Determination of Optical Constants and Carrier Effective Mass of Semiconductors

By using reflectivity and absorption measurements in the region 5 to 35 micron, the effect of free carriers on the optical constants has been determined for n- and p-type germanium, silicon, and indium antimonide, and for n-type indium arsenide. The contribution of the free carriers to the electric susceptibility is obtained from the optical constants. A carrier effective mass, mₛ, is defined in terms of the susceptibility, and the significance of mₛ is considered for four different types of energy band structure. The experimental values of mₛ are compared with those calculated by using data from other experiments. Good agreement was found for n- and p-type silicon, n-type germanium, and p-type indium antimonide. In p-type germanium, the susceptibility due to transitions between the overlapping bands in the valence band was taken into account. However, the resulting mₛ, for a sample of {~}10¹⁹ cm^-3 impurity concentration, is larger by a factor of 1.8 than that calculated by using cyclotron resonance data. In n-type indium antimonide mₛ increases with carrier concentration. If one assumes mₛ to be energy-dependent, the shape of the conduction band calculated is consistent with previously reported measurements of the shift of the intrinsic absorption edge with electron concentrations. In the case of n-type indium arsenide, mₛ differs from the effective mass reported from thermoelectric measurements but gives good agreement with the values determined from the shift of the intrinsic absorption edge for an impure specimen.