Infrared Absorption by Conduction Electrons in Germanium

Abstract

A quantum mechanical theory of infrared absorption by conduction electrons in germanium due to intravalley lattice scattering is developed which takes into account the multivalley structure of the conduction band as well as the present knowledge about intravalley lattice scattering. Within the framework of the deformation-potential theory the calculation can be performed without any serious approximations for all relevant wavelengths and all relevant temperatures. The final result for the absorption constant due to scattering by acoustical modes contains the two deformation-potential constants and may be of help for their quantitative determination. If their numerical values as known at present are used for the numerical evaluation of the absorption constant at $\lambda ={10}^{-3\mathrm{}}$ cm and $T=78\mathrm{}°$K, the result is too low by a factor of about 5 as compared to the experimental result of Fan and Spitzer. If this discrepancy is ascribed to the influence of the optical modes, an estimate may be made of the strength of the coupling of a conduction electron to these modes. On the basis of a simpler model, impurity scattering is also considered and regions of impurity concentration, wavelength, and temperature are indicated where impurity scattering may be neglected. Besides the determination of the deformation potential constants, the theory may be useful for the exploration of the band structure and the various scattering mechanisms and also for the study of impurity-bandconduction phenomena. The general limits of validity of the theory are indicated.