Surface structure of electron-hole drops in germanium and silicon

Density-functional formalism of Hohenberg and Kohn is generalized for the case of a multicomponent plasma. Using the self-consistent Kohn-Sham equations for electrons and holes and the local-density approximation for the exchange-correlation potential, we investigate the surface characteristics of the electron-hole liquid in six configurations of Ge and Si. We denote these configurations by $X({\nu }_e;{\nu }_h)$, where $X$ is either Ge or Si, and ${\nu }_e$ and ${\nu }_h$ are the number of occupied electron and hole bands, respectively. In normal Ge, i.e., Ge(4;2), the value of surface tension $\sigma$ is found to be 3.7 × ${10}^{-4\mathrm{}}$ erg/${\mathrm{cm}}^2$. When Ge is subject to a uniform stress of about 3.5 kg/${\mathrm{mm}}^2$ along the direction, i.e., in Ge(1;2), $\sigma$ is calculated to be 1.0 × ${10}^{-4\mathrm{}}$ erg/${\mathrm{cm}}^2$. Under a very large uniaxial stress on Ge, i.e., Ge(1;1), $\sigma$ is found to be a factor of 20 smaller than in Ge(4;2). The charge on the electron-hole drop (EHD) is also studied in the above-mentioned systems. In accordance with the experiment of Pokrovsky and Svistunova, we find that the EHD is negative in Ge(4;2) and positive in Ge(1;2). It is predicted that the drop will sustain a negative charge in Ge(1;1). Calculations for surfacetension and charge on the EHD are also reported in three configurations of silicon. The value of $\sigma$ in unstressed Si, denoted by Si(6;2), is obtained to be 87.4 × ${10}^{-4\mathrm{}}$ erg/${\mathrm{cm}}^2$. Application of an intermediate stress along the direction leads to the configuration Si(2;2). The value of $\sigma$ in Si(2;2) is found to be 32.8 × ${10}^{-4\mathrm{}}$ erg/${\mathrm{cm}}^2$. In the presence of a large stress, i.e., in Si(2;1), the surface tension is a factor of 8 smaller than in Si(6;2). Calculation of the charge reveals that the EHD is negative in both Si(6;2) and Si(2;1). Within the limits of accuracy of our calculation we find the drop is almost neutral in Si(2;2).