Optical functions of silicon between 1.7 and 4.7 eV at elevated temperatures

Polarization modulation ellipsometry has been used to determine the optical functions of silicon at elevated temperatures up to 1000 K. The $E_1$, $E_0^{\prime }$, and $E_2$ features move monotonically to lower energies as the temperature is increased. A fit of the $E_0^{\prime }$ and $E_2$ peak positions to the empirical formulation of Varshni is obtained; it is found that the critical points of the joint density of states for the $E_0^{\prime }$ and $E_2$ gaps move somewhat differently from the indirect gap, although the difference is not large.