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 ∼${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$ 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.