Phonon-assisted electron relaxation in multi-valley semiconductors

Electronic decay in multi-valley semiconductors was a hot topic of semiconductor research in late 50ths and 60ths due to its direct relation to electronic distributions in semiconductor devices for electronics and optoelectronics. Different theoretical propositions have been explored in order to find an adequate description of experimentally observed anomalous fast rates of electronic capture onto charge centers, such as dopants, in semiconductors. Most of commonly accepted theories consider electronic capture as a multi-step, “cascade” process of phonon-assisted gradual relaxation of an electron through ladders of excited states of impurity centers. Individual steps in the cascade model are accompanied by emission of intravalley acoustic phonons and obey the energy and momentum conservation law, making relaxation steps between the closest in energy states as most probable. This point of view has been reconsidered recently due to experimental results indicating that the cascade model of intracenter relaxation fails for multi-valley semiconductors, such as silicon. In these media a dominant contribution in intracenter relaxation occurs from an electron interaction with intervalley phonons and enhanced around the energy resonances between the phonons and impurity states. This results in appearance of alternative relaxation stairs with different probabilities and in effect causes fast relaxation rates observed experimentally. Our experiments on determination of lifetimes of most longliving excited states of shallow donors in silicon show that the longest individual relaxation steps do not exceed a couple of hundreds ps. Specific combinations of significantly different relaxation rates cause existence of short- and longliving states of impurity centers in multi-valley semiconductors. The latter can be used for creation of inverted electronic distributions inside the centers with resulting amplification of light, dominantly in the terahertz frequency range, where intervalley phonons hold their frequencies. The experimentally observed relaxation rates of some excited states of shallow donor centers in silicon have been used for the proof of different theoretical descriptions of intracenter relaxation taking into account interaction with intervalley phonons.