Phonon Overheating in Quantum Dots: Low Electronic Densities
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0959-M17-17
Phonon Overheating in Quantum Dots: Low Electronic Densities Karel Král Dept. of Cond. Matter Theory, Institute of Physics, Academy of Sciences of Czech Republic, Na Slovance 2, Prague 8, 188221, Czech Republic
ABSTRACT The electronic coupling to the longitudinal optical phonons has been recently used to interpret theoretically the electronic energy relaxation in quantum dots. In this theory the LO phonon modes served as a reservoir, on which the electron executes multiple scattering acts. Quite reasonably such a phonon subsystem is expected to be passive, namely, in a long-time limit of development, the whole system should be able to achieve such a stationary state, in which the statistical distributions of both subsystems, electron and phonons, do not change in time. We remind briefly that the recent approach to the relaxation in quantum dots has led to a non-passivity of such a reservoir. We remind as well the method of a partial elimination of the phonon overheating effect by using the Lang-Firsov transformation. Then we apply such a modified relaxation theory to the electronic relaxation at low electronic densities in quantum dots and come to conclusions concerning the role of e-LO scattering mechanism. We show that the modified theory of relaxation gives a plausible dependence of relaxation rate on temperature of sample. We also come to conclusions that at low levels of electronic excitation of quantum dot sample the electron-LO phonon mechanism can become relatively weak with respect to other relaxation mechanisms not supporting the electronic up-conversion effect. INTRODUCTION The lasing of small zero-dimensional systems of quantum dots is an attractive topic at present. Among the interesting problems there is the lasing of some of the quantum dot structures from the higher excited states [1]-[3]. We have reported recently our theoretical calculations of such effects in quantum dot samples, namely of the effect of electronic up-conversion and of the effect of an incomplete depopulation of the electronic excited states after excitation by a laser pulse [4]. In these works the up-conversion effect was interpreted with help of the mechanism based on multiple scattering (MS) of electrons on the longitudinal optical (LO) phonons, which was earlier shown to be able to explain the effect of the rapid relaxation of electronic energy in individual quantum dots. Although this line of interpretation of the electronic relaxation effect in quantum dots has not yet become completely understood, it provides a rather plausible explanation of the relaxation measurements in a broad range of energies, not only under the condition of the electronic energy level separations being close to the LO phonon energy. This remarkable property of theoretical formulas for the electronic relaxation is obtained with help of quantum kinetic equations for electronic relaxation based on self-consistent Born approximation to electronic self-energy and on the the instant collisions approximation to the collision integral of the kin
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