Carrier concentration is a critical parameter in semiconductor wafer selection because it determines electrical conductivity, resistivity, and device performance. UniversityWafer, Inc. supplies silicon, GaP, GaAs, SiC, Ge, and other semiconductor substrates with precisely controlled doping levels and carrier concentrations for integrated circuits, optoelectronics, RF devices, MEMS, solar cells, and advanced materials research. Researchers can specify carrier concentration, resistivity, crystal orientation, and wafer thickness to optimize their device performance.
Carrier concentration is the number of mobile electrons or holes per unit volume in a semiconductor and is typically expressed in cm-3. It is an important electrical parameter because, together with carrier mobility, it determines the electrical conductivity and resistivity of semiconductor material.
Semiconductor conductivity can be expressed as:
σ = q(nμn + pμp)
where q is the elementary charge, n and p are the electron and hole concentrations, and μn and μp are the corresponding carrier mobilities.
In materials such as silicon, gallium phosphide (GaP), gallium arsenide (GaAs), and silicon carbide (SiC), equilibrium carrier concentration depends on factors including doping, temperature, band structure, band-gap energy, dopant ionization, compensation, and defects.
In an intrinsic semiconductor, the equilibrium electron and hole concentrations are equal:
n = p = ni
The intrinsic carrier concentration depends strongly on temperature and band-gap energy. For example, crystalline silicon has an intrinsic carrier concentration on the order of 1010 cm-3 at 300 K, whereas GaP has a much lower intrinsic carrier concentration because its band gap is substantially larger.
In a doped semiconductor, the actual electron and hole concentrations generally differ from ni. Donor and acceptor dopants change the majority-carrier population, while compensation and incomplete dopant ionization can also affect the measured free-carrier concentration.
UniversityWafer, Inc. supplies semiconductor substrates with specified electrical and physical properties such as carrier concentration, resistivity, conductivity type, orientation, thickness, and surface finish for research and device development.
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Researchers may require gallium phosphide (GaP) substrates with specified electrical properties for optoelectronics, semiconductor-device research, photonics, and epitaxial growth.
GaP is an indirect-band-gap III-V semiconductor with a room-temperature band gap of approximately 2.26 eV. Its intrinsic carrier concentration at 300 K is extremely low, so the electrical properties of practical GaP wafers are usually governed much more strongly by electrically active dopants, compensation, defects, and impurities than by intrinsic carrier generation.
One researcher requested the following epi-ready 2-inch GaP wafers:
High-Resistivity / Semi-Insulating GaP
N-Type GaP
The researcher also requested a single evaluation wafer to assess substrate quality before ordering the full quantity.
Important: carrier concentration and dopant concentration are related but are not necessarily identical. The number of electrically active free carriers can differ from the chemical dopant concentration because of factors such as incomplete ionization, compensation, defects, and temperature.
Likewise, a semi-insulating wafer should be characterized primarily by its very high electrical resistivity and low free-carrier conductivity rather than by a carrier-concentration value alone.
Reference #264285 for specifications and pricing.
Carrier concentration helps determine the electrical behavior of a semiconductor, but it must be considered together with carrier mobility, resistivity, band structure, device geometry, and operating temperature.
By controlling donor or acceptor doping, engineers can tailor the majority-carrier concentration for particular device regions. Different applications may require very different carrier concentrations.
Carrier concentration therefore plays an important role in applications including:
One of the most common methods for measuring carrier concentration in semiconductor wafers is the Hall effect. A Hall measurement can provide the majority-carrier type, Hall carrier concentration, and Hall mobility when the appropriate sample geometry and measurement conditions are used.
Combining carrier-concentration and mobility measurements also allows researchers to evaluate electrical conductivity and resistivity. Other electrical and optical techniques may be used depending on the semiconductor, doping level, layer thickness, and device structure.
UniversityWafer supplies a range of semiconductor materials that may be specified by conductivity type, resistivity, carrier concentration, dopant, and related electrical properties, subject to current inventory and manufacturing capability.
Carrier concentration is the number of mobile charge carriers per unit volume in a semiconductor and is typically expressed in cm-3. Electrons in the conduction band and holes in the valence band can both contribute to electrical conduction.
Electron concentration is commonly represented by n, while hole concentration is represented by p. Carrier concentration is an important semiconductor property because, together with carrier mobility, it determines electrical conductivity:
σ = q(nμn + pμp)
where q is the elementary charge, μn is electron mobility, and μp is hole mobility.
Carrier concentration depends on factors including temperature, doping, dopant ionization, compensation, defects, and the semiconductor's electronic band structure.
An intrinsic semiconductor is an ideally pure or sufficiently uncompensated semiconductor in which the equilibrium electron and hole populations are governed primarily by thermal generation rather than intentional doping.
At thermal equilibrium in an intrinsic semiconductor:
n = p = ni
where ni is the intrinsic carrier concentration.
An extrinsic semiconductor has intentionally introduced donor or acceptor dopants that modify the equilibrium electron and hole concentrations.
In ordinary n-type material, electrons are the majority carriers and holes are the minority carriers. In ordinary p-type material, holes are the majority carriers and electrons are the minority carriers.
Doping is the controlled introduction of electrically active impurities into a semiconductor to modify its carrier concentrations and electrical properties.
In silicon, group-V elements such as phosphorus, arsenic, and antimony can act as donor dopants. Donors can provide electrons to the conduction band, producing n-type material.
Group-III elements such as boron can act as acceptor dopants in silicon. Acceptors increase the hole concentration, producing p-type material.
Dopant concentration and free-carrier concentration are not always identical. Their relationship depends on dopant ionization, compensation, temperature, defects, and doping level. At sufficiently high doping levels, semiconductor behavior can also become degenerate.
Carrier concentration and resistivity are closely related, but carrier concentration alone does not determine resistivity. Resistivity is the reciprocal of conductivity:
ρ = 1 / σ = 1 / [q(nμn + pμp)]
Therefore, both carrier concentration and carrier mobility must be considered.
Increasing the majority-carrier concentration often reduces resistivity, but heavy doping can also reduce carrier mobility because of increased ionized-impurity scattering. The relationship is therefore not perfectly proportional across all doping levels.
Carrier concentration and resistivity specifications are important when selecting wafers for applications such as:
Under thermal equilibrium, a nondegenerate semiconductor can be described by the law of mass action:
np = ni2
Here, n is the equilibrium electron concentration, p is the equilibrium hole concentration, and ni is the intrinsic carrier concentration at the same temperature.
This relationship shows that increasing the equilibrium concentration of one carrier type through ordinary doping generally decreases the equilibrium concentration of the other carrier type.
The simple relationship np = ni2 applies under thermal equilibrium and nondegenerate semiconductor conditions. More complete statistical treatments are required for strongly degenerate materials or systems driven significantly out of equilibrium.
For a nondegenerate intrinsic semiconductor, the intrinsic carrier concentration can be written approximately as:
ni = √(NCNV) exp[-Eg/(2kBT)]
where:
This relationship explains why intrinsic carrier concentration is strongly temperature dependent and why semiconductor materials with larger band gaps generally have much lower intrinsic carrier concentrations at a given temperature, all else being comparable.
Temperature has a strong effect on carrier populations, but the behavior should be distinguished between intrinsic and doped semiconductors.
In an intrinsic semiconductor, increasing temperature generates more electron-hole pairs by thermal excitation, causing ni to increase rapidly.
A doped semiconductor can exhibit several temperature regimes:
The temperatures associated with these regimes depend on the semiconductor material, dopant species, doping concentration, compensation, and band structure.
The band gap strongly influences intrinsic carrier concentration.
At a given temperature, a smaller band gap generally allows thermal excitation of electron-hole pairs more readily and therefore results in a higher intrinsic carrier concentration. A larger band gap generally results in a much lower intrinsic carrier concentration.
This is one reason wide-band-gap semiconductors such as silicon carbide (SiC) and gallium nitride (GaN) can maintain very low intrinsic carrier concentrations at temperatures where narrower-band-gap semiconductors experience much stronger intrinsic carrier generation.
Band gap alone, however, does not determine the actual conductivity of a doped wafer. Doping, mobility, compensation, defects, and temperature must also be considered.
Carrier concentration is an important design parameter in photovoltaic devices, but maximum solar-cell efficiency is not achieved simply by maximizing the number of carriers.
Controlled doping is used to establish junctions, built-in electric fields, contact regions, and other device structures. Doping concentration also affects properties such as recombination, minority-carrier lifetime, mobility, junction behavior, and series resistance.
Solar-cell design therefore requires balancing carrier concentration, carrier lifetime, mobility, recombination, optical absorption, junction design, and contact resistance.
The Hall effect is widely used to characterize carrier concentration in semiconductor materials. Hall measurements can provide information about majority-carrier type, Hall carrier concentration, and Hall mobility when the appropriate measurement model and sample conditions are satisfied.
Resistivity measurements can be combined with Hall measurements to obtain a more complete picture of a wafer's electrical properties.
Depending on the semiconductor and device structure, other techniques may also be used to characterize doping or carrier distributions.
Controlled carrier concentrations are important throughout semiconductor technology, including:
UniversityWafer, Inc. supplies semiconductor substrates with electrical specifications that can include conductivity type, dopant, resistivity, and carrier concentration, depending on the material and available product.
Materials used for semiconductor research include silicon, gallium phosphide, gallium arsenide, germanium, silicon carbide, gallium nitride, indium phosphide, and other compound semiconductor substrates.
When selecting a wafer, researchers should distinguish between chemical dopant concentration, electrically active dopant concentration, free-carrier concentration, and resistivity. These quantities are related, but they are not interchangeable.