Optical Absorption Edge of Compensated Germanium

The optical absorption of heavily doped and closely compensated Ge is calculated using a Halperin-Lax band-tail model and an ad hoc matrix element. The only adjustable parameter is an effective temperature $T_{\mathrm{ion}}$ for the contribution of the position correlations of the ions to the screening; $T_{\mathrm{ion}}$ is estimated to be about 7000 °K. The results are in reasonable agreement with experiment; direct transitions at $k=0\mathrm{}$ make the dominant contribution to the edge.