How this calculator works
The nondegenerate equilibrium model combines thermal excitation across a band gap with conduction and valence densities of states. Presets supply only the 300 K density-of-states values; enter the band gap at your chosen temperature, for example about 1.12 eV for silicon, 0.66 eV for germanium or 1.424 eV for GaAs at 300 K. Density of states is scaled as T^(3/2), holding effective masses fixed. Temperature inversion holds the entered band gap fixed, so it does not incorporate the real temperature dependence of band gap. Doping, degeneracy and non-equilibrium generation are excluded.
Formula
ni = sqrt(Nc Nv) exp[-Eg/(2 kB T)]; Nc,v(T) = Nc,v(300 K)(T/300 K)^(3/2); kB = 8.617333262145 x 10^-5 eV/K.
Worked example
With Nc = Nv = 10^24/m3, T = 300 K and Eg = 0.1190528587 eV, the exponential factor is about 0.1, giving ni about 10^23/m3. Halving that band gap gives approximately 3.16228 x 10^23/m3.
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Frequently asked questions
Are carriers per cm3 or per m3?
Both are shown. One cubic metre contains one million cubic centimetres, so divide per-m3 concentration by one million to obtain per-cm3.
Do presets change the band gap automatically?
No. Presets supply density-of-states parameters only. Enter the band gap for the actual temperature and material.
Can I use this for a heavily doped semiconductor?
It estimates intrinsic equilibrium concentration. A heavily doped semiconductor may need Fermi-Dirac statistics and charge neutrality.