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

Abstract

The complex dielectric function \ensuremath{\epsilon}(\ensuremath{\omega}) 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 ${d}^{2}$\ensuremath{\epsilon}/d${\ensuremath{\omega}}^{2}$ 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, \ensuremath{\alpha}-Sn, and heavy III-V or II-VI compounds a two-dimensional critical point yields the best representation.