Properties of the electron-hole liquid in GaP

Abstract

An investigation of the luminescence of the polar III-V semiconductor GaP under conditions of high excitation intensity. (${\mathrm{I}}_{\mathrm{exc}}$\ensuremath{\le} 10 MW/${\mathrm{cm}}^{2}$) as a function of the excitation intensity, the temperature, and the time after excitation is presented. Evidence is given from time-delayed spectra that at temperatures ${T}_{c}\ensuremath{\lesssim}45$ K a phase transition from an electron-hole plasma (EHP) to an electron-hole liquid (EHL) occurs. The prominent luminescence band detected in the region of 2.26 eV is proved to be composed of recombination radiation originating from both the EHL and the EHP, a fact that is found to be decisive for a quantitative understanding of the experimental results. The ground-state properties of the EHL are calculated including the effect of the camel's-back-like conduction-band minimum. It is shown to be more important than the electron-phonon interaction correction of the exchange, yielding a ground state energy of 33.3 meV, a binding energy of 14 meV, and a density of 8.6 \ifmmode\times\else\texttimes\fi{} ${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. An independent determination of ${E}_{B}$ from a lineshape fit gives the value 17.5 meV. The high density of states for electrons arising from the camel's back is also shown to strongly influence the ratio of the electron and hole Fermi energies of the EHL, yielding a value of $\frac{{E}_{F}^{h}}{{E}_{F}^{e}}\ensuremath{\simeq}4.9$, which should give rise to a strong charging of the drops in GaP. Following a suggestion by Hensel et al., a universal scaling law relating the critical temperature ${T}_{c}$ and the low-temperature density ${n}_{0}$ is firmly established for the four best-known materials that exhibit this electronic phase transition and the constant $\ensuremath{\beta}=\frac{\sqrt{{n}_{0}}}{{T}_{c}}$ is given as (7.0\ifmmode\pm\else\textpm\fi{}0.5) \ifmmode\times\else\texttimes\fi{} ${10}^{7}$ ${\mathrm{cm}}^{\ensuremath{-}3/2}$${\mathrm{K}}^{\ensuremath{-}1}$.