Physics Book - User contributions [en]

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2024-04-15T03:35:42Z

Idumitriu3:

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2024-04-15T03:33:49Z

Idumitriu3:

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Idumitriu3:

Semiconductor Devices

2024-04-15T03:30:21Z

Idumitriu3: /* Determining Semiconductor Resistivity and Conductivity */

Last edited by Irene Dumitriu (Spring 2024)

===What are Semiconductors?===

Semiconductor devices are electronic components with the electronic properties of semiconductors. Silicon, germanium, gallium arsenide, organic semiconductors are among the most common semiconductors used in these devices. Semiconductors are materials that are neither good conductors or good insulators. They have a good conductivity between conductors (these tend to be metals) and nonconductors (these insulators tend to be ceramics). Semiconductors do not have to originate organically - the most common semiconductor material are pure elements such as silicon and germanium, but impurities are often added to control the conductivity levels. This process is called doping. The doped semiconductors are called extrinsic semiconductors while pure, impurity-free semiconductors are called intrinsic semiconductors. Intrinsic semiconductors are less conductive than metals as they have a lower amount of charge carriers, or electrons or holes, that can move across the band gap. Extrinsic semiconductors can have higher or lower conductivity depending on the doping.

The conductivity of these semiconductors can also be impacted by environmental changes such as temperature changes. Electrical conductivity depends on two factors: charge-carrier mobility and the concentration of mobile charge carriers. Charge carriers are free electrons or holes that are able to move freely throughout a material, and their mobility is the speed at which these electrons move in a certain direction under the application of a voltage. The free electrons are responsible for determining a current as a current is defined as the rate of electrons flowing through a material in a unit of time. In semiconductors, the charge carrier mobility is negligible as the temperature directly impacts mainly the charge carrier concentration. The band gap theory helps explain how charge carriers move in semiconductors. Unlike metals, semiconductors have a gap between the conduction band and the valence band where the electrons sit without excitation. As temperature increases, these electrons gain energy until they have enough energy to cross the band gap and into the conduction band, decreasing resistivity and increasing conductivity. This behavior is observed mainly in intrinsic semiconductors. In extrinsic semiconductors, the type of doping can affect the conductivity negatively or positively.

Due to low cost, reliability, ability to control conductivity, and compactness, semiconductors are used for a wide range of applications. They also have a wide range of current and voltage handling capabilities, contributing to their suitability for a number of operations. They are commonly found in power devices, optical sensors, and light emitters. Perhaps more importantly, they are readily integrated into microelectronic uses as key elements for the majority of electronic systems, including communications, consumer, data-processing, and industrial-control equipment.

[[File:Intelthing.jpg|frame|border|right|A raw board with many transistors in it!]]
[[File:transistor.png|frame|none|left|An fully built integrated circuit.]]

==The Main Idea==

Semiconductors work by using the electric properties of the p-n junction that makes up a diode. The junction is formed through a process called doping. Doping involves turning silicon into a conductor by changing the behavior of its electrons. In n-type doping, a phosphorus/arsenic impurity is introduced so that the valence will have free electrons to allow a electric current to flow. Since extra electrons are negative in charge, this type of doping is called n-type doping referred to by "n" in the p-n junction. In the p-type doping, a boron/gallium impurity is introduced to the silicon lattice so the valence will have an empty electron orbital. Because the empty area implies the absence of an electron and thus creates a positive charge, "p" was assigned as the name of the doping type.

[[File:n-type.gif|frame|border|right|N-Type Material]]

[[File:p-type.png|frame|none|left|P-Type Material]]

The two most useful forms of semiconductor devices are diodes and transistors. Diodes are the simplest semiconductor device, which conducts current easily in one direction but conducts almost no current in the other direction. These are made by joining two pieces of semiconducting material, a junction called a "p-n" junction. One of the pieces contains a small amount of boron and the other contains a small amount of phosphorus. Transistors are constructed through two semiconducting junctions, or "p-n" junctions. These are the most common elements in digital circuits. The conductivity of these semiconductors can be controlled by introduction of an electric or magnetic field, by exposure to light or heat, or by mechanical deformation of a doped monocrystalline grid. Due to this, semiconductors are extremely useful and can be altered to fit specific purposes.

===Semiconductors & Applications in Solid-State Physics===

The key principle that is often used in solid-state physics is the carrier effective mass. This refers to the mass a particle (within the semiconductor) seems to have when interacting with other identical particles in a thermal distribution. This constant is simplified version of the band theory and influences measurable properties of a solid, including the efficiency of the devices that semiconductors are used in for example, solar cell efficiency and integrated circuit speed. So, how do we actually measure the carrier effective masses in a semiconductor?

Large parts of the simplicity of the free electron gas model can be saved by assigning effective masses to the carriers. Only electrons and holes at the band edges (characterized by a wave vector kex) participate in the generation - recombination process that is the hallmark of semiconductors. A particle's effective mass is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles over long distances can be very different from their motion in a vacuum. The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass. Sometimes the effective mass can be considered to be a simple constant of a material, however, the value of effective mass depends on the purpose for which it is used, and can vary depending on a number of factors. For electrons or electron holes in a solid, the effective mass is usually stated in units of the rest mass of an electron, me (9.11×10−31 kg). In these units it is usually in the range 0.01 to 10, but can also be lower or higher—for example, reaching 1,000 in exotic heavy fermion materials, or anywhere from zero to infinity (depending on definition) in graphene. The effective mass of a semiconductor is obtained by fitting the actual electron diagram around the conduction band minimum or the valence band maximum by a parabola - this is called an E-K diagram (shown below). It shows the relationship between the energy and momentum of available quantum mechanical states for electrons in the material. As it simplifies the more general band theory, the electronic effective mass can be seen as an important basic parameter that influences measurable properties of a solid, including everything from the efficiency of a solar cell to the speed of an integrated circuit.

[[File:IMG 2424.jpg|Diagram of an EK diagram|350 px|]]

===Detecting Doping===

Secondary ion mass spectroscopy (SIMS) is a very powerful technique for the analysis of impurities in solids. SIMS can be utilized for semiconductor dopant profiling. The technique relies on removal of material from a solid by sputtering and on analysis of the sputtered ionized species; all elements are detected. SIMS can detect dopant densities as low as 10^14 cm^-3. The dopant density profile that is generated is based on the ion signal versus time plot. The time axis is converted to a depth axis by measuring the depth of the crater at the end of the measurement assuming a constant sputtering rate. For example, boron is implanted into silicon at a given energy and dose to create a standard. The secondary ion signal is calibrated by assuming the total amount of boron in the sample to equal to the implanted boron. The unknown sample of B implanted into silicon is then compared to the standard. However, there is limited dynamic range of the SIMS instrument that can contribute to slightly deeper junctions and discrepancies in the lowly doped portions of the profile. When sputtering from a highly doped region to a lowly doped region, the crater walls still contain the entire doping density profile. SIMS also measures total dopant density, regardless of activation. Thus going back to the silicon-boron example, the dopant profile shows dependence of electrical activation of boron implanted into silicon on implant dose and activation temperature.

[[File:Sims-technique-schematic.png|frame|none|left|Example of SIMS]]

===Determining Semiconductor Resistivity and Conductivity===

Methods for determining the resistivity and conductivity of material involve galvanostatic or potentiostatic tests. In a galvanostatic test, a constant current is applied and the voltage is measured. In a potentiostatic test, a constant voltage is applied and the current is measured. An electrochemical analyzer can be used with either a 2-point or 4-point method. With the 2-point method, there can be contact resistance between the material and the wires, falsely increasing the resistivity. The 4-point technique overcomes this issue by using four wires. A current is conducted and measured through the endpoints of the bar while two wires are connected to the inner points of the bar so that they can measure the voltage produced across the inner bar. Once the data is collected, Ohm’s law can be used to calculate the resistance where the resistance is 1/slope of the current vs. voltage graph. Resistivity is
<math>
𝜌 = R \ {\frac{A}{L}}
</math>, where R is the resistance, A is the cross-sectional area, and L is the length. Conductivity is
<math>
𝜎 = 𝜌^{-1}
</math>.

[[File:2pp_vs_4pp_resistivity.png|frame|border|center|The 2-point method vs. the 4-point method in determining the resistivity of sample.]]

However, this method only works for bulk materials. If the semiconductor is in the form of a thin film, then a 4-point colinear probe can be used instead. The method works by measuring the resistance of the material by applying a current through the two outer probes and measuring the voltage of the two inner probes. The resistivity and conductivity calculations are more complicated for thin films as correction factors need to be applied in order to adjust the data for the film thickness, the probe's placement, and other factors. For example, a correction factor needs to be used when the thickness is less than or equal to half the probe spacing. If this is true, then the resistivity is
<math>
𝜌 = (R)\ (2𝜋)\ (s)\ (F1)
</math> where s is the spacing and F1 is the correction factor.

===A Mathematical Model===

Semiconductors operate based on the concept of thermal energy exciting electrons and causing them to jump to the next higher (unoccupied) energy band.
These electrons can pick up energy (and drift speed) from an applied electric field. The filled energy band is called the “valence” band, and the nearly unoccupied higher energy band is called the “conduction” band. The number of electrons excited into the conduction band is proportional to a value called the Boltzmann constant, equivalent to the value:
<math>
e^{-E_{\text{gap}} / k_B T}
</math>.
Therefore, high conductivity (corrosponding to a favorable Boltzmann factor) can be calculated according to
<math>
T = 2 \pi \sqrt{\frac{m}{k}}
</math>,
where <math>m</math> is the mass of the object in kilograms, <math>k</math> is the spring constant, and <math>T</math> is the period of oscillation in seconds. In addition, the total conventional current in a semiconductor can be calculated, according to the equation
<math>
I = e n_n A u_n E + e n_p A u_p E
</math>.

===A Conceptual Model===
The following diagram demonstrates how electron excitement in semiconductors works. Semiconductors are materials with small band gaps between the valence band and conduction bands. As you can see, a small amount of thermal energy is needed to promote an electron to the conduction band in a semiconductor.

[[File:conceptual.png|frame|none|left|A Conceptual Model of the Semiconductor]]

===A Computational Model===

[https://phet.colorado.edu/sims/cheerpj/semiconductor/latest/semiconductor.html?simulation=semiconductor Semiconductor Simulation]

==History==
'''1874'''
Ferdinand Braun discovers that current flows freely in only one direction when a metal point and a galena crystal are put together.

'''1901'''
Jagadis Bose takes ownership of the discovery of the semiconductor crystal for detecting radio waves.

'''1940'''
Russell Ohl discovers the p-n junction.

'''1940s'''
Semiconductors were used only as two-terminal devices, such as rectifiers and photodiodes. They were most commonly used as detectors in radios, through devices called "cat's whiskers". During the era of WWII, researchers worked with semiconductors and cat's whiskers to make more effective diodes.

'''1947'''
William Shockley and John Bardeen worked together to create a triode-like semiconductor: the first transistor. They realized that if there were some way to control the flow of the electrons from the emitter to the collector of this newly discovered diode, an amplifier could be built.The first transistor was officially created on the 23rd of December, 1947.

'''1956'''
John Bardeen, William Shockley, and another researcher named Walter Houser Brattain were credited for the invention and awarded a Nobel Prize for physics in 1956 for their work. After this, the utilization of semiconductors soon advanced to even more complicated applications.

'''1960s'''
In the late 1960s, transistors moved from being germanium based to silicon based. Gordon K Teal was most responsible for this advancement, and his company, Texas Instruments, profited greatly. Portable radios are just one popular invention that benefited from silicon based semiconductors. Now, silicon based semiconductors constitute more than 95 percent of all semiconductor hardware sold worldwide.

'''1970s'''
Silicon technology is modernized and the race to fit all semiconductor processor technology into one chip is most active.

'''2000'''
Nobel Prize in physics awarded to Zhores I. Alferov and Herbert Kroemer for developing semiconductor heterostructures used in high-speed- and opto-electronics and half to Jack S. Kilby "for his part in the invention of the integrated circuit."

[[File:transistorwork.png|frame|none|none|John Bardeen, William Shockley, and Walter Houser Brattain, winners of the Nobel Prize for their invention of the transistor, are pictured above.]]

===Connectedness===

Semiconductors are crucial to modern technology, and are used for memory storage as well as so many other technological innovations. This technology is used every day by millions of people for thousands of different applications. Most people in the world have used semiconductors in one way or another, even if they weren't aware of it. It is specifically connected to the major of Biomedical Engineering through memory storage and the complex computer programs used every day to conduct business and create simulations for the furthering of biomedical research. All industrial applications of semiconductors are very applicable, from amplifiers to transistors to silicon disks. Without semiconductors, much of the technology that the general population relies on today would not be possible.

Semiconductors are used in essentially every part of this technological and electronically-dependent world we live in today. They have both conductor and insulator properties and includes all of the metal we see in wires. Computers, phones, and other electronic devices all use semiconductors to fulfill their functions such as communication and efficiency. The most important aspect of semiconductors is utilization, which is shown through the use of switches. Inside electronic devices, the switches exist in extremely large numbers, which is why electronic devices process information in an incredible speed with surprising efficiency.

Semiconductors are connected to chemical engineering largely through their industrial creation. The process of depositing each layer of material onto the wafer is a chemical process controlled by deposition of gaseous metals onto the wafer. There are an incredible variety of steps from material preparation to packaging which can be optimized by an eager chemical engineer.

Another example that was discussed previously on this page is the usage of silicon in photovoltaic devices. Silicon is used because it is the first semiconductor that was commercialized successfully. Many commercial companies are very proficient in making silicon devices, so the silicon is not necessarily used because it is the best material for harnessing the electricity from the photovoltaic effect. The silicon crystals allow the power to reach the external electrical circuit, but the silicon doesn't absorb sunlight as efficiently because it needs to be ten to one hundred times thicker than an advanced thin-film cell. It is also favored because of the low maintenance. A unique oxide forms when silicon is exposed to high temperatures that serves to neutralize defects on the silicon surface. The frontier for replacing the silicon looks quite bleak because of the practicality of manufacturing silicon crystalline semiconductors, but new research is being conducted on using silicon with lower purity or combining it with other semiconductor materials.

==Types of Semiconductors==

===Diodes===

[[File:Diode_current_wiki.png|314px|thumb|right|top|IV Characteristic of a Diode]]

Diodes are really great! In a simple sense, they can give you a "point of no return" in your circuit (but they can actually do much more than that).
Three interesting things should be observed from the IV characteristic shown to the right:

# For small positive voltages and above, the diode does not limit the current (the line is almost vertical)!
# For small to larger negative voltages, the diode resists current (the line is almost flat).
# For a large negative voltage (the breakdown voltage) the diode gives up (no one is perfect).

We can formally define this line with the Shockley Diode Equation, which formalizes this observation:

<math display="block">
I = I_S \left( e^{\frac{V_D}{n V_T}} - 1 \right)
</math> where

<math>I</math> is the diode current,

<math>I_S</math> is the reverse bias saturation current (or scale current),

<math>V_D</math> is the voltage across the diode,

<math>V_T</math> is the thermal voltage, and

<math>n</math> is the ideality factor, (1 if the diode is ideal, greater than 1 if it is imperfect).

A great practical use for diodes is a rectifier:

[[File:Gratz.rectifier.en.svg|frame|border|center|Diodes groups the positive and negative signals together]]

This makes sure that when a positive voltage appears on either line, it is redirected to a single positive line, and the same for the negatives.
BAM! AC to DC, that's pretty easy, you can charge your phone with that.
In reality a capacitor is added in parallel with the load to try to smooth out the ripples.
A voltage regulator after the rectifying step is also a popular choice, depending on the needs of the application.

Another super useful application is that of a back up power supply: simply connect two supplies in parallel with the positive terminals buffered with diodes. The higher of the two voltages is always used and the transition between supplies is seamless.

===Zener Diodes===

Some diodes (Zener) are made to have small breakdown voltages.
Since during breakdown the IV curve is almost vertical (it's really an exponential), the current is independent (almost) from voltage.
You can then wire up a Zener diode in reverse to a point in the circuit, and it will accept as much current as it needs to to reach that
breakdown voltage. Because of this a great practical use for Zener diodes is a voltage regulator since the voltage is set when the diode is
manufactured and does not change greatly with a varying power supply.

===Bipolar Junction Transistors===

[[Image:BJT NPN symbol (case).svg|75px|thumb|NPN BJT]]
[[Image:BJT PNP symbol (case).svg|75px|thumb|PNP BJT]]

Shortly after the invention of the first transistor (which was OK), the BJT landed, which was the first transistor to be prolific in the field.
It was made using two alternating NP junctions as shown below:

[[File:NPN BJT (Planar) Cross-section.svg|frame|border|center|NPN BJT (Planar) Cross-section]]

Really transistors (and by extension all that is needed for a computer to be built) are amplifiers (OK, to build all computers you need an inverting amplifier, but one can be built using the BJT).
If one is used to thinking of them as an electrically-controlled switch, you can simply think of a switch as an amplifier with a gain of <math>\infty</math>.

A simple model of a BJT is a linear current-controlled current source, i.e. the base to emitter (B to E) current <math>I_{BE}</math> is proportional to
the collector to emitter (C to E) current <math>I_{CE}</math>. The proportionality constant <math>\beta</math> can be thought of as the "gain" of the
transistor. This gives a relationship of <math>I_{CE} = \beta I_{BE}</math>.

[[File:Current-Voltage relationship of BJT.png|thumb|right|Current-Voltage relationship of BJT]]

Sadly there is no source of infinite power, so the output to our amplifier tops off when it can't supply any more power.
This can be seen with the graph on the right.
The simple model then only works for the tiny linear part at the start of the graph, even so its not ''that'' linear.
The BJT proved to be power hungry, pretty non-linear and sensitive to the environment (temperature, etc.).
These growing pains lead to a new development, called the MOSFET.

===MOSFETs===

MOSFETs are the coolest, they are less power-hungy and easier to work with when compared to BJTs.
Instead of having a current control, which uses power and gets the control and the output signal coupled together,
a MOSFET's output is controlled by the electric Field (the F in MOSFET) the control signal creates on one of the plates of the MOSFET.
Since the control signal and the output are electrically disconnected (as you would see in a capacitor) there is much less power draw
from this type of transistor.

We can see how linear this thing is with its IV characteristic: <math>I_D= \mu_n C_{ox}\frac{W}{L} \left( (V_{GS}-V_{th})V_{DS}-\frac{V_{DS}^2}{2} \right)</math>

Apart from the control signal <math>V_{DS}</math> and constants, the voltage across the output portion of the MOSFET is linearly related to the current!
This means that the MOSFET behaves like a voltage controlled resistor, and a resistor is something much easier to analyse and work with.

Most circuits with an enormous amount of transistors these days use primarily MOSFETs. BJTs are still useful for temperature and light sensing
applications.

==Industrial Semiconductor Fabrication==

Semiconductors are mass produced in specialized factories called foundries or fabs. The process consists of multiple chemical and photolithographic steps which add layers to a wafer usually made of silicon. The entire process usually takes around 2 months but it can last up to 4.

The semiconductor product is rated by the size of the chip's process gate length, where processes with smaller gate lengths are typically harder to make. There are 10-20 different sized chips being fabricated around the world as of 2018. There is an immense amount of attention and money being dedicated to improving semiconductor fabrication process efficiency.

[[File:feol.png|frame|none|left|Steps to fabricate a semiconductor device]]

==Examples==

===Simple===
[[File:Cat'swhiskerdetector.jpg]]

A simple application of a semiconductor would be the Cat's Whisker detector for radios, invented in the early 1900s.

===Moderate===
[[File:Opticallsensor.jpg]]

Optical sensors are moderately difficult applications of semiconductors. Optical sensors are electronic detectors that convert light into an electronic signal. They are used in many industrial and consumer applications. An example would include lamps that turn on automatically in response to darkness.

===Difficult===

[[File:Complicated_semiconductor.jpg]]

A very complicated application of a semiconductor is its use in modern cellular phone devices, such as its use here in the iPhone 6.

== See also ==

Related Wiki pages:

-Transformers

-Resistors and conductivity

-Superconductors

-Electric Fields

-Transformers from a physics standpoint

===Further reading===

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

===External links===

Wikipedia page about semiconductors:

https://en.wikipedia.org/wiki/Semiconductor_device

Encyclopedia entry about semiconductors, including the history of semiconductors:

http://www.britannica.com/technology/semiconductor-device

Information about Diodes:

https://en.wikipedia.org/wiki/Diode

Information about BJTs:

https://en.wikipedia.org/wiki/Bipolar_junction_transistor

Information about MOSFETs:

https://en.wikipedia.org/wiki/MOSFET

Semiconductor Device Fabrication

https://en.wikipedia.org/wiki/Semiconductor_device_fabrication

==References==
Brain, Marshall. "How Semiconductors Work." HowStuffWorks. N.p., 25 Apr. 2001. Web. 27 Nov. 2016.

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Electronics and Semiconductor. (n.d.). Retrieved December 3, 2015, from http://www.plm.automation.siemens.com/en_us/electronics-semiconductor/devices/

Huculak, M. (2014, September 19). IPhone 6 and iPhone 6 Plus get teardown by iFixit • The Windows Site for Enthusiasts - Pureinfotech. Retrieved December 3, 2015, from http://pureinfotech.com/2014/09/19/iphone-6-iphone-6-plus-get-teardown-ifixit/

Introduction to Secondary Ion Mass Spectrometry (SIMS) technique. (n.d.). Retrieved November 15, 2020, from https://www.cameca.com/products/sims/technique

John Bardeen, William Shockley and Walter Brattain at Bell Labs, 1948. (n.d.). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/John_Bardeen#/media/File:Bardeen_Shockley_Brattain_1948.JPG

The Nobel Prize in Physics 1956. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/1956/summary/>

The Nobel Prize in Physics 2000. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/2000/summary/>

เซ็นเซอร์แสง (Optical Sensor) - Elec-Za.com. (2014, July 28). Retrieved December 3, 2015, from http://www.elec-za.com/เซ็นเซอร์แสง-optical-sensor/

Semiconductor device. (2015, November 30). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/Semiconductor_device

Semiconductor Fabrication. (25 November 2018). http://www.iue.tuwien.ac.at/phd/rovitto/node10.html

Shah, A. (2013, May 13). Intel loses ground as world's top semiconductor company, survey says. Retrieved December 3, 2015, from http://www.pcworld.com/article/2038645/intel-loses-ground-as-worlds-top-semiconductor-company-survey-says.html

Shaw, R. (2014, November 1). The cat's-whisker detector. Retrieved December 3, 2015, from http://rileyjshaw.com/blog/the-cat's-whisker-detector/

Sze, S. (2015, October 1). Semiconductor device | electronics. Retrieved December 3, 2015, from http://www.britannica.com/technology/semiconductor-device

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

"Timeline." Timeline | The Silicon Engine | Computer History Museum. The Silicon Engine, n.d. Web. 27 Nov. 2016.

[[Category:Simple Circuits]]

Semiconductor Devices

2024-04-15T02:51:16Z

Idumitriu3: /* Determining Semiconductor Resistivity and Conductivity */

Last edited by Irene Dumitriu (Spring 2024)

===What are Semiconductors?===

Semiconductor devices are electronic components with the electronic properties of semiconductors. Silicon, germanium, gallium arsenide, organic semiconductors are among the most common semiconductors used in these devices. Semiconductors are materials that are neither good conductors or good insulators. They have a good conductivity between conductors (these tend to be metals) and nonconductors (these insulators tend to be ceramics). Semiconductors do not have to originate organically - the most common semiconductor material are pure elements such as silicon and germanium, but impurities are often added to control the conductivity levels. This process is called doping. The doped semiconductors are called extrinsic semiconductors while pure, impurity-free semiconductors are called intrinsic semiconductors. Intrinsic semiconductors are less conductive than metals as they have a lower amount of charge carriers, or electrons or holes, that can move across the band gap. Extrinsic semiconductors can have higher or lower conductivity depending on the doping.

The conductivity of these semiconductors can also be impacted by environmental changes such as temperature changes. Electrical conductivity depends on two factors: charge-carrier mobility and the concentration of mobile charge carriers. Charge carriers are free electrons or holes that are able to move freely throughout a material, and their mobility is the speed at which these electrons move in a certain direction under the application of a voltage. The free electrons are responsible for determining a current as a current is defined as the rate of electrons flowing through a material in a unit of time. In semiconductors, the charge carrier mobility is negligible as the temperature directly impacts mainly the charge carrier concentration. The band gap theory helps explain how charge carriers move in semiconductors. Unlike metals, semiconductors have a gap between the conduction band and the valence band where the electrons sit without excitation. As temperature increases, these electrons gain energy until they have enough energy to cross the band gap and into the conduction band, decreasing resistivity and increasing conductivity. This behavior is observed mainly in intrinsic semiconductors. In extrinsic semiconductors, the type of doping can affect the conductivity negatively or positively.

Due to low cost, reliability, ability to control conductivity, and compactness, semiconductors are used for a wide range of applications. They also have a wide range of current and voltage handling capabilities, contributing to their suitability for a number of operations. They are commonly found in power devices, optical sensors, and light emitters. Perhaps more importantly, they are readily integrated into microelectronic uses as key elements for the majority of electronic systems, including communications, consumer, data-processing, and industrial-control equipment.

[[File:Intelthing.jpg|frame|border|right|A raw board with many transistors in it!]]
[[File:transistor.png|frame|none|left|An fully built integrated circuit.]]

==The Main Idea==

Semiconductors work by using the electric properties of the p-n junction that makes up a diode. The junction is formed through a process called doping. Doping involves turning silicon into a conductor by changing the behavior of its electrons. In n-type doping, a phosphorus/arsenic impurity is introduced so that the valence will have free electrons to allow a electric current to flow. Since extra electrons are negative in charge, this type of doping is called n-type doping referred to by "n" in the p-n junction. In the p-type doping, a boron/gallium impurity is introduced to the silicon lattice so the valence will have an empty electron orbital. Because the empty area implies the absence of an electron and thus creates a positive charge, "p" was assigned as the name of the doping type.

[[File:n-type.gif|frame|border|right|N-Type Material]]

[[File:p-type.png|frame|none|left|P-Type Material]]

The two most useful forms of semiconductor devices are diodes and transistors. Diodes are the simplest semiconductor device, which conducts current easily in one direction but conducts almost no current in the other direction. These are made by joining two pieces of semiconducting material, a junction called a "p-n" junction. One of the pieces contains a small amount of boron and the other contains a small amount of phosphorus. Transistors are constructed through two semiconducting junctions, or "p-n" junctions. These are the most common elements in digital circuits. The conductivity of these semiconductors can be controlled by introduction of an electric or magnetic field, by exposure to light or heat, or by mechanical deformation of a doped monocrystalline grid. Due to this, semiconductors are extremely useful and can be altered to fit specific purposes.

===Semiconductors & Applications in Solid-State Physics===

The key principle that is often used in solid-state physics is the carrier effective mass. This refers to the mass a particle (within the semiconductor) seems to have when interacting with other identical particles in a thermal distribution. This constant is simplified version of the band theory and influences measurable properties of a solid, including the efficiency of the devices that semiconductors are used in for example, solar cell efficiency and integrated circuit speed. So, how do we actually measure the carrier effective masses in a semiconductor?

Large parts of the simplicity of the free electron gas model can be saved by assigning effective masses to the carriers. Only electrons and holes at the band edges (characterized by a wave vector kex) participate in the generation - recombination process that is the hallmark of semiconductors. A particle's effective mass is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles over long distances can be very different from their motion in a vacuum. The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass. Sometimes the effective mass can be considered to be a simple constant of a material, however, the value of effective mass depends on the purpose for which it is used, and can vary depending on a number of factors. For electrons or electron holes in a solid, the effective mass is usually stated in units of the rest mass of an electron, me (9.11×10−31 kg). In these units it is usually in the range 0.01 to 10, but can also be lower or higher—for example, reaching 1,000 in exotic heavy fermion materials, or anywhere from zero to infinity (depending on definition) in graphene. The effective mass of a semiconductor is obtained by fitting the actual electron diagram around the conduction band minimum or the valence band maximum by a parabola - this is called an E-K diagram (shown below). It shows the relationship between the energy and momentum of available quantum mechanical states for electrons in the material. As it simplifies the more general band theory, the electronic effective mass can be seen as an important basic parameter that influences measurable properties of a solid, including everything from the efficiency of a solar cell to the speed of an integrated circuit.

[[File:IMG 2424.jpg|Diagram of an EK diagram|350 px|]]

===Detecting Doping===

Secondary ion mass spectroscopy (SIMS) is a very powerful technique for the analysis of impurities in solids. SIMS can be utilized for semiconductor dopant profiling. The technique relies on removal of material from a solid by sputtering and on analysis of the sputtered ionized species; all elements are detected. SIMS can detect dopant densities as low as 10^14 cm^-3. The dopant density profile that is generated is based on the ion signal versus time plot. The time axis is converted to a depth axis by measuring the depth of the crater at the end of the measurement assuming a constant sputtering rate. For example, boron is implanted into silicon at a given energy and dose to create a standard. The secondary ion signal is calibrated by assuming the total amount of boron in the sample to equal to the implanted boron. The unknown sample of B implanted into silicon is then compared to the standard. However, there is limited dynamic range of the SIMS instrument that can contribute to slightly deeper junctions and discrepancies in the lowly doped portions of the profile. When sputtering from a highly doped region to a lowly doped region, the crater walls still contain the entire doping density profile. SIMS also measures total dopant density, regardless of activation. Thus going back to the silicon-boron example, the dopant profile shows dependence of electrical activation of boron implanted into silicon on implant dose and activation temperature.

[[File:Sims-technique-schematic.png|frame|none|left|Example of SIMS]]

===Determining Semiconductor Resistivity and Conductivity===

Methods for determining the resistivity and conductivity of material involve galvanostatic or potentiostatic tests. In a galvanostatic test, a constant current is applied and the voltage is measured. In a potentiostatic test, a constant voltage is applied and the current is measured. An electrochemical analyzer can be used with either a 2-point or 4-point method. With the 2-point method, there can be contact resistance between the material and the wires, falsely increasing the resistivity. The 4-point technique overcomes this issue by using four wires. A current is conducted and measured through the endpoints of the bar while two wires are connected to the inner points of the bar so that they can measure voltage produced across the inner bar. Once the data is collected, Ohm’s law can be used to calculate the resistivity with the voltage and resistance where the resistance is the 1/slope of the current vs. voltage graph.

[[File:2pp_vs_4pp_resistivity.png|frame|border|center|The 2-point method vs. the 4-point method in determining the resistivity of sample.]]

===A Mathematical Model===

Semiconductors operate based on the concept of thermal energy exciting electrons and causing them to jump to the next higher (unoccupied) energy band.
These electrons can pick up energy (and drift speed) from an applied electric field. The filled energy band is called the “valence” band, and the nearly unoccupied higher energy band is called the “conduction” band. The number of electrons excited into the conduction band is proportional to a value called the Boltzmann constant, equivalent to the value:
<math>
e^{-E_{\text{gap}} / k_B T}
</math>.
Therefore, high conductivity (corrosponding to a favorable Boltzmann factor) can be calculated according to
<math>
T = 2 \pi \sqrt{\frac{m}{k}}
</math>,
where <math>m</math> is the mass of the object in kilograms, <math>k</math> is the spring constant, and <math>T</math> is the period of oscillation in seconds. In addition, the total conventional current in a semiconductor can be calculated, according to the equation
<math>
I = e n_n A u_n E + e n_p A u_p E
</math>.

===A Conceptual Model===
The following diagram demonstrates how electron excitement in semiconductors works. Semiconductors are materials with small band gaps between the valence band and conduction bands. As you can see, a small amount of thermal energy is needed to promote an electron to the conduction band in a semiconductor.

[[File:conceptual.png|frame|none|left|A Conceptual Model of the Semiconductor]]

===A Computational Model===

[https://phet.colorado.edu/sims/cheerpj/semiconductor/latest/semiconductor.html?simulation=semiconductor Semiconductor Simulation]

==History==
'''1874'''
Ferdinand Braun discovers that current flows freely in only one direction when a metal point and a galena crystal are put together.

'''1901'''
Jagadis Bose takes ownership of the discovery of the semiconductor crystal for detecting radio waves.

'''1940'''
Russell Ohl discovers the p-n junction.

'''1940s'''
Semiconductors were used only as two-terminal devices, such as rectifiers and photodiodes. They were most commonly used as detectors in radios, through devices called "cat's whiskers". During the era of WWII, researchers worked with semiconductors and cat's whiskers to make more effective diodes.

'''1947'''
William Shockley and John Bardeen worked together to create a triode-like semiconductor: the first transistor. They realized that if there were some way to control the flow of the electrons from the emitter to the collector of this newly discovered diode, an amplifier could be built.The first transistor was officially created on the 23rd of December, 1947.

'''1956'''
John Bardeen, William Shockley, and another researcher named Walter Houser Brattain were credited for the invention and awarded a Nobel Prize for physics in 1956 for their work. After this, the utilization of semiconductors soon advanced to even more complicated applications.

'''1960s'''
In the late 1960s, transistors moved from being germanium based to silicon based. Gordon K Teal was most responsible for this advancement, and his company, Texas Instruments, profited greatly. Portable radios are just one popular invention that benefited from silicon based semiconductors. Now, silicon based semiconductors constitute more than 95 percent of all semiconductor hardware sold worldwide.

'''1970s'''
Silicon technology is modernized and the race to fit all semiconductor processor technology into one chip is most active.

'''2000'''
Nobel Prize in physics awarded to Zhores I. Alferov and Herbert Kroemer for developing semiconductor heterostructures used in high-speed- and opto-electronics and half to Jack S. Kilby "for his part in the invention of the integrated circuit."

[[File:transistorwork.png|frame|none|none|John Bardeen, William Shockley, and Walter Houser Brattain, winners of the Nobel Prize for their invention of the transistor, are pictured above.]]

===Connectedness===

Semiconductors are crucial to modern technology, and are used for memory storage as well as so many other technological innovations. This technology is used every day by millions of people for thousands of different applications. Most people in the world have used semiconductors in one way or another, even if they weren't aware of it. It is specifically connected to the major of Biomedical Engineering through memory storage and the complex computer programs used every day to conduct business and create simulations for the furthering of biomedical research. All industrial applications of semiconductors are very applicable, from amplifiers to transistors to silicon disks. Without semiconductors, much of the technology that the general population relies on today would not be possible.

Semiconductors are used in essentially every part of this technological and electronically-dependent world we live in today. They have both conductor and insulator properties and includes all of the metal we see in wires. Computers, phones, and other electronic devices all use semiconductors to fulfill their functions such as communication and efficiency. The most important aspect of semiconductors is utilization, which is shown through the use of switches. Inside electronic devices, the switches exist in extremely large numbers, which is why electronic devices process information in an incredible speed with surprising efficiency.

Semiconductors are connected to chemical engineering largely through their industrial creation. The process of depositing each layer of material onto the wafer is a chemical process controlled by deposition of gaseous metals onto the wafer. There are an incredible variety of steps from material preparation to packaging which can be optimized by an eager chemical engineer.

Another example that was discussed previously on this page is the usage of silicon in photovoltaic devices. Silicon is used because it is the first semiconductor that was commercialized successfully. Many commercial companies are very proficient in making silicon devices, so the silicon is not necessarily used because it is the best material for harnessing the electricity from the photovoltaic effect. The silicon crystals allow the power to reach the external electrical circuit, but the silicon doesn't absorb sunlight as efficiently because it needs to be ten to one hundred times thicker than an advanced thin-film cell. It is also favored because of the low maintenance. A unique oxide forms when silicon is exposed to high temperatures that serves to neutralize defects on the silicon surface. The frontier for replacing the silicon looks quite bleak because of the practicality of manufacturing silicon crystalline semiconductors, but new research is being conducted on using silicon with lower purity or combining it with other semiconductor materials.

==Types of Semiconductors==

===Diodes===

[[File:Diode_current_wiki.png|314px|thumb|right|top|IV Characteristic of a Diode]]

Diodes are really great! In a simple sense, they can give you a "point of no return" in your circuit (but they can actually do much more than that).
Three interesting things should be observed from the IV characteristic shown to the right:

# For small positive voltages and above, the diode does not limit the current (the line is almost vertical)!
# For small to larger negative voltages, the diode resists current (the line is almost flat).
# For a large negative voltage (the breakdown voltage) the diode gives up (no one is perfect).

We can formally define this line with the Shockley Diode Equation, which formalizes this observation:

<math display="block">
I = I_S \left( e^{\frac{V_D}{n V_T}} - 1 \right)
</math> where

<math>I</math> is the diode current,

<math>I_S</math> is the reverse bias saturation current (or scale current),

<math>V_D</math> is the voltage across the diode,

<math>V_T</math> is the thermal voltage, and

<math>n</math> is the ideality factor, (1 if the diode is ideal, greater than 1 if it is imperfect).

A great practical use for diodes is a rectifier:

[[File:Gratz.rectifier.en.svg|frame|border|center|Diodes groups the positive and negative signals together]]

This makes sure that when a positive voltage appears on either line, it is redirected to a single positive line, and the same for the negatives.
BAM! AC to DC, that's pretty easy, you can charge your phone with that.
In reality a capacitor is added in parallel with the load to try to smooth out the ripples.
A voltage regulator after the rectifying step is also a popular choice, depending on the needs of the application.

Another super useful application is that of a back up power supply: simply connect two supplies in parallel with the positive terminals buffered with diodes. The higher of the two voltages is always used and the transition between supplies is seamless.

===Zener Diodes===

Some diodes (Zener) are made to have small breakdown voltages.
Since during breakdown the IV curve is almost vertical (it's really an exponential), the current is independent (almost) from voltage.
You can then wire up a Zener diode in reverse to a point in the circuit, and it will accept as much current as it needs to to reach that
breakdown voltage. Because of this a great practical use for Zener diodes is a voltage regulator since the voltage is set when the diode is
manufactured and does not change greatly with a varying power supply.

===Bipolar Junction Transistors===

[[Image:BJT NPN symbol (case).svg|75px|thumb|NPN BJT]]
[[Image:BJT PNP symbol (case).svg|75px|thumb|PNP BJT]]

Shortly after the invention of the first transistor (which was OK), the BJT landed, which was the first transistor to be prolific in the field.
It was made using two alternating NP junctions as shown below:

[[File:NPN BJT (Planar) Cross-section.svg|frame|border|center|NPN BJT (Planar) Cross-section]]

Really transistors (and by extension all that is needed for a computer to be built) are amplifiers (OK, to build all computers you need an inverting amplifier, but one can be built using the BJT).
If one is used to thinking of them as an electrically-controlled switch, you can simply think of a switch as an amplifier with a gain of <math>\infty</math>.

A simple model of a BJT is a linear current-controlled current source, i.e. the base to emitter (B to E) current <math>I_{BE}</math> is proportional to
the collector to emitter (C to E) current <math>I_{CE}</math>. The proportionality constant <math>\beta</math> can be thought of as the "gain" of the
transistor. This gives a relationship of <math>I_{CE} = \beta I_{BE}</math>.

[[File:Current-Voltage relationship of BJT.png|thumb|right|Current-Voltage relationship of BJT]]

Sadly there is no source of infinite power, so the output to our amplifier tops off when it can't supply any more power.
This can be seen with the graph on the right.
The simple model then only works for the tiny linear part at the start of the graph, even so its not ''that'' linear.
The BJT proved to be power hungry, pretty non-linear and sensitive to the environment (temperature, etc.).
These growing pains lead to a new development, called the MOSFET.

===MOSFETs===

MOSFETs are the coolest, they are less power-hungy and easier to work with when compared to BJTs.
Instead of having a current control, which uses power and gets the control and the output signal coupled together,
a MOSFET's output is controlled by the electric Field (the F in MOSFET) the control signal creates on one of the plates of the MOSFET.
Since the control signal and the output are electrically disconnected (as you would see in a capacitor) there is much less power draw
from this type of transistor.

We can see how linear this thing is with its IV characteristic: <math>I_D= \mu_n C_{ox}\frac{W}{L} \left( (V_{GS}-V_{th})V_{DS}-\frac{V_{DS}^2}{2} \right)</math>

Apart from the control signal <math>V_{DS}</math> and constants, the voltage across the output portion of the MOSFET is linearly related to the current!
This means that the MOSFET behaves like a voltage controlled resistor, and a resistor is something much easier to analyse and work with.

Most circuits with an enormous amount of transistors these days use primarily MOSFETs. BJTs are still useful for temperature and light sensing
applications.

==Industrial Semiconductor Fabrication==

Semiconductors are mass produced in specialized factories called foundries or fabs. The process consists of multiple chemical and photolithographic steps which add layers to a wafer usually made of silicon. The entire process usually takes around 2 months but it can last up to 4.

The semiconductor product is rated by the size of the chip's process gate length, where processes with smaller gate lengths are typically harder to make. There are 10-20 different sized chips being fabricated around the world as of 2018. There is an immense amount of attention and money being dedicated to improving semiconductor fabrication process efficiency.

[[File:feol.png|frame|none|left|Steps to fabricate a semiconductor device]]

==Examples==

===Simple===
[[File:Cat'swhiskerdetector.jpg]]

A simple application of a semiconductor would be the Cat's Whisker detector for radios, invented in the early 1900s.

===Moderate===
[[File:Opticallsensor.jpg]]

Optical sensors are moderately difficult applications of semiconductors. Optical sensors are electronic detectors that convert light into an electronic signal. They are used in many industrial and consumer applications. An example would include lamps that turn on automatically in response to darkness.

===Difficult===

[[File:Complicated_semiconductor.jpg]]

A very complicated application of a semiconductor is its use in modern cellular phone devices, such as its use here in the iPhone 6.

== See also ==

Related Wiki pages:

-Transformers

-Resistors and conductivity

-Superconductors

-Electric Fields

-Transformers from a physics standpoint

===Further reading===

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

===External links===

Wikipedia page about semiconductors:

https://en.wikipedia.org/wiki/Semiconductor_device

Encyclopedia entry about semiconductors, including the history of semiconductors:

http://www.britannica.com/technology/semiconductor-device

Information about Diodes:

https://en.wikipedia.org/wiki/Diode

Information about BJTs:

https://en.wikipedia.org/wiki/Bipolar_junction_transistor

Information about MOSFETs:

https://en.wikipedia.org/wiki/MOSFET

Semiconductor Device Fabrication

https://en.wikipedia.org/wiki/Semiconductor_device_fabrication

==References==
Brain, Marshall. "How Semiconductors Work." HowStuffWorks. N.p., 25 Apr. 2001. Web. 27 Nov. 2016.

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Electronics and Semiconductor. (n.d.). Retrieved December 3, 2015, from http://www.plm.automation.siemens.com/en_us/electronics-semiconductor/devices/

Huculak, M. (2014, September 19). IPhone 6 and iPhone 6 Plus get teardown by iFixit • The Windows Site for Enthusiasts - Pureinfotech. Retrieved December 3, 2015, from http://pureinfotech.com/2014/09/19/iphone-6-iphone-6-plus-get-teardown-ifixit/

Introduction to Secondary Ion Mass Spectrometry (SIMS) technique. (n.d.). Retrieved November 15, 2020, from https://www.cameca.com/products/sims/technique

John Bardeen, William Shockley and Walter Brattain at Bell Labs, 1948. (n.d.). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/John_Bardeen#/media/File:Bardeen_Shockley_Brattain_1948.JPG

The Nobel Prize in Physics 1956. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/1956/summary/>

The Nobel Prize in Physics 2000. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/2000/summary/>

เซ็นเซอร์แสง (Optical Sensor) - Elec-Za.com. (2014, July 28). Retrieved December 3, 2015, from http://www.elec-za.com/เซ็นเซอร์แสง-optical-sensor/

Semiconductor device. (2015, November 30). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/Semiconductor_device

Semiconductor Fabrication. (25 November 2018). http://www.iue.tuwien.ac.at/phd/rovitto/node10.html

Shah, A. (2013, May 13). Intel loses ground as world's top semiconductor company, survey says. Retrieved December 3, 2015, from http://www.pcworld.com/article/2038645/intel-loses-ground-as-worlds-top-semiconductor-company-survey-says.html

Shaw, R. (2014, November 1). The cat's-whisker detector. Retrieved December 3, 2015, from http://rileyjshaw.com/blog/the-cat's-whisker-detector/

Sze, S. (2015, October 1). Semiconductor device | electronics. Retrieved December 3, 2015, from http://www.britannica.com/technology/semiconductor-device

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

"Timeline." Timeline | The Silicon Engine | Computer History Museum. The Silicon Engine, n.d. Web. 27 Nov. 2016.

[[Category:Simple Circuits]]

File:2pp vs 4pp resistivity.png

2024-04-15T02:46:52Z

Idumitriu3:

Semiconductor Devices

2024-04-15T02:45:27Z

Idumitriu3: /* Determining Semiconductor Resistivity and Conductivity */

Last edited by Irene Dumitriu (Spring 2024)

===What are Semiconductors?===

Semiconductor devices are electronic components with the electronic properties of semiconductors. Silicon, germanium, gallium arsenide, organic semiconductors are among the most common semiconductors used in these devices. Semiconductors are materials that are neither good conductors or good insulators. They have a good conductivity between conductors (these tend to be metals) and nonconductors (these insulators tend to be ceramics). Semiconductors do not have to originate organically - the most common semiconductor material are pure elements such as silicon and germanium, but impurities are often added to control the conductivity levels. This process is called doping. The doped semiconductors are called extrinsic semiconductors while pure, impurity-free semiconductors are called intrinsic semiconductors. Intrinsic semiconductors are less conductive than metals as they have a lower amount of charge carriers, or electrons or holes, that can move across the band gap. Extrinsic semiconductors can have higher or lower conductivity depending on the doping.

The conductivity of these semiconductors can also be impacted by environmental changes such as temperature changes. Electrical conductivity depends on two factors: charge-carrier mobility and the concentration of mobile charge carriers. Charge carriers are free electrons or holes that are able to move freely throughout a material, and their mobility is the speed at which these electrons move in a certain direction under the application of a voltage. The free electrons are responsible for determining a current as a current is defined as the rate of electrons flowing through a material in a unit of time. In semiconductors, the charge carrier mobility is negligible as the temperature directly impacts mainly the charge carrier concentration. The band gap theory helps explain how charge carriers move in semiconductors. Unlike metals, semiconductors have a gap between the conduction band and the valence band where the electrons sit without excitation. As temperature increases, these electrons gain energy until they have enough energy to cross the band gap and into the conduction band, decreasing resistivity and increasing conductivity. This behavior is observed mainly in intrinsic semiconductors. In extrinsic semiconductors, the type of doping can affect the conductivity negatively or positively.

Due to low cost, reliability, ability to control conductivity, and compactness, semiconductors are used for a wide range of applications. They also have a wide range of current and voltage handling capabilities, contributing to their suitability for a number of operations. They are commonly found in power devices, optical sensors, and light emitters. Perhaps more importantly, they are readily integrated into microelectronic uses as key elements for the majority of electronic systems, including communications, consumer, data-processing, and industrial-control equipment.

[[File:Intelthing.jpg|frame|border|right|A raw board with many transistors in it!]]
[[File:transistor.png|frame|none|left|An fully built integrated circuit.]]

==The Main Idea==

Semiconductors work by using the electric properties of the p-n junction that makes up a diode. The junction is formed through a process called doping. Doping involves turning silicon into a conductor by changing the behavior of its electrons. In n-type doping, a phosphorus/arsenic impurity is introduced so that the valence will have free electrons to allow a electric current to flow. Since extra electrons are negative in charge, this type of doping is called n-type doping referred to by "n" in the p-n junction. In the p-type doping, a boron/gallium impurity is introduced to the silicon lattice so the valence will have an empty electron orbital. Because the empty area implies the absence of an electron and thus creates a positive charge, "p" was assigned as the name of the doping type.

[[File:n-type.gif|frame|border|right|N-Type Material]]

[[File:p-type.png|frame|none|left|P-Type Material]]

The two most useful forms of semiconductor devices are diodes and transistors. Diodes are the simplest semiconductor device, which conducts current easily in one direction but conducts almost no current in the other direction. These are made by joining two pieces of semiconducting material, a junction called a "p-n" junction. One of the pieces contains a small amount of boron and the other contains a small amount of phosphorus. Transistors are constructed through two semiconducting junctions, or "p-n" junctions. These are the most common elements in digital circuits. The conductivity of these semiconductors can be controlled by introduction of an electric or magnetic field, by exposure to light or heat, or by mechanical deformation of a doped monocrystalline grid. Due to this, semiconductors are extremely useful and can be altered to fit specific purposes.

===Semiconductors & Applications in Solid-State Physics===

The key principle that is often used in solid-state physics is the carrier effective mass. This refers to the mass a particle (within the semiconductor) seems to have when interacting with other identical particles in a thermal distribution. This constant is simplified version of the band theory and influences measurable properties of a solid, including the efficiency of the devices that semiconductors are used in for example, solar cell efficiency and integrated circuit speed. So, how do we actually measure the carrier effective masses in a semiconductor?

Large parts of the simplicity of the free electron gas model can be saved by assigning effective masses to the carriers. Only electrons and holes at the band edges (characterized by a wave vector kex) participate in the generation - recombination process that is the hallmark of semiconductors. A particle's effective mass is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles over long distances can be very different from their motion in a vacuum. The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass. Sometimes the effective mass can be considered to be a simple constant of a material, however, the value of effective mass depends on the purpose for which it is used, and can vary depending on a number of factors. For electrons or electron holes in a solid, the effective mass is usually stated in units of the rest mass of an electron, me (9.11×10−31 kg). In these units it is usually in the range 0.01 to 10, but can also be lower or higher—for example, reaching 1,000 in exotic heavy fermion materials, or anywhere from zero to infinity (depending on definition) in graphene. The effective mass of a semiconductor is obtained by fitting the actual electron diagram around the conduction band minimum or the valence band maximum by a parabola - this is called an E-K diagram (shown below). It shows the relationship between the energy and momentum of available quantum mechanical states for electrons in the material. As it simplifies the more general band theory, the electronic effective mass can be seen as an important basic parameter that influences measurable properties of a solid, including everything from the efficiency of a solar cell to the speed of an integrated circuit.

[[File:IMG 2424.jpg|Diagram of an EK diagram|350 px|]]

===Detecting Doping===

Secondary ion mass spectroscopy (SIMS) is a very powerful technique for the analysis of impurities in solids. SIMS can be utilized for semiconductor dopant profiling. The technique relies on removal of material from a solid by sputtering and on analysis of the sputtered ionized species; all elements are detected. SIMS can detect dopant densities as low as 10^14 cm^-3. The dopant density profile that is generated is based on the ion signal versus time plot. The time axis is converted to a depth axis by measuring the depth of the crater at the end of the measurement assuming a constant sputtering rate. For example, boron is implanted into silicon at a given energy and dose to create a standard. The secondary ion signal is calibrated by assuming the total amount of boron in the sample to equal to the implanted boron. The unknown sample of B implanted into silicon is then compared to the standard. However, there is limited dynamic range of the SIMS instrument that can contribute to slightly deeper junctions and discrepancies in the lowly doped portions of the profile. When sputtering from a highly doped region to a lowly doped region, the crater walls still contain the entire doping density profile. SIMS also measures total dopant density, regardless of activation. Thus going back to the silicon-boron example, the dopant profile shows dependence of electrical activation of boron implanted into silicon on implant dose and activation temperature.

[[File:Sims-technique-schematic.png|frame|none|left|Example of SIMS]]

===Determining Semiconductor Resistivity and Conductivity===

Methods for determining the resistivity and conductivity of material involve galvanostatic or potentiostatic tests. In a galvanostatic test, a constant current is applied and the voltage is measured. In a potentiostatic test, a constant voltage is applied and the current is measured. An electrochemical analyzer can be used with either a 2-point or 4-point method. With the 2-point method, there can be contact resistance between the material and the wires, falsely increasing the resistivity. The 4-point technique overcomes this issue by using four wires. A current is conducted and measured through the endpoints of the bar while two wires are connected to the inner points of the bar so that they can measure voltage produced across the inner bar. Once the data is collected, Ohm’s law can be used to calculate the resistivity with the voltage and resistance where the resistance is the 1/slope of the current vs. voltage graph.

===A Mathematical Model===

Semiconductors operate based on the concept of thermal energy exciting electrons and causing them to jump to the next higher (unoccupied) energy band.
These electrons can pick up energy (and drift speed) from an applied electric field. The filled energy band is called the “valence” band, and the nearly unoccupied higher energy band is called the “conduction” band. The number of electrons excited into the conduction band is proportional to a value called the Boltzmann constant, equivalent to the value:
<math>
e^{-E_{\text{gap}} / k_B T}
</math>.
Therefore, high conductivity (corrosponding to a favorable Boltzmann factor) can be calculated according to
<math>
T = 2 \pi \sqrt{\frac{m}{k}}
</math>,
where <math>m</math> is the mass of the object in kilograms, <math>k</math> is the spring constant, and <math>T</math> is the period of oscillation in seconds. In addition, the total conventional current in a semiconductor can be calculated, according to the equation
<math>
I = e n_n A u_n E + e n_p A u_p E
</math>.

===A Conceptual Model===
The following diagram demonstrates how electron excitement in semiconductors works. Semiconductors are materials with small band gaps between the valence band and conduction bands. As you can see, a small amount of thermal energy is needed to promote an electron to the conduction band in a semiconductor.

[[File:conceptual.png|frame|none|left|A Conceptual Model of the Semiconductor]]

===A Computational Model===

[https://phet.colorado.edu/sims/cheerpj/semiconductor/latest/semiconductor.html?simulation=semiconductor Semiconductor Simulation]

==History==
'''1874'''
Ferdinand Braun discovers that current flows freely in only one direction when a metal point and a galena crystal are put together.

'''1901'''
Jagadis Bose takes ownership of the discovery of the semiconductor crystal for detecting radio waves.

'''1940'''
Russell Ohl discovers the p-n junction.

'''1940s'''
Semiconductors were used only as two-terminal devices, such as rectifiers and photodiodes. They were most commonly used as detectors in radios, through devices called "cat's whiskers". During the era of WWII, researchers worked with semiconductors and cat's whiskers to make more effective diodes.

'''1947'''
William Shockley and John Bardeen worked together to create a triode-like semiconductor: the first transistor. They realized that if there were some way to control the flow of the electrons from the emitter to the collector of this newly discovered diode, an amplifier could be built.The first transistor was officially created on the 23rd of December, 1947.

'''1956'''
John Bardeen, William Shockley, and another researcher named Walter Houser Brattain were credited for the invention and awarded a Nobel Prize for physics in 1956 for their work. After this, the utilization of semiconductors soon advanced to even more complicated applications.

'''1960s'''
In the late 1960s, transistors moved from being germanium based to silicon based. Gordon K Teal was most responsible for this advancement, and his company, Texas Instruments, profited greatly. Portable radios are just one popular invention that benefited from silicon based semiconductors. Now, silicon based semiconductors constitute more than 95 percent of all semiconductor hardware sold worldwide.

'''1970s'''
Silicon technology is modernized and the race to fit all semiconductor processor technology into one chip is most active.

'''2000'''
Nobel Prize in physics awarded to Zhores I. Alferov and Herbert Kroemer for developing semiconductor heterostructures used in high-speed- and opto-electronics and half to Jack S. Kilby "for his part in the invention of the integrated circuit."

[[File:transistorwork.png|frame|none|none|John Bardeen, William Shockley, and Walter Houser Brattain, winners of the Nobel Prize for their invention of the transistor, are pictured above.]]

===Connectedness===

Semiconductors are crucial to modern technology, and are used for memory storage as well as so many other technological innovations. This technology is used every day by millions of people for thousands of different applications. Most people in the world have used semiconductors in one way or another, even if they weren't aware of it. It is specifically connected to the major of Biomedical Engineering through memory storage and the complex computer programs used every day to conduct business and create simulations for the furthering of biomedical research. All industrial applications of semiconductors are very applicable, from amplifiers to transistors to silicon disks. Without semiconductors, much of the technology that the general population relies on today would not be possible.

Semiconductors are used in essentially every part of this technological and electronically-dependent world we live in today. They have both conductor and insulator properties and includes all of the metal we see in wires. Computers, phones, and other electronic devices all use semiconductors to fulfill their functions such as communication and efficiency. The most important aspect of semiconductors is utilization, which is shown through the use of switches. Inside electronic devices, the switches exist in extremely large numbers, which is why electronic devices process information in an incredible speed with surprising efficiency.

Semiconductors are connected to chemical engineering largely through their industrial creation. The process of depositing each layer of material onto the wafer is a chemical process controlled by deposition of gaseous metals onto the wafer. There are an incredible variety of steps from material preparation to packaging which can be optimized by an eager chemical engineer.

Another example that was discussed previously on this page is the usage of silicon in photovoltaic devices. Silicon is used because it is the first semiconductor that was commercialized successfully. Many commercial companies are very proficient in making silicon devices, so the silicon is not necessarily used because it is the best material for harnessing the electricity from the photovoltaic effect. The silicon crystals allow the power to reach the external electrical circuit, but the silicon doesn't absorb sunlight as efficiently because it needs to be ten to one hundred times thicker than an advanced thin-film cell. It is also favored because of the low maintenance. A unique oxide forms when silicon is exposed to high temperatures that serves to neutralize defects on the silicon surface. The frontier for replacing the silicon looks quite bleak because of the practicality of manufacturing silicon crystalline semiconductors, but new research is being conducted on using silicon with lower purity or combining it with other semiconductor materials.

==Types of Semiconductors==

===Diodes===

[[File:Diode_current_wiki.png|314px|thumb|right|top|IV Characteristic of a Diode]]

Diodes are really great! In a simple sense, they can give you a "point of no return" in your circuit (but they can actually do much more than that).
Three interesting things should be observed from the IV characteristic shown to the right:

# For small positive voltages and above, the diode does not limit the current (the line is almost vertical)!
# For small to larger negative voltages, the diode resists current (the line is almost flat).
# For a large negative voltage (the breakdown voltage) the diode gives up (no one is perfect).

We can formally define this line with the Shockley Diode Equation, which formalizes this observation:

<math display="block">
I = I_S \left( e^{\frac{V_D}{n V_T}} - 1 \right)
</math> where

<math>I</math> is the diode current,

<math>I_S</math> is the reverse bias saturation current (or scale current),

<math>V_D</math> is the voltage across the diode,

<math>V_T</math> is the thermal voltage, and

<math>n</math> is the ideality factor, (1 if the diode is ideal, greater than 1 if it is imperfect).

A great practical use for diodes is a rectifier:

[[File:Gratz.rectifier.en.svg|frame|border|center|Diodes groups the positive and negative signals together]]

This makes sure that when a positive voltage appears on either line, it is redirected to a single positive line, and the same for the negatives.
BAM! AC to DC, that's pretty easy, you can charge your phone with that.
In reality a capacitor is added in parallel with the load to try to smooth out the ripples.
A voltage regulator after the rectifying step is also a popular choice, depending on the needs of the application.

Another super useful application is that of a back up power supply: simply connect two supplies in parallel with the positive terminals buffered with diodes. The higher of the two voltages is always used and the transition between supplies is seamless.

===Zener Diodes===

Some diodes (Zener) are made to have small breakdown voltages.
Since during breakdown the IV curve is almost vertical (it's really an exponential), the current is independent (almost) from voltage.
You can then wire up a Zener diode in reverse to a point in the circuit, and it will accept as much current as it needs to to reach that
breakdown voltage. Because of this a great practical use for Zener diodes is a voltage regulator since the voltage is set when the diode is
manufactured and does not change greatly with a varying power supply.

===Bipolar Junction Transistors===

[[Image:BJT NPN symbol (case).svg|75px|thumb|NPN BJT]]
[[Image:BJT PNP symbol (case).svg|75px|thumb|PNP BJT]]

Shortly after the invention of the first transistor (which was OK), the BJT landed, which was the first transistor to be prolific in the field.
It was made using two alternating NP junctions as shown below:

[[File:NPN BJT (Planar) Cross-section.svg|frame|border|center|NPN BJT (Planar) Cross-section]]

Really transistors (and by extension all that is needed for a computer to be built) are amplifiers (OK, to build all computers you need an inverting amplifier, but one can be built using the BJT).
If one is used to thinking of them as an electrically-controlled switch, you can simply think of a switch as an amplifier with a gain of <math>\infty</math>.

A simple model of a BJT is a linear current-controlled current source, i.e. the base to emitter (B to E) current <math>I_{BE}</math> is proportional to
the collector to emitter (C to E) current <math>I_{CE}</math>. The proportionality constant <math>\beta</math> can be thought of as the "gain" of the
transistor. This gives a relationship of <math>I_{CE} = \beta I_{BE}</math>.

[[File:Current-Voltage relationship of BJT.png|thumb|right|Current-Voltage relationship of BJT]]

Sadly there is no source of infinite power, so the output to our amplifier tops off when it can't supply any more power.
This can be seen with the graph on the right.
The simple model then only works for the tiny linear part at the start of the graph, even so its not ''that'' linear.
The BJT proved to be power hungry, pretty non-linear and sensitive to the environment (temperature, etc.).
These growing pains lead to a new development, called the MOSFET.

===MOSFETs===

MOSFETs are the coolest, they are less power-hungy and easier to work with when compared to BJTs.
Instead of having a current control, which uses power and gets the control and the output signal coupled together,
a MOSFET's output is controlled by the electric Field (the F in MOSFET) the control signal creates on one of the plates of the MOSFET.
Since the control signal and the output are electrically disconnected (as you would see in a capacitor) there is much less power draw
from this type of transistor.

We can see how linear this thing is with its IV characteristic: <math>I_D= \mu_n C_{ox}\frac{W}{L} \left( (V_{GS}-V_{th})V_{DS}-\frac{V_{DS}^2}{2} \right)</math>

Apart from the control signal <math>V_{DS}</math> and constants, the voltage across the output portion of the MOSFET is linearly related to the current!
This means that the MOSFET behaves like a voltage controlled resistor, and a resistor is something much easier to analyse and work with.

Most circuits with an enormous amount of transistors these days use primarily MOSFETs. BJTs are still useful for temperature and light sensing
applications.

==Industrial Semiconductor Fabrication==

Semiconductors are mass produced in specialized factories called foundries or fabs. The process consists of multiple chemical and photolithographic steps which add layers to a wafer usually made of silicon. The entire process usually takes around 2 months but it can last up to 4.

The semiconductor product is rated by the size of the chip's process gate length, where processes with smaller gate lengths are typically harder to make. There are 10-20 different sized chips being fabricated around the world as of 2018. There is an immense amount of attention and money being dedicated to improving semiconductor fabrication process efficiency.

[[File:feol.png|frame|none|left|Steps to fabricate a semiconductor device]]

==Examples==

===Simple===
[[File:Cat'swhiskerdetector.jpg]]

A simple application of a semiconductor would be the Cat's Whisker detector for radios, invented in the early 1900s.

===Moderate===
[[File:Opticallsensor.jpg]]

Optical sensors are moderately difficult applications of semiconductors. Optical sensors are electronic detectors that convert light into an electronic signal. They are used in many industrial and consumer applications. An example would include lamps that turn on automatically in response to darkness.

===Difficult===

[[File:Complicated_semiconductor.jpg]]

A very complicated application of a semiconductor is its use in modern cellular phone devices, such as its use here in the iPhone 6.

== See also ==

Related Wiki pages:

-Transformers

-Resistors and conductivity

-Superconductors

-Electric Fields

-Transformers from a physics standpoint

===Further reading===

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

===External links===

Wikipedia page about semiconductors:

https://en.wikipedia.org/wiki/Semiconductor_device

Encyclopedia entry about semiconductors, including the history of semiconductors:

http://www.britannica.com/technology/semiconductor-device

Information about Diodes:

https://en.wikipedia.org/wiki/Diode

Information about BJTs:

https://en.wikipedia.org/wiki/Bipolar_junction_transistor

Information about MOSFETs:

https://en.wikipedia.org/wiki/MOSFET

Semiconductor Device Fabrication

https://en.wikipedia.org/wiki/Semiconductor_device_fabrication

==References==
Brain, Marshall. "How Semiconductors Work." HowStuffWorks. N.p., 25 Apr. 2001. Web. 27 Nov. 2016.

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Electronics and Semiconductor. (n.d.). Retrieved December 3, 2015, from http://www.plm.automation.siemens.com/en_us/electronics-semiconductor/devices/

Huculak, M. (2014, September 19). IPhone 6 and iPhone 6 Plus get teardown by iFixit • The Windows Site for Enthusiasts - Pureinfotech. Retrieved December 3, 2015, from http://pureinfotech.com/2014/09/19/iphone-6-iphone-6-plus-get-teardown-ifixit/

Introduction to Secondary Ion Mass Spectrometry (SIMS) technique. (n.d.). Retrieved November 15, 2020, from https://www.cameca.com/products/sims/technique

John Bardeen, William Shockley and Walter Brattain at Bell Labs, 1948. (n.d.). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/John_Bardeen#/media/File:Bardeen_Shockley_Brattain_1948.JPG

The Nobel Prize in Physics 1956. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/1956/summary/>

The Nobel Prize in Physics 2000. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/2000/summary/>

เซ็นเซอร์แสง (Optical Sensor) - Elec-Za.com. (2014, July 28). Retrieved December 3, 2015, from http://www.elec-za.com/เซ็นเซอร์แสง-optical-sensor/

Semiconductor device. (2015, November 30). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/Semiconductor_device

Semiconductor Fabrication. (25 November 2018). http://www.iue.tuwien.ac.at/phd/rovitto/node10.html

Shah, A. (2013, May 13). Intel loses ground as world's top semiconductor company, survey says. Retrieved December 3, 2015, from http://www.pcworld.com/article/2038645/intel-loses-ground-as-worlds-top-semiconductor-company-survey-says.html

Shaw, R. (2014, November 1). The cat's-whisker detector. Retrieved December 3, 2015, from http://rileyjshaw.com/blog/the-cat's-whisker-detector/

Sze, S. (2015, October 1). Semiconductor device | electronics. Retrieved December 3, 2015, from http://www.britannica.com/technology/semiconductor-device

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

"Timeline." Timeline | The Silicon Engine | Computer History Museum. The Silicon Engine, n.d. Web. 27 Nov. 2016.

[[Category:Simple Circuits]]

Conductivity and Resistivity

2024-04-15T02:44:20Z

Idumitriu3: Undo revision 46278 by Idumitriu3 (talk)

'''This page was constructed from an amalgamation of [[Conductivity]] and [[Resistivity]], then edited by '''Islombek Kadirov, Fall 2023''''''

In the field of electrical engineering and materials science, conductivity refers to the ability of a material to conduct electric current. It is quantitatively measured as the ratio of the current density to the electric field causing the current flow. This property varies among different materials, significantly influencing their applications in various industries.

Resistivity, on the other hand, is the inverse of conductivity. It quantifies how strongly a material opposes the flow of electric current. The relationship between resistivity and conductivity is reciprocal, allowing for interchangeability in calculations and analyses, provided the inverse nature and corresponding units are properly accounted for.

Electrical conductivity is a measure of a material's capability to allow the passage of electric current. It indicates how easily electricity can traverse through a given material. This concept is analogous to thermal conductivity, which determines the efficiency with which thermal energy, commonly in the form of heat, can move through a material. Both electrical and thermal conductivity provide crucial insights into the behavior of materials under different energy transfer scenarios, making them fundamental properties in various fields, including materials science, electrical engineering, and thermal engineering.<ref> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html </ref>.

==Main Idea==

[[File:Conductance Of Materials.png|shows electron current and free electrons|500 px|]]
<ref>http://www.schoolphysics.co.uk/age16-19/glance/Electricity%20and%20magnetism/Conductance_/index.html</ref>

In the accompanying image, the interrelated nature of conductance and resistance is visually represented, illustrating how various factors influence these electrical properties. The image exemplifies how the density of atoms within a material can impact the movement of electrons. This visual aid serves to demonstrate the effect of atomic density on electron mobility, thereby affecting the material's conductance and resistance.

In the first material depicted, the atoms are more widely spaced, providing a greater area for the movement of free electrons. This phenomenon is identified as resistance. The conductance of the material is influenced by the transfer of these free electrons; a higher rate of free electron passage in a given timeframe correlates with increased conductivity. Due to the pronounced movement of free electrons, this material demonstrates lower resistance and higher conductivity, making it more efficient in transferring heat or energy. Consequently, it is often utilized as a conductor.

In the second material, the atoms are positioned closer together, resulting in reduced space for the movement of free electrons, a characteristic known as resistance. The conductance of this material is consequently affected by the limited transfer of free electrons. The fewer free electrons that pass through within a given timeframe, the less conductive the material is. Due to this diminished movement of free electrons, the material exhibits greater resistance and reduced conductivity, leading to less efficient heat or energy transfer. Such properties render this material more suitable for use as an insulator.

A conductor is a type of material that offers minimal resistance to the flow of electric current, making it highly efficient for conducting electricity. It's important to note that the resistivity of a material is influenced not only by the presence of free electrons but also by the temperature at which the material is maintained. Variations in temperature can significantly alter a material's resistive properties, affecting its ability to conduct electricity. This interplay between electron mobility and temperature is a crucial factor in determining the overall conductive or resistive behavior of a material.

An insulator is a material that exhibits high resistance to the flow of electric current, effectively preventing or significantly hindering the passage of electricity. Semiconductors, on the other hand, are materials that possess properties of both conductors and insulators, allowing them to conduct electricity under certain conditions. Common examples of conductive materials include metals, known for their low resistivity and high conductivity. Insulators typically comprise materials like wood or plastics, which have high resistivity and are used to prevent unwanted flow of electric current <ref> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/conins.html </ref>. Semiconductors, though more rare compared to conductors and insulators, play a crucial role in modern technology, particularly in the construction of transistors. These components are essential in all computers and a wide range of electronic devices. The most commonly used semiconductor material is doped silicon, which, through the process of doping, acquires the necessary electrical properties to efficiently control and amplify electronic signals. This characteristic makes semiconductors indispensable in the realm of digital electronics and integrated circuits <ref> https://electronics.howstuffworks.com/diode.htm </ref>. Beyond conductors, insulators, and semiconductors, there is another notable category known as superconductors. The phenomenon of superconductivity, discovered in 1911, is a quantum mechanical marvel that allows for the unimpeded flow of electric current, making superconductors highly valuable for applications requiring efficient energy transmission, powerful electromagnets, and advanced technologies like magnetic resonance imaging (MRI) and particle accelerators, and these unique materials exhibit zero electrical resistance under specific conditions, typically at extremely low temperatures and/or under high pressures <ref> https://home.cern/science/engineering/superconductivity </ref>, and there also exist a host of other materials with odd behaviors.

[[Units For Conductivity and Resistivity:]]

The units used to express conductivity and resistivity are indeed based on the familiar Ohm, a unit of electrical resistance. Conductivity, which measures how easily a material allows the flow of electric current, is typically expressed in Siemens per meter (S/m). On the other hand, resistivity, representing how much a material resists the flow of electric current, is measured in ohm-meters (Ω·m). These units provide a standardized way to quantify and compare the electrical properties of different materials, crucial for applications in electrical engineering and materials science. Expressed in terms of SI base units, the unit of resistivity becomes <math> \frac{kg\cdot m^3}{s^3\cdot A^2} = \frac{kg\cdot m^3}{s\cdot C^2} </math>.

[[Factors that influence the resistivity of an object:]]

~Material Composition: Different materials inherently have different levels of resistivity. For instance, metals typically have lower resistivity than insulators like plastic or wood.

~Temperature: Generally, for conductors, resistivity increases with temperature. In semiconductors and insulators, the effect can be more complex.

~Impurities and Material Defects: The presence of impurities and defects in a material can significantly alter its resistivity. This is particularly notable in semiconductors, where doping with impurities is used to control resistivity.

~ Physical Structure: The microscopic structure of a material, including its crystal structure and the presence of grain boundaries, can affect resistivity.

~Pressure: Applying pressure to a material can change its resistivity, though this effect is generally less significant than temperature or material composition.

===Mathematical Method===

The relationship between conductivity and resistivity is a fundamental concept in the field of materials science and electrical engineering. Here's how they are related:

<math> \sigma = \frac{1}{\rho} </math>

By convention, we have <math> \sigma </math> as the conductivity, and <math> \rho </math> as the resistivity.

[[File:Resistivity geometry.svg|Resistivity geometry|300 px|right]]

Conductivity and Resistivity are intrinsic material properties, influenced primarily by chemical composition and structural attributes, but also sensitive to temperature and other environmental conditions. In practical applications, these values are either predetermined constants used in calculations or derived outcomes from specific equations. The focus thus lies in understanding the relevant equations that govern these properties. A key equation relates resistivity to resistance in an idealized manner, providing a foundational understanding for analyzing the electrical characteristics of different materials. This relationship is crucial for the design and analysis of electrical and electronic systems, where accurate knowledge of material properties is essential.

<math> R = \frac{\rho L}{A} </math>

In this context, the resistance of a wire is denoted as <math> R </math>, the length of the wire is <math> L </math>, <math> rho </math> is equal to resistivity and the variable <math>A </math> is its cross sectional area. This formulation presupposes a well-defined length of the wire aligned with the direction of electric current flow and a specific cross-sectional area perpendicular to the current's direction. These parameters are essential in determining the wire's resistance characteristics, especially in the context of electrical and electronic engineering.

Adjusting the area of a conductor can be achieved by making additional connections to it within a circuit. For instance, if there is a current flowing from North to South through a conductor, attaching a second conductor parallel to the first effectively doubles the area of the conductor. This modification impacts the overall resistance of the circuit, as the cross-sectional area is a key factor in determining resistance. By increasing the area through parallel connections, the resistance is reduced, allowing more current to flow through the circuit.

As seen by the equation <math> R = \frac{\rho L}{A} </math>, doubling the Area would cut the resistance in half and effectively double the conductance of the circuit containing the conductors seeing that <math> \sigma = \frac{1}{\rho} </math>

<p>In the realm of electrical engineering, a standard wire exemplifies a practical application of Ohm's Law. This fundamental law delineates the correlation between the flow of electric charge and the electric field responsible for this flow. Ohm's Law is articulated through two essential equations:</p>

<p>The first equation explicitly states the relationship:</p>

<math>\vec{J} = \sigma \vec{E}</math>

<p>Here, <math>\vec{J}</math> represents the current density, and <math>\vec{E}</math> signifies the electric field. The concept of current density refers to the amount of charge traversing a specified cross-sectional area within a certain time frame, measured in SI units as <math>\frac{A}{m^2} = \frac{C}{m^2 \cdot s}</math>. This elucidates that current density is a 'density' with 'area' in its denominator.</p>

<p>Another aspect related to Ohm's Law is the "skin effect," which elucidates the interplay between current density and the radius of a wire. It posits that a larger wire radius leads to increased current density. This effect is integral to understanding Ohm's Law in practical scenarios.</p>

<p>Another commonly used form of Ohm's Law is expressed as:</p>

<math>V = I R</math>

<p>Where <math>V</math> is the electric potential, <math>I</math> the current, and <math>R</math> the resistance. This version of the law is widely employed in various electrical engineering applications.</p>

===Computational Method===

This topic is largely conceptual and algebraic, so there is relatively little modeling to be done. However, [https://colab.research.google.com/drive/1hR-F7dQk4ZadIB3DEhZZPvnTmmGpj1hQ this] program is designed to create plots of the relationship between resistance, resistivity, length and cross sectional area.

[[Code shows the relationship between:]]

Resistance and length across different fixed points

Resistance and area across different fixed points

Furthermore, [https://phet.colorado.edu/sims/html/resistance-in-a-wire/latest/resistance-in-a-wire_en.html this] external program provides a good visual demonstration of the relationship that acts as a good simulation for altering either the volume, conductance, current, or area of an object to see how the resistance will be altered (but unfortunately the source code is not accessible).

==Examples==

===Simple===
'''Example Number 1'''

A semi conductive material has a resistivity of <math> 200 \; \Omega\cdot m </math>. What is its conductivity?

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

Since conductivity is the reciprocal of resistivity,

<math> \sigma = \frac{1}{\rho} = \frac{1}{200 \; \Omega \cdot m} = 0.005 \frac{1}{\Omega \cdot m} </math>

</div></div>

'''Example Number 1.2'''

A copper wire has a resistivity of <math> 1.68 \times 10^{-8} \; \Omega\cdot m </math> at room temperature. Determine its conductivity.

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

Given that conductivity is the inverse of resistivity,

<math> \sigma = \frac{1}{\rho} = \frac{1}{1.68 \times 10^{-8} \; \Omega \cdot m} = 5.95 \times 10^{7} \frac{1}{\Omega \cdot m} </math>

This result indicates high conductivity, characteristic of copper.

</div></div>

'''Example Number 1.3'''

Calculate the resistivity of an aluminum material with a conductivity of <math> 3.5 \times 10^{7} \frac{1}{\Omega \cdot m} </math>.

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

Since resistivity is the reciprocal of conductivity,

<math> \rho = \frac{1}{\sigma} = \frac{1}{3.5 \times 10^{7} \frac{1}{\Omega \cdot m}} = 2.86 \times 10^{-8} \; \Omega\cdot m </math>

This value of resistivity is typical for aluminum.

</div></div>

'''Example Number 2'''

An unknown material is used in the creation of a video game console.

Part A: How would the amount of free electrons in the material affect the conductance of the material?

Part B: Would the material's conductance increase or decrease if you put the material in the freezer as opposed to room temperature?

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution For Part A</div>
<div class="mw-collapsible-content">

The conductance of a material is directly influenced by the number of free electrons available for conduction. A higher number of free electrons implies lower resistance, as conductance is inversely related to resistivity (<math> \sigma = \frac{1}{\rho} </math>). Therefore, an increase in free electrons results in higher conductance.

</div></div>

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution For Part B</div>
<div class="mw-collapsible-content">

Lowering the temperature of a material typically increases its resistivity, as free electron movement is slowed. This results in a decrease in conductance. In colder environments (like a freezer), the slowed electron movement leads to increased resistance and consequently, decreased conductance in the material.

</div></div>

===Middling===

'''Example Number 1'''

An electric potential of <math> 120 V </math> is applied to a circular wire of length <math> 2 \cdot 10^4 \; m </math> and radius <math> 0.001 m </math>. The current is equal to <math> 1.11 \; A </math>. Determine the resistivity, and match it to an elemental metal using an appropriate table (such as <ref> http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/elecon.html </ref>)

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

We have Ohm's Law

<math> V = I R </math>

and so plugging in our definition for resistance in terms of resistivity gives that

<math> V = \frac{I \rho L}{A} </math>

which we rearrange to get

<math> \rho = \frac{ V A}{I L} </math>

plugging all of the values in gives an answer of <math>\rho = 1.7 \cdot 10^{-8} \; \Omega \cdot m </math>, which is the resistivity of copper.

</div></div>

'''Example Number 2'''

A student wishes to cut a wire in order to reach a specific potential difference.

Given what we know about Ohm's law, a student discovers that the wire she is using in a circuit to light a light bulb has a resistance of <math> \rho = 2.0 \cdot 10^{-7} \; \Omega \cdot m </math> and a radius of .002 meters. The current in the circuit is equal to 1 Amepere. The student then realizes that in order for the light bulb to be lit, there must be an electric potential across the light bulb of at least 100 Volts. Given that there are no other resistors in the circuit, determine the necessary length of the wire that she would need to cut in order for the potential difference of the wire to equal 100 Volts.

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

We can start by rearranging Ohm's Law

Ohms Law is equal to

<math> V = I R </math>

and so plugging in our definition for resistance in terms of resistivity gives that

<math> V = \frac{I \rho L}{A} </math>

which we rearrange to get

<math> \rho = \frac{ V A}{I L} </math> like in example 1

If the equation is even more rearranged in order to find the necessary length she needs to cut of the wire to get a potential difference, the equation would be

<math> L= \frac{ V* A}{I*rho} </math>

The next step is to use the radius of the wire in the given problem to find the area

Area= pi*r^2

If you plug in the numbers you get <math>L=100*(pi*(.002)^2)/(2.0 \cdot 10^{-7}*1)</math>

This gives you a necessary length of 6.28 \cdot 10^{5} meters

</div></div>

===Difficult===

One cubic meter of a fictional material with resistivity <math> \rho = 10^{-5} \; \Omega \cdot m </math> is formed into a shape with uniform cross sectional area (such that volume is equal to the base times the height) for which the resistance to current run lengthwise is equal to <math> 10 \; \Omega</math>. Determine the dimensions (length and cross sectional area) of the shape, presuming that it follows Ohm's law and the equation for resistance given above.

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

As the clarification hints, it is necessary to use a little basic geometry to solve this problem, namely

<math> V = L \cdot A </math>

So we lay out the standard formula

<math> R = \frac{\rho L}{A} </math>

Then multiply both numerator and denominator by <math> L </math> to obtain

<math> R = \frac{\rho L^2}{A L} = \frac{\rho L^2}{V} </math>

From here it is simply rearrangement to find that

<math> L = \sqrt{\frac{R V}{\rho}} = \sqrt{\frac{(1 \;m^3)(10 \;\Omega)}{10^{-5} \; \Omega \cdot m }} = 10^2 \; m </math>

With the length determined, it is then straightforward to conclude that <math> A = 10^{-2} \; m^2 </math>, and the cross-section can take any shape which has that enclosed area.

</div></div>

==Connectedness==

<p>Every time an electrical system has been created, an understanding of conductivity and resistivity had to be determined.</p>

<p>Since conductivity and resistivity are related, it is reasonable to assume that wires or components with low electric resistivity make good conductors due to their ability to effectively transmit electricity and heat. Conversely, materials with high electric resistivity are less efficient at conducting and are often used as insulators.</p>

<p>This concept has significant applications in real life, including:</p>
<ul>
<li><strong>[[Home insulation:]]</strong> Utilizing materials with high resistivity to maintain indoor temperature.</li>
<li><strong>[[Cooking:]]</strong> Employing pots, pans, and other metallic objects with low resistivity for efficient heat transfer, allowing food to cook evenly without direct exposure to the stove's heat source.</li>
<li><strong>[[Electronic Devices:]]</strong> Using materials with high resistivity in electronic devices to regulate temperature and prevent overheating, caused by the constant flow of electrical current.</li>
</ul>

[[Measuring Conductivity]]

To measure conductivity<ref>https://gpg.geosci.xyz/content/physical_properties/physical_properties_conductivity.html</ref>, a sample of the material is placed in between two metallic electrodes, either made of copper or granite.
Ohm's law is then used to calculate the numerical value of the resistance of the circuit.

[[File:Resistance.jpg|Electrical Conductivity of Various Metals|350 px|]]<ref>https://gpg.geosci.xyz/content/physical_properties/induced_polarization_physical_properties_duplicate.html</ref>

This is done through monitoring the current that is produced from the loop and the <math>delta V</math> that can be measured through the attachment of an ammeter to the copper or granite circuit.
The stronger conductors would have a higher <health>delta V<delta V> value and/or a lower I, a larger convection current.

==History==

<p>The study of conductivity and resistivity has a rich history, marked by significant contributions from various scientists. One of the earliest contributors was Stephen Gray, who along with Ganvil Wheler, observed that electricity could be transmitted over distances and that different materials had varying effectiveness in conducting electricity. This early observation, contrasting the conductivity between silk and brass wires, laid the groundwork for future studies [9].</p>

<p>While the 18th century saw notable advancements in understanding electricity, including the work of Benjamin Franklin, these developments were more closely tied to broader aspects of electrical science rather than specifically to conductivity and resistivity.</p>

<p>The early 19th century marked a pivotal moment in the study of resistivity and conductivity. Antoine Becquerel, the grandfather of Henri Becquerel who later became renowned for his work in radioactivity alongside Marie Skłodowska Curie and Pierre Curie, formulated an equation to determine resistance from resistivity and geometry [10]. This breakthrough provided a more quantitative approach to understanding how electrical resistance was influenced by material properties and structural dimensions.</p>

<p>Following Becquerel's work, Georg Ohm, a German physicist, proposed a theorem relating current, potential, and resistance. Although his initial proposition was incorrect, he soon revised it, leading to the formulation of Ohm's law. Despite initial skepticism and poor reception due to philosophical differences and confusion over the definitions of resistance, current, and potential, Ohm's work eventually gained acceptance and recognition, transforming our understanding of electrical resistance and its relationship to current and voltage.</p>

<p>This period marked a crucial era in the study of electrical properties, as scientists began to establish the fundamental principles that would shape our modern understanding of electrical conductivity and resistivity.</p>

==See Also==
If you are interested in learning more about this topic or want further clarification about concepts, check out these resources!

===Further reading===
The textbook Matter and Interaction by Chabay and Sherwood has some discussion of conductivity and resistivity:
*Chapter 14 discusses conductors and insulators with some specifics about polarization and charge. Page 548 includes a specific definition for both.
*Page 771 talks about conductivity
*Page 773 talks about resistance in relation to conductivity and geometry
*Page 775 talks about semiconductors
The textbook Electricity and Magnetism by Purcell also covers conductivity and resistivity:
*Chapter 3.1 covers conductors and insulators
*Chapter 4.6 covers semiconductors

===External links===
*Table of electrical resistivity and conductivity values for different materials: https://www.thoughtco.com/table-of-electrical-resistivity-conductivity-608499
*Resistivity and conductivity explanation: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html
*Khan Academy video on resistivity and conductivity https://www.khanacademy.org/science/ap-physics-1/ap-circuits-topic/current-ap/v/resistivity-and-conductivity
*Resistivity, An explanation (Youtube Video By Brian Swarthout) https://youtu.be/dRtNvUQC7c8

==References==

<references/>

Semiconductor Devices

2024-04-15T02:42:56Z

Idumitriu3: /* Detecting Doping */

Last edited by Irene Dumitriu (Spring 2024)

===What are Semiconductors?===

Semiconductor devices are electronic components with the electronic properties of semiconductors. Silicon, germanium, gallium arsenide, organic semiconductors are among the most common semiconductors used in these devices. Semiconductors are materials that are neither good conductors or good insulators. They have a good conductivity between conductors (these tend to be metals) and nonconductors (these insulators tend to be ceramics). Semiconductors do not have to originate organically - the most common semiconductor material are pure elements such as silicon and germanium, but impurities are often added to control the conductivity levels. This process is called doping. The doped semiconductors are called extrinsic semiconductors while pure, impurity-free semiconductors are called intrinsic semiconductors. Intrinsic semiconductors are less conductive than metals as they have a lower amount of charge carriers, or electrons or holes, that can move across the band gap. Extrinsic semiconductors can have higher or lower conductivity depending on the doping.

The conductivity of these semiconductors can also be impacted by environmental changes such as temperature changes. Electrical conductivity depends on two factors: charge-carrier mobility and the concentration of mobile charge carriers. Charge carriers are free electrons or holes that are able to move freely throughout a material, and their mobility is the speed at which these electrons move in a certain direction under the application of a voltage. The free electrons are responsible for determining a current as a current is defined as the rate of electrons flowing through a material in a unit of time. In semiconductors, the charge carrier mobility is negligible as the temperature directly impacts mainly the charge carrier concentration. The band gap theory helps explain how charge carriers move in semiconductors. Unlike metals, semiconductors have a gap between the conduction band and the valence band where the electrons sit without excitation. As temperature increases, these electrons gain energy until they have enough energy to cross the band gap and into the conduction band, decreasing resistivity and increasing conductivity. This behavior is observed mainly in intrinsic semiconductors. In extrinsic semiconductors, the type of doping can affect the conductivity negatively or positively.

Due to low cost, reliability, ability to control conductivity, and compactness, semiconductors are used for a wide range of applications. They also have a wide range of current and voltage handling capabilities, contributing to their suitability for a number of operations. They are commonly found in power devices, optical sensors, and light emitters. Perhaps more importantly, they are readily integrated into microelectronic uses as key elements for the majority of electronic systems, including communications, consumer, data-processing, and industrial-control equipment.

[[File:Intelthing.jpg|frame|border|right|A raw board with many transistors in it!]]
[[File:transistor.png|frame|none|left|An fully built integrated circuit.]]

==The Main Idea==

Semiconductors work by using the electric properties of the p-n junction that makes up a diode. The junction is formed through a process called doping. Doping involves turning silicon into a conductor by changing the behavior of its electrons. In n-type doping, a phosphorus/arsenic impurity is introduced so that the valence will have free electrons to allow a electric current to flow. Since extra electrons are negative in charge, this type of doping is called n-type doping referred to by "n" in the p-n junction. In the p-type doping, a boron/gallium impurity is introduced to the silicon lattice so the valence will have an empty electron orbital. Because the empty area implies the absence of an electron and thus creates a positive charge, "p" was assigned as the name of the doping type.

[[File:n-type.gif|frame|border|right|N-Type Material]]

[[File:p-type.png|frame|none|left|P-Type Material]]

The two most useful forms of semiconductor devices are diodes and transistors. Diodes are the simplest semiconductor device, which conducts current easily in one direction but conducts almost no current in the other direction. These are made by joining two pieces of semiconducting material, a junction called a "p-n" junction. One of the pieces contains a small amount of boron and the other contains a small amount of phosphorus. Transistors are constructed through two semiconducting junctions, or "p-n" junctions. These are the most common elements in digital circuits. The conductivity of these semiconductors can be controlled by introduction of an electric or magnetic field, by exposure to light or heat, or by mechanical deformation of a doped monocrystalline grid. Due to this, semiconductors are extremely useful and can be altered to fit specific purposes.

===Semiconductors & Applications in Solid-State Physics===

The key principle that is often used in solid-state physics is the carrier effective mass. This refers to the mass a particle (within the semiconductor) seems to have when interacting with other identical particles in a thermal distribution. This constant is simplified version of the band theory and influences measurable properties of a solid, including the efficiency of the devices that semiconductors are used in for example, solar cell efficiency and integrated circuit speed. So, how do we actually measure the carrier effective masses in a semiconductor?

Large parts of the simplicity of the free electron gas model can be saved by assigning effective masses to the carriers. Only electrons and holes at the band edges (characterized by a wave vector kex) participate in the generation - recombination process that is the hallmark of semiconductors. A particle's effective mass is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles over long distances can be very different from their motion in a vacuum. The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass. Sometimes the effective mass can be considered to be a simple constant of a material, however, the value of effective mass depends on the purpose for which it is used, and can vary depending on a number of factors. For electrons or electron holes in a solid, the effective mass is usually stated in units of the rest mass of an electron, me (9.11×10−31 kg). In these units it is usually in the range 0.01 to 10, but can also be lower or higher—for example, reaching 1,000 in exotic heavy fermion materials, or anywhere from zero to infinity (depending on definition) in graphene. The effective mass of a semiconductor is obtained by fitting the actual electron diagram around the conduction band minimum or the valence band maximum by a parabola - this is called an E-K diagram (shown below). It shows the relationship between the energy and momentum of available quantum mechanical states for electrons in the material. As it simplifies the more general band theory, the electronic effective mass can be seen as an important basic parameter that influences measurable properties of a solid, including everything from the efficiency of a solar cell to the speed of an integrated circuit.

[[File:IMG 2424.jpg|Diagram of an EK diagram|350 px|]]

===Detecting Doping===

Secondary ion mass spectroscopy (SIMS) is a very powerful technique for the analysis of impurities in solids. SIMS can be utilized for semiconductor dopant profiling. The technique relies on removal of material from a solid by sputtering and on analysis of the sputtered ionized species; all elements are detected. SIMS can detect dopant densities as low as 10^14 cm^-3. The dopant density profile that is generated is based on the ion signal versus time plot. The time axis is converted to a depth axis by measuring the depth of the crater at the end of the measurement assuming a constant sputtering rate. For example, boron is implanted into silicon at a given energy and dose to create a standard. The secondary ion signal is calibrated by assuming the total amount of boron in the sample to equal to the implanted boron. The unknown sample of B implanted into silicon is then compared to the standard. However, there is limited dynamic range of the SIMS instrument that can contribute to slightly deeper junctions and discrepancies in the lowly doped portions of the profile. When sputtering from a highly doped region to a lowly doped region, the crater walls still contain the entire doping density profile. SIMS also measures total dopant density, regardless of activation. Thus going back to the silicon-boron example, the dopant profile shows dependence of electrical activation of boron implanted into silicon on implant dose and activation temperature.

[[File:Sims-technique-schematic.png|frame|none|left|Example of SIMS]]

===Determining Semiconductor Resistivity and Conductivity===

===A Mathematical Model===

Semiconductors operate based on the concept of thermal energy exciting electrons and causing them to jump to the next higher (unoccupied) energy band.
These electrons can pick up energy (and drift speed) from an applied electric field. The filled energy band is called the “valence” band, and the nearly unoccupied higher energy band is called the “conduction” band. The number of electrons excited into the conduction band is proportional to a value called the Boltzmann constant, equivalent to the value:
<math>
e^{-E_{\text{gap}} / k_B T}
</math>.
Therefore, high conductivity (corrosponding to a favorable Boltzmann factor) can be calculated according to
<math>
T = 2 \pi \sqrt{\frac{m}{k}}
</math>,
where <math>m</math> is the mass of the object in kilograms, <math>k</math> is the spring constant, and <math>T</math> is the period of oscillation in seconds. In addition, the total conventional current in a semiconductor can be calculated, according to the equation
<math>
I = e n_n A u_n E + e n_p A u_p E
</math>.

===A Conceptual Model===
The following diagram demonstrates how electron excitement in semiconductors works. Semiconductors are materials with small band gaps between the valence band and conduction bands. As you can see, a small amount of thermal energy is needed to promote an electron to the conduction band in a semiconductor.

[[File:conceptual.png|frame|none|left|A Conceptual Model of the Semiconductor]]

===A Computational Model===

[https://phet.colorado.edu/sims/cheerpj/semiconductor/latest/semiconductor.html?simulation=semiconductor Semiconductor Simulation]

==History==
'''1874'''
Ferdinand Braun discovers that current flows freely in only one direction when a metal point and a galena crystal are put together.

'''1901'''
Jagadis Bose takes ownership of the discovery of the semiconductor crystal for detecting radio waves.

'''1940'''
Russell Ohl discovers the p-n junction.

'''1940s'''
Semiconductors were used only as two-terminal devices, such as rectifiers and photodiodes. They were most commonly used as detectors in radios, through devices called "cat's whiskers". During the era of WWII, researchers worked with semiconductors and cat's whiskers to make more effective diodes.

'''1947'''
William Shockley and John Bardeen worked together to create a triode-like semiconductor: the first transistor. They realized that if there were some way to control the flow of the electrons from the emitter to the collector of this newly discovered diode, an amplifier could be built.The first transistor was officially created on the 23rd of December, 1947.

'''1956'''
John Bardeen, William Shockley, and another researcher named Walter Houser Brattain were credited for the invention and awarded a Nobel Prize for physics in 1956 for their work. After this, the utilization of semiconductors soon advanced to even more complicated applications.

'''1960s'''
In the late 1960s, transistors moved from being germanium based to silicon based. Gordon K Teal was most responsible for this advancement, and his company, Texas Instruments, profited greatly. Portable radios are just one popular invention that benefited from silicon based semiconductors. Now, silicon based semiconductors constitute more than 95 percent of all semiconductor hardware sold worldwide.

'''1970s'''
Silicon technology is modernized and the race to fit all semiconductor processor technology into one chip is most active.

'''2000'''
Nobel Prize in physics awarded to Zhores I. Alferov and Herbert Kroemer for developing semiconductor heterostructures used in high-speed- and opto-electronics and half to Jack S. Kilby "for his part in the invention of the integrated circuit."

[[File:transistorwork.png|frame|none|none|John Bardeen, William Shockley, and Walter Houser Brattain, winners of the Nobel Prize for their invention of the transistor, are pictured above.]]

===Connectedness===

Semiconductors are crucial to modern technology, and are used for memory storage as well as so many other technological innovations. This technology is used every day by millions of people for thousands of different applications. Most people in the world have used semiconductors in one way or another, even if they weren't aware of it. It is specifically connected to the major of Biomedical Engineering through memory storage and the complex computer programs used every day to conduct business and create simulations for the furthering of biomedical research. All industrial applications of semiconductors are very applicable, from amplifiers to transistors to silicon disks. Without semiconductors, much of the technology that the general population relies on today would not be possible.

Semiconductors are used in essentially every part of this technological and electronically-dependent world we live in today. They have both conductor and insulator properties and includes all of the metal we see in wires. Computers, phones, and other electronic devices all use semiconductors to fulfill their functions such as communication and efficiency. The most important aspect of semiconductors is utilization, which is shown through the use of switches. Inside electronic devices, the switches exist in extremely large numbers, which is why electronic devices process information in an incredible speed with surprising efficiency.

Semiconductors are connected to chemical engineering largely through their industrial creation. The process of depositing each layer of material onto the wafer is a chemical process controlled by deposition of gaseous metals onto the wafer. There are an incredible variety of steps from material preparation to packaging which can be optimized by an eager chemical engineer.

Another example that was discussed previously on this page is the usage of silicon in photovoltaic devices. Silicon is used because it is the first semiconductor that was commercialized successfully. Many commercial companies are very proficient in making silicon devices, so the silicon is not necessarily used because it is the best material for harnessing the electricity from the photovoltaic effect. The silicon crystals allow the power to reach the external electrical circuit, but the silicon doesn't absorb sunlight as efficiently because it needs to be ten to one hundred times thicker than an advanced thin-film cell. It is also favored because of the low maintenance. A unique oxide forms when silicon is exposed to high temperatures that serves to neutralize defects on the silicon surface. The frontier for replacing the silicon looks quite bleak because of the practicality of manufacturing silicon crystalline semiconductors, but new research is being conducted on using silicon with lower purity or combining it with other semiconductor materials.

==Types of Semiconductors==

===Diodes===

[[File:Diode_current_wiki.png|314px|thumb|right|top|IV Characteristic of a Diode]]

Diodes are really great! In a simple sense, they can give you a "point of no return" in your circuit (but they can actually do much more than that).
Three interesting things should be observed from the IV characteristic shown to the right:

# For small positive voltages and above, the diode does not limit the current (the line is almost vertical)!
# For small to larger negative voltages, the diode resists current (the line is almost flat).
# For a large negative voltage (the breakdown voltage) the diode gives up (no one is perfect).

We can formally define this line with the Shockley Diode Equation, which formalizes this observation:

<math display="block">
I = I_S \left( e^{\frac{V_D}{n V_T}} - 1 \right)
</math> where

<math>I</math> is the diode current,

<math>I_S</math> is the reverse bias saturation current (or scale current),

<math>V_D</math> is the voltage across the diode,

<math>V_T</math> is the thermal voltage, and

<math>n</math> is the ideality factor, (1 if the diode is ideal, greater than 1 if it is imperfect).

A great practical use for diodes is a rectifier:

[[File:Gratz.rectifier.en.svg|frame|border|center|Diodes groups the positive and negative signals together]]

This makes sure that when a positive voltage appears on either line, it is redirected to a single positive line, and the same for the negatives.
BAM! AC to DC, that's pretty easy, you can charge your phone with that.
In reality a capacitor is added in parallel with the load to try to smooth out the ripples.
A voltage regulator after the rectifying step is also a popular choice, depending on the needs of the application.

Another super useful application is that of a back up power supply: simply connect two supplies in parallel with the positive terminals buffered with diodes. The higher of the two voltages is always used and the transition between supplies is seamless.

===Zener Diodes===

Some diodes (Zener) are made to have small breakdown voltages.
Since during breakdown the IV curve is almost vertical (it's really an exponential), the current is independent (almost) from voltage.
You can then wire up a Zener diode in reverse to a point in the circuit, and it will accept as much current as it needs to to reach that
breakdown voltage. Because of this a great practical use for Zener diodes is a voltage regulator since the voltage is set when the diode is
manufactured and does not change greatly with a varying power supply.

===Bipolar Junction Transistors===

[[Image:BJT NPN symbol (case).svg|75px|thumb|NPN BJT]]
[[Image:BJT PNP symbol (case).svg|75px|thumb|PNP BJT]]

Shortly after the invention of the first transistor (which was OK), the BJT landed, which was the first transistor to be prolific in the field.
It was made using two alternating NP junctions as shown below:

[[File:NPN BJT (Planar) Cross-section.svg|frame|border|center|NPN BJT (Planar) Cross-section]]

Really transistors (and by extension all that is needed for a computer to be built) are amplifiers (OK, to build all computers you need an inverting amplifier, but one can be built using the BJT).
If one is used to thinking of them as an electrically-controlled switch, you can simply think of a switch as an amplifier with a gain of <math>\infty</math>.

A simple model of a BJT is a linear current-controlled current source, i.e. the base to emitter (B to E) current <math>I_{BE}</math> is proportional to
the collector to emitter (C to E) current <math>I_{CE}</math>. The proportionality constant <math>\beta</math> can be thought of as the "gain" of the
transistor. This gives a relationship of <math>I_{CE} = \beta I_{BE}</math>.

[[File:Current-Voltage relationship of BJT.png|thumb|right|Current-Voltage relationship of BJT]]

Sadly there is no source of infinite power, so the output to our amplifier tops off when it can't supply any more power.
This can be seen with the graph on the right.
The simple model then only works for the tiny linear part at the start of the graph, even so its not ''that'' linear.
The BJT proved to be power hungry, pretty non-linear and sensitive to the environment (temperature, etc.).
These growing pains lead to a new development, called the MOSFET.

===MOSFETs===

MOSFETs are the coolest, they are less power-hungy and easier to work with when compared to BJTs.
Instead of having a current control, which uses power and gets the control and the output signal coupled together,
a MOSFET's output is controlled by the electric Field (the F in MOSFET) the control signal creates on one of the plates of the MOSFET.
Since the control signal and the output are electrically disconnected (as you would see in a capacitor) there is much less power draw
from this type of transistor.

We can see how linear this thing is with its IV characteristic: <math>I_D= \mu_n C_{ox}\frac{W}{L} \left( (V_{GS}-V_{th})V_{DS}-\frac{V_{DS}^2}{2} \right)</math>

Apart from the control signal <math>V_{DS}</math> and constants, the voltage across the output portion of the MOSFET is linearly related to the current!
This means that the MOSFET behaves like a voltage controlled resistor, and a resistor is something much easier to analyse and work with.

Most circuits with an enormous amount of transistors these days use primarily MOSFETs. BJTs are still useful for temperature and light sensing
applications.

==Industrial Semiconductor Fabrication==

Semiconductors are mass produced in specialized factories called foundries or fabs. The process consists of multiple chemical and photolithographic steps which add layers to a wafer usually made of silicon. The entire process usually takes around 2 months but it can last up to 4.

The semiconductor product is rated by the size of the chip's process gate length, where processes with smaller gate lengths are typically harder to make. There are 10-20 different sized chips being fabricated around the world as of 2018. There is an immense amount of attention and money being dedicated to improving semiconductor fabrication process efficiency.

[[File:feol.png|frame|none|left|Steps to fabricate a semiconductor device]]

==Examples==

===Simple===
[[File:Cat'swhiskerdetector.jpg]]

A simple application of a semiconductor would be the Cat's Whisker detector for radios, invented in the early 1900s.

===Moderate===
[[File:Opticallsensor.jpg]]

Optical sensors are moderately difficult applications of semiconductors. Optical sensors are electronic detectors that convert light into an electronic signal. They are used in many industrial and consumer applications. An example would include lamps that turn on automatically in response to darkness.

===Difficult===

[[File:Complicated_semiconductor.jpg]]

A very complicated application of a semiconductor is its use in modern cellular phone devices, such as its use here in the iPhone 6.

== See also ==

Related Wiki pages:

-Transformers

-Resistors and conductivity

-Superconductors

-Electric Fields

-Transformers from a physics standpoint

===Further reading===

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

===External links===

Wikipedia page about semiconductors:

https://en.wikipedia.org/wiki/Semiconductor_device

Encyclopedia entry about semiconductors, including the history of semiconductors:

http://www.britannica.com/technology/semiconductor-device

Information about Diodes:

https://en.wikipedia.org/wiki/Diode

Information about BJTs:

https://en.wikipedia.org/wiki/Bipolar_junction_transistor

Information about MOSFETs:

https://en.wikipedia.org/wiki/MOSFET

Semiconductor Device Fabrication

https://en.wikipedia.org/wiki/Semiconductor_device_fabrication

==References==
Brain, Marshall. "How Semiconductors Work." HowStuffWorks. N.p., 25 Apr. 2001. Web. 27 Nov. 2016.

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Electronics and Semiconductor. (n.d.). Retrieved December 3, 2015, from http://www.plm.automation.siemens.com/en_us/electronics-semiconductor/devices/

Huculak, M. (2014, September 19). IPhone 6 and iPhone 6 Plus get teardown by iFixit • The Windows Site for Enthusiasts - Pureinfotech. Retrieved December 3, 2015, from http://pureinfotech.com/2014/09/19/iphone-6-iphone-6-plus-get-teardown-ifixit/

Introduction to Secondary Ion Mass Spectrometry (SIMS) technique. (n.d.). Retrieved November 15, 2020, from https://www.cameca.com/products/sims/technique

John Bardeen, William Shockley and Walter Brattain at Bell Labs, 1948. (n.d.). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/John_Bardeen#/media/File:Bardeen_Shockley_Brattain_1948.JPG

The Nobel Prize in Physics 1956. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/1956/summary/>

The Nobel Prize in Physics 2000. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/2000/summary/>

เซ็นเซอร์แสง (Optical Sensor) - Elec-Za.com. (2014, July 28). Retrieved December 3, 2015, from http://www.elec-za.com/เซ็นเซอร์แสง-optical-sensor/

Semiconductor device. (2015, November 30). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/Semiconductor_device

Semiconductor Fabrication. (25 November 2018). http://www.iue.tuwien.ac.at/phd/rovitto/node10.html

Shah, A. (2013, May 13). Intel loses ground as world's top semiconductor company, survey says. Retrieved December 3, 2015, from http://www.pcworld.com/article/2038645/intel-loses-ground-as-worlds-top-semiconductor-company-survey-says.html

Shaw, R. (2014, November 1). The cat's-whisker detector. Retrieved December 3, 2015, from http://rileyjshaw.com/blog/the-cat's-whisker-detector/

Sze, S. (2015, October 1). Semiconductor device | electronics. Retrieved December 3, 2015, from http://www.britannica.com/technology/semiconductor-device

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

"Timeline." Timeline | The Silicon Engine | Computer History Museum. The Silicon Engine, n.d. Web. 27 Nov. 2016.

[[Category:Simple Circuits]]

Conductivity and Resistivity

2024-04-14T23:55:18Z

Idumitriu3:

'''This page was constructed from an amalgamation of [[Conductivity]] and [[Resistivity]], then edited by '''Irene Dumitriu, Spring 2024''''''

In the field of electrical engineering and materials science, conductivity refers to the ability of a material to conduct electric current. It is quantitatively measured as the ratio of the current density to the electric field causing the current flow. This property varies among different materials, significantly influencing their applications in various industries.

Resistivity, on the other hand, is the inverse of conductivity. It quantifies how strongly a material opposes the flow of electric current. The relationship between resistivity and conductivity is reciprocal, allowing for interchangeability in calculations and analyses, provided the inverse nature and corresponding units are properly accounted for.

Electrical conductivity is a measure of a material's capability to allow the passage of electric current. It indicates how easily electricity can traverse through a given material. This concept is analogous to thermal conductivity, which determines the efficiency with which thermal energy, commonly in the form of heat, can move through a material. Both electrical and thermal conductivity provide crucial insights into the behavior of materials under different energy transfer scenarios, making them fundamental properties in various fields, including materials science, electrical engineering, and thermal engineering.<ref> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html </ref>.

Methods for determining the resistivity and conductivity of material involve galvanostatic or potentiostatic tests. In a galvanostatic test, a constant current is applied and the voltage is measured. In a potentiostatic test, a constant voltage is applied and the current is measured. An electrochemical analyzer can be used with either a 2-point or 4-point method. With the two point method, there can be contact resistance between the material and the wires, falsely increasing the resistivity. The four-point technique overcomes this issue by using four wires. A current is conducted and measured through the endpoints of the bar while two wires are connected to the inner points of the bar so that they can measure the voltage produced across the inner bar. Once the data is collected, Ohm’s law can be used to calculate the resistivity with the voltage and resistance where the resistance is the 1/slope of the current vs. voltage graph.

==Main Idea==

[[File:Conductance Of Materials.png|shows electron current and free electrons|500 px|]]
<ref>http://www.schoolphysics.co.uk/age16-19/glance/Electricity%20and%20magnetism/Conductance_/index.html</ref>

In the accompanying image, the interrelated nature of conductance and resistance is visually represented, illustrating how various factors influence these electrical properties. The image exemplifies how the density of atoms within a material can impact the movement of electrons. This visual aid serves to demonstrate the effect of atomic density on electron mobility, thereby affecting the material's conductance and resistance.

In the first material depicted, the atoms are more widely spaced, providing a greater area for the movement of free electrons. This phenomenon is identified as resistance. The conductance of the material is influenced by the transfer of these free electrons; a higher rate of free electron passage in a given timeframe correlates with increased conductivity. Due to the pronounced movement of free electrons, this material demonstrates lower resistance and higher conductivity, making it more efficient in transferring heat or energy. Consequently, it is often utilized as a conductor.

In the second material, the atoms are positioned closer together, resulting in reduced space for the movement of free electrons, a characteristic known as resistance. The conductance of this material is consequently affected by the limited transfer of free electrons. The fewer free electrons that pass through within a given timeframe, the less conductive the material is. Due to this diminished movement of free electrons, the material exhibits greater resistance and reduced conductivity, leading to less efficient heat or energy transfer. Such properties render this material more suitable for use as an insulator.

A conductor is a type of material that offers minimal resistance to the flow of electric current, making it highly efficient for conducting electricity. It's important to note that the resistivity of a material is influenced not only by the presence of free electrons but also by the temperature at which the material is maintained. Variations in temperature can significantly alter a material's resistive properties, affecting its ability to conduct electricity. This interplay between electron mobility and temperature is a crucial factor in determining the overall conductive or resistive behavior of a material.

An insulator is a material that exhibits high resistance to the flow of electric current, effectively preventing or significantly hindering the passage of electricity. Semiconductors, on the other hand, are materials that possess properties of both conductors and insulators, allowing them to conduct electricity under certain conditions. Common examples of conductive materials include metals, known for their low resistivity and high conductivity. Insulators typically comprise materials like wood or plastics, which have high resistivity and are used to prevent unwanted flow of electric current <ref> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/conins.html </ref>. Semiconductors, though more rare compared to conductors and insulators, play a crucial role in modern technology, particularly in the construction of transistors. These components are essential in all computers and a wide range of electronic devices. The most commonly used semiconductor material is doped silicon, which, through the process of doping, acquires the necessary electrical properties to efficiently control and amplify electronic signals. This characteristic makes semiconductors indispensable in the realm of digital electronics and integrated circuits <ref> https://electronics.howstuffworks.com/diode.htm </ref>. Beyond conductors, insulators, and semiconductors, there is another notable category known as superconductors. The phenomenon of superconductivity, discovered in 1911, is a quantum mechanical marvel that allows for the unimpeded flow of electric current, making superconductors highly valuable for applications requiring efficient energy transmission, powerful electromagnets, and advanced technologies like magnetic resonance imaging (MRI) and particle accelerators, and these unique materials exhibit zero electrical resistance under specific conditions, typically at extremely low temperatures and/or under high pressures <ref> https://home.cern/science/engineering/superconductivity </ref>, and there also exist a host of other materials with odd behaviors.

[[Units For Conductivity and Resistivity:]]

The units used to express conductivity and resistivity are indeed based on the familiar Ohm, a unit of electrical resistance. Conductivity, which measures how easily a material allows the flow of electric current, is typically expressed in Siemens per meter (S/m). On the other hand, resistivity, representing how much a material resists the flow of electric current, is measured in ohm-meters (Ω·m). These units provide a standardized way to quantify and compare the electrical properties of different materials, crucial for applications in electrical engineering and materials science. Expressed in terms of SI base units, the unit of resistivity becomes <math> \frac{kg\cdot m^3}{s^3\cdot A^2} = \frac{kg\cdot m^3}{s\cdot C^2} </math>.

[[Factors that influence the resistivity of an object:]]

~Material Composition: Different materials inherently have different levels of resistivity. For instance, metals typically have lower resistivity than insulators like plastic or wood.

~Temperature: Generally, for conductors, resistivity increases with temperature. In semiconductors and insulators, the effect can be more complex.

~Impurities and Material Defects: The presence of impurities and defects in a material can significantly alter its resistivity. This is particularly notable in semiconductors, where doping with impurities is used to control resistivity.

~ Physical Structure: The microscopic structure of a material, including its crystal structure and the presence of grain boundaries, can affect resistivity.

~Pressure: Applying pressure to a material can change its resistivity, though this effect is generally less significant than temperature or material composition.

===Mathematical Method===

The relationship between conductivity and resistivity is a fundamental concept in the field of materials science and electrical engineering. Here's how they are related:

<math> \sigma = \frac{1}{\rho} </math>

By convention, we have <math> \sigma </math> as the conductivity, and <math> \rho </math> as the resistivity.

[[File:Resistivity geometry.svg|Resistivity geometry|300 px|right]]

Conductivity and Resistivity are intrinsic material properties, influenced primarily by chemical composition and structural attributes, but also sensitive to temperature and other environmental conditions. In practical applications, these values are either predetermined constants used in calculations or derived outcomes from specific equations. The focus thus lies in understanding the relevant equations that govern these properties. A key equation relates resistivity to resistance in an idealized manner, providing a foundational understanding for analyzing the electrical characteristics of different materials. This relationship is crucial for the design and analysis of electrical and electronic systems, where accurate knowledge of material properties is essential.

<math> R = \frac{\rho L}{A} </math>

In this context, the resistance of a wire is denoted as <math> R </math>, the length of the wire is <math> L </math>, <math> rho </math> is equal to resistivity and the variable <math>A </math> is its cross sectional area. This formulation presupposes a well-defined length of the wire aligned with the direction of electric current flow and a specific cross-sectional area perpendicular to the current's direction. These parameters are essential in determining the wire's resistance characteristics, especially in the context of electrical and electronic engineering.

Adjusting the area of a conductor can be achieved by making additional connections to it within a circuit. For instance, if there is a current flowing from North to South through a conductor, attaching a second conductor parallel to the first effectively doubles the area of the conductor. This modification impacts the overall resistance of the circuit, as the cross-sectional area is a key factor in determining resistance. By increasing the area through parallel connections, the resistance is reduced, allowing more current to flow through the circuit.

As seen by the equation <math> R = \frac{\rho L}{A} </math>, doubling the Area would cut the resistance in half and effectively double the conductance of the circuit containing the conductors seeing that <math> \sigma = \frac{1}{\rho} </math>

<p>In the realm of electrical engineering, a standard wire exemplifies a practical application of Ohm's Law. This fundamental law delineates the correlation between the flow of electric charge and the electric field responsible for this flow. Ohm's Law is articulated through two essential equations:</p>

<p>The first equation explicitly states the relationship:</p>

<math>\vec{J} = \sigma \vec{E}</math>

<p>Here, <math>\vec{J}</math> represents the current density, and <math>\vec{E}</math> signifies the electric field. The concept of current density refers to the amount of charge traversing a specified cross-sectional area within a certain time frame, measured in SI units as <math>\frac{A}{m^2} = \frac{C}{m^2 \cdot s}</math>. This elucidates that current density is a 'density' with 'area' in its denominator.</p>

<p>Another aspect related to Ohm's Law is the "skin effect," which elucidates the interplay between current density and the radius of a wire. It posits that a larger wire radius leads to increased current density. This effect is integral to understanding Ohm's Law in practical scenarios.</p>

<p>Another commonly used form of Ohm's Law is expressed as:</p>

<math>V = I R</math>

<p>Where <math>V</math> is the electric potential, <math>I</math> the current, and <math>R</math> the resistance. This version of the law is widely employed in various electrical engineering applications.</p>

===Computational Method===

This topic is largely conceptual and algebraic, so there is relatively little modeling to be done. However, [https://colab.research.google.com/drive/1hR-F7dQk4ZadIB3DEhZZPvnTmmGpj1hQ this] program is designed to create plots of the relationship between resistance, resistivity, length and cross sectional area.

[[Code shows the relationship between:]]

Resistance and length across different fixed points

Resistance and area across different fixed points

Furthermore, [https://phet.colorado.edu/sims/html/resistance-in-a-wire/latest/resistance-in-a-wire_en.html this] external program provides a good visual demonstration of the relationship that acts as a good simulation for altering either the volume, conductance, current, or area of an object to see how the resistance will be altered (but unfortunately the source code is not accessible).

==Examples==

===Simple===
'''Example Number 1'''

A semi conductive material has a resistivity of <math> 200 \; \Omega\cdot m </math>. What is its conductivity?

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

Since conductivity is the reciprocal of resistivity,

<math> \sigma = \frac{1}{\rho} = \frac{1}{200 \; \Omega \cdot m} = 0.005 \frac{1}{\Omega \cdot m} </math>

</div></div>

'''Example Number 1.2'''

A copper wire has a resistivity of <math> 1.68 \times 10^{-8} \; \Omega\cdot m </math> at room temperature. Determine its conductivity.

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

Given that conductivity is the inverse of resistivity,

<math> \sigma = \frac{1}{\rho} = \frac{1}{1.68 \times 10^{-8} \; \Omega \cdot m} = 5.95 \times 10^{7} \frac{1}{\Omega \cdot m} </math>

This result indicates high conductivity, characteristic of copper.

</div></div>

'''Example Number 1.3'''

Calculate the resistivity of an aluminum material with a conductivity of <math> 3.5 \times 10^{7} \frac{1}{\Omega \cdot m} </math>.

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

Since resistivity is the reciprocal of conductivity,

<math> \rho = \frac{1}{\sigma} = \frac{1}{3.5 \times 10^{7} \frac{1}{\Omega \cdot m}} = 2.86 \times 10^{-8} \; \Omega\cdot m </math>

This value of resistivity is typical for aluminum.

</div></div>

'''Example Number 2'''

An unknown material is used in the creation of a video game console.

Part A: How would the amount of free electrons in the material affect the conductance of the material?

Part B: Would the material's conductance increase or decrease if you put the material in the freezer as opposed to room temperature?

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution For Part A</div>
<div class="mw-collapsible-content">

The conductance of a material is directly influenced by the number of free electrons available for conduction. A higher number of free electrons implies lower resistance, as conductance is inversely related to resistivity (<math> \sigma = \frac{1}{\rho} </math>). Therefore, an increase in free electrons results in higher conductance.

</div></div>

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution For Part B</div>
<div class="mw-collapsible-content">

Lowering the temperature of a material typically increases its resistivity, as free electron movement is slowed. This results in a decrease in conductance. In colder environments (like a freezer), the slowed electron movement leads to increased resistance and consequently, decreased conductance in the material.

</div></div>

===Middling===

'''Example Number 1'''

An electric potential of <math> 120 V </math> is applied to a circular wire of length <math> 2 \cdot 10^4 \; m </math> and radius <math> 0.001 m </math>. The current is equal to <math> 1.11 \; A </math>. Determine the resistivity, and match it to an elemental metal using an appropriate table (such as <ref> http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/elecon.html </ref>)

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

We have Ohm's Law

<math> V = I R </math>

and so plugging in our definition for resistance in terms of resistivity gives that

<math> V = \frac{I \rho L}{A} </math>

which we rearrange to get

<math> \rho = \frac{ V A}{I L} </math>

plugging all of the values in gives an answer of <math>\rho = 1.7 \cdot 10^{-8} \; \Omega \cdot m </math>, which is the resistivity of copper.

</div></div>

'''Example Number 2'''

A student wishes to cut a wire in order to reach a specific potential difference.

Given what we know about Ohm's law, a student discovers that the wire she is using in a circuit to light a light bulb has a resistance of <math> \rho = 2.0 \cdot 10^{-7} \; \Omega \cdot m </math> and a radius of .002 meters. The current in the circuit is equal to 1 Amepere. The student then realizes that in order for the light bulb to be lit, there must be an electric potential across the light bulb of at least 100 Volts. Given that there are no other resistors in the circuit, determine the necessary length of the wire that she would need to cut in order for the potential difference of the wire to equal 100 Volts.

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

We can start by rearranging Ohm's Law

Ohms Law is equal to

<math> V = I R </math>

and so plugging in our definition for resistance in terms of resistivity gives that

<math> V = \frac{I \rho L}{A} </math>

which we rearrange to get

<math> \rho = \frac{ V A}{I L} </math> like in example 1

If the equation is even more rearranged in order to find the necessary length she needs to cut of the wire to get a potential difference, the equation would be

<math> L= \frac{ V* A}{I*rho} </math>

The next step is to use the radius of the wire in the given problem to find the area

Area= pi*r^2

If you plug in the numbers you get <math>L=100*(pi*(.002)^2)/(2.0 \cdot 10^{-7}*1)</math>

This gives you a necessary length of 6.28 \cdot 10^{5} meters

</div></div>

===Difficult===

One cubic meter of a fictional material with resistivity <math> \rho = 10^{-5} \; \Omega \cdot m </math> is formed into a shape with uniform cross sectional area (such that volume is equal to the base times the height) for which the resistance to current run lengthwise is equal to <math> 10 \; \Omega</math>. Determine the dimensions (length and cross sectional area) of the shape, presuming that it follows Ohm's law and the equation for resistance given above.

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

As the clarification hints, it is necessary to use a little basic geometry to solve this problem, namely

<math> V = L \cdot A </math>

So we lay out the standard formula

<math> R = \frac{\rho L}{A} </math>

Then multiply both numerator and denominator by <math> L </math> to obtain

<math> R = \frac{\rho L^2}{A L} = \frac{\rho L^2}{V} </math>

From here it is simply rearrangement to find that

<math> L = \sqrt{\frac{R V}{\rho}} = \sqrt{\frac{(1 \;m^3)(10 \;\Omega)}{10^{-5} \; \Omega \cdot m }} = 10^2 \; m </math>

With the length determined, it is then straightforward to conclude that <math> A = 10^{-2} \; m^2 </math>, and the cross-section can take any shape which has that enclosed area.

</div></div>

==Connectedness==

<p>Every time an electrical system has been created, an understanding of conductivity and resistivity had to be determined.</p>

<p>Since conductivity and resistivity are related, it is reasonable to assume that wires or components with low electric resistivity make good conductors due to their ability to effectively transmit electricity and heat. Conversely, materials with high electric resistivity are less efficient at conducting and are often used as insulators.</p>

<p>This concept has significant applications in real life, including:</p>
<ul>
<li><strong>[[Home insulation:]]</strong> Utilizing materials with high resistivity to maintain indoor temperature.</li>
<li><strong>[[Cooking:]]</strong> Employing pots, pans, and other metallic objects with low resistivity for efficient heat transfer, allowing food to cook evenly without direct exposure to the stove's heat source.</li>
<li><strong>[[Electronic Devices:]]</strong> Using materials with high resistivity in electronic devices to regulate temperature and prevent overheating, caused by the constant flow of electrical current.</li>
</ul>

[[Measuring Conductivity]]

To measure conductivity<ref>https://gpg.geosci.xyz/content/physical_properties/physical_properties_conductivity.html</ref>, a sample of the material is placed in between two metallic electrodes, either made of copper or granite.
Ohm's law is then used to calculate the numerical value of the resistance of the circuit.

[[File:Resistance.jpg|Electrical Conductivity of Various Metals|350 px|]]<ref>https://gpg.geosci.xyz/content/physical_properties/induced_polarization_physical_properties_duplicate.html</ref>

This is done through monitoring the current that is produced from the loop and the <math>delta V</math> that can be measured through the attachment of an ammeter to the copper or granite circuit.
The stronger conductors would have a higher <health>delta V<delta V> value and/or a lower I, a larger convection current.

==History==

<p>The study of conductivity and resistivity has a rich history, marked by significant contributions from various scientists. One of the earliest contributors was Stephen Gray, who along with Ganvil Wheler, observed that electricity could be transmitted over distances and that different materials had varying effectiveness in conducting electricity. This early observation, contrasting the conductivity between silk and brass wires, laid the groundwork for future studies [9].</p>

<p>While the 18th century saw notable advancements in understanding electricity, including the work of Benjamin Franklin, these developments were more closely tied to broader aspects of electrical science rather than specifically to conductivity and resistivity.</p>

<p>The early 19th century marked a pivotal moment in the study of resistivity and conductivity. Antoine Becquerel, the grandfather of Henri Becquerel who later became renowned for his work in radioactivity alongside Marie Skłodowska Curie and Pierre Curie, formulated an equation to determine resistance from resistivity and geometry [10]. This breakthrough provided a more quantitative approach to understanding how electrical resistance was influenced by material properties and structural dimensions.</p>

<p>Following Becquerel's work, Georg Ohm, a German physicist, proposed a theorem relating current, potential, and resistance. Although his initial proposition was incorrect, he soon revised it, leading to the formulation of Ohm's law. Despite initial skepticism and poor reception due to philosophical differences and confusion over the definitions of resistance, current, and potential, Ohm's work eventually gained acceptance and recognition, transforming our understanding of electrical resistance and its relationship to current and voltage.</p>

<p>This period marked a crucial era in the study of electrical properties, as scientists began to establish the fundamental principles that would shape our modern understanding of electrical conductivity and resistivity.</p>

==See Also==
If you are interested in learning more about this topic or want further clarification about concepts, check out these resources!

===Further reading===
The textbook Matter and Interaction by Chabay and Sherwood has some discussion of conductivity and resistivity:
*Chapter 14 discusses conductors and insulators with some specifics about polarization and charge. Page 548 includes a specific definition for both.
*Page 771 talks about conductivity
*Page 773 talks about resistance in relation to conductivity and geometry
*Page 775 talks about semiconductors
The textbook Electricity and Magnetism by Purcell also covers conductivity and resistivity:
*Chapter 3.1 covers conductors and insulators
*Chapter 4.6 covers semiconductors

===External links===
*Table of electrical resistivity and conductivity values for different materials: https://www.thoughtco.com/table-of-electrical-resistivity-conductivity-608499
*Resistivity and conductivity explanation: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html
*Khan Academy video on resistivity and conductivity https://www.khanacademy.org/science/ap-physics-1/ap-circuits-topic/current-ap/v/resistivity-and-conductivity
*Resistivity, An explanation (Youtube Video By Brian Swarthout) https://youtu.be/dRtNvUQC7c8

==References==

<references/>

Semiconductor Devices

2024-04-14T22:20:37Z

Idumitriu3:

Last edited by Irene Dumitriu (Spring 2024)

===What are Semiconductors?===

Semiconductor devices are electronic components with the electronic properties of semiconductors. Silicon, germanium, gallium arsenide, organic semiconductors are among the most common semiconductors used in these devices. Semiconductors are materials that are neither good conductors or good insulators. They have a good conductivity between conductors (these tend to be metals) and nonconductors (these insulators tend to be ceramics). Semiconductors do not have to originate organically - the most common semiconductor material are pure elements such as silicon and germanium, but impurities are often added to control the conductivity levels. This process is called doping. The doped semiconductors are called extrinsic semiconductors while pure, impurity-free semiconductors are called intrinsic semiconductors. Intrinsic semiconductors are less conductive than metals as they have a lower amount of charge carriers, or electrons or holes, that can move across the band gap. Extrinsic semiconductors can have higher or lower conductivity depending on the doping.

The conductivity of these semiconductors can also be impacted by environmental changes such as temperature changes. Electrical conductivity depends on two factors: charge-carrier mobility and the concentration of mobile charge carriers. Charge carriers are free electrons or holes that are able to move freely throughout a material, and their mobility is the speed at which these electrons move in a certain direction under the application of a voltage. The free electrons are responsible for determining a current as a current is defined as the rate of electrons flowing through a material in a unit of time. In semiconductors, the charge carrier mobility is negligible as the temperature directly impacts mainly the charge carrier concentration. The band gap theory helps explain how charge carriers move in semiconductors. Unlike metals, semiconductors have a gap between the conduction band and the valence band where the electrons sit without excitation. As temperature increases, these electrons gain energy until they have enough energy to cross the band gap and into the conduction band, decreasing resistivity and increasing conductivity. This behavior is observed mainly in intrinsic semiconductors. In extrinsic semiconductors, the type of doping can affect the conductivity negatively or positively.

Due to low cost, reliability, ability to control conductivity, and compactness, semiconductors are used for a wide range of applications. They also have a wide range of current and voltage handling capabilities, contributing to their suitability for a number of operations. They are commonly found in power devices, optical sensors, and light emitters. Perhaps more importantly, they are readily integrated into microelectronic uses as key elements for the majority of electronic systems, including communications, consumer, data-processing, and industrial-control equipment.

[[File:Intelthing.jpg|frame|border|right|A raw board with many transistors in it!]]
[[File:transistor.png|frame|none|left|An fully built integrated circuit.]]

==The Main Idea==

Semiconductors work by using the electric properties of the p-n junction that makes up a diode. The junction is formed through a process called doping. Doping involves turning silicon into a conductor by changing the behavior of its electrons. In n-type doping, a phosphorus/arsenic impurity is introduced so that the valence will have free electrons to allow a electric current to flow. Since extra electrons are negative in charge, this type of doping is called n-type doping referred to by "n" in the p-n junction. In the p-type doping, a boron/gallium impurity is introduced to the silicon lattice so the valence will have an empty electron orbital. Because the empty area implies the absence of an electron and thus creates a positive charge, "p" was assigned as the name of the doping type.

[[File:n-type.gif|frame|border|right|N-Type Material]]

[[File:p-type.png|frame|none|left|P-Type Material]]

The two most useful forms of semiconductor devices are diodes and transistors. Diodes are the simplest semiconductor device, which conducts current easily in one direction but conducts almost no current in the other direction. These are made by joining two pieces of semiconducting material, a junction called a "p-n" junction. One of the pieces contains a small amount of boron and the other contains a small amount of phosphorus. Transistors are constructed through two semiconducting junctions, or "p-n" junctions. These are the most common elements in digital circuits. The conductivity of these semiconductors can be controlled by introduction of an electric or magnetic field, by exposure to light or heat, or by mechanical deformation of a doped monocrystalline grid. Due to this, semiconductors are extremely useful and can be altered to fit specific purposes.

===Semiconductors & Applications in Solid-State Physics===

The key principle that is often used in solid-state physics is the carrier effective mass. This refers to the mass a particle (within the semiconductor) seems to have when interacting with other identical particles in a thermal distribution. This constant is simplified version of the band theory and influences measurable properties of a solid, including the efficiency of the devices that semiconductors are used in for example, solar cell efficiency and integrated circuit speed. So, how do we actually measure the carrier effective masses in a semiconductor?

Large parts of the simplicity of the free electron gas model can be saved by assigning effective masses to the carriers. Only electrons and holes at the band edges (characterized by a wave vector kex) participate in the generation - recombination process that is the hallmark of semiconductors. A particle's effective mass is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles over long distances can be very different from their motion in a vacuum. The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass. Sometimes the effective mass can be considered to be a simple constant of a material, however, the value of effective mass depends on the purpose for which it is used, and can vary depending on a number of factors. For electrons or electron holes in a solid, the effective mass is usually stated in units of the rest mass of an electron, me (9.11×10−31 kg). In these units it is usually in the range 0.01 to 10, but can also be lower or higher—for example, reaching 1,000 in exotic heavy fermion materials, or anywhere from zero to infinity (depending on definition) in graphene. The effective mass of a semiconductor is obtained by fitting the actual electron diagram around the conduction band minimum or the valence band maximum by a parabola - this is called an E-K diagram (shown below). It shows the relationship between the energy and momentum of available quantum mechanical states for electrons in the material. As it simplifies the more general band theory, the electronic effective mass can be seen as an important basic parameter that influences measurable properties of a solid, including everything from the efficiency of a solar cell to the speed of an integrated circuit.

[[File:IMG 2424.jpg|Diagram of an EK diagram|350 px|]]

===Detecting Doping===

Secondary ion mass spectroscopy (SIMS) is a very powerful technique for the analysis of impurities in solids. SIMS can be utilized for semiconductor dopant profiling. The technique relies on removal of material from a solid by sputtering and on analysis of the sputtered ionized species; all elements are detected. SIMS can detect dopant densities as low as 10^14 cm^-3. The dopant density profile that is generated is based on the ion signal versus time plot. The time axis is converted to a depth axis by measuring the depth of the crater at the end of the measurement assuming a constant sputtering rate. For example, boron is implanted into silicon at a given energy and dose to create a standard. The secondary ion signal is calibrated by assuming the total amount of boron in the sample to equal to the implanted boron. The unknown sample of B implanted into silicon is then compared to the standard. However, there is limited dynamic range of the SIMS instrument that can contribute to slightly deeper junctions and discrepancies in the lowly doped portions of the profile. When sputtering from a highly doped region to a lowly doped region, the crater walls still contain the entire doping density profile. SIMS also measures total dopant density, regardless of activation. Thus going back to the silicon-boron example, the dopant profile shows dependence of electrical activation of boron implanted into silicon on implant dose and activation temperature.

[[File:Sims-technique-schematic.png|frame|none|left|Example of SIMS]]

===A Mathematical Model===

Semiconductors operate based on the concept of thermal energy exciting electrons and causing them to jump to the next higher (unoccupied) energy band.
These electrons can pick up energy (and drift speed) from an applied electric field. The filled energy band is called the “valence” band, and the nearly unoccupied higher energy band is called the “conduction” band. The number of electrons excited into the conduction band is proportional to a value called the Boltzmann constant, equivalent to the value:
<math>
e^{-E_{\text{gap}} / k_B T}
</math>.
Therefore, high conductivity (corrosponding to a favorable Boltzmann factor) can be calculated according to
<math>
T = 2 \pi \sqrt{\frac{m}{k}}
</math>,
where <math>m</math> is the mass of the object in kilograms, <math>k</math> is the spring constant, and <math>T</math> is the period of oscillation in seconds. In addition, the total conventional current in a semiconductor can be calculated, according to the equation
<math>
I = e n_n A u_n E + e n_p A u_p E
</math>.

===A Conceptual Model===
The following diagram demonstrates how electron excitement in semiconductors works. Semiconductors are materials with small band gaps between the valence band and conduction bands. As you can see, a small amount of thermal energy is needed to promote an electron to the conduction band in a semiconductor.

[[File:conceptual.png|frame|none|left|A Conceptual Model of the Semiconductor]]

===A Computational Model===

[https://phet.colorado.edu/sims/cheerpj/semiconductor/latest/semiconductor.html?simulation=semiconductor Semiconductor Simulation]

==History==
'''1874'''
Ferdinand Braun discovers that current flows freely in only one direction when a metal point and a galena crystal are put together.

'''1901'''
Jagadis Bose takes ownership of the discovery of the semiconductor crystal for detecting radio waves.

'''1940'''
Russell Ohl discovers the p-n junction.

'''1940s'''
Semiconductors were used only as two-terminal devices, such as rectifiers and photodiodes. They were most commonly used as detectors in radios, through devices called "cat's whiskers". During the era of WWII, researchers worked with semiconductors and cat's whiskers to make more effective diodes.

'''1947'''
William Shockley and John Bardeen worked together to create a triode-like semiconductor: the first transistor. They realized that if there were some way to control the flow of the electrons from the emitter to the collector of this newly discovered diode, an amplifier could be built.The first transistor was officially created on the 23rd of December, 1947.

'''1956'''
John Bardeen, William Shockley, and another researcher named Walter Houser Brattain were credited for the invention and awarded a Nobel Prize for physics in 1956 for their work. After this, the utilization of semiconductors soon advanced to even more complicated applications.

'''1960s'''
In the late 1960s, transistors moved from being germanium based to silicon based. Gordon K Teal was most responsible for this advancement, and his company, Texas Instruments, profited greatly. Portable radios are just one popular invention that benefited from silicon based semiconductors. Now, silicon based semiconductors constitute more than 95 percent of all semiconductor hardware sold worldwide.

'''1970s'''
Silicon technology is modernized and the race to fit all semiconductor processor technology into one chip is most active.

'''2000'''
Nobel Prize in physics awarded to Zhores I. Alferov and Herbert Kroemer for developing semiconductor heterostructures used in high-speed- and opto-electronics and half to Jack S. Kilby "for his part in the invention of the integrated circuit."

[[File:transistorwork.png|frame|none|none|John Bardeen, William Shockley, and Walter Houser Brattain, winners of the Nobel Prize for their invention of the transistor, are pictured above.]]

===Connectedness===

Semiconductors are crucial to modern technology, and are used for memory storage as well as so many other technological innovations. This technology is used every day by millions of people for thousands of different applications. Most people in the world have used semiconductors in one way or another, even if they weren't aware of it. It is specifically connected to the major of Biomedical Engineering through memory storage and the complex computer programs used every day to conduct business and create simulations for the furthering of biomedical research. All industrial applications of semiconductors are very applicable, from amplifiers to transistors to silicon disks. Without semiconductors, much of the technology that the general population relies on today would not be possible.

Semiconductors are used in essentially every part of this technological and electronically-dependent world we live in today. They have both conductor and insulator properties and includes all of the metal we see in wires. Computers, phones, and other electronic devices all use semiconductors to fulfill their functions such as communication and efficiency. The most important aspect of semiconductors is utilization, which is shown through the use of switches. Inside electronic devices, the switches exist in extremely large numbers, which is why electronic devices process information in an incredible speed with surprising efficiency.

Semiconductors are connected to chemical engineering largely through their industrial creation. The process of depositing each layer of material onto the wafer is a chemical process controlled by deposition of gaseous metals onto the wafer. There are an incredible variety of steps from material preparation to packaging which can be optimized by an eager chemical engineer.

Another example that was discussed previously on this page is the usage of silicon in photovoltaic devices. Silicon is used because it is the first semiconductor that was commercialized successfully. Many commercial companies are very proficient in making silicon devices, so the silicon is not necessarily used because it is the best material for harnessing the electricity from the photovoltaic effect. The silicon crystals allow the power to reach the external electrical circuit, but the silicon doesn't absorb sunlight as efficiently because it needs to be ten to one hundred times thicker than an advanced thin-film cell. It is also favored because of the low maintenance. A unique oxide forms when silicon is exposed to high temperatures that serves to neutralize defects on the silicon surface. The frontier for replacing the silicon looks quite bleak because of the practicality of manufacturing silicon crystalline semiconductors, but new research is being conducted on using silicon with lower purity or combining it with other semiconductor materials.

==Types of Semiconductors==

===Diodes===

[[File:Diode_current_wiki.png|314px|thumb|right|top|IV Characteristic of a Diode]]

Diodes are really great! In a simple sense, they can give you a "point of no return" in your circuit (but they can actually do much more than that).
Three interesting things should be observed from the IV characteristic shown to the right:

# For small positive voltages and above, the diode does not limit the current (the line is almost vertical)!
# For small to larger negative voltages, the diode resists current (the line is almost flat).
# For a large negative voltage (the breakdown voltage) the diode gives up (no one is perfect).

We can formally define this line with the Shockley Diode Equation, which formalizes this observation:

<math display="block">
I = I_S \left( e^{\frac{V_D}{n V_T}} - 1 \right)
</math> where

<math>I</math> is the diode current,

<math>I_S</math> is the reverse bias saturation current (or scale current),

<math>V_D</math> is the voltage across the diode,

<math>V_T</math> is the thermal voltage, and

<math>n</math> is the ideality factor, (1 if the diode is ideal, greater than 1 if it is imperfect).

A great practical use for diodes is a rectifier:

[[File:Gratz.rectifier.en.svg|frame|border|center|Diodes groups the positive and negative signals together]]

This makes sure that when a positive voltage appears on either line, it is redirected to a single positive line, and the same for the negatives.
BAM! AC to DC, that's pretty easy, you can charge your phone with that.
In reality a capacitor is added in parallel with the load to try to smooth out the ripples.
A voltage regulator after the rectifying step is also a popular choice, depending on the needs of the application.

Another super useful application is that of a back up power supply: simply connect two supplies in parallel with the positive terminals buffered with diodes. The higher of the two voltages is always used and the transition between supplies is seamless.

===Zener Diodes===

Some diodes (Zener) are made to have small breakdown voltages.
Since during breakdown the IV curve is almost vertical (it's really an exponential), the current is independent (almost) from voltage.
You can then wire up a Zener diode in reverse to a point in the circuit, and it will accept as much current as it needs to to reach that
breakdown voltage. Because of this a great practical use for Zener diodes is a voltage regulator since the voltage is set when the diode is
manufactured and does not change greatly with a varying power supply.

===Bipolar Junction Transistors===

[[Image:BJT NPN symbol (case).svg|75px|thumb|NPN BJT]]
[[Image:BJT PNP symbol (case).svg|75px|thumb|PNP BJT]]

Shortly after the invention of the first transistor (which was OK), the BJT landed, which was the first transistor to be prolific in the field.
It was made using two alternating NP junctions as shown below:

[[File:NPN BJT (Planar) Cross-section.svg|frame|border|center|NPN BJT (Planar) Cross-section]]

Really transistors (and by extension all that is needed for a computer to be built) are amplifiers (OK, to build all computers you need an inverting amplifier, but one can be built using the BJT).
If one is used to thinking of them as an electrically-controlled switch, you can simply think of a switch as an amplifier with a gain of <math>\infty</math>.

A simple model of a BJT is a linear current-controlled current source, i.e. the base to emitter (B to E) current <math>I_{BE}</math> is proportional to
the collector to emitter (C to E) current <math>I_{CE}</math>. The proportionality constant <math>\beta</math> can be thought of as the "gain" of the
transistor. This gives a relationship of <math>I_{CE} = \beta I_{BE}</math>.

[[File:Current-Voltage relationship of BJT.png|thumb|right|Current-Voltage relationship of BJT]]

Sadly there is no source of infinite power, so the output to our amplifier tops off when it can't supply any more power.
This can be seen with the graph on the right.
The simple model then only works for the tiny linear part at the start of the graph, even so its not ''that'' linear.
The BJT proved to be power hungry, pretty non-linear and sensitive to the environment (temperature, etc.).
These growing pains lead to a new development, called the MOSFET.

===MOSFETs===

MOSFETs are the coolest, they are less power-hungy and easier to work with when compared to BJTs.
Instead of having a current control, which uses power and gets the control and the output signal coupled together,
a MOSFET's output is controlled by the electric Field (the F in MOSFET) the control signal creates on one of the plates of the MOSFET.
Since the control signal and the output are electrically disconnected (as you would see in a capacitor) there is much less power draw
from this type of transistor.

We can see how linear this thing is with its IV characteristic: <math>I_D= \mu_n C_{ox}\frac{W}{L} \left( (V_{GS}-V_{th})V_{DS}-\frac{V_{DS}^2}{2} \right)</math>

Apart from the control signal <math>V_{DS}</math> and constants, the voltage across the output portion of the MOSFET is linearly related to the current!
This means that the MOSFET behaves like a voltage controlled resistor, and a resistor is something much easier to analyse and work with.

Most circuits with an enormous amount of transistors these days use primarily MOSFETs. BJTs are still useful for temperature and light sensing
applications.

==Industrial Semiconductor Fabrication==

Semiconductors are mass produced in specialized factories called foundries or fabs. The process consists of multiple chemical and photolithographic steps which add layers to a wafer usually made of silicon. The entire process usually takes around 2 months but it can last up to 4.

The semiconductor product is rated by the size of the chip's process gate length, where processes with smaller gate lengths are typically harder to make. There are 10-20 different sized chips being fabricated around the world as of 2018. There is an immense amount of attention and money being dedicated to improving semiconductor fabrication process efficiency.

[[File:feol.png|frame|none|left|Steps to fabricate a semiconductor device]]

==Examples==

===Simple===
[[File:Cat'swhiskerdetector.jpg]]

A simple application of a semiconductor would be the Cat's Whisker detector for radios, invented in the early 1900s.

===Moderate===
[[File:Opticallsensor.jpg]]

Optical sensors are moderately difficult applications of semiconductors. Optical sensors are electronic detectors that convert light into an electronic signal. They are used in many industrial and consumer applications. An example would include lamps that turn on automatically in response to darkness.

===Difficult===

[[File:Complicated_semiconductor.jpg]]

A very complicated application of a semiconductor is its use in modern cellular phone devices, such as its use here in the iPhone 6.

== See also ==

Related Wiki pages:

-Transformers

-Resistors and conductivity

-Superconductors

-Electric Fields

-Transformers from a physics standpoint

===Further reading===

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

===External links===

Wikipedia page about semiconductors:

https://en.wikipedia.org/wiki/Semiconductor_device

Encyclopedia entry about semiconductors, including the history of semiconductors:

http://www.britannica.com/technology/semiconductor-device

Information about Diodes:

https://en.wikipedia.org/wiki/Diode

Information about BJTs:

https://en.wikipedia.org/wiki/Bipolar_junction_transistor

Information about MOSFETs:

https://en.wikipedia.org/wiki/MOSFET

Semiconductor Device Fabrication

https://en.wikipedia.org/wiki/Semiconductor_device_fabrication

==References==
Brain, Marshall. "How Semiconductors Work." HowStuffWorks. N.p., 25 Apr. 2001. Web. 27 Nov. 2016.

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Electronics and Semiconductor. (n.d.). Retrieved December 3, 2015, from http://www.plm.automation.siemens.com/en_us/electronics-semiconductor/devices/

Huculak, M. (2014, September 19). IPhone 6 and iPhone 6 Plus get teardown by iFixit • The Windows Site for Enthusiasts - Pureinfotech. Retrieved December 3, 2015, from http://pureinfotech.com/2014/09/19/iphone-6-iphone-6-plus-get-teardown-ifixit/

Introduction to Secondary Ion Mass Spectrometry (SIMS) technique. (n.d.). Retrieved November 15, 2020, from https://www.cameca.com/products/sims/technique

John Bardeen, William Shockley and Walter Brattain at Bell Labs, 1948. (n.d.). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/John_Bardeen#/media/File:Bardeen_Shockley_Brattain_1948.JPG

The Nobel Prize in Physics 1956. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/1956/summary/>

The Nobel Prize in Physics 2000. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/2000/summary/>

เซ็นเซอร์แสง (Optical Sensor) - Elec-Za.com. (2014, July 28). Retrieved December 3, 2015, from http://www.elec-za.com/เซ็นเซอร์แสง-optical-sensor/

Semiconductor device. (2015, November 30). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/Semiconductor_device

Semiconductor Fabrication. (25 November 2018). http://www.iue.tuwien.ac.at/phd/rovitto/node10.html

Shah, A. (2013, May 13). Intel loses ground as world's top semiconductor company, survey says. Retrieved December 3, 2015, from http://www.pcworld.com/article/2038645/intel-loses-ground-as-worlds-top-semiconductor-company-survey-says.html

Shaw, R. (2014, November 1). The cat's-whisker detector. Retrieved December 3, 2015, from http://rileyjshaw.com/blog/the-cat's-whisker-detector/

Sze, S. (2015, October 1). Semiconductor device | electronics. Retrieved December 3, 2015, from http://www.britannica.com/technology/semiconductor-device

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

"Timeline." Timeline | The Silicon Engine | Computer History Museum. The Silicon Engine, n.d. Web. 27 Nov. 2016.

[[Category:Simple Circuits]]

Semiconductor Devices

2024-04-14T22:20:10Z

Idumitriu3: /* What are Semiconductors? */

Last edited by Megha Sharma (Fall 2020)

===What are Semiconductors?===

Semiconductor devices are electronic components with the electronic properties of semiconductors. Silicon, germanium, gallium arsenide, organic semiconductors are among the most common semiconductors used in these devices. Semiconductors are materials that are neither good conductors or good insulators. They have a good conductivity between conductors (these tend to be metals) and nonconductors (these insulators tend to be ceramics). Semiconductors do not have to originate organically - the most common semiconductor material are pure elements such as silicon and germanium, but impurities are often added to control the conductivity levels. This process is called doping. The doped semiconductors are called extrinsic semiconductors while pure, impurity-free semiconductors are called intrinsic semiconductors. Intrinsic semiconductors are less conductive than metals as they have a lower amount of charge carriers, or electrons or holes, that can move across the band gap. Extrinsic semiconductors can have higher or lower conductivity depending on the doping.

The conductivity of these semiconductors can also be impacted by environmental changes such as temperature changes. Electrical conductivity depends on two factors: charge-carrier mobility and the concentration of mobile charge carriers. Charge carriers are free electrons or holes that are able to move freely throughout a material, and their mobility is the speed at which these electrons move in a certain direction under the application of a voltage. The free electrons are responsible for determining a current as a current is defined as the rate of electrons flowing through a material in a unit of time. In semiconductors, the charge carrier mobility is negligible as the temperature directly impacts mainly the charge carrier concentration. The band gap theory helps explain how charge carriers move in semiconductors. Unlike metals, semiconductors have a gap between the conduction band and the valence band where the electrons sit without excitation. As temperature increases, these electrons gain energy until they have enough energy to cross the band gap and into the conduction band, decreasing resistivity and increasing conductivity. This behavior is observed mainly in intrinsic semiconductors. In extrinsic semiconductors, the type of doping can affect the conductivity negatively or positively.

Due to low cost, reliability, ability to control conductivity, and compactness, semiconductors are used for a wide range of applications. They also have a wide range of current and voltage handling capabilities, contributing to their suitability for a number of operations. They are commonly found in power devices, optical sensors, and light emitters. Perhaps more importantly, they are readily integrated into microelectronic uses as key elements for the majority of electronic systems, including communications, consumer, data-processing, and industrial-control equipment.

[[File:Intelthing.jpg|frame|border|right|A raw board with many transistors in it!]]
[[File:transistor.png|frame|none|left|An fully built integrated circuit.]]

==The Main Idea==

Semiconductors work by using the electric properties of the p-n junction that makes up a diode. The junction is formed through a process called doping. Doping involves turning silicon into a conductor by changing the behavior of its electrons. In n-type doping, a phosphorus/arsenic impurity is introduced so that the valence will have free electrons to allow a electric current to flow. Since extra electrons are negative in charge, this type of doping is called n-type doping referred to by "n" in the p-n junction. In the p-type doping, a boron/gallium impurity is introduced to the silicon lattice so the valence will have an empty electron orbital. Because the empty area implies the absence of an electron and thus creates a positive charge, "p" was assigned as the name of the doping type.

[[File:n-type.gif|frame|border|right|N-Type Material]]

[[File:p-type.png|frame|none|left|P-Type Material]]

The two most useful forms of semiconductor devices are diodes and transistors. Diodes are the simplest semiconductor device, which conducts current easily in one direction but conducts almost no current in the other direction. These are made by joining two pieces of semiconducting material, a junction called a "p-n" junction. One of the pieces contains a small amount of boron and the other contains a small amount of phosphorus. Transistors are constructed through two semiconducting junctions, or "p-n" junctions. These are the most common elements in digital circuits. The conductivity of these semiconductors can be controlled by introduction of an electric or magnetic field, by exposure to light or heat, or by mechanical deformation of a doped monocrystalline grid. Due to this, semiconductors are extremely useful and can be altered to fit specific purposes.

===Semiconductors & Applications in Solid-State Physics===

The key principle that is often used in solid-state physics is the carrier effective mass. This refers to the mass a particle (within the semiconductor) seems to have when interacting with other identical particles in a thermal distribution. This constant is simplified version of the band theory and influences measurable properties of a solid, including the efficiency of the devices that semiconductors are used in for example, solar cell efficiency and integrated circuit speed. So, how do we actually measure the carrier effective masses in a semiconductor?

Large parts of the simplicity of the free electron gas model can be saved by assigning effective masses to the carriers. Only electrons and holes at the band edges (characterized by a wave vector kex) participate in the generation - recombination process that is the hallmark of semiconductors. A particle's effective mass is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles over long distances can be very different from their motion in a vacuum. The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass. Sometimes the effective mass can be considered to be a simple constant of a material, however, the value of effective mass depends on the purpose for which it is used, and can vary depending on a number of factors. For electrons or electron holes in a solid, the effective mass is usually stated in units of the rest mass of an electron, me (9.11×10−31 kg). In these units it is usually in the range 0.01 to 10, but can also be lower or higher—for example, reaching 1,000 in exotic heavy fermion materials, or anywhere from zero to infinity (depending on definition) in graphene. The effective mass of a semiconductor is obtained by fitting the actual electron diagram around the conduction band minimum or the valence band maximum by a parabola - this is called an E-K diagram (shown below). It shows the relationship between the energy and momentum of available quantum mechanical states for electrons in the material. As it simplifies the more general band theory, the electronic effective mass can be seen as an important basic parameter that influences measurable properties of a solid, including everything from the efficiency of a solar cell to the speed of an integrated circuit.

[[File:IMG 2424.jpg|Diagram of an EK diagram|350 px|]]

===Detecting Doping===

Secondary ion mass spectroscopy (SIMS) is a very powerful technique for the analysis of impurities in solids. SIMS can be utilized for semiconductor dopant profiling. The technique relies on removal of material from a solid by sputtering and on analysis of the sputtered ionized species; all elements are detected. SIMS can detect dopant densities as low as 10^14 cm^-3. The dopant density profile that is generated is based on the ion signal versus time plot. The time axis is converted to a depth axis by measuring the depth of the crater at the end of the measurement assuming a constant sputtering rate. For example, boron is implanted into silicon at a given energy and dose to create a standard. The secondary ion signal is calibrated by assuming the total amount of boron in the sample to equal to the implanted boron. The unknown sample of B implanted into silicon is then compared to the standard. However, there is limited dynamic range of the SIMS instrument that can contribute to slightly deeper junctions and discrepancies in the lowly doped portions of the profile. When sputtering from a highly doped region to a lowly doped region, the crater walls still contain the entire doping density profile. SIMS also measures total dopant density, regardless of activation. Thus going back to the silicon-boron example, the dopant profile shows dependence of electrical activation of boron implanted into silicon on implant dose and activation temperature.

[[File:Sims-technique-schematic.png|frame|none|left|Example of SIMS]]

===A Mathematical Model===

Semiconductors operate based on the concept of thermal energy exciting electrons and causing them to jump to the next higher (unoccupied) energy band.
These electrons can pick up energy (and drift speed) from an applied electric field. The filled energy band is called the “valence” band, and the nearly unoccupied higher energy band is called the “conduction” band. The number of electrons excited into the conduction band is proportional to a value called the Boltzmann constant, equivalent to the value:
<math>
e^{-E_{\text{gap}} / k_B T}
</math>.
Therefore, high conductivity (corrosponding to a favorable Boltzmann factor) can be calculated according to
<math>
T = 2 \pi \sqrt{\frac{m}{k}}
</math>,
where <math>m</math> is the mass of the object in kilograms, <math>k</math> is the spring constant, and <math>T</math> is the period of oscillation in seconds. In addition, the total conventional current in a semiconductor can be calculated, according to the equation
<math>
I = e n_n A u_n E + e n_p A u_p E
</math>.

===A Conceptual Model===
The following diagram demonstrates how electron excitement in semiconductors works. Semiconductors are materials with small band gaps between the valence band and conduction bands. As you can see, a small amount of thermal energy is needed to promote an electron to the conduction band in a semiconductor.

[[File:conceptual.png|frame|none|left|A Conceptual Model of the Semiconductor]]

===A Computational Model===

[https://phet.colorado.edu/sims/cheerpj/semiconductor/latest/semiconductor.html?simulation=semiconductor Semiconductor Simulation]

==History==
'''1874'''
Ferdinand Braun discovers that current flows freely in only one direction when a metal point and a galena crystal are put together.

'''1901'''
Jagadis Bose takes ownership of the discovery of the semiconductor crystal for detecting radio waves.

'''1940'''
Russell Ohl discovers the p-n junction.

'''1940s'''
Semiconductors were used only as two-terminal devices, such as rectifiers and photodiodes. They were most commonly used as detectors in radios, through devices called "cat's whiskers". During the era of WWII, researchers worked with semiconductors and cat's whiskers to make more effective diodes.

'''1947'''
William Shockley and John Bardeen worked together to create a triode-like semiconductor: the first transistor. They realized that if there were some way to control the flow of the electrons from the emitter to the collector of this newly discovered diode, an amplifier could be built.The first transistor was officially created on the 23rd of December, 1947.

'''1956'''
John Bardeen, William Shockley, and another researcher named Walter Houser Brattain were credited for the invention and awarded a Nobel Prize for physics in 1956 for their work. After this, the utilization of semiconductors soon advanced to even more complicated applications.

'''1960s'''
In the late 1960s, transistors moved from being germanium based to silicon based. Gordon K Teal was most responsible for this advancement, and his company, Texas Instruments, profited greatly. Portable radios are just one popular invention that benefited from silicon based semiconductors. Now, silicon based semiconductors constitute more than 95 percent of all semiconductor hardware sold worldwide.

'''1970s'''
Silicon technology is modernized and the race to fit all semiconductor processor technology into one chip is most active.

'''2000'''
Nobel Prize in physics awarded to Zhores I. Alferov and Herbert Kroemer for developing semiconductor heterostructures used in high-speed- and opto-electronics and half to Jack S. Kilby "for his part in the invention of the integrated circuit."

[[File:transistorwork.png|frame|none|none|John Bardeen, William Shockley, and Walter Houser Brattain, winners of the Nobel Prize for their invention of the transistor, are pictured above.]]

===Connectedness===

Semiconductors are crucial to modern technology, and are used for memory storage as well as so many other technological innovations. This technology is used every day by millions of people for thousands of different applications. Most people in the world have used semiconductors in one way or another, even if they weren't aware of it. It is specifically connected to the major of Biomedical Engineering through memory storage and the complex computer programs used every day to conduct business and create simulations for the furthering of biomedical research. All industrial applications of semiconductors are very applicable, from amplifiers to transistors to silicon disks. Without semiconductors, much of the technology that the general population relies on today would not be possible.

Semiconductors are used in essentially every part of this technological and electronically-dependent world we live in today. They have both conductor and insulator properties and includes all of the metal we see in wires. Computers, phones, and other electronic devices all use semiconductors to fulfill their functions such as communication and efficiency. The most important aspect of semiconductors is utilization, which is shown through the use of switches. Inside electronic devices, the switches exist in extremely large numbers, which is why electronic devices process information in an incredible speed with surprising efficiency.

Semiconductors are connected to chemical engineering largely through their industrial creation. The process of depositing each layer of material onto the wafer is a chemical process controlled by deposition of gaseous metals onto the wafer. There are an incredible variety of steps from material preparation to packaging which can be optimized by an eager chemical engineer.

Another example that was discussed previously on this page is the usage of silicon in photovoltaic devices. Silicon is used because it is the first semiconductor that was commercialized successfully. Many commercial companies are very proficient in making silicon devices, so the silicon is not necessarily used because it is the best material for harnessing the electricity from the photovoltaic effect. The silicon crystals allow the power to reach the external electrical circuit, but the silicon doesn't absorb sunlight as efficiently because it needs to be ten to one hundred times thicker than an advanced thin-film cell. It is also favored because of the low maintenance. A unique oxide forms when silicon is exposed to high temperatures that serves to neutralize defects on the silicon surface. The frontier for replacing the silicon looks quite bleak because of the practicality of manufacturing silicon crystalline semiconductors, but new research is being conducted on using silicon with lower purity or combining it with other semiconductor materials.

==Types of Semiconductors==

===Diodes===

[[File:Diode_current_wiki.png|314px|thumb|right|top|IV Characteristic of a Diode]]

Diodes are really great! In a simple sense, they can give you a "point of no return" in your circuit (but they can actually do much more than that).
Three interesting things should be observed from the IV characteristic shown to the right:

# For small positive voltages and above, the diode does not limit the current (the line is almost vertical)!
# For small to larger negative voltages, the diode resists current (the line is almost flat).
# For a large negative voltage (the breakdown voltage) the diode gives up (no one is perfect).

We can formally define this line with the Shockley Diode Equation, which formalizes this observation:

<math display="block">
I = I_S \left( e^{\frac{V_D}{n V_T}} - 1 \right)
</math> where

<math>I</math> is the diode current,

<math>I_S</math> is the reverse bias saturation current (or scale current),

<math>V_D</math> is the voltage across the diode,

<math>V_T</math> is the thermal voltage, and

<math>n</math> is the ideality factor, (1 if the diode is ideal, greater than 1 if it is imperfect).

A great practical use for diodes is a rectifier:

[[File:Gratz.rectifier.en.svg|frame|border|center|Diodes groups the positive and negative signals together]]

This makes sure that when a positive voltage appears on either line, it is redirected to a single positive line, and the same for the negatives.
BAM! AC to DC, that's pretty easy, you can charge your phone with that.
In reality a capacitor is added in parallel with the load to try to smooth out the ripples.
A voltage regulator after the rectifying step is also a popular choice, depending on the needs of the application.

Another super useful application is that of a back up power supply: simply connect two supplies in parallel with the positive terminals buffered with diodes. The higher of the two voltages is always used and the transition between supplies is seamless.

===Zener Diodes===

Some diodes (Zener) are made to have small breakdown voltages.
Since during breakdown the IV curve is almost vertical (it's really an exponential), the current is independent (almost) from voltage.
You can then wire up a Zener diode in reverse to a point in the circuit, and it will accept as much current as it needs to to reach that
breakdown voltage. Because of this a great practical use for Zener diodes is a voltage regulator since the voltage is set when the diode is
manufactured and does not change greatly with a varying power supply.

===Bipolar Junction Transistors===

[[Image:BJT NPN symbol (case).svg|75px|thumb|NPN BJT]]
[[Image:BJT PNP symbol (case).svg|75px|thumb|PNP BJT]]

Shortly after the invention of the first transistor (which was OK), the BJT landed, which was the first transistor to be prolific in the field.
It was made using two alternating NP junctions as shown below:

[[File:NPN BJT (Planar) Cross-section.svg|frame|border|center|NPN BJT (Planar) Cross-section]]

Really transistors (and by extension all that is needed for a computer to be built) are amplifiers (OK, to build all computers you need an inverting amplifier, but one can be built using the BJT).
If one is used to thinking of them as an electrically-controlled switch, you can simply think of a switch as an amplifier with a gain of <math>\infty</math>.

A simple model of a BJT is a linear current-controlled current source, i.e. the base to emitter (B to E) current <math>I_{BE}</math> is proportional to
the collector to emitter (C to E) current <math>I_{CE}</math>. The proportionality constant <math>\beta</math> can be thought of as the "gain" of the
transistor. This gives a relationship of <math>I_{CE} = \beta I_{BE}</math>.

[[File:Current-Voltage relationship of BJT.png|thumb|right|Current-Voltage relationship of BJT]]

Sadly there is no source of infinite power, so the output to our amplifier tops off when it can't supply any more power.
This can be seen with the graph on the right.
The simple model then only works for the tiny linear part at the start of the graph, even so its not ''that'' linear.
The BJT proved to be power hungry, pretty non-linear and sensitive to the environment (temperature, etc.).
These growing pains lead to a new development, called the MOSFET.

===MOSFETs===

MOSFETs are the coolest, they are less power-hungy and easier to work with when compared to BJTs.
Instead of having a current control, which uses power and gets the control and the output signal coupled together,
a MOSFET's output is controlled by the electric Field (the F in MOSFET) the control signal creates on one of the plates of the MOSFET.
Since the control signal and the output are electrically disconnected (as you would see in a capacitor) there is much less power draw
from this type of transistor.

We can see how linear this thing is with its IV characteristic: <math>I_D= \mu_n C_{ox}\frac{W}{L} \left( (V_{GS}-V_{th})V_{DS}-\frac{V_{DS}^2}{2} \right)</math>

Apart from the control signal <math>V_{DS}</math> and constants, the voltage across the output portion of the MOSFET is linearly related to the current!
This means that the MOSFET behaves like a voltage controlled resistor, and a resistor is something much easier to analyse and work with.

Most circuits with an enormous amount of transistors these days use primarily MOSFETs. BJTs are still useful for temperature and light sensing
applications.

==Industrial Semiconductor Fabrication==

Semiconductors are mass produced in specialized factories called foundries or fabs. The process consists of multiple chemical and photolithographic steps which add layers to a wafer usually made of silicon. The entire process usually takes around 2 months but it can last up to 4.

The semiconductor product is rated by the size of the chip's process gate length, where processes with smaller gate lengths are typically harder to make. There are 10-20 different sized chips being fabricated around the world as of 2018. There is an immense amount of attention and money being dedicated to improving semiconductor fabrication process efficiency.

[[File:feol.png|frame|none|left|Steps to fabricate a semiconductor device]]

==Examples==

===Simple===
[[File:Cat'swhiskerdetector.jpg]]

A simple application of a semiconductor would be the Cat's Whisker detector for radios, invented in the early 1900s.

===Moderate===
[[File:Opticallsensor.jpg]]

Optical sensors are moderately difficult applications of semiconductors. Optical sensors are electronic detectors that convert light into an electronic signal. They are used in many industrial and consumer applications. An example would include lamps that turn on automatically in response to darkness.

===Difficult===

[[File:Complicated_semiconductor.jpg]]

A very complicated application of a semiconductor is its use in modern cellular phone devices, such as its use here in the iPhone 6.

== See also ==

Related Wiki pages:

-Transformers

-Resistors and conductivity

-Superconductors

-Electric Fields

-Transformers from a physics standpoint

===Further reading===

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

===External links===

Wikipedia page about semiconductors:

https://en.wikipedia.org/wiki/Semiconductor_device

Encyclopedia entry about semiconductors, including the history of semiconductors:

http://www.britannica.com/technology/semiconductor-device

Information about Diodes:

https://en.wikipedia.org/wiki/Diode

Information about BJTs:

https://en.wikipedia.org/wiki/Bipolar_junction_transistor

Information about MOSFETs:

https://en.wikipedia.org/wiki/MOSFET

Semiconductor Device Fabrication

https://en.wikipedia.org/wiki/Semiconductor_device_fabrication

==References==
Brain, Marshall. "How Semiconductors Work." HowStuffWorks. N.p., 25 Apr. 2001. Web. 27 Nov. 2016.

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Electronics and Semiconductor. (n.d.). Retrieved December 3, 2015, from http://www.plm.automation.siemens.com/en_us/electronics-semiconductor/devices/

Huculak, M. (2014, September 19). IPhone 6 and iPhone 6 Plus get teardown by iFixit • The Windows Site for Enthusiasts - Pureinfotech. Retrieved December 3, 2015, from http://pureinfotech.com/2014/09/19/iphone-6-iphone-6-plus-get-teardown-ifixit/

Introduction to Secondary Ion Mass Spectrometry (SIMS) technique. (n.d.). Retrieved November 15, 2020, from https://www.cameca.com/products/sims/technique

John Bardeen, William Shockley and Walter Brattain at Bell Labs, 1948. (n.d.). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/John_Bardeen#/media/File:Bardeen_Shockley_Brattain_1948.JPG

The Nobel Prize in Physics 1956. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/1956/summary/>

The Nobel Prize in Physics 2000. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/2000/summary/>

เซ็นเซอร์แสง (Optical Sensor) - Elec-Za.com. (2014, July 28). Retrieved December 3, 2015, from http://www.elec-za.com/เซ็นเซอร์แสง-optical-sensor/

Semiconductor device. (2015, November 30). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/Semiconductor_device

Semiconductor Fabrication. (25 November 2018). http://www.iue.tuwien.ac.at/phd/rovitto/node10.html

Shah, A. (2013, May 13). Intel loses ground as world's top semiconductor company, survey says. Retrieved December 3, 2015, from http://www.pcworld.com/article/2038645/intel-loses-ground-as-worlds-top-semiconductor-company-survey-says.html

Shaw, R. (2014, November 1). The cat's-whisker detector. Retrieved December 3, 2015, from http://rileyjshaw.com/blog/the-cat's-whisker-detector/

Sze, S. (2015, October 1). Semiconductor device | electronics. Retrieved December 3, 2015, from http://www.britannica.com/technology/semiconductor-device

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

"Timeline." Timeline | The Silicon Engine | Computer History Museum. The Silicon Engine, n.d. Web. 27 Nov. 2016.

[[Category:Simple Circuits]]

Semiconductor Devices

2024-04-14T22:11:30Z

Idumitriu3: /* What are Semiconductors? */

Last edited by Megha Sharma (Fall 2020)

===What are Semiconductors?===

Semiconductor devices are electronic components with the electronic properties of semiconductors. Silicon, germanium, gallium arsenide, organic semiconductors are among the most common semiconductors used in these devices. Semiconductors are materials that are neither good conductors or good insulators. They have a good conductivity between conductors (these tend to be metals) and nonconductors (these insulators tend to be ceramics). Semiconductors do not have to originate organically - the most common semiconductor material are pure elements such as silicon and germanium, but impurities are often added to control the conductivity levels. This process is called doping. The doped semiconductors are called extrinsic semiconductors while pure, impurity-free semiconductors are called intrinsic semiconductors. Intrinsic semiconductors are less conductive than metals as they have a lower amount of charge carriers, or electrons or holes, that can move across the band gap. Extrinsic semiconductors can have higher or lower conductivity depending on the doping.

Due to low cost, reliability, ability to control conductivity, and compactness, semiconductors are used for a wide range of applications. They also have a wide range of current and voltage handling capabilities, contributing to their suitability for a number of operations. They are commonly found in power devices, optical sensors, and light emitters. Perhaps more importantly, they are readily integrated into microelectronic uses as key elements for the majority of electronic systems, including communications, consumer, data-processing, and industrial-control equipment.

[[File:Intelthing.jpg|frame|border|right|A raw board with many transistors in it!]]
[[File:transistor.png|frame|none|left|An fully built integrated circuit.]]

==The Main Idea==

Semiconductors work by using the electric properties of the p-n junction that makes up a diode. The junction is formed through a process called doping. Doping involves turning silicon into a conductor by changing the behavior of its electrons. In n-type doping, a phosphorus/arsenic impurity is introduced so that the valence will have free electrons to allow a electric current to flow. Since extra electrons are negative in charge, this type of doping is called n-type doping referred to by "n" in the p-n junction. In the p-type doping, a boron/gallium impurity is introduced to the silicon lattice so the valence will have an empty electron orbital. Because the empty area implies the absence of an electron and thus creates a positive charge, "p" was assigned as the name of the doping type.

[[File:n-type.gif|frame|border|right|N-Type Material]]

[[File:p-type.png|frame|none|left|P-Type Material]]

The two most useful forms of semiconductor devices are diodes and transistors. Diodes are the simplest semiconductor device, which conducts current easily in one direction but conducts almost no current in the other direction. These are made by joining two pieces of semiconducting material, a junction called a "p-n" junction. One of the pieces contains a small amount of boron and the other contains a small amount of phosphorus. Transistors are constructed through two semiconducting junctions, or "p-n" junctions. These are the most common elements in digital circuits. The conductivity of these semiconductors can be controlled by introduction of an electric or magnetic field, by exposure to light or heat, or by mechanical deformation of a doped monocrystalline grid. Due to this, semiconductors are extremely useful and can be altered to fit specific purposes.

===Semiconductors & Applications in Solid-State Physics===

The key principle that is often used in solid-state physics is the carrier effective mass. This refers to the mass a particle (within the semiconductor) seems to have when interacting with other identical particles in a thermal distribution. This constant is simplified version of the band theory and influences measurable properties of a solid, including the efficiency of the devices that semiconductors are used in for example, solar cell efficiency and integrated circuit speed. So, how do we actually measure the carrier effective masses in a semiconductor?

Large parts of the simplicity of the free electron gas model can be saved by assigning effective masses to the carriers. Only electrons and holes at the band edges (characterized by a wave vector kex) participate in the generation - recombination process that is the hallmark of semiconductors. A particle's effective mass is the mass that it seems to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles over long distances can be very different from their motion in a vacuum. The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass. Sometimes the effective mass can be considered to be a simple constant of a material, however, the value of effective mass depends on the purpose for which it is used, and can vary depending on a number of factors. For electrons or electron holes in a solid, the effective mass is usually stated in units of the rest mass of an electron, me (9.11×10−31 kg). In these units it is usually in the range 0.01 to 10, but can also be lower or higher—for example, reaching 1,000 in exotic heavy fermion materials, or anywhere from zero to infinity (depending on definition) in graphene. The effective mass of a semiconductor is obtained by fitting the actual electron diagram around the conduction band minimum or the valence band maximum by a parabola - this is called an E-K diagram (shown below). It shows the relationship between the energy and momentum of available quantum mechanical states for electrons in the material. As it simplifies the more general band theory, the electronic effective mass can be seen as an important basic parameter that influences measurable properties of a solid, including everything from the efficiency of a solar cell to the speed of an integrated circuit.

[[File:IMG 2424.jpg|Diagram of an EK diagram|350 px|]]

===Detecting Doping===

Secondary ion mass spectroscopy (SIMS) is a very powerful technique for the analysis of impurities in solids. SIMS can be utilized for semiconductor dopant profiling. The technique relies on removal of material from a solid by sputtering and on analysis of the sputtered ionized species; all elements are detected. SIMS can detect dopant densities as low as 10^14 cm^-3. The dopant density profile that is generated is based on the ion signal versus time plot. The time axis is converted to a depth axis by measuring the depth of the crater at the end of the measurement assuming a constant sputtering rate. For example, boron is implanted into silicon at a given energy and dose to create a standard. The secondary ion signal is calibrated by assuming the total amount of boron in the sample to equal to the implanted boron. The unknown sample of B implanted into silicon is then compared to the standard. However, there is limited dynamic range of the SIMS instrument that can contribute to slightly deeper junctions and discrepancies in the lowly doped portions of the profile. When sputtering from a highly doped region to a lowly doped region, the crater walls still contain the entire doping density profile. SIMS also measures total dopant density, regardless of activation. Thus going back to the silicon-boron example, the dopant profile shows dependence of electrical activation of boron implanted into silicon on implant dose and activation temperature.

[[File:Sims-technique-schematic.png|frame|none|left|Example of SIMS]]

===A Mathematical Model===

Semiconductors operate based on the concept of thermal energy exciting electrons and causing them to jump to the next higher (unoccupied) energy band.
These electrons can pick up energy (and drift speed) from an applied electric field. The filled energy band is called the “valence” band, and the nearly unoccupied higher energy band is called the “conduction” band. The number of electrons excited into the conduction band is proportional to a value called the Boltzmann constant, equivalent to the value:
<math>
e^{-E_{\text{gap}} / k_B T}
</math>.
Therefore, high conductivity (corrosponding to a favorable Boltzmann factor) can be calculated according to
<math>
T = 2 \pi \sqrt{\frac{m}{k}}
</math>,
where <math>m</math> is the mass of the object in kilograms, <math>k</math> is the spring constant, and <math>T</math> is the period of oscillation in seconds. In addition, the total conventional current in a semiconductor can be calculated, according to the equation
<math>
I = e n_n A u_n E + e n_p A u_p E
</math>.

===A Conceptual Model===
The following diagram demonstrates how electron excitement in semiconductors works. Semiconductors are materials with small band gaps between the valence band and conduction bands. As you can see, a small amount of thermal energy is needed to promote an electron to the conduction band in a semiconductor.

[[File:conceptual.png|frame|none|left|A Conceptual Model of the Semiconductor]]

===A Computational Model===

[https://phet.colorado.edu/sims/cheerpj/semiconductor/latest/semiconductor.html?simulation=semiconductor Semiconductor Simulation]

==History==
'''1874'''
Ferdinand Braun discovers that current flows freely in only one direction when a metal point and a galena crystal are put together.

'''1901'''
Jagadis Bose takes ownership of the discovery of the semiconductor crystal for detecting radio waves.

'''1940'''
Russell Ohl discovers the p-n junction.

'''1940s'''
Semiconductors were used only as two-terminal devices, such as rectifiers and photodiodes. They were most commonly used as detectors in radios, through devices called "cat's whiskers". During the era of WWII, researchers worked with semiconductors and cat's whiskers to make more effective diodes.

'''1947'''
William Shockley and John Bardeen worked together to create a triode-like semiconductor: the first transistor. They realized that if there were some way to control the flow of the electrons from the emitter to the collector of this newly discovered diode, an amplifier could be built.The first transistor was officially created on the 23rd of December, 1947.

'''1956'''
John Bardeen, William Shockley, and another researcher named Walter Houser Brattain were credited for the invention and awarded a Nobel Prize for physics in 1956 for their work. After this, the utilization of semiconductors soon advanced to even more complicated applications.

'''1960s'''
In the late 1960s, transistors moved from being germanium based to silicon based. Gordon K Teal was most responsible for this advancement, and his company, Texas Instruments, profited greatly. Portable radios are just one popular invention that benefited from silicon based semiconductors. Now, silicon based semiconductors constitute more than 95 percent of all semiconductor hardware sold worldwide.

'''1970s'''
Silicon technology is modernized and the race to fit all semiconductor processor technology into one chip is most active.

'''2000'''
Nobel Prize in physics awarded to Zhores I. Alferov and Herbert Kroemer for developing semiconductor heterostructures used in high-speed- and opto-electronics and half to Jack S. Kilby "for his part in the invention of the integrated circuit."

[[File:transistorwork.png|frame|none|none|John Bardeen, William Shockley, and Walter Houser Brattain, winners of the Nobel Prize for their invention of the transistor, are pictured above.]]

===Connectedness===

Semiconductors are crucial to modern technology, and are used for memory storage as well as so many other technological innovations. This technology is used every day by millions of people for thousands of different applications. Most people in the world have used semiconductors in one way or another, even if they weren't aware of it. It is specifically connected to the major of Biomedical Engineering through memory storage and the complex computer programs used every day to conduct business and create simulations for the furthering of biomedical research. All industrial applications of semiconductors are very applicable, from amplifiers to transistors to silicon disks. Without semiconductors, much of the technology that the general population relies on today would not be possible.

Semiconductors are used in essentially every part of this technological and electronically-dependent world we live in today. They have both conductor and insulator properties and includes all of the metal we see in wires. Computers, phones, and other electronic devices all use semiconductors to fulfill their functions such as communication and efficiency. The most important aspect of semiconductors is utilization, which is shown through the use of switches. Inside electronic devices, the switches exist in extremely large numbers, which is why electronic devices process information in an incredible speed with surprising efficiency.

Semiconductors are connected to chemical engineering largely through their industrial creation. The process of depositing each layer of material onto the wafer is a chemical process controlled by deposition of gaseous metals onto the wafer. There are an incredible variety of steps from material preparation to packaging which can be optimized by an eager chemical engineer.

Another example that was discussed previously on this page is the usage of silicon in photovoltaic devices. Silicon is used because it is the first semiconductor that was commercialized successfully. Many commercial companies are very proficient in making silicon devices, so the silicon is not necessarily used because it is the best material for harnessing the electricity from the photovoltaic effect. The silicon crystals allow the power to reach the external electrical circuit, but the silicon doesn't absorb sunlight as efficiently because it needs to be ten to one hundred times thicker than an advanced thin-film cell. It is also favored because of the low maintenance. A unique oxide forms when silicon is exposed to high temperatures that serves to neutralize defects on the silicon surface. The frontier for replacing the silicon looks quite bleak because of the practicality of manufacturing silicon crystalline semiconductors, but new research is being conducted on using silicon with lower purity or combining it with other semiconductor materials.

==Types of Semiconductors==

===Diodes===

[[File:Diode_current_wiki.png|314px|thumb|right|top|IV Characteristic of a Diode]]

Diodes are really great! In a simple sense, they can give you a "point of no return" in your circuit (but they can actually do much more than that).
Three interesting things should be observed from the IV characteristic shown to the right:

# For small positive voltages and above, the diode does not limit the current (the line is almost vertical)!
# For small to larger negative voltages, the diode resists current (the line is almost flat).
# For a large negative voltage (the breakdown voltage) the diode gives up (no one is perfect).

We can formally define this line with the Shockley Diode Equation, which formalizes this observation:

<math display="block">
I = I_S \left( e^{\frac{V_D}{n V_T}} - 1 \right)
</math> where

<math>I</math> is the diode current,

<math>I_S</math> is the reverse bias saturation current (or scale current),

<math>V_D</math> is the voltage across the diode,

<math>V_T</math> is the thermal voltage, and

<math>n</math> is the ideality factor, (1 if the diode is ideal, greater than 1 if it is imperfect).

A great practical use for diodes is a rectifier:

[[File:Gratz.rectifier.en.svg|frame|border|center|Diodes groups the positive and negative signals together]]

This makes sure that when a positive voltage appears on either line, it is redirected to a single positive line, and the same for the negatives.
BAM! AC to DC, that's pretty easy, you can charge your phone with that.
In reality a capacitor is added in parallel with the load to try to smooth out the ripples.
A voltage regulator after the rectifying step is also a popular choice, depending on the needs of the application.

Another super useful application is that of a back up power supply: simply connect two supplies in parallel with the positive terminals buffered with diodes. The higher of the two voltages is always used and the transition between supplies is seamless.

===Zener Diodes===

Some diodes (Zener) are made to have small breakdown voltages.
Since during breakdown the IV curve is almost vertical (it's really an exponential), the current is independent (almost) from voltage.
You can then wire up a Zener diode in reverse to a point in the circuit, and it will accept as much current as it needs to to reach that
breakdown voltage. Because of this a great practical use for Zener diodes is a voltage regulator since the voltage is set when the diode is
manufactured and does not change greatly with a varying power supply.

===Bipolar Junction Transistors===

[[Image:BJT NPN symbol (case).svg|75px|thumb|NPN BJT]]
[[Image:BJT PNP symbol (case).svg|75px|thumb|PNP BJT]]

Shortly after the invention of the first transistor (which was OK), the BJT landed, which was the first transistor to be prolific in the field.
It was made using two alternating NP junctions as shown below:

[[File:NPN BJT (Planar) Cross-section.svg|frame|border|center|NPN BJT (Planar) Cross-section]]

Really transistors (and by extension all that is needed for a computer to be built) are amplifiers (OK, to build all computers you need an inverting amplifier, but one can be built using the BJT).
If one is used to thinking of them as an electrically-controlled switch, you can simply think of a switch as an amplifier with a gain of <math>\infty</math>.

A simple model of a BJT is a linear current-controlled current source, i.e. the base to emitter (B to E) current <math>I_{BE}</math> is proportional to
the collector to emitter (C to E) current <math>I_{CE}</math>. The proportionality constant <math>\beta</math> can be thought of as the "gain" of the
transistor. This gives a relationship of <math>I_{CE} = \beta I_{BE}</math>.

[[File:Current-Voltage relationship of BJT.png|thumb|right|Current-Voltage relationship of BJT]]

Sadly there is no source of infinite power, so the output to our amplifier tops off when it can't supply any more power.
This can be seen with the graph on the right.
The simple model then only works for the tiny linear part at the start of the graph, even so its not ''that'' linear.
The BJT proved to be power hungry, pretty non-linear and sensitive to the environment (temperature, etc.).
These growing pains lead to a new development, called the MOSFET.

===MOSFETs===

MOSFETs are the coolest, they are less power-hungy and easier to work with when compared to BJTs.
Instead of having a current control, which uses power and gets the control and the output signal coupled together,
a MOSFET's output is controlled by the electric Field (the F in MOSFET) the control signal creates on one of the plates of the MOSFET.
Since the control signal and the output are electrically disconnected (as you would see in a capacitor) there is much less power draw
from this type of transistor.

We can see how linear this thing is with its IV characteristic: <math>I_D= \mu_n C_{ox}\frac{W}{L} \left( (V_{GS}-V_{th})V_{DS}-\frac{V_{DS}^2}{2} \right)</math>

Apart from the control signal <math>V_{DS}</math> and constants, the voltage across the output portion of the MOSFET is linearly related to the current!
This means that the MOSFET behaves like a voltage controlled resistor, and a resistor is something much easier to analyse and work with.

Most circuits with an enormous amount of transistors these days use primarily MOSFETs. BJTs are still useful for temperature and light sensing
applications.

==Industrial Semiconductor Fabrication==

Semiconductors are mass produced in specialized factories called foundries or fabs. The process consists of multiple chemical and photolithographic steps which add layers to a wafer usually made of silicon. The entire process usually takes around 2 months but it can last up to 4.

The semiconductor product is rated by the size of the chip's process gate length, where processes with smaller gate lengths are typically harder to make. There are 10-20 different sized chips being fabricated around the world as of 2018. There is an immense amount of attention and money being dedicated to improving semiconductor fabrication process efficiency.

[[File:feol.png|frame|none|left|Steps to fabricate a semiconductor device]]

==Examples==

===Simple===
[[File:Cat'swhiskerdetector.jpg]]

A simple application of a semiconductor would be the Cat's Whisker detector for radios, invented in the early 1900s.

===Moderate===
[[File:Opticallsensor.jpg]]

Optical sensors are moderately difficult applications of semiconductors. Optical sensors are electronic detectors that convert light into an electronic signal. They are used in many industrial and consumer applications. An example would include lamps that turn on automatically in response to darkness.

===Difficult===

[[File:Complicated_semiconductor.jpg]]

A very complicated application of a semiconductor is its use in modern cellular phone devices, such as its use here in the iPhone 6.

== See also ==

Related Wiki pages:

-Transformers

-Resistors and conductivity

-Superconductors

-Electric Fields

-Transformers from a physics standpoint

===Further reading===

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

===External links===

Wikipedia page about semiconductors:

https://en.wikipedia.org/wiki/Semiconductor_device

Encyclopedia entry about semiconductors, including the history of semiconductors:

http://www.britannica.com/technology/semiconductor-device

Information about Diodes:

https://en.wikipedia.org/wiki/Diode

Information about BJTs:

https://en.wikipedia.org/wiki/Bipolar_junction_transistor

Information about MOSFETs:

https://en.wikipedia.org/wiki/MOSFET

Semiconductor Device Fabrication

https://en.wikipedia.org/wiki/Semiconductor_device_fabrication

==References==
Brain, Marshall. "How Semiconductors Work." HowStuffWorks. N.p., 25 Apr. 2001. Web. 27 Nov. 2016.

Chabay, Sherwood. (n.d.). Matter and Interactions (4th ed., Vol. 2). Raleigh, North Carolina: Wiley.

Electronics and Semiconductor. (n.d.). Retrieved December 3, 2015, from http://www.plm.automation.siemens.com/en_us/electronics-semiconductor/devices/

Huculak, M. (2014, September 19). IPhone 6 and iPhone 6 Plus get teardown by iFixit • The Windows Site for Enthusiasts - Pureinfotech. Retrieved December 3, 2015, from http://pureinfotech.com/2014/09/19/iphone-6-iphone-6-plus-get-teardown-ifixit/

Introduction to Secondary Ion Mass Spectrometry (SIMS) technique. (n.d.). Retrieved November 15, 2020, from https://www.cameca.com/products/sims/technique

John Bardeen, William Shockley and Walter Brattain at Bell Labs, 1948. (n.d.). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/John_Bardeen#/media/File:Bardeen_Shockley_Brattain_1948.JPG

The Nobel Prize in Physics 1956. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/1956/summary/>

The Nobel Prize in Physics 2000. NobelPrize.org. Nobel Media AB 2018. Sun. 25 Nov 2018. <https://www.nobelprize.org/prizes/physics/2000/summary/>

เซ็นเซอร์แสง (Optical Sensor) - Elec-Za.com. (2014, July 28). Retrieved December 3, 2015, from http://www.elec-za.com/เซ็นเซอร์แสง-optical-sensor/

Semiconductor device. (2015, November 30). Retrieved December 3, 2015, from https://en.wikipedia.org/wiki/Semiconductor_device

Semiconductor Fabrication. (25 November 2018). http://www.iue.tuwien.ac.at/phd/rovitto/node10.html

Shah, A. (2013, May 13). Intel loses ground as world's top semiconductor company, survey says. Retrieved December 3, 2015, from http://www.pcworld.com/article/2038645/intel-loses-ground-as-worlds-top-semiconductor-company-survey-says.html

Shaw, R. (2014, November 1). The cat's-whisker detector. Retrieved December 3, 2015, from http://rileyjshaw.com/blog/the-cat's-whisker-detector/

Sze, S. (2015, October 1). Semiconductor device | electronics. Retrieved December 3, 2015, from http://www.britannica.com/technology/semiconductor-device

Sze, S. (1981). Physics of semiconductor devices (2nd ed.). New York: Wiley.

"Timeline." Timeline | The Silicon Engine | Computer History Museum. The Silicon Engine, n.d. Web. 27 Nov. 2016.

[[Category:Simple Circuits]]

Ductility

2024-04-14T21:51:02Z

Idumitriu3:

Edited by Irene Dumitriu (Spring 2024)
==The Main Idea==

Ductility is a solids ability to deform under tensile stress. It is similar to [[malleability]], which characterizes a materials ability to deform under an applied stress. Both of these are plastic properties of materials. While they are often similar, sometimes a materials ductility is independent from its malleability[1]. Ductility is the percentage of plastic deformation right before fracture, where plastic deformation means permanent deformation or change in shape of a solid body without fracture under the action of a sustained force[10]. Materials with low ductility are defined as brittle. Materials with metallic bonds have much higher ductility due to the mobile electrons that tend to deform, rather than fracture. Therefore, the most common ductile materials are steel, copper, gold and aluminum. Ductility is an important property in material science and metal-working industries, where solids are deformed and molded with outside forces. Ductile materials can absorb a large amount of energy before they start to show signs of deformation, whereas brittle materials tend to show deformations and cracks relatively easily.[8]
[[File:Cast iron tensile test.JPG|thumb|Fig. 1- Highly brittle fracture]]
[[File:Al tensile test.jpg|thumb| Fig. 2- Semi-ductile fracture]]

Environmental factors can also affect the ductility of a material. A temperature increase causes a material to stretch, and thus increases ductility. A temperature decreases leads to brittle and fragile behavior of the material and as such decreases ductility. Generally, low temperatures adversely affect the tensile toughness of many metals. Similarly, pressure can be used to control ductile-brittle effects. Sufficiently large superimposed pressure can convert a generally brittle material into a ductile material.[11]

Metals like aluminum, gold, silver, and copper have a face-centered cubic crystal lattice structure, and most do not experience a shift from ductile to brittle behavior. Other metals, like iron, chromium, and tungsten, have a body-centered cubic crystal structure and experience a sharp shift in ductility. [7]

On the other hand, plastics can also experience variation in ductility through being categorized as a thermoplastic or thermoset. A thermoplastic is a polymer that upon heating becomes moldable and when cooled regains its rigidity through solidifying. Thermoplastics can further be categorized as either amorphous or semicrystalline. In amorphous polymers, the polymer chains are randomly arranged with no long-range ordering and are described as glassy. While in the semicrystalline state, the polymer contains both amorphous and crystalline regions. These crystalline regions involve tightly packed and ordered polymer chains. The molecular differences between these two types of thermoplastics can impact the ductility. For example in amorphous thermoplastics, the ductility is mainly determined by the polymer chain mobility where the chains can glide past each other to accommodate for deformation before fracturing. In semicrystalline materials, the crystalline regions, as they are are ordered in specific directions, allow for easier chain gliding and provide reinforcement to the material. In addition to thermoplastics, thermosets are another polymer category in which the polymer chains are held together by crosslinks. Due to these crosslinks, thermosets tend to be less ductile materials as these linkages don’t allow the material to experience the same amount of percent elongation in comparison to thermoplastics. Therefore, like metals, plastics also experience variation in ductility due to molecular arrangements and morphology.

The Ductile - Brittle Transition Temperature (DBTT) is the temperature at which the fracture energy passes below a predetermined value (typically 40 J) or the point at which the material absorbs 15 ft*lb of impact energy during fracture[7]. The Ductile - Brittle Transition Temperature is an important consideration when determining which material to select, when said material is subjected to mechanical stresses (as shown at https://www.doitpoms.ac.uk/tlplib/BD6/images/graph0.gif). A low DBTT is integral for designs which will need to function in low temperatures [7].

The Ductile to Brittle Transition can also occur when dislocation motion occurs. Dislocation is defined as areas where the atoms are out of position in the crystal structure[12]. The stress required to move a dislocation depends on the atomic bonding, crystal structure, and obstacles. If the stress required to move the dislocation is too high, the metal will fail instead and form cracks or other deformations instead and the failure will be brittle[6].

===A Mathematical Model===

Mathematically, ductility can be defined as the fracture strain, or the tensile strain along one axis that causes a fracture to occur. Fractures range from brittle fractures (Fig. 1) to fully ductile fractures (Fig. 2), resulting in very different physical appearances associated with the different types. This can be modeled on a stress/strain curve (https://www.nde-ed.org/EducationResources/CommunityCollege/Materials/Graphics/Mechanical/Brittle-Ductile.gif) showing where fracture occurs along the graph.

Quantitatively being able to measure ductility is important with regards to comparing ductility between different materials. Ductility can be measured through two main methods: percent elongation and percent reduction of area[5]. The formulas can be found below: (http://www.engineersedge.com/material_science/ductility.htm)[2]

Percent Elongation = (Final Gage Length - Initial Gage Length) / Initial Gage Length

<math>\% elongation = \frac{L_f - L_o}{L_o} \cdot 100 </math>

Percent Reduction of Area = (Area of Original Cross Section - Minimum Final Area) / Area of Original Cross Section
<math> \% Area \ Reduction = \frac{Decrease \ in \ Area}{Original \ Area} </math>

===A Computational Model===

This [https://trinket.io/glowscript/71966b1570 Ductility Demonstration] illustrates the general concept of ductility as a material's ability to undergo some plastic deformation (in this case via stretching a beam), up until some fracture point where the material loses its integrity. On a related note, to learn more about types of plastic deformation, similar to this computational model, see the attached diagram of necking. Necking is a type of deformation often associated with ductile materials. This concept is illustrated in the diagram and additionally within the animation present with the "Ductility Demonstration" computational model!
[[File:Schematic Diagram of Necking.png|thumb|Schematic Diagram of Necking]]

[[File:Lundqvist ductility.png|glowscriptductility]]

==Connectedness==
Stress-Strain Testing Background:

When a material experiences forces such as stress and strain, understanding its performance under such conditions is critical to performance
and application. The general calculation for normal stress is taken by dividing the force by the area, as seen below. Similarly, strain can be considered as the elongation over original length.

<math>\sigma = \frac{F}{A} </math>

<math>\varepsilon = \frac{\Delta L}{L} </math>

Hooke's Law:

<math>\sigma = Modulus \ of \ Elasticity \cdot \varepsilon </math>

Modulus of elasticity is a property of the material itself, and is a material’s resistance to elastic deformation (non-permanent). From these equations, the behavior of a material undergoing deformation may be determined.

Based on a material’s modulus of elasticity, a material can be categorized as either “brittle” or “ductile”. A brittle material does not bend, and fractures comparatively quickly. Ductile materials can be easily bent and are comparatively difficult to fracture.

[[File:Stress strain comparison brittle ductile.svg|Stress strain comparison brittle ductile|750px|Image: 750 pixels]]]

[14]
The common points that a ductile material experiences during deformation are identified below. One important characteristic to note is that fracture strength is typically lower than the Ultimate strength of the material. A ductile material is able to withstand additional elongation (strain) even after ultimate strength has been achieved.

[[File:Stress strain ductile.svg|Stress strain ductile|750px|Image: 750 pixels]]

[15]
This knowledge provides a background to how stress-strain testing is conducted.
Different materials are placed inside a stress-strain testing rig. A load is continuously applied to the material until material fracture. A force transducer, combined with a position sensor, allow for the determination of key characteristics. This data allows for further examination using the equations and principles explained above.

[[File:SS John W Brown.jpg|thumb|Image of the SS John W Brown, one of only two surviving World War II Liberty Ships]]
Having a solid understanding of ductility and material processes is crucial for material scientists, physicists, mechanical engineers, and several other professions and research disciplines. Understanding the ductility of various materials is incredibly important for having a holistic understanding of a project and for performing proper materials selection and analysis. This is exemplified in materials that have a high applied tensile strength. Significant brittle fractures can cause a great deal of damage and lack of structural integrity. This was seen in Liberty Ships in World War 2, where ships had hull cracks and other significant defects due to the cold temperatures of the water. This ultimately caused the ship's materials to be more brittle in composition. As time progressed, several ships were lost due to brittle fractures, demonstrating the importance of solid materials understanding and the real-world impact that technical oversights can have.[13]

==History==
Percy Williams Bridgman's findings on tensile strength and material properties led to much of what is known about ductility, including that it is highly influenced by temperature and pressure. These findings led him to win the 1946 Nobel Prize in physics.[4]

[[File:Bridgman.jpg|Bridgman|center|Image on center|50px|Image: 50 pixels|frame| Percy William Bridgman]]]

== See also ==

*[[Malleability]]
*[[Temperature]]
*[[Pressure]]

===Further reading===

https://en.wikipedia.org/wiki/Ductility

===External links===

[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

[1]https://en.wikipedia.org/wiki/Ductility
[2]https://en.wikibooks.org/wiki/Advanced_Structural_Analysis/Part_I_-_Theory/Materials/Properties/Ductility
[3]https://en.wikipedia.org/wiki/Ductility#/media/File:Ductility.svg
[4]https://en.wikipedia.org/wiki/Percy_Williams_Bridgman
[5]http://www.engineersedge.com/material_science/ductility.htm
[6]https://www.doitpoms.ac.uk/tlplib/BD6/ductile-to-brittle.php
[7]http://www.spartaengineering.com/effects-of-low-temperature-on-performance-of-steel-equipment/
[8]http://people.clarkson.edu/~isuni/Chap-7.pdf
[9]http://www.etomica.org/app/modules/sites/MaterialFracture/Background1.html
[10]https://www.merriam-webster.com/dictionary/plastic%20deformation
[11]http://www.failurecriteria.com/theductile-britt.html
[12]https://www.nde-ed.org/EducationResources/CommunityCollege/Materials/Structure/linear_defects.htm
[13]https://en.wikipedia.org/wiki/Liberty_ship
[14]https://www.researchgate.net/figure/Engineering-Stress-Strain-curve-for-both-Brittle-and-Ductile-material-Source_fig4_326753159
[15]https://www.instructables.com/Steps-to-Analyzing-a-Materials-Properties-from-its/

[[Category: Properties of Matter ]]

Ductility

2024-04-14T21:50:03Z

Idumitriu3: /* The Main Idea */

Edited by Ryan Lundqvist (Fall 2023)
==The Main Idea==

Ductility is a solids ability to deform under tensile stress. It is similar to [[malleability]], which characterizes a materials ability to deform under an applied stress. Both of these are plastic properties of materials. While they are often similar, sometimes a materials ductility is independent from its malleability[1]. Ductility is the percentage of plastic deformation right before fracture, where plastic deformation means permanent deformation or change in shape of a solid body without fracture under the action of a sustained force[10]. Materials with low ductility are defined as brittle. Materials with metallic bonds have much higher ductility due to the mobile electrons that tend to deform, rather than fracture. Therefore, the most common ductile materials are steel, copper, gold and aluminum. Ductility is an important property in material science and metal-working industries, where solids are deformed and molded with outside forces. Ductile materials can absorb a large amount of energy before they start to show signs of deformation, whereas brittle materials tend to show deformations and cracks relatively easily.[8]
[[File:Cast iron tensile test.JPG|thumb|Fig. 1- Highly brittle fracture]]
[[File:Al tensile test.jpg|thumb| Fig. 2- Semi-ductile fracture]]

Environmental factors can also affect the ductility of a material. A temperature increase causes a material to stretch, and thus increases ductility. A temperature decreases leads to brittle and fragile behavior of the material and as such decreases ductility. Generally, low temperatures adversely affect the tensile toughness of many metals. Similarly, pressure can be used to control ductile-brittle effects. Sufficiently large superimposed pressure can convert a generally brittle material into a ductile material.[11]

Metals like aluminum, gold, silver, and copper have a face-centered cubic crystal lattice structure, and most do not experience a shift from ductile to brittle behavior. Other metals, like iron, chromium, and tungsten, have a body-centered cubic crystal structure and experience a sharp shift in ductility. [7]

On the other hand, plastics can also experience variation in ductility through being categorized as a thermoplastic or thermoset. A thermoplastic is a polymer that upon heating becomes moldable and when cooled regains its rigidity through solidifying. Thermoplastics can further be categorized as either amorphous or semicrystalline. In amorphous polymers, the polymer chains are randomly arranged with no long-range ordering and are described as glassy. While in the semicrystalline state, the polymer contains both amorphous and crystalline regions. These crystalline regions involve tightly packed and ordered polymer chains. The molecular differences between these two types of thermoplastics can impact the ductility. For example in amorphous thermoplastics, the ductility is mainly determined by the polymer chain mobility where the chains can glide past each other to accommodate for deformation before fracturing. In semicrystalline materials, the crystalline regions, as they are are ordered in specific directions, allow for easier chain gliding and provide reinforcement to the material. In addition to thermoplastics, thermosets are another polymer category in which the polymer chains are held together by crosslinks. Due to these crosslinks, thermosets tend to be less ductile materials as these linkages don’t allow the material to experience the same amount of percent elongation in comparison to thermoplastics. Therefore, like metals, plastics also experience variation in ductility due to molecular arrangements and morphology.

The Ductile - Brittle Transition Temperature (DBTT) is the temperature at which the fracture energy passes below a predetermined value (typically 40 J) or the point at which the material absorbs 15 ft*lb of impact energy during fracture[7]. The Ductile - Brittle Transition Temperature is an important consideration when determining which material to select, when said material is subjected to mechanical stresses (as shown at https://www.doitpoms.ac.uk/tlplib/BD6/images/graph0.gif). A low DBTT is integral for designs which will need to function in low temperatures [7].

The Ductile to Brittle Transition can also occur when dislocation motion occurs. Dislocation is defined as areas where the atoms are out of position in the crystal structure[12]. The stress required to move a dislocation depends on the atomic bonding, crystal structure, and obstacles. If the stress required to move the dislocation is too high, the metal will fail instead and form cracks or other deformations instead and the failure will be brittle[6].

===A Mathematical Model===

Mathematically, ductility can be defined as the fracture strain, or the tensile strain along one axis that causes a fracture to occur. Fractures range from brittle fractures (Fig. 1) to fully ductile fractures (Fig. 2), resulting in very different physical appearances associated with the different types. This can be modeled on a stress/strain curve (https://www.nde-ed.org/EducationResources/CommunityCollege/Materials/Graphics/Mechanical/Brittle-Ductile.gif) showing where fracture occurs along the graph.

Quantitatively being able to measure ductility is important with regards to comparing ductility between different materials. Ductility can be measured through two main methods: percent elongation and percent reduction of area[5]. The formulas can be found below: (http://www.engineersedge.com/material_science/ductility.htm)[2]

Percent Elongation = (Final Gage Length - Initial Gage Length) / Initial Gage Length

<math>\% elongation = \frac{L_f - L_o}{L_o} \cdot 100 </math>

Percent Reduction of Area = (Area of Original Cross Section - Minimum Final Area) / Area of Original Cross Section
<math> \% Area \ Reduction = \frac{Decrease \ in \ Area}{Original \ Area} </math>

===A Computational Model===

This [https://trinket.io/glowscript/71966b1570 Ductility Demonstration] illustrates the general concept of ductility as a material's ability to undergo some plastic deformation (in this case via stretching a beam), up until some fracture point where the material loses its integrity. On a related note, to learn more about types of plastic deformation, similar to this computational model, see the attached diagram of necking. Necking is a type of deformation often associated with ductile materials. This concept is illustrated in the diagram and additionally within the animation present with the "Ductility Demonstration" computational model!
[[File:Schematic Diagram of Necking.png|thumb|Schematic Diagram of Necking]]

[[File:Lundqvist ductility.png|glowscriptductility]]

==Connectedness==
Stress-Strain Testing Background:

When a material experiences forces such as stress and strain, understanding its performance under such conditions is critical to performance
and application. The general calculation for normal stress is taken by dividing the force by the area, as seen below. Similarly, strain can be considered as the elongation over original length.

<math>\sigma = \frac{F}{A} </math>

<math>\varepsilon = \frac{\Delta L}{L} </math>

Hooke's Law:

<math>\sigma = Modulus \ of \ Elasticity \cdot \varepsilon </math>

Modulus of elasticity is a property of the material itself, and is a material’s resistance to elastic deformation (non-permanent). From these equations, the behavior of a material undergoing deformation may be determined.

Based on a material’s modulus of elasticity, a material can be categorized as either “brittle” or “ductile”. A brittle material does not bend, and fractures comparatively quickly. Ductile materials can be easily bent and are comparatively difficult to fracture.

[[File:Stress strain comparison brittle ductile.svg|Stress strain comparison brittle ductile|750px|Image: 750 pixels]]]

[14]
The common points that a ductile material experiences during deformation are identified below. One important characteristic to note is that fracture strength is typically lower than the Ultimate strength of the material. A ductile material is able to withstand additional elongation (strain) even after ultimate strength has been achieved.

[[File:Stress strain ductile.svg|Stress strain ductile|750px|Image: 750 pixels]]

[15]
This knowledge provides a background to how stress-strain testing is conducted.
Different materials are placed inside a stress-strain testing rig. A load is continuously applied to the material until material fracture. A force transducer, combined with a position sensor, allow for the determination of key characteristics. This data allows for further examination using the equations and principles explained above.

[[File:SS John W Brown.jpg|thumb|Image of the SS John W Brown, one of only two surviving World War II Liberty Ships]]
Having a solid understanding of ductility and material processes is crucial for material scientists, physicists, mechanical engineers, and several other professions and research disciplines. Understanding the ductility of various materials is incredibly important for having a holistic understanding of a project and for performing proper materials selection and analysis. This is exemplified in materials that have a high applied tensile strength. Significant brittle fractures can cause a great deal of damage and lack of structural integrity. This was seen in Liberty Ships in World War 2, where ships had hull cracks and other significant defects due to the cold temperatures of the water. This ultimately caused the ship's materials to be more brittle in composition. As time progressed, several ships were lost due to brittle fractures, demonstrating the importance of solid materials understanding and the real-world impact that technical oversights can have.[13]

==History==
Percy Williams Bridgman's findings on tensile strength and material properties led to much of what is known about ductility, including that it is highly influenced by temperature and pressure. These findings led him to win the 1946 Nobel Prize in physics.[4]

[[File:Bridgman.jpg|Bridgman|center|Image on center|50px|Image: 50 pixels|frame| Percy William Bridgman]]]

== See also ==

*[[Malleability]]
*[[Temperature]]
*[[Pressure]]

===Further reading===

https://en.wikipedia.org/wiki/Ductility

===External links===

[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

[1]https://en.wikipedia.org/wiki/Ductility
[2]https://en.wikibooks.org/wiki/Advanced_Structural_Analysis/Part_I_-_Theory/Materials/Properties/Ductility
[3]https://en.wikipedia.org/wiki/Ductility#/media/File:Ductility.svg
[4]https://en.wikipedia.org/wiki/Percy_Williams_Bridgman
[5]http://www.engineersedge.com/material_science/ductility.htm
[6]https://www.doitpoms.ac.uk/tlplib/BD6/ductile-to-brittle.php
[7]http://www.spartaengineering.com/effects-of-low-temperature-on-performance-of-steel-equipment/
[8]http://people.clarkson.edu/~isuni/Chap-7.pdf
[9]http://www.etomica.org/app/modules/sites/MaterialFracture/Background1.html
[10]https://www.merriam-webster.com/dictionary/plastic%20deformation
[11]http://www.failurecriteria.com/theductile-britt.html
[12]https://www.nde-ed.org/EducationResources/CommunityCollege/Materials/Structure/linear_defects.htm
[13]https://en.wikipedia.org/wiki/Liberty_ship
[14]https://www.researchgate.net/figure/Engineering-Stress-Strain-curve-for-both-Brittle-and-Ductile-material-Source_fig4_326753159
[15]https://www.instructables.com/Steps-to-Analyzing-a-Materials-Properties-from-its/

[[Category: Properties of Matter ]]