Impurity Band in Semiconductors with Small Effective Mass

The energy levels of ordered impurities in semiconductors are formally equivalent to the energy levels of metallic hydrogen if a number of simplifying approximations are made. An approximate calculation of the energy states for the 1s band of metallic hydrogen is carried out for smaller lattice constants than those considered by Wigner and Huntington, or by Baltensperger. A simple transformation of the distance and energy scales converts the calculation for metallic hydrogen to one applying to impurities in a semiconductor, if values for the effective mass and the dielectric constant are given. Experimental results for the optical energy gap in InAs are reported as a function of impurity concentration. The effective mass required to fit the optical data for InSb published by other workers is about 0. 03m, as compared to the value 0. 013m found by cyclotron resonance measurements.