Theory of femtosecond photon-echo decay in semiconductors.

Abstract

We investigate a mechanism responsible for the observed very short times of the photon-echo decay (of the order of a few femtoseconds) in semiconductors. It is associated with the loss of phase memory as a result of the interaction of the interband mixed state with an unscreened random Coulomb potential of the photocarriers and/or charged impurities. A time characteristic of a system of interacting electrons is found. This is the time of phase breaking ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$, which we calculate within the eikonal approximation using diagrammatic techniques. ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$ is shown to be typically much shorter than both the time of electron-electron collisions and the period of plasma oscillations. We demonstrate that the screening of Coulomb potential cannot be built up during this time. ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$ is proportional to ${\mathit{n}}^{\mathrm{\ensuremath{-}}1/\mathit{d}}$ (where n is the carrier concentration and d the dimensionality of a system), which is consistent with the experimental results. The derived law of echo decay of the form exp[-(\ensuremath{\tau}/${\mathrm{\ensuremath{\tau}}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$${)}^{\mathit{d}}$] agrees with the results of numerical simulation, although it does not agree with the existing results of physical experiment. We believe that such a disagreement is of a fundamental nature and manifests a basic need for further experimental and theoretical work.