Multi-channel electron intracenter relaxation in hydrogen-like donors in silicon

Abstract

Electronic relaxation on ionized and neutral impurity centers in silicon has been thoroughly studied over last 60 years. Because electronic capture in silicon determines speed and efficiency of optoelectronic and electronic devices this study was mostly driven by silicon-based electronics. Nowadays, an understanding of relaxation processes in doped silicon becomes actual for the development of impurity-based silicon lasers. For a long time the cascade model of electronic capture has been accepted as mostly adequate for description of intracenter relaxation in silicon. The cascade model based on the assumption that a free carrier is captured first in a highly excited state with a large orbit radius. Then the carriers go down the ‘‘ladder’’ of closely spaced energy levels under simultaneous emission/absorption of acoustic phonons. We have carried out experiments on intracenter excitation of silicon crystals doped by hydrogen-like donors. The analysis of observed emission spectra of the n-Si terahertz intracenter lasers together with the laser thresholds as well as empirical data for lifetimes of particular excited states allows to estimate different schemes of intracenter relaxation. The most important result is evidence of different specific channels for electron relaxation through low lying donor states. The dominating relaxation channels strongly depend on the initial energy distribution of the nonequilibrium carriers. A relaxation step may exceed not only the energy gap to an adjacent lower-lying donor level but also the Lax´s characteristic energy step as set by the energy and momentum conservation requirements for intravalley acoustic phonons. The latter indicates on significant contribution of intervalley phonons for such a relaxation that fits to the theoretical calculation of relaxation rates in n-Si with assistance of intervalley acoustic phonons. Intracenter relaxation rates of a number of channels have been estimated from experimental data. The fastest channels for intracenter relaxation onto the ground state of hydrogen-like donors have characteristic relaxation rates above 1e10/s, and in the case of resonant interaction of donors with intervalley phonons – above 1e11/s. Multi-channel relaxation scheme can explain experimentally observed relatively short lifetimes of nonequilibrium electronic distributions in excited donor states of Si:P and Si:As: 100-205 ps.