Semiconductor Bandgap
Bandgap energy and absorption edge vs temperature using the Varshni equation. Direct vs indirect gap materials.
Bandgap Energy vs Temperature
Absorption Edge Wavelength vs Temperature (shaded: visible, 380–750 nm)
Eg(T) = Eg0 − αT² / (T + β)
λedge = hc / Eg = 1239.84 / Eg(eV) nm
Eg(InxGa1−xAs) = (1−x)·Eg,GaAs + x·Eg,InAs − 0.477·x(1−x) eV
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Varshni E_g(T) = E_g(0) − αT²/(T + β) with Sze's sets for Si and Ge and Vurgaftman's for the III–V compounds (GaP: indirect X gap; GaN: wurtzite). In₀.₅₃Ga₀.₄₇As interpolates the GaAs and InAs gaps with bowing 0.477 eV. The fits are made for roughly 0–500 K; the slider goes to 700 K. The absorption edge hc/E_g ignores excitons and the Urbach tail.
- Varshni Y. P. (1967). Temperature dependence of the energy gap in semiconductors. Physica 34, 149–154. doi:10.1016/0031-8914(67)90062-6
- Vurgaftman I., Meyer J. R., Ram-Mohan L. R. (2001). Band parameters for III–V compound semiconductors and their alloys. J. Appl. Phys. 89, 5815–5875. Varshni sets (Tables I–X) and the Ga₁₋ₓInₓAs bowing C = 0.477 eV (Table XIII). doi:10.1063/1.1368156
- Sze S. M. (1981). Physics of Semiconductor Devices, 2nd ed. Wiley, ch. 1. Si (1.17 eV, 4.73e-4 eV/K, 636 K) and Ge (0.7437 eV, 4.774e-4 eV/K, 235 K), as tabulated in V. Palankovski, PhD thesis, TU Wien (2000), §3.3.1.1. iue.tuwien.ac.at