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.

• Received 6 December 1982

DOI:https://doi.org/10.1103/PhysRevB.27.7466