Temperature-dependent refractive index of semiconductors

A single-oscillator Lorentz model is applied to four different semiconductors having diamond-like crystal structure to describe the temperature dependence of their refractive index between 300 and 600  K. Theoretical results are compared to previous experiments and to experiments carried out in this study for Si, Ge, GaAs, and InP. An efficient experimental method is also presented, enabling fast measurements of the refractive index of materials. Using the Yu-Brooks formalism and the energy bandgap at the X-point of the Brillouin zone, the temperature-dependent refractive indices are calculated and they agree well with experiments, particularly, considering the simplicity of the Lorentz model. However, there are discrepancies between the theory and experiment at high temperatures (near 600 K) in certain cases. This discrepancy may be due to the single-oscillator approximation. Additionally the effect of “self-energy” on the temperature dependence of the energy bandgap, such as the temperature-dependent damping of the oscillation of electrons, can be significant at higher temperatures.