Collision broadening in the exciton gas outside the electron-hole droplets in Ge

Abstract

A broadening of both the recombination luminescence and absorption spectra of indirect excitons in Ge is observed. This broadening is found to be density dependent consistent with an exciton-exciton collision process. An effective exciton collision radius of 220 \ifmmode\pm\else\textpm\fi{} 80 \AA{} is measured in agreement with theoretical estimates. Density-modulated absorption spectra also indicate an apparent red shift of the exciton energy at high carrier densities. A detailed analysis of the exciton line shape leads to a better understanding of the thermodynamics of the coexisting electron-hole liquid and exciton gas, provides improved values of the binding energy, $\ensuremath{\varphi}=1.8\ifmmode\pm\else\textpm\fi{}0.2$ meV, and the ground-state energy per pair, ${E}_{G}=\ensuremath{-}5.9\ifmmode\pm\else\textpm\fi{}0.3$ meV, and gives the most nearly complete description of the gas-liquid phase boundary. The complications due to density gradients which arise from surface excitation with be briefly discussed.