Combined Investigation of Nonuniform-Field Electroreflectance and Surface Galvanomagnetic Properties in Germanium

Abstract

"Dry" electroreflectance (ER) spectra have been taken near the fundamental edge of intrinsic germanium for comparison with the theory of the Franz-Keldysh effect in nonuniform electric fields. The theory presented by Aspnes and Frova in a previous paper applies quite generally to one-dimensional inhomogeneities induced by any kind of nonuniform perturbation in a medium, and shows that the inhomogeneity causes a mixing of the real and imaginary parts of the dielectric function which results in changes in the line shapes of optical spectra. Typical nonuniform perturbations are space-charge or depletion-region electric fields (which occur in $p\ensuremath{-}n$ junctions or surface electro-optic effects), gradients in carrier density (such as in photo-reflectance experiments), or gradients in stress, impurity concentration, temperature, etc. For the specific case of surface-barrier ER in an intrinsic semiconductor, the field nonuniformity increases with increasing magnitude of the surface electric field. ER spectra therefore depend drastically on this magnitude and provide a convenient test of the validity of the nonuniform-field theory. The results presented here, obtained with square-wave zero-to-peak modulation, clearly demonstrate that the theory describes the main features of ER in semiconductors. As an example, the measured crossover of the heights of the first and third ER peaks is found to occur almost at the predicted value of the field. The quantitative comparison of theory and experiment requires an accurate measurement of the value of the surface field as a function of electrode voltage. This has been done by performing combined measurements of field-effect-induced changes in the Hall coefficient and conductivity of the sample. Use of the Hall-coefficient data enables the surface mobility to be obtained directly from experiment, so that the excess carrier concentration, and therefore the surface potential and field, can be determined without making assumptions as to the value of the surface mobility. From these data, it has also been possible to obtain information about the nature of the scattering mechanisms which determine the surface mobility. A number of other observations are presented and discussed.