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

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 ±{} 80 {} 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, φ=1.8±0.2 meV, and the ground-state energy per pair, EG=-5.9±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.