Binding energy of the electron-hole liquid in quantum wells

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Abstract
The binding energy and equilibrium density of the quasi-two-dimensional (2D) electron-hole metallic liquid at zero temperature is calculated for GaAs(001) and Ge(001) quantum wells as a function of well width, mass ratio, and electron-band anisotropy. The band-gap renormalization of the electron-hole plasma is calculated for several well widths as a function of density. The calculations are based on an extension to the quasi-2D case (finite well thickness) of the random-phase approximation theory (3D) of Brinkman and Rice, and on a particular model potential used previously for calculating the biexciton binding energy. It is found that the liquid is stable relative to biexcitons for all Ge quantum wells and for GaAs wells of thickness >220 Å. The results in the 2D limit (zero thickness) are in qualitative but not quantitative agreement with those of Kuramoto and Kamimura.