Temperature dependence of the dielectric function and interband critical points in silicon

The complex dielectric function ε(ω) of Si was measured ellipsometrically in the 1.7–5.7-eV photon-energy range at temperatures between 30 and 820 K. The observed structures are analyzed by fitting the second-derivative spectrum $d^2$ε/d${\omega }^2$ with analytic critical-point line shapes. Results for the temperature dependence of the parameters of these critical points, labeled $E_0^{\mathcal{’}}$, $E_1$, $E_2$, and $E_1^{\mathcal{’}}$, are presented. The data show good agreement with microscopic calculations for the energy shift and the broadening of interband transitions with temperature based on the electron-phonon interaction. The character of the $E_1$ transitions in semiconductors is analyzed. We find that for Si and light III-V or II-VI compounds an excitonic line shape represents best the experimental data, whereas for Ge, α-Sn, and heavy III-V or II-VI compounds a two-dimensional critical point yields the best representation.