Dynamical screening in the cooling theory of high-density electron-hole plasmas

We calculate the LO-phonon emission rate and the energy transfer from carriers to the lattice using a dynamical screening of the electron-phonon interactions in the random-phase approximation. We consider a three-dimensional homogeneous plasma. Because of the computational difficulties encountered when screening dynamically, we restrict our study to the partly thermalized regime. We analyze particularly the LO-phonon emission rates by electrons and holes at room temperature and at liquid-helium temperature. Electrons are more sensitive than holes to dynamical effects. Contrary to the results deduced in the static approximation, we conclude from our general study that the screening of the LO-phonon emission has no significant effect on the cooling up to the density rho/sub c/, corresponding to the resonance of LO phonons with plasmons, determined by the equation (h/2π)ω/sub LO/≅(h/2π)ω/sub pl/(rho/sub c/). Here, (h/2π)ω/sub LO/ and (h/2π)ω/sub pl/(rho/sub c/) are, respectively, the LO-phonon energy and the plasmon energy. In GaAs, rho/sub c/≅(5--7) x 10/sup 17/ cm/sup -3/. At plasma densities higher than rho/sub c/, the dynamical screening tends to the static one, but the effect depends quantitatively on the plasma temperature