Nucleation Phenomena in Electron‐Hole Drop Formation in Ge and Si: I. Nucleation Rates

A general nucleation theory for liquids possessing finite lifetimes, specifically for the condensation of electron‐hole drops (EHD) from a gas of free excitons (FE), is presented. The theory is developed for both homogeneous and inhomogeneous nucleation in Ge and Si. In Part I explicit expressions are derived for the steady‐state rates of formation J+ and breakup J− of macroscopic EHD, and for the EHD size distribution in dynamic equilibrium. It is found that the FE‐EHD system above T ≈ 1.3 K in Ge is characterized by metastable states for which the equilibration time is extremely long. The expressions for J+ and J− yield two sharp excitation thresholds. In Part II these results are applied to quantitatively predict for EHD the metastable time behavior, a procedure for measuring the surface tension, the phase diagram, and the EHD radius as a function of temperature. In Part III experimental luminescence data are presented for Ge which support this theory and accurately determine the surface tension.