PHONON EXCESS HEATING IN ELECTRONIC RELAXATION THEORY IN QUANTUM DOTS
Abstract
When the usual operator of the Fröhlich's coupling between electrons and longitudinal optical phonons of semiconductor single quantum dot is used to calculate electronic energy relaxation, a permanent phonon generation in quantum dot is obtained, leading to an artificial effect of permanent heating up of the lattice. The mechanism of the phonon heating is identified here with the influence of the transverse part of the interaction operator. This part is responsible first of all for a tendency to build the polaronic well of an electron in a quantum dot. The effect of overheating is shown to be possibly eliminated to a considerable extent upon removing the transverse part of the interaction with the help of the Lang–Firsov canonical transformation and upon modifying accordingly the longitudinal part of the coupling. The resulting electronic relaxation and optical phonon generation is demonstrated numerically in a relatively simple approximation to electron and phonon self-energy, in which the model of quantum dot is reduced to an electron coupled to a single-LO-phonon mode. It is interesting to see that the removal of the phonon overheating based on the application of the Lang–Firsov canonical transformation has a rather small influence on electronic characteristics calculated with electronic transport equations. In this sense, the long-time limit properties of the electronic subsystem, like the electronic up-conversion and incomplete depopulation effect, calculated earlier, remain nearly untouched.
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