Semiconductor Calculator

Calculate resistivity, carrier concentration, mobility, and other key semiconductor parameters with temperature dependence. Essential tool for physics and electronics engineers.

Carrier Concentration
Resistivity & Conductivity
Mobility Calculator
Silicon (Si)
Germanium (Ge)
Gallium Arsenide (GaAs)
Indium Gallium Arsenide (InGaAs)
Silicon Carbide (SiC)
Semiconductor Type:
Intrinsic
Extrinsic

Carrier Concentration Formulas:

Intrinsic Carrier Concentration: ni = √(NcNv) exp(-Eg/2kT)

Extrinsic (N-type): n ≈ Nd, p ≈ ni2/Nd

Extrinsic (P-type): p ≈ Na, n ≈ ni2/Na

K
Absolute temperature in Kelvin (typically 300K for room temperature)
eV
Band gap energy in electron volts (material-specific)

Resistivity and Conductivity Formulas:

Resistivity: ρ = 1/(q(μnn + μpp))

Conductivity: σ = 1/ρ = q(μnn + μpp)

Where: q = electron charge (1.602×10-19 C), μ = mobility, n/p = carrier concentration

cm-3
Electron concentration in conduction band
cm²/V·s
Electron mobility (material and doping dependent)
cm-3
Hole concentration in valence band
cm²/V·s
Hole mobility (material and doping dependent)

Mobility Calculation:

Mobility can be calculated from resistivity and carrier concentration:

μ = 1/(qρn) for n-type, μ = 1/(qρp) for p-type

Where: q = electron charge (1.602×10-19 C), ρ = resistivity, n/p = carrier concentration

Ω·cm
Resistivity in ohm-centimeters
cm-3
Majority carrier concentration
Electrons (n-type)
Holes (p-type)
Calculating...

Understanding Semiconductor Physics

Semiconductors are materials with electrical conductivity between conductors (metals) and insulators. Their conductivity can be controlled by doping, temperature, and electric fields, making them essential for electronic devices.

Key Semiconductor Parameters:

  • Carrier Concentration (n, p): Number of free electrons (n) and holes (p) per unit volume
  • Mobility (μ): How quickly charge carriers move in response to an electric field
  • Resistivity (ρ): Measure of how strongly a material opposes electric current
  • Conductivity (σ): Reciprocal of resistivity, measure of how easily current flows
  • Band Gap (Eg): Energy difference between valence and conduction bands

Common Semiconductor Materials

Material Band Gap (eV) Electron Mobility (cm²/V·s) Hole Mobility (cm²/V·s) Applications
Silicon (Si) 1.12 1400 450 Integrated circuits, solar cells
Germanium (Ge) 0.67 3900 1900 Infrared optics, high-speed circuits
Gallium Arsenide (GaAs) 1.42 8500 400 High-frequency devices, LEDs
InGaAs 0.75-1.42 10000-14000 200-500 Fiber optics, photodetectors
Silicon Carbide (SiC) 2.3-3.3 900 120 High-temperature, high-power devices

Fundamental Formulas

Intrinsic Carrier Concentration
ni = √(NcNv) × exp(-Eg/2kT)

Where:

  • Nc = Effective density of states in conduction band
  • Nv = Effective density of states in valence band
  • Eg = Band gap energy
  • k = Boltzmann constant (8.617×10-5 eV/K)
  • T = Absolute temperature in Kelvin
Resistivity and Conductivity
ρ = 1/σ = 1/[q(μnn + μpp)]

Where:

  • ρ = Resistivity (Ω·cm)
  • σ = Conductivity (S/cm)
  • q = Electron charge (1.602×10-19 C)
  • μn, μp = Electron and hole mobilities (cm²/V·s)
  • n, p = Electron and hole concentrations (cm-3)

Temperature Effects

1

Intrinsic Carrier Concentration: Increases exponentially with temperature as ni ∝ T3/2exp(-Eg/2kT)

2

Mobility: Decreases with temperature due to increased phonon scattering (μ ∝ T-3/2 for lattice scattering)

3

Band Gap: Generally decreases with increasing temperature (Eg decreases as T increases)

Doping Effects

  • N-type doping: Adds donor atoms (e.g., P, As in Si) that donate free electrons
  • P-type doping: Adds acceptor atoms (e.g., B, Ga in Si) that create free holes
  • Carrier concentration: In extrinsic semiconductors, majority carrier concentration ≈ doping concentration
  • Minority carriers: Minority carrier concentration = ni2/majority carrier concentration
  • Mobility degradation: High doping concentrations reduce carrier mobility due to ionized impurity scattering

Engineering Note: Semiconductor parameters vary significantly with material, doping concentration, and temperature. Always consult material-specific data sheets for precise values in engineering applications.

Frequently Asked Questions

Intrinsic semiconductors are pure materials with no intentional doping. Their carrier concentrations (n and p) are equal and determined by temperature. Extrinsic semiconductors are doped with impurities to increase either electron (n-type) or hole (p-type) concentration, making them useful for electronic devices.

At high doping concentrations, ionized impurity scattering becomes significant. The charged dopant ions create Coulomb potential that scatters charge carriers, reducing their mobility. This effect is more pronounced at low temperatures where lattice scattering is reduced.

For intrinsic semiconductors, resistivity decreases with temperature because carrier concentration increases exponentially. For extrinsic semiconductors at low to moderate temperatures, resistivity may initially increase with temperature (due to mobility decrease) then decrease at higher temperatures (when intrinsic carriers dominate). At very high temperatures, all semiconductors become intrinsic.

Band gap energy determines many semiconductor properties: (1) Electrical conductivity - larger band gap means fewer intrinsic carriers; (2) Optical properties - determines the wavelength of light the material can absorb or emit; (3) Temperature stability - materials with larger band gaps maintain semiconducting properties at higher temperatures; (4) Breakdown voltage - wider band gap materials can withstand higher electric fields.

Silicon dominates the semiconductor industry due to several advantages: (1) Abundance - silicon is the second most abundant element in Earth's crust; (2) Native oxide - SiO2 forms an excellent insulator crucial for MOSFETs; (3) Mature processing - decades of development have optimized silicon processing; (4) Suitable band gap - 1.12 eV provides good thermal stability and low leakage; (5) Good thermal conductivity - helps dissipate heat from devices.