Evidence for separate Mott and liquid-gas transitions in photoexcited, strained germanium

The phase diagram of photoexcited electron-hole ($e-h$) pairs, which are confined to a strain well in stressed Ge, is investigated via measurements of energy spectra and spatial distributions of $e-h$ recombination luminescence. From calculated fits to the energy spectra, we determined that the liquid-gas (LG) critical temperature was 4.5±0.2 K. However, above 3.7 K, we observed excess luminescence between the typical free-excition (FE) and $e-h$-liquid (EHL) lines. In addition, measurements of the actual spatial distributions of the $e-h$ pairs indicate that sharp changes in density occur even at temperatures well above the measured LG critical temperature. We were able to quantitatively explain all of our data by assuming the presence of three phases separated by two phase transitions: a low-density FE gas separated by a Mott (metal-insulator) transition from an intermediate-density $e-h$ gas (EHG) which in turn condenses into an EHL with still higher density. In this interpretation, the line of Mott transitions between the FE and EHG phases is determined to begin at a triple-point temperature of 3.7±0.2 K and end at a critical point at 6.5±0.5 K and density (9±3) × ${10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$. A simple theory for the Mott transition gives a critical-point temperature of 5.4 K and density of 3.4×${10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Other interpretations of our data such as inhomogeneous strain broadening or the existence of excitonic complexes are considered but shown to be inadequate. However, the apparent small density difference between the FE and EHG phases makes it impossible to rule out the possibility that the Mott transition is actually continuous above the LG critical temperature. This last explanation is considered unlikely due to the temperature range over which the Mott transition is observed to remain sharp.