Glossary of Terms
acceptor
Dopant atoms that, when added to the semiconductor, have the effect of removing free electrons from the system at sufficiently high temperatures.
Auger recombination
Auger recombination becomes important at high nonequilibrium carrier densities since the process requires three carriers. For example, when two electrons collide the collision can result in the recombination of one of the electrons with a hole. The energy released by the transition is transferred to the surviving electron, which subsequently returns to equilibrium as it undergoes collisions with the lattice.
avalanche breakdown
See impact ionization.
band
A collection of states that can be occupied by electrons, spanning a discrete range of energies.
band bending
A shift in the energy levels associated with the band structure as a function of position in space. Band bending is usually caused by electric fields originating from space charge layers in the semiconductor.
band gap
A range of energies in which no states are available for electrons to occupy.
band gap narrowing
A reduction in the band gap of a heavily doped semiconductor resulting from the merging of the impurity band with the conduction or valence band.
base (transistor)
See bipolar transistor.
basis
The specific pattern of atoms that is repeated periodically at each point in a lattice.
bipolar transistor/bipolar junction transistor/BJT
A transistor that uses two back to back p–n junctions to achieve power amplification. These transistors can be of the type PNP or NPN. There are three terminals in a bipolar transistor: the emitter, the base, and the collector, each of which is connected to one of the differently doped regions of the semiconductor (the base is connected to the region between the collector and emitter). During operation, a small current flowing between the base and the emitter usually controls a much larger current between the collector and emitter terminals, either to amplify a signal or to implement a switch.
Bloch’s theorem
A theorem that describes restrictions on the form of the electron wave function in a periodic potential.
Bloch wave function/Bloch state
A wave function that satisfies Bloch’s theorem.
Boltzmann equation
A partial differential equation that, for semiconductors, describes the evolution of the hole and electron distribution functions.
body (transistor)
See field effect transistor.
collector (transistor)
See bipolar transistor.
conduction band
A band with a range of energies that lie just above the band gap in which the Fermi level lies.
degenerate semiconductor
A semiconductor where Fermi–Dirac statistics are required to describe the carrier distribution functions.
depletion region
A region of the semiconductor, usually at a p–n junction or metal– semiconductor contact, in which the carrier concentration is greatly suppressed at equilibrium. There is usually a space charge and corresponding electric field associated with the depletion region.
density of states
The number of states per unit energy (or, in some cases, per unit volume of k-space) that can be occupied by electrons.
diode
A two terminal device with much lower resistance when current flows in one direction (the forward direction) than when it flows in the other direction (the reverse direction).
direct recombination
This recombination process is possible in direct band gap semiconductors and occurs when electron–hole pairs recombine with the emission of photons (with an energy close to the band gap).
donors
Dopant atoms which, when added to the semiconductor, have the effect of adding additional free electrons to the system at sufficiently high temperatures.
dopants
Impurities that are deliberately added to a semiconductor in order to modify the conductivity of the material.
drain (transistor)
See field effect transistor.
drift–diffusion equations
Equations describing the migration and diffusion of electrons and holes in a semiconductor under the influence of applied fields, temperature gradients, or concentration gradients.
electron distribution function
A function that determines the fraction of available states that are full as a function of energy.
electron quasi-Fermi level
See quasi-Fermi level.
electrons
An elementary particle with a negative elementary electric charge.
emitter (transistor)
See bipolar transistor.
Fermi–Dirac distribution
The general form of the electron (or hole) distribution function in equilibrium.
Fermi–Dirac statistics
Electron or hole statistics that are described by the Fermi–Dirac distribution.
Fermi level
The energy associated with states which, at a specified temperature, have a 50% probability of being occupied. The Fermi level is the chemical potential for electrons.
Fermi surface
The surface in k-space that corresponds to the Fermi level.
field effect transistor
A transistor that uses an electric field to alter the geometry of a conducting channel adjacent to the surface of a semiconductor. Usually the field is applied to the surface of a semiconductor in an oppositely doped region (sometimes connected to the body terminal) between two doped-like regions of semiconductor (connected to the source and the drain terminals). The field results from a voltage applied to a terminal referred to as the gate. In a MOSFET, the field produces band bending near the surface of the semiconductor, resulting in an inversion layer, which produces a conducting channel between the source and the drain. The extent of the channel is controlled by the applied field allowing the channel resistance to be modulated. For a JFET or MESFET, the field is applied to a p–n junction or a Schottky contact, altering the size of the depletion layer and consequently modifying the channel thickness.
Gaussian doping
A distribution of dopants where the concentration decays from a peak value following a Gaussian distribution.
generation
A process by which electron hole pairs are created.
gate (transistor)
See field effect transistor.
heterojunction
An interface between two different semiconductors.
hole distribution function
A function which determines fraction of available states which are empty as a function of energy.
hole quasi-Fermi level
See quasi-Fermi level.
holes
Particles evoked to simplify the computation of current from bands that are almost completely full of electrons.
impact ionization
A carrier generation mechanism that occurs when the carriers are accelerated by the electric field between collisions to velocities where the energies are greater than the gap energy, these can dissipate enough energy during collisions that additional electron hole pairs can be generated. This process is referred to as impact ionization and is responsible for the phenomenon of avalanche breakdown.
incomplete ionization
For semiconductors with a wideband gap or for conventional semiconductors at low temperatures, the thermal energy is not sufficient to completely ionize the dopant atoms and only a fraction of the dopants are ionized. This situation is referred to as incomplete ionization.
insulator
A solid that has no observable conductivity at temperatures below its melting point. The band structure of insulators is such that there are only completely full or completely empty bands, and a band gap of sufficient size exists between the full and empty bands that there is negligible thermal excitation.
inversion layer
A layer of semiconductor in which band bending leads to a change of the material from n-type to p-type or vice versa.
JFET (Junction Field Effect Transistor)
A field effect transistor in which the electric field is applied to the semiconductor by a biased p–n junction.
k-space
The space in which the wave vectors of the electron wave function (usually denoted k), are defined.
lattice
A set of points in space that are all identical due to the periodicity of the structure represented.
Maxwell–Boltzmann distribution
The limit of the Fermi–Dirac distribution when the Fermi energy is several times the thermal energy within the band gap.
Maxwell–Boltzmann statistics
Electron or hole statistics that are described by the Maxwell–Boltzmann distribution.
metal
A solid with good electric conductivity. A metal has one or more partially filled bands.
MESFET (metal semiconductor field effect transistor)
A field effect transistor in which the electric field is applied to the semiconductor by a Schottky contact.
mobility
A quantity (strictly a tensor) relating the velocity of electrons or holes to the applied electric field.
MOSFET (metal oxide semiconductor field effect transistor)
A field effect transistor in which the electric field is applied to the semiconductor by a metal contact (or in some cases a heavily doped polysilicon) separated from the semiconductor by an insulator (often silicon oxide).
nearly free electron model
A quantum mechanical model for the behavior of electrons moving in a weakly periodic potential.
nondegenerate semiconductor
A semiconductor in which it is sufficient to use Maxwell–Boltzmann statistics to describe the carrier distribution functions.
n-type
A region of semiconductor where the number of donors exceeds the number of acceptors.
ohmic contact
A contact between a metal and a semiconductor that has a linear IV characteristic.
p-type
A region of semiconductor where the number of acceptors exceeds the number of donors.
p–n junction
A junction between p- and n- type regions of a semiconductor.
Pauli exclusion principle
The Pauli exclusion principle states that two fermions (such as electrons) cannot occupy the same quantum mechanical state. A consequence of the principle is that each state in a crystal can be occupied only by two electrons, one spin up and another spin down.
quasi-Fermi level
Net current flows and/or thermal gradients in a semiconductor represent nonequilibrium conditions and consequently the concept of the Fermi level (derived from equilibrium thermodynamics) does not apply to these processes. However, in many devices it is possible to assume a collective (and different) quasi-equilibrium for electrons and holes, since the relaxation time for scattering within the band is much less than that for recombination processes. The electron and hole quasi-Fermi levels are the Fermi levels associated with these two quasi-equilibrium populations.
recombination
A process by which electrons and holes recombine, resulting in a return of the system to equilibrium.
rectifier
A device with much lower resistance when current flows in one direction (the forward direction) than when it flows in the other direction (the reverse direction).
reciprocal lattice
The lattice obtained by taking the Fourier transform of the lattice in real space. The reciprocal lattice is a set of vectors in k-space.
Schottky contact
A metal semiconductor contact where the barrier height and width is sufficient to result in rectifying behavior.
Schrödinger equation
A partial differential equation that describes the evolution of the wave function.
semiclassical model
A model that describes the dynamics of electrons moving in periodic solids in between collisions.
semiconductor
A solid that is an insulator at zero temperature but that has observable conductivity at temperatures below its melting point. The conductivity results from a significant number of electrons that are thermally excited across the band gap; consequently the gap energy must be of the same order as the thermal energy (most important semiconductors have a gap energy of less than 2 eV).
Shockley–Read–Hall recombination
This recombination mechanism is important in indirect band gap semiconductors, such as silicon and germanium (for these materials direct recombination is not possible). A defect (usually with an energy close to the mid-gap) is involved in the process. An electron or hole is first trapped by the defect and then emitted into the valence/conduction band, resulting in a reduction in the number of available carriers. The carrier energy is typically converted to heat.
source (transistor)
See field effect transistor.
spin
An intrinsic form of angular momentum carried by elementary particles. The electron spin can take two values, +1/2 and -1/2, frequently referred to as up and down, respectively.
transistor
A device used to amplify or switch electrical signals.
valence band
A band with a range of energies that lie just below the band gap in which the Fermi-level lies.
wave function
A complex-valued function that describes the quantum state of a particle. The modulus squared of the wave function represents the probability density of finding a given particle in a given region of space at a particular time.