Varshniligningen

Varshni's equation, or Varshni's law, is an empirical relation that describes how the electronic band gap of a semiconductor varies with temperature. The equation is written as Eg(T) = Eg(0) - α T^2 / (T + β), where Eg(0) is the band gap at 0 kelvin, T is the absolute temperature, and α and β are material-dependent constants determined by fits to experimental data. The model captures the general trend that Eg decreases with increasing temperature due to lattice expansion and electron-phonon interactions.

The coefficients α and β are empirical and vary between materials; α is typically on the order of 10^-4 to 10^-3 eV/K, while β is of the order of tens to hundreds of kelvin. The equation is widely used in device modeling and simulations to estimate band gaps in the absence of direct measurements, and applies to many common semiconductors such as Si, Ge, GaAs, and InP within a moderate temperature range.

Varshni introduced the relation in 1967. While it provides a convenient and simple description, it is not a fundamental law and its accuracy is limited. It often reproduces the general trend but can deviate at very low or very high temperatures or for materials with complex phonon spectra or strong nonparabolicity of the bands. More detailed models that include specific phonon populations or anharmonic effects are used when higher accuracy is required.