Model of electron-hole droplet condensation in semiconductors

Abstract

The phase diagram for electron-hole droplet condensation is addressed, and detailed calculations are given for the elemental systems Ge and Si with varying uniaxial strain which have properties that vary systematically over relatively wide ranges. A model based on noninteracting droplet fluctuations is used to describe the phase diagram. This model expresses the liquid and gas densities in terms of properties of the low-temperature liquid phase, most notably its surface tension. Detailed microscopic calculations based on a gradient expansion of the free energy are given for the temperature-dependent surface tension of droplets in six model systems involving Ge and Si with uniaxial strain; these are zero strain, intermediate strain sufficient to remove the electron-band degeneracy, and large strain which also removes the hole-band degeneracy. Phase diagrams are given for these systems and show changes corresponding to the systematic decrease in the electron-hole droplet binding energy with increasing uniaxial strain. The resulting critical temperatures and densities are compared to the results of new calculations based on the uniform plasma approach to the critical point. The phase diagrams, including the values of the critical parameters, are in good agreement with experiment for unstressed Ge and Si and for Ge with fairly large uniaxial dress. The model provides a parameter which characterizes the shape of the phase diagram, and systematic changes in shape with strain are obtained.