Strain-confined electron-hole liquid in germanium

Previous experiments in pure germanium at low temperatures have shown that high densities of photo-produced electron-hole pairs condense into a metallic liquid phase—typically manifested as small electron-hole droplets (EHD). The energy, pair density, and lifetime of an EHD can be significantly modified by applying a stress to the crystal. Due to the lowering of the indirect band edge with strain, droplets, free excitons, and carriers are accelerated in a strain gradient approximately towards a point of maximum shear strain. We show that by appropriately stressing a crystal, it is possible to create inside the crystal a shear strain maximum, i.e., a potential well, into which droplets, excitons, and carriers are attracted, causing them to coalesce into a macroscopic mass of electron-hole liquid with diameter up to a millimeter. Using the known deformation potentials and anisotropies of germanium, we calculate numerically the stress tensor, the band-edge shift, and the electron-hole liquid energy vs position in an inhomogeneously stressed crystal. We report photographic data on large drops in Ge and compare these data to the strain theory. A two-dimensional numerical calculation is in essential agreement with the observed drop locations. Due to the anisotropy of the band-edge shift with strain, we find that it is possible to form one, two, or four electron-hole drops beneath the stress contact area by applying stress along $〈111〉$, $〈110〉$, and $〈100〉$ crystal axes, respectively. In addition we have observed birefringence patterns in these same crystals which yield strain distributions in accord with the above theory and photographic data. Theoretical calculations of the birefringence also agree with observations. Thus the macroscopic features (i.e., position, shape, and number) of the large strain-confined drops can be understood in terms of the known deformation properties of germanium.