Thermodynamics of excitonic molecules in silicon

The first spatially controlled thermodynamic measurements of a system of free excitons (FE) and excitonic molecules (EM) are reported. Both excitonic phases are confined to Gaussian spatial distributions in a strain-induced potential well. This parabolic well affords a simple analytic description of the thermal expansion of the gases. Recombination emission from the ultrapure Si is detected with spatial, spectral, and time resolution over the temperature range 3.5-10 K. The system is well described by a chemical equilibrium between two ideal gases at the lattice temperature: we observe the quadratic dependence of the EM density on the FE density and the expected form of thermal activation. In addition, the EM-FE thermalization time is found to be much less than the recombination times. The thermodynamically determined binding energy, ${\phi }_{\mathrm{EM}}^t=1.53\mathrm{}\pm 0.10$ meV, is in excellent agreement with our measured spectroscopic value ${\phi }_{\mathrm{EM}}^s=1.46\mathrm{}\pm 0.09$ meV. These values are several times larger than the most recent theoretical estimates.