Semiconductor bandgap and carriers calculator
Calculate bandgap, equilibrium carriers, Fermi level and conductivity for Si, Ge and GaAs.
Silicon: 300 K; Bandgap Eg = 1.125 eV
| Bandgap Eg | 1.125 eV |
|---|---|
| Intrinsic carriers ni | 8.143e+9 cm-3 |
| Electrons n | 8.143e+9 cm-3 |
| Holes p | 8.143e+9 cm-3 |
| Fermi level above valence edge | 0.5567 eV |
| Conductivity (fixed 300 K mobilities) | 2.414e-6 S/cm |
At 300 K, silicon has a bandgap of about 1.125 eV. Choose Si, Ge or GaAs to calculate temperature-dependent bandgap and intrinsic carriers, then add signed net doping to estimate the Fermi level and conductivity.
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Example: What are the bandgap and intrinsic carriers of silicon at 300 K?
Eg(T) = Eg(0) – alpha T^2/(T + beta); ni = sqrt(Nc Nv) exp[-Eg/(2 kB T)]. Charge neutrality: n – p = ND – NA; np = ni^2. EF – Ev = kB T ln(Nv/p); conductivity = q(n mu_n + p mu_p).
Intrinsic material reference at 300 K
| Material | Bandgap Eg (eV) | Intrinsic carriers ni (cm-3) | Electron mobility at 300 K (cm2/V/s) | Hole mobility at 300 K (cm2/V/s) |
|---|---|---|---|---|
| Silicon | 1.125 | 8.143e+9 | 1400 | 450 |
| Germanium | 0.6634 | 2.033e+13 | 3900 | 1900 |
| Gallium arsenide | 1.422 | 2.044e+6 | 8800 | 400 |
Cite this
ScienceShot. Semiconductor bandgap and carriers calculator. https://scienceshot.com/semiconductor-bandgap-calculator.
More formats
ScienceShot. (2026). Semiconductor bandgap and carriers calculator [Online calculator]. https://scienceshot.com/semiconductor-bandgap-calculator
@misc{scienceshot-semiconductor-bandgap-calculator-2026,
author = {{ScienceShot}},
title = {{Semiconductor bandgap and carriers calculator}},
year = {2026},
note = {Online calculator},
url = {https://scienceshot.com/semiconductor-bandgap-calculator}
}Sources: C. D. Thurmond, The standard thermodynamic functions for the formation of electrons and holes in Ge, Si, GaAs, and GaP, Journal of the Electrochemical Society 122, 1133 (1975); B. Van Zeghbroeck, Principles of Semiconductor Devices (2011), Appendix 3: Material Parameters (300 K); CODATA 2018, NIST.
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