Kinetics of electron-hole droplet clouds: The role of thermalization phonons

Abstract

This paper presents a detailed analysis of the phonon wind which is responsible for the large cloud of electron-hole droplets often observed in Ge. The phonons are separated into two categories: $T$ phonons, produced by the initial thermalization of the hot carriers, and $R$ phonons, produced when an electron-hole pair recombine nonradiatively. It is shown that, while most of the $T$-phonon energy is effectively lost in an initial optical-phonon cascade, there is a residual energy given off to acoustic phonons when the carriers have cooled to within a single optical-phonon energy of the band edge. These phonons, which represent less than one percent of the total phonon energy, produce all of the characteristic features of the phonon wind. Without the $T$ phonons, the cloud density would not saturate, but would continue to grow as the laser power increased, and the cloud volume would not increase with power. Also, since the $T$ phonons reach steady state in essentially the thermalization time, the phonon wind is present in full force almost from the moment the drops condense, causing a rapid initial growth of the cloud. In addition to kinetic equations describing cloud buildup, more detailed models of the thermalization process are presented, in order to estimate the time evolution of the condensation and the magnitude of the wind. The theoretical prediction is in good agreement with experiments (except at high-absorption-power pulsed experiments, in which the wind is greatly enhanced). The number of $R$ phonons is harder to estimate; because they are spread out over the entire volume of the cloud, their effects are greatly diluted, and they make very little contribution to the characteristic features of the phonon wind. An analysis of previous experiments suggests that $R$ phonons may be as much as five times as numerous as $T$ phonons.