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Intrinsic Semiconductor Carrier Concentration Calculator — result sheet
Estimate equilibrium intrinsic carrier concentration from effective density of states, band gap, and temperature.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Scale Nc and Nv by (T/Tref)^(3/2), then calculate nᵢ = √(NcNv) exp[−Eg/(2kBT)] with kB = 8.617333262×10⁻⁵ eV/K.
The result is an equilibrium, nondegenerate semiconductor estimate. Effective density-of-states inputs remain visible because carrier concentration depends on material parameters as well as temperature and band gap.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Effective Nc at reference temperature — cm⁻³; minimum 1.0E-6; maximum 1.0E+30
- Effective Nv at reference temperature — cm⁻³; minimum 1.0E-6; maximum 1.0E+30
- Band-gap energy — eV; minimum 1.0E-6; maximum 20
- Temperature — K; minimum 1.0E-6; maximum 5000
- Reference temperature for Nc and Nv — K; minimum 1.0E-6; maximum 5000
Worked example
| Input | Value |
|---|---|
| Effective Nc at reference temperature | 2.8E+19 |
| Effective Nv at reference temperature | 1.04E+19 |
| Band-gap energy | 1.12 |
| Temperature | 300 |
| Reference temperature for Nc and Nv | 300 |
The silicon-like defaults give an intrinsic carrier concentration of about 6.68×10⁹ cm⁻³ under this supplied density-of-states approximation.
Assumptions and limits
- Nc and Nv follow a T^(3/2) effective-mass scaling from the stated reference temperature.
- The semiconductor is in equilibrium and nondegenerate with a single supplied band gap.
- The band gap is entered in electronvolts and temperature is absolute kelvin.
- Doping, compensation, incomplete ionization, band-gap narrowing, composition, strain, and device bias are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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