Hydrodynamic approach to electron-hole droplet nucleation and stability

A hydrodynamic model for the nonequilibrium thermodynamics of electron-hole droplets in semiconductors is presented. It predicts droplet properties at densities and temperatures where the assumptions of nucleation kinetics fail. It is an extension to finite lifetimes of the Cahn-Hilliard theories of critical droplets and spinodal decomposition. As in finite-lifetime nucleation kinetics both critical and stable droplets are found to exist above a minimum supersaturation which must become large at low temperatures. However, stable droplets differ both quantitatively and qualitatively from the capillarity approximation commonly assumed in nucleation kinetics. For example, they may be characterized by a velocity profile which peaks in the surface region. Among other novel predictions are that: (i) a maximum supersaturation before phase separation is given by the spinodal line; (ii) stable droplets continue to exist at temperatures approaching $T_c$ but their properties are strongly affected by impurity and phonon scattering; and (iii) at very low temperatures critical droplets are too small for hysteresis, but stable droplet properties are calculated. Quantitative predictions are made by the principle of corresponding states.