Electric field

From Wikipedia, the free encyclopedia

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

 

Electric field of a positive point electric charge suspended over an infinite sheet of conducting material. The field is depicted by electric field lines, lines which follow the direction of the electric field in space.

 

An electric field surrounds an electric charge, and exerts force on other charges in the field, attracting or repelling them. Electric field is sometimes abbreviated as E-field. The electric field is defined mathematically as a vector field that associates to each point in space the (electrostatic or Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point. The SI unit for electric field strength is volt per meter (V/m). Newtons per coulomb (N/C) is also used as a unit of electric field strength. Electric fields are created by electric charges, or by time-varying magnetic fields. Electric fields are important in many areas of physics, and are exploited practically in electrical technology. On an atomic scale, the electric field is responsible for the attractive force between the atomic nucleus and electrons that holds atoms together, and the forces between atoms that cause chemical bonding. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces (or interactions) of nature. 

Definition

From Coulomb's law a particle with electric charge ${\displaystyle q_{1}}$ at position ${\displaystyle {\boldsymbol {x}}_{1}}$ exerts a force on a particle with charge ${\displaystyle q_{0}}$ at position ${\displaystyle {\boldsymbol {x}}_{0}}$ of

${\displaystyle {\boldsymbol {F}}={1 \over 4\pi \varepsilon _{0}}{q_{1}q_{0} \over ({\boldsymbol {x}}_{1}-{\boldsymbol {x}}_{0})^{2}}{\hat {\boldsymbol {r}}}_{1,0}}$

where ${\displaystyle {\boldsymbol {r}}_{1,0}}$ is the unit vector in the direction from point ${\displaystyle {\boldsymbol {x}}_{1}}$ to point ${\displaystyle {\boldsymbol {x}}_{0}}$, and ε₀ is the electric constant (also known as "the absolute permittivity of free space") in C² m⁻² N⁻¹

When the charges ${\displaystyle q_{0}}$ and ${\displaystyle q_{1}}$ have the same sign this force is positive, directed away from the other charge, indicating the particles repel each other. When the charges have unlike signs the force is negative, indicating the particles attract. To make it easy to calculate the Coulomb force on any charge at position ${\displaystyle {\boldsymbol {x}}_{0}}$ this expression can be divided by ${\displaystyle q_{0}}$, leaving an expression that only depends on the other charge (the source charge)

${\displaystyle {\boldsymbol {E}}({\boldsymbol {x}}_{0})={{\boldsymbol {F}} \over q_{0}}={1 \over 4\pi \varepsilon _{0}}{q_{1} \over ({\boldsymbol {x}}_{1}-{\boldsymbol {x}}_{0})^{2}}{\hat {\boldsymbol {r}}}_{1,0}}$

This is the electric field at point ${\displaystyle {\boldsymbol {x}}_{0}}$ due to the point charge ${\displaystyle q_{1}}$; it is a vector equal to the Coulomb force per unit charge that a positive point charge would experience at the position ${\displaystyle {\boldsymbol {x}}_{0}}$. Since this formula gives the electric field magnitude and direction at any point ${\displaystyle {\boldsymbol {x}}_{0}}$ in space (except at the location of the charge itself, ${\displaystyle {\boldsymbol {x}}_{1}}$, where it becomes infinite) it defines a vector field. From the above formula it can be seen that the electric field due to a point charge is everywhere directed away from the charge if it is positive, and toward the charge if it is negative, and its magnitude decreases with the inverse square of the distance from the charge. 

If there are multiple charges, the resultant Coulomb force on a charge can be found by summing the vectors of the forces due to each charge. This shows the electric field obeys the superposition principle: the total electric field at a point due to a collection of charges is just equal to the vector sum of the electric fields at that point due to the individual charges.

${\displaystyle {\boldsymbol {E}}({\boldsymbol {x}})={\boldsymbol {E}}_{1}({\boldsymbol {x}})+{\boldsymbol {E}}_{2}({\boldsymbol {x}})+{\boldsymbol {E}}_{3}({\boldsymbol {x}})+\cdots ={1 \over 4\pi \varepsilon _{0}}{q_{1} \over ({\boldsymbol {x}}_{1}-{\boldsymbol {x}})^{2}}{\hat {\boldsymbol {r}}}_{1}+{1 \over 4\pi \varepsilon _{0}}{q_{2} \over ({\boldsymbol {x}}_{2}-{\boldsymbol {x}})^{2}}{\hat {\boldsymbol {r}}}_{2}+{1 \over 4\pi \varepsilon _{0}}{q_{3} \over ({\boldsymbol {x}}_{3}-{\boldsymbol {x}})^{2}}{\hat {\boldsymbol {r}}}_{3}+\cdots }$

${\displaystyle {\boldsymbol {E}}({\boldsymbol {x}})={1 \over 4\pi \varepsilon _{0}}\sum _{k=1}^{N}{q_{k} \over ({\boldsymbol {x}}_{k}-{\boldsymbol {x}})^{2}}{\hat {\boldsymbol {r}}}_{k}}$

where ${\displaystyle {\boldsymbol {{\hat {r}}_{k}}}}$ is the unit vector in the direction from point ${\displaystyle {\boldsymbol {x}}_{k}}$ to point ${\displaystyle {\boldsymbol {x}}}$.

This is the definition of the electric field due to the point source charges ${\displaystyle q_{1},\ldots ,q_{N}}$. It diverges and becomes infinite at the locations of the charges themselves, and so is not defined there. 

Evidence of an electric field: styrofoam peanuts clinging to a cat's fur due to static electricity. The triboelectric effect causes an electrostatic charge to build up on the fur due to the cat's motions. The electric field of the charge causes polarization of the molecules of the styrofoam due to electrostatic induction, resulting in a slight attraction of the light plastic pieces to the charged fur. This effect is also the cause of static cling in clothes.

 

The Coulomb force on a charge of magnitude ${\displaystyle q}$ at any point in space is equal to the product of the charge and the electric field at that point

${\displaystyle {\boldsymbol {F}}=q{\boldsymbol {E}}}$

The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m); in terms of the SI base units they are kg⋅m⋅s⁻³⋅A⁻¹

 

The electric field due to a continuous distribution of charge ${\displaystyle \rho ({\boldsymbol {x}})}$ in space (where ${\displaystyle \rho }$ is the charge density in coulombs per cubic meter) can be calculated by considering the charge ${\displaystyle \rho ({\boldsymbol {x}}')dV}$ in each small volume of space ${\displaystyle dV}$ at point ${\displaystyle {\boldsymbol {x}}'}$ as a point charge, and calculating its electric field ${\displaystyle d{\boldsymbol {E}}({\boldsymbol {x}})}$ at point ${\displaystyle {\boldsymbol {x}}}$

${\displaystyle d{\boldsymbol {E}}({\boldsymbol {x}})={1 \over 4\pi \varepsilon _{0}}{\rho ({\boldsymbol {x}}')dV \over ({\boldsymbol {x}}'-{\boldsymbol {x}})^{2}}{\hat {\boldsymbol {r}}}'}$

where ${\displaystyle {\hat {\boldsymbol {r}}}'}$ is the unit vector pointing from ${\displaystyle {\boldsymbol {x}}'}$ to ${\displaystyle {\boldsymbol {x}}}$, then adding up the contributions from all the increments of volume by integrating over the volume of the charge distribution ${\displaystyle V}$

${\displaystyle {\boldsymbol {E}}({\boldsymbol {x}})={1 \over 4\pi \varepsilon _{0}}\iiint \limits _{V}\,{\rho ({\boldsymbol {x}}')dV \over ({\boldsymbol {x}}'-{\boldsymbol {x}})^{2}}{\hat {\boldsymbol {r}}}'$

Sources

Causes and description

Electric fields are caused by electric charges, described by Gauss's law, or varying magnetic fields, described by Faraday's law of induction. Together, these laws are enough to define the behavior of the electric field as a function of charge repartition and magnetic field. However, since the magnetic field is described as a function of electric field, the equations of both fields are coupled and together form Maxwell's equations that describe both fields as a function of charges and currents.

In the special case of a steady state (stationary charges and currents), the Maxwell-Faraday inductive effect disappears. The resulting two equations (Gauss's law ${\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{0}}}}$ and Faraday's law with no induction term ${\displaystyle \nabla \times \mathbf {E} =0}$), taken together, are equivalent to Coulomb's law, written as ${\displaystyle {\boldsymbol {E}}({\boldsymbol {r}})={1 \over 4\pi \varepsilon _{0}}\int \rho ({\boldsymbol {r'}}){{\boldsymbol {r}}-{\boldsymbol {r'}} \over |{\boldsymbol {r}}-{\boldsymbol {r'}}|^{3}}d^{3}r'}$ for a charge density ${\displaystyle \mathbf {\rho } (\mathbf {r} )}$ (${\displaystyle \mathbf {r} }$ is position in space). Notice that ${\displaystyle \varepsilon _{0}}$, the vacuum electric permittivity, must be substituted with ${\displaystyle \varepsilon }$, permittivity, when charges are in non-empty media. 

Continuous vs. discrete charge representation

The electric field (lines with arrows) of a charge (+) induces surface charges (red and blue areas) on metal objects due to electrostatic induction.

 

The equations of electromagnetism are best described in a continuous description. However, charges are sometimes best described as discrete points; for example, some models may describe electrons as point sources where charge density is infinite on an infinitesimal section of space. 

A charge ${\displaystyle q}$ located at ${\displaystyle \mathbf {r_{0}} }$ can be described mathematically as a charge density ${\displaystyle \rho (\mathbf {r} )=q\delta (\mathbf {r-r_{0}} )}$, where the Dirac delta function (in three dimensions) is used. Conversely, a charge distribution can be approximated by many small point charges. 

Superposition principle

Electric fields satisfy the superposition principle, because Maxwell's equations are linear. As a result, if ${\displaystyle \mathbf {E} _{1}}$ and ${\displaystyle \mathbf {E} _{2}}$ are the electric fields resulting from distribution of charges ${\displaystyle \rho _{1}}$ and ${\displaystyle \rho _{2}}$, a distribution of charges ${\displaystyle \rho _{1}+\rho _{2}}$ will create an electric field ${\displaystyle \mathbf {E} _{1}+\mathbf {E} _{2}}$; for instance, Coulomb's law is linear in charge density as well. 

This principle is useful to calculate the field created by multiple point charges. If charges ${\displaystyle q_{1},q_{2},...,q_{n}}$ are stationary in space at ${\displaystyle \mathbf {r} _{1},\mathbf {r} _{2},...\mathbf {r} _{n}}$, in the absence of currents, the superposition principle proves that the resulting field is the sum of fields generated by each particle as described by Coulomb's law:

${\displaystyle \mathbf {E} (\mathbf {r} )=\sum _{i=1}^{N}\mathbf {E} _{i}(\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\sum _{i=1}^{N}q_{i}{\frac {\mathbf {r} -\mathbf {r} _{i}}{|\mathbf {r} -\mathbf {r} _{i}|^{3}}}}$

Electrostatic fields

Illustration of the electric field surrounding a positive (red) and a negative (blue) charge

Electrostatic fields are electric fields which do not change with time, which happens when charges and currents are stationary. In that case, Coulomb's law fully describes the field.

Electric potential

If a system is static, such that magnetic fields are not time-varying, then by Faraday's law, the electric field is curl-free. In this case, one can define an electric potential, that is, a function ${\displaystyle \Phi }$ such that ${\displaystyle \mathbf {E} =-\nabla \Phi }$. This is analogous to the gravitational potential. 

Parallels between electrostatic and gravitational fields

Coulomb's law, which describes the interaction of electric charges:

${\displaystyle \mathbf {F} =q\left({\frac {Q}{4\pi \varepsilon _{0}}}{\frac {\mathbf {\hat {r}} }{|\mathbf {r} |^{2}}}\right)=q\mathbf {E} }$

is similar to Newton's law of universal gravitation:

${\displaystyle \mathbf {F} =m\left(-GM{\frac {\mathbf {\hat {r}} }{|\mathbf {r} |^{2}}}\right)=m\mathbf {g} }$

(where ${\displaystyle \mathbf {\hat {r}} =\mathbf {\frac {r}{|r|}} }$).

This suggests similarities between the electric field E and the gravitational field g, or their associated potentials. Mass is sometimes called "gravitational charge".

Electrostatic and gravitational forces both are central, conservative and obey an inverse-square law.

Uniform fields

A uniform field is one in which the electric field is constant at every point. It can be approximated by placing two conducting plates parallel to each other and maintaining a voltage (potential difference) between them; it is only an approximation because of boundary effects (near the edge of the planes, electric field is distorted because the plane does not continue). Assuming infinite planes, the magnitude of the electric field E is:

${\displaystyle E=-{\frac {V}{d}}}$

where ΔV is the potential difference between the plates and d is the distance separating the plates. The negative sign arises as positive charges repel, so a positive charge will experience a force away from the positively charged plate, in the opposite direction to that in which the voltage increases. In micro- and nano-applications, for instance in relation to semiconductors, a typical magnitude of an electric field is in the order of 10⁶ V⋅m⁻¹, achieved by applying a voltage of the order of 1 volt between conductors spaced 1 µm apart. 

Electrodynamic fields

Electrodynamic fields are electric fields which do change with time, for instance when charges are in motion. 

The electric field cannot be described independently of the magnetic field in that case. If A is the magnetic vector potential, defined so that ${\displaystyle \mathbf {B} =\nabla \times \mathbf {A} }$, one can still define an electric potential ${\displaystyle \Phi }$ such that:

${\displaystyle \mathbf {E} =-\nabla \Phi -{\frac {\partial \mathbf {A} }{\partial t}}}$

One can recover Faraday's law of induction by taking the curl of that equation

${\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial (\nabla \times \mathbf {A} )}{\partial t}}=-{\frac {\partial \mathbf {B} }{\partial t}}}$

which justifies, a posteriori, the previous form for E. 

Energy in the electric field

The total energy per unit volume stored by the electromagnetic field is

${\displaystyle u_{EM}={\frac {\varepsilon }{2}}|\mathbf {E} |^{2}+{\frac {1}{2\mu }}|\mathbf {B} |^{2}}$

where ε is the permittivity of the medium in which the field exists, ${\displaystyle \mu }$ its magnetic permeability, and E and B are the electric and magnetic field vectors. 

As E and B fields are coupled, it would be misleading to split this expression into "electric" and "magnetic" contributions. However, in the steady-state case, the fields are no longer coupled. It makes sense in that case to compute the electrostatic energy per unit volume:

${\displaystyle u_{ES}={\frac {1}{2}}\varepsilon |\mathbf {E} |^{2}\,,}$

The total energy U stored in the electric field in a given volume V is therefore

${\displaystyle U_{ES}={\frac {1}{2}}\varepsilon \int _{V}|\mathbf {E} |^{2}\,\mathrm {d} V\,,}$

Further extensions

Definitive equation of vector fields

In the presence of matter, it is helpful to extend the notion of the electric field into three vector fields:

${\displaystyle \mathbf {D} =\varepsilon _{0}\mathbf {E} +\mathbf {P} \!}$

where P is the electric polarization – the volume density of electric dipole moments, and D is the electric displacement field. Since E and P are defined separately, this equation can be used to define D. The physical interpretation of D is not as clear as E (effectively the field applied to the material) or P (induced field due to the dipoles in the material), but still serves as a convenient mathematical simplification, since Maxwell's equations can be simplified in terms of free charges and currents. 

Constitutive relation

The E and D fields are related by the permittivity of the material, ε.

For linear, homogeneous, isotropic materials E and D are proportional and constant throughout the region, there is no position dependence: For inhomogeneous materials, there is a position dependence throughout the material:

${\displaystyle \mathbf {D(r)} =\varepsilon \mathbf {E(r)} }$

For anisotropic materials the E and D fields are not parallel, and so E and D are related by the permittivity tensor (a 2nd order tensor field), in component form:

${\displaystyle D_{i}=\varepsilon _{ij}E_{j}}$

For non-linear media, E and D are not proportional. Materials can have varying extents of linearity, homogeneity and isotropy.

Field-effect transistor

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Field-effect_transistor

 

Cross-sectional view of a field-effect transistor, showing source, gate and drain terminals

 

The field-effect transistor (FET) is a type of transistor which uses an electric field to control the flow of current. FETs are devices with three terminals: source, gate, and drain. FETs control the flow of current by the application of a voltage to the gate, which in turn alters the conductivity between the drain and source. 

FETs are also known as unipolar transistors since they involve single-carrier-type operation. That is, FETs use electrons or holes as charge carriers in their operation, but not both. Many different types of field effect transistors exist. Field effect transistors generally display very high input impedance at low frequencies. The most widely used field-effect transistor is the MOSFET (metal-oxide-semiconductor field-effect transistor). 

History

Julius Edgar Lilienfeld proposed the concept of a field-effect transistor in 1925.

 

The concept of a field-effect transistor (FET) was first patented by Austro-Hungarian physicist Julius Edgar Lilienfeld in 1925 and by Oskar Heil in 1934, but they were unable to build a working practical semiconducting device based on the concept. The transistor effect was later observed and explained by John Bardeen and Walter Houser Brattain while working under William Shockley at Bell Labs in 1947, shortly after the 17-year patent expired. Shockley initially attempted to build a working FET, by trying to modulate the conductivity of a semiconductor, but was unsuccessful, mainly due to problems with the surface states, the dangling bond, and the germanium and copper compound materials. In the course of trying to understand the mysterious reasons behind their failure to build a working FET, this led to Bardeen and Brattain instead building a point-contact transistor in 1947, which was followed by Shockley's bipolar junction transistor in 1948.

The first FET device to be successfully built was the junction field-effect transistor (JFET). A JFET was first patented by Heinrich Welker in 1945. The static induction transistor (SIT), a type of JFET with a short channel, was invented by Japanese engineers Jun-ichi Nishizawa and Y. Watanabe in 1950. Following Shockley's theoretical treatment on the JFET in 1952, a working practical JFET was built by George F. Dacey and Ian M. Ross in 1953. However, the JFET still had issues affecting junction transistors in general. Junction transistors were relatively bulky devices that were difficult to manufacture on a mass-production basis, which limited them to a number of specialised applications. The insulated-gate field-effect transistor (IGFET) was theorized as a potential alternative to junction transistors, but researchers were unable to build working IGFETs, largely due to the troublesome surface state barrier that prevented the external electric field from penetrating into the material. By the mid-1950s, researchers had largely given up on the FET concept, and instead focused on bipolar junction transistor (BJT) technology.

Metal-oxide-semiconductor FET (MOSFET)

Mohamed Atalla (top) and Dawon Kahng (bottom) invented the MOSFET (MOS field-effect transistor) in 1959.

 

A breakthrough in FET research came with the work of Egyptian engineer Mohamed Atalla in the late 1950s. He investigated the surface properties of silicon semiconductors at Bell Labs, where he adopted a new method of semiconductor device fabrication, coating a silicon wafer with an insulating layer of silicon oxide, so that electricity could reliably penetrate to the conducting silicon below, overcoming the surface states that prevented electricity from reaching the semiconducting layer. This is known as surface passivation, a method that became critical to the semiconductor industry as it made mass-production of silicon integrated circuits possible. Building on his surface passivation method, he developed the metal–oxide–semiconductor (MOS) process, which he presented in 1957. He later proposed the MOS process could be used to build the first working silicon FET, which he began working on building with the help of his Korean colleague Dawon Kahng.

The metal–oxide–semiconductor field-effect transistor (MOSFET) was invented by Mohamed Atalla and Dawon Kahng in 1959. The MOSFET largely superseded both the bipolar transistor and the JFET, and had a profound effect on digital electronic development. With its high scalability, and much lower power consumption and higher density than bipolar junction transistors, the MOSFET made it possible to build high-density integrated circuits. The MOSFET is also capable of handling higher power than the JFET. The MOSFET was the first truly compact transistor that could be miniaturised and mass-produced for a wide range of uses. The MOSFET thus became the most common type of transistor in computers, electronics, and communications technology (such as smartphones). The US Patent and Trademark Office calls it a "groundbreaking invention that transformed life and culture around the world".

CMOS (complementary MOS), a semiconductor device fabrication process for MOSFETs, was developed by Chih-Tang Sah and Frank Wanlass at Fairchild Semiconductor in 1963. The first report of a floating-gate MOSFET was made by Dawon Kahng and Simon Sze in 1967. A double-gate MOSFET was first demonstrated in 1984 by Electrotechnical Laboratory researchers Toshihiro Sekigawa and Yutaka Hayashi. FinFET (fin field-effect transistor), a type of 3D non-planar multi-gate MOSFET, originated from the research of Digh Hisamoto and his team at Hitachi Central Research Laboratory in 1989.

Basic information

FETs can be majority-charge-carrier devices, in which the current is carried predominantly by majority carriers, or minority-charge-carrier devices, in which the current is mainly due to a flow of minority carriers. The device consists of an active channel through which charge carriers, electrons or holes, flow from the source to the drain. Source and drain terminal conductors are connected to the semiconductor through ohmic contacts. The conductivity of the channel is a function of the potential applied across the gate and source terminals.

The FET's three terminals are:

1. source (S), through which the carriers enter the channel. Conventionally, current entering the channel at S is designated by I_S.
2. drain (D), through which the carriers leave the channel. Conventionally, current entering the channel at D is designated by I_D. Drain-to-source voltage is V_DS.
3. gate (G), the terminal that modulates the channel conductivity. By applying voltage to G, one can control I_D.
   

More about terminals

Cross section of an n-type MOSFET

 

All FETs have source, drain, and gate terminals that correspond roughly to the emitter, collector, and base of BJTs. Most FETs have a fourth terminal called the body, base, bulk, or substrate. This fourth terminal serves to bias the transistor into operation; it is rare to make non-trivial use of the body terminal in circuit designs, but its presence is important when setting up the physical layout of an integrated circuit. The size of the gate, length L in the diagram, is the distance between source and drain. The width is the extension of the transistor, in the direction perpendicular to the cross section in the diagram (i.e., into/out of the screen). Typically the width is much larger than the length of the gate. A gate length of 1 µm limits the upper frequency to about 5 GHz, 0.2 µm to about 30 GHz. 

The names of the terminals refer to their functions. The gate terminal may be thought of as controlling the opening and closing of a physical gate. This gate permits electrons to flow through or blocks their passage by creating or eliminating a channel between the source and drain. Electron-flow from the source terminal towards the drain terminal is influenced by an applied voltage. The body simply refers to the bulk of the semiconductor in which the gate, source and drain lie. Usually the body terminal is connected to the highest or lowest voltage within the circuit, depending on the type of the FET. The body terminal and the source terminal are sometimes connected together since the source is often connected to the highest or lowest voltage within the circuit, although there are several uses of FETs which do not have such a configuration, such as transmission gates and cascode circuits. 

Effect of gate voltage on current

I–V characteristics and output plot of a JFET n-channel transistor.

 

Simulation result for right side: formation of inversion channel (electron density) and left side: current-gate voltage curve (transfer characteristics) in an n-channel nanowire MOSFET. Note that the threshold voltage for this device lies around 0.45 V.

 

FET conventional symbol types

 

The FET controls the flow of electrons (or electron holes) from the source to drain by affecting the size and shape of a "conductive channel" created and influenced by voltage (or lack of voltage) applied across the gate and source terminals. (For simplicity, this discussion assumes that the body and source are connected.) This conductive channel is the "stream" through which electrons flow from source to drain. 

n-channel FET

In an n-channel "depletion-mode" device, a negative gate-to-source voltage causes a depletion region to expand in width and encroach on the channel from the sides, narrowing the channel. If the active region expands to completely close the channel, the resistance of the channel from source to drain becomes large, and the FET is effectively turned off like a switch (see right figure, when there is very small current). This is called "pinch-off", and the voltage at which it occurs is called the "pinch-off voltage". Conversely, a positive gate-to-source voltage increases the channel size and allows electrons to flow easily (see right figure, when there is a conduction channel and current is large). 

In an n-channel "enhancement-mode" device, a conductive channel does not exist naturally within the transistor, and a positive gate-to-source voltage is necessary to create one. The positive voltage attracts free-floating electrons within the body towards the gate, forming a conductive channel. But first, enough electrons must be attracted near the gate to counter the dopant ions added to the body of the FET; this forms a region with no mobile carriers called a depletion region, and the voltage at which this occurs is referred to as the threshold voltage of the FET. Further gate-to-source voltage increase will attract even more electrons towards the gate which are able to create a conductive channel from source to drain; this process is called inversion. 

p-channel FET

In a p-channel "depletion-mode" device, a positive voltage from gate to body widens the depletion layer by forcing electrons to the gate-insulator/semiconductor interface, leaving exposed a carrier-free region of immobile, positively charged acceptor ions.

Conversely, in a p-channel "enhancement-mode" device, a conductive region does not exist and negative voltage must be used to generate a conduction channel. 

Effect of drain-to-source voltage on channel

For either enhancement- or depletion-mode devices, at drain-to-source voltages much less than gate-to-source voltages, changing the gate voltage will alter the channel resistance, and drain current will be proportional to drain voltage (referenced to source voltage). In this mode the FET operates like a variable resistor and the FET is said to be operating in a linear mode or ohmic mode.

If drain-to-source voltage is increased, this creates a significant asymmetrical change in the shape of the channel due to a gradient of voltage potential from source to drain. The shape of the inversion region becomes "pinched-off" near the drain end of the channel. If drain-to-source voltage is increased further, the pinch-off point of the channel begins to move away from the drain towards the source. The FET is said to be in saturation mode; although some authors refer to it as active mode, for a better analogy with bipolar transistor operating regions. The saturation mode, or the region between ohmic and saturation, is used when amplification is needed. The in-between region is sometimes considered to be part of the ohmic or linear region, even where drain current is not approximately linear with drain voltage. 

Even though the conductive channel formed by gate-to-source voltage no longer connects source to drain during saturation mode, carriers are not blocked from flowing. Considering again an n-channel enhancement-mode device, a depletion region exists in the p-type body, surrounding the conductive channel and drain and source regions. The electrons which comprise the channel are free to move out of the channel through the depletion region if attracted to the drain by drain-to-source voltage. The depletion region is free of carriers and has a resistance similar to silicon. Any increase of the drain-to-source voltage will increase the distance from drain to the pinch-off point, increasing the resistance of the depletion region in proportion to the drain-to-source voltage applied. This proportional change causes the drain-to-source current to remain relatively fixed, independent of changes to the drain-to-source voltage, quite unlike its ohmic behavior in the linear mode of operation. Thus, in saturation mode, the FET behaves as a constant-current source rather than as a resistor, and can effectively be used as a voltage amplifier. In this case, the gate-to-source voltage determines the level of constant current through the channel.

Composition

FETs can be constructed from various semiconductors—silicon is by far the most common. Most FETs are made by using conventional bulk semiconductor processing techniques, using a single crystal semiconductor wafer as the active region, or channel.

Among the more unusual body materials are amorphous silicon, polycrystalline silicon or other amorphous semiconductors in thin-film transistors or organic field-effect transistors (OFETs) that are based on organic semiconductors; often, OFET gate insulators and electrodes are made of organic materials, as well. Such FETs are manufactured using a variety of materials such as silicon carbide (SiC), gallium arsenide (GaAs), gallium nitride (GaN), and indium gallium arsenide (InGaAs). 

In June 2011, IBM announced that it had successfully used graphene-based FETs in an integrated circuit. These transistors are capable of about 2.23 GHz cutoff frequency, much higher than standard silicon FETs.

Types

Depletion-type FETs under typical voltages: JFET, poly-silicon MOSFET, double-gate MOSFET, metal-gate MOSFET, MESFET.

  Depletion

  Electrons

  Holes

  Metal

  Insulator

Top: source, bottom: drain, left: gate, right: bulk. Voltages that lead to channel formation are not shown.

 

The channel of a FET is doped to produce either an n-type semiconductor or a p-type semiconductor. The drain and source may be doped of opposite type to the channel, in the case of enhancement mode FETs, or doped of similar type to the channel as in depletion mode FETs. Field-effect transistors are also distinguished by the method of insulation between channel and gate. Types of FETs include:

• The MOSFET (metal–oxide–semiconductor field-effect transistor) utilizes an insulator (typically SiO₂) between the gate and the body. This is by far the most common type of FET.
  • The DGMOSFET (dual-gate MOSFET) or DGMOS, a MOSFET with two insulated gates.
  • The IGBT (insulated-gate bipolar transistor) is a device for power control. It has a structure akin to a MOSFET coupled with a bipolar-like main conduction channel. These are commonly used for the 200–3000 V drain-to-source voltage range of operation. Power MOSFETs are still the device of choice for drain-to-source voltages of 1 to 200 V.
  • The MNOS (metal–nitride–oxide–semiconductor transistor) utilizes an nitride-oxide layer insulator between the gate and the body.
  • The ISFET (ion-sensitive field-effect transistor) can be used to measure ion concentrations in a solution; when the ion concentration (such as H⁺, see pH electrode) changes, the current through the transistor will change accordingly.
  • The BioFET (Biologically sensitive field-effect transistor) is a class of sensors/biosensors based on ISFET technology which are utilized to detect charged molecules; when a charged molecule is present, changes in the electrostatic field at the BioFET surface result in a measurable change in current through the transistor. These include enzyme modified FETs (EnFETs), immunologically modified FETs (ImmunoFETs), gene-modified FETs (GenFETs), DNAFETs, cell-based BioFETs (CPFETs), beetle/chip FETs (BeetleFETs), and FETs based on ion-channels/protein binding.
  • The DNAFET (DNA field-effect transistor) is a specialized FET that acts as a biosensor, by using a gate made of single-strand DNA molecules to detect matching DNA strands.
• The JFET (junction field-effect transistor) uses a reverse biased p–n junction to separate the gate from the body.
  • The static induction transistor (SIT) is a type of JFET with a short channel.
• The DEPFET is a FET formed in a fully depleted substrate and acts as a sensor, amplifier and memory node at the same time. It can be used as an image (photon) sensor.
• The FREDFET (fast-reverse or fast-recovery epitaxial diode FET) is a specialized FET designed to provide a very fast recovery (turn-off) of the body diode.
• The HIGFET (heterostructure insulated-gate field-effect transistor) is now used mainly in research.
• The MODFET (modulation-doped field-effect transistor) is a high-electron-mobility transistor using a quantum well structure formed by graded doping of the active region.
• The TFET (tunnel field-effect transistor) is based on band-to-band tunneling.
• The HEMT (high-electron-mobility transistor), also called a HFET (heterostructure FET), can be made using bandgap engineering in a ternary semiconductor such as AlGaAs. The fully depleted wide-band-gap material forms the isolation between gate and body.
• The MESFET (metal–semiconductor field-effect transistor) substitutes the p–n junction of the JFET with a Schottky barrier; and is used in GaAs and other III-V semiconductor materials.
• The NOMFET is a nanoparticle organic memory field-effect transistor.
• The GNRFET (graphene nanoribbon field-effect transistor) uses a graphene nanoribbon for its channel.
• The VeSFET (vertical-slit field-effect transistor) is a square-shaped junctionless FET with a narrow slit connecting the source and drain at opposite corners. Two gates occupy the other corners, and control the current through the slit.
• The CNTFET (carbon nanotube field-effect transistor).
• The OFET (organic field-effect transistor) uses an organic semiconductor in its channel.
• The QFET (quantum field effect transistor) takes advantage of quantum tunneling to greatly increase the speed of transistor operation by eliminating the traditional transistor's area of electron conduction.
• The SB-FET (Schottky-barrier field-effect transistor) is a field-effect transistor with metallic source and drain contact electrodes, which create Schottky barriers at both the source-channel and drain-channel interfaces.
• The GFET is a highly sensitive graphene-based field effect transistor used as biosensors and chemical sensors. Due to the 2 dimensional structure of graphene, along with its physical properties, GFETs offer increased sensitivity, and reduced instances of 'false positives' in sensing applications
• The Fe FET uses a ferroelectric between the gate, allowing the transistor to retain its state in the absence of bias - such devices may have application as non-volatile memory.
  

Advantages

The FET has high gate-to-main current resistance, on the order of 100 MΩ or more, providing a high degree of isolation between control and flow. Because base current noise will increase with shaping time, a FET typically produces less noise than a bipolar junction transistor (BJT), and is found in noise-sensitive electronics such as tuners and low-noise amplifiers for VHF and satellite receivers. It is relatively immune to radiation. It exhibits no offset voltage at zero drain current and makes an excellent signal chopper. It typically has better thermal stability than a BJT. Because they are controlled by gate charge, once the gate is closed or open, there is no additional power draw, as there would be with a bipolar junction transistor or with non-latching relays in some states. This allows extremely low-power switching, which in turn allows greater miniaturization of circuits because heat dissipation needs are reduced compared to other types of switches. 

Disadvantages

A field-effect transistor has a relatively low gain–bandwidth product compared to a BJT. The MOSFET is very susceptible to overload voltages, thus requiring special handling during installation. The fragile insulating layer of the MOSFET between the gate and channel makes it vulnerable to electrostatic discharge or changes to threshold voltage during handling. This is not usually a problem after the device has been installed in a properly designed circuit. 

FETs often have a very low "on" resistance and have a high "off" resistance. However, the intermediate resistances are significant, and so FETs can dissipate large amounts of power while switching. Thus efficiency can put a premium on switching quickly, but this can cause transients that can excite stray inductances and generate significant voltages that can couple to the gate and cause unintentional switching. FET circuits can therefore require very careful layout and can involve trades between switching speed and power dissipation. There is also a trade-off between voltage rating and "on" resistance, so high-voltage FETs have a relatively high "on" resistance and hence conduction losses.

Failure modes

FETs are relatively robust, especially when operated within the temperature and electrical limitations defined by the manufacturer (proper derating). However, modern FET devices can often incorporate a body diode. If the characteristics of the body diode are not taken into consideration, the FET can experience slow body diode behavior, where a parasitic transistor will turn on and allow high current to be drawn from drain to source when the FET is off.

Uses

The most commonly used FET is the MOSFET. The CMOS (complementary metal oxide semiconductor) process technology is the basis for modern digital integrated circuits. This process technology uses an arrangement where the (usually "enhancement-mode") p-channel MOSFET and n-channel MOSFET are connected in series such that when one is on, the other is off. 

In FETs, electrons can flow in either direction through the channel when operated in the linear mode. The naming convention of drain terminal and source terminal is somewhat arbitrary, as the devices are typically (but not always) built symmetrical from source to drain. This makes FETs suitable for switching analog signals between paths (multiplexing). With this concept, one can construct a solid-state mixing board, for example. FET is commonly used as an amplifier. For example, due to its large input resistance and low output resistance, it is effective as a buffer in common-drain (source follower) configuration.

IGBTs are used in switching internal combustion engine ignition coils, where fast switching and voltage blocking capabilities are important.

Source-gated transistor

Source-gated transistors are more robust to manufacturing and environmental issues in large-area electronics such as display screens, but are slower in operation than FETs.