The light Raman scattering as the origin of the frequency threshold on the carrier multiplication efficiency in quantum dots

Abstract

The carrier multiplication (CM) process generated from single photon absorption in spherical quantum dots is studied theoretically taking into account as the perturbations the electron-radiation and the Coulomb electron-electron interaction. New aspects related with Raman scattering phenomena accompanying the light absorption were revealed. Side by side with the creation of two or more electron-hole (e-h) pairs the Raman scattering photons can appear. A semiconductor with simple parabolic e-h bands and impenetrable spherical symmetry quantum dots with strong size quantization were considered. In these conditions the band-to-band quantum transitions lead to creation of e-h pairs with the same quantum numbers <i>l, n, m</i> of the envelope functions. Only such type wave functions of the e-h pairs with the same quantum numbers <i>l, n, m</i> were used as the real and virtual electron states in the frame of the perturbation theory. The photon states are also introduced. First of all the probability to create two e-h pairs was studied in the scheme, when the first step is the obligatory participation of electron-photon interaction followed by the second step involving the electron-electron interaction. Side by side with this variant, the process of light absorption with the creation of two e-h pairs accompanied by a Raman scattered photon was studied. In this case the second step of the perturbation theory is also based on the electron-radiation interaction. In the first obligatory step the resonant part of the electron-radiation interaction is used, whereas in the second step the antiresonant part is engaged. In difference on the first variant this second process leads to smooth absorption band shape and can explain the existence of the threshold on the frequency dependence of the CM quantum efficiency in the photon frequency region corresponding to creation of two e-h pairs.