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, m_s, is defined in terms of the susceptibility, and the significance of m_s is considered for four different types of energy band structure. The experimental values of m_s 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 m_s, 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 m_s increases with carrier concentration. If one assumes m_s 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, m_s 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.