Hot electrons and core hole screening

Two problems are discussed with respect to the applicability of linear response theory. In Part I, high-field transport in solids is treated analytically in one dimension for optical phonon scattering, for arbitrary field strength. The problem is thus highly nonlinear in field, while linearized in the carrier concentration, which in turn implies neglecting carrier-carrier scattering. Results are obtained for a constant field profile. The results show the well-known velocity saturation behavior in a realistic way, thus emphasizing the critical role of optical phonons in this phenomenon. A Maxwellian distribution is found at all fields; in some cases the electron temperature is lower than the lattice temperature. Runaway is shown to result from forward (polar) scattering, but not for isotropic scattering. The formalism developed for the high-field problem is also applied to the transient relaxation of carriers under photoexcitation; the results are compared with experiment. In Part II, the dynamic screening of a suddenly-created core hole in a metal is examined in the linear ap proximation. The photoelectron is neglected; the results are thus valid for photon energies well above threshold. The time and space dependence of the screening charge, for high and low electron gas density, is obtained by numerical integration over the spectral function of the dynamic dielectric function. The integral is broken into a plasmon part and an electron-hole pair (e-h) part, from the corresponding regions of the spectral function. The e-h part is found to be more heavily damped, and much larger in amplitude (×30) than the plasmon part; however, both parts respond on essentially the same time scale given bj' the inverse plasma frequency. Addition of local-field corrections to the RPA is found to have little effect on the results. Transients in screening are found to be larger and more persistent for low density than for high density. However, in either case transients are not predicted to persist to times on the order of the core hole lifetime from x-ray emission.