Temperature dependence of the electron-hole-liquid luminescence in Si

Abstract

Detailed measurements and line-shape fits of the combined LO- and TO-phonon assisted electron-hole condensate luminescence lines from laser-excited, high-purity Si are reported in the temperature range from 2.2 to 13.0°K. These data permit a determination of the liquid density $n$, chemical potential $\mu$, the Fermi energy $E_F$, and the work function $\phi$, as functions of temperature. Fitting of these data to the $T^2$ dependence expected from Fermi-liquid theory gives $n\left(T\right)=[3.33\mathrm{}\pm 0.03-(1.5\pm 0.5)\times {10}^{-3\mathrm{}}{T}^2]\times {10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$; $\mu \mathrm{}\left(T\right)=\left[\right(1088.7\mathrm{}\pm 0.1)+\hslash {\omega }_{\mathrm{p}\mathrm{}\mathrm{h}}^{\mathrm{TO}}-(5.9\mathrm{}\pm 1.1)\times {10}^{-3\mathrm{}}{T}^2]$ meV; $E_F\mathrm{}\left(T\right)=[22.2\mathrm{}\pm 0.1-(8.0\pm 2.2)\times {10}^{-3\mathrm{}}{T}^2]$ meV; and $\phi \mathrm{}\left(T\right)=[8.21\mathrm{}\pm 0.1+(5.9\pm 8.2)\times {10}^{-3\mathrm{}}{T}^2]$ meV, where $T$ is in degrees Kelvin, and $\hslash {\omega }_{\mathrm{p}\mathrm{}\mathrm{h}}^{\mathrm{TO}}$ is the energy of the TO phonon assisting in the recombination. Analysis of the temperature dependence of the density gives a value for the second derivative of the ground-state energy per pair with respect to a density of 4.9 × ${10}^{-37\mathrm{}}$ meV ${\mathrm{cm}}^6$. The value of the density and work function at zero temperature, and the values of the coefficients of the various $T^2$ terms are compared with various theoretical calculations.