Universal features in degenerate and nondegenerate hot-carrier screening.

Abstract

The quantum-transport-equation approach, which was used to calculate nonequilibrium screening in the nondegenerate regime [Phys. Rev. B 39, 8468 (1989)], is extended to study nonequilibrium screening in the highly degenerate regime. We obtain an expression for the nonequilibrium electric susceptibility \ensuremath{\chi}(q,\ensuremath{\omega})=\ensuremath{\delta}n(q,\ensuremath{\omega})/\ensuremath{\delta}U(q,\ensuremath{\omega}) for a degenerate system in the presence of a large static electric field, within the relaxation-time approximation. Using the drift-diffusion equation as modified by Thornber and Price to include gradients of the field, we show that in both degenerate and nondegenerate systems, when the drift velocity exceeds a critical velocity ${\mathit{v}}_{\mathit{c}}$ (${\mathit{v}}_{\mathit{c}}$=${\mathit{v}}_{\mathit{F}}$/ \ensuremath{\surd}6 and ${\mathit{v}}_{\mathit{c}}$= \ensuremath{\surd}${\mathit{k}}_{\mathit{B}}$T/2m for the degenerate and nondegenerate cases, respectively), the real part of \ensuremath{\chi}(q, \ensuremath{\omega}=0) is positive for small q. The fact that Re[\ensuremath{\chi}(q, \ensuremath{\omega}=0)]>0 suggests that, with the proper device configuration, instabilities with respect to density perturbations might be possible. Since the large-q limit of the nonequilbrium \ensuremath{\chi} is the nonequilibrium Lindhard form of the susceptibility, ${\mathrm{\ensuremath{\chi}}}_{\mathrm{NL}}$, we scale \ensuremath{\chi} by ${\mathrm{\ensuremath{\chi}}}_{\mathrm{NL}}$. The ratio \ensuremath{\chi}(q)/${\mathrm{\ensuremath{\chi}}}_{\mathrm{NL}}$(q) is a universal function, independent of both the degeneracy and the value of ${\mathit{mv}}_{\mathit{c}}^{2}$\ensuremath{\tau}/\ensuremath{\Elzxh} (the product of the wave vector and mean free path of a carrier with velocity ${\mathit{v}}_{\mathit{c}}$), for 0${\mathit{v}}_{\mathit{d}}$/${\mathit{v}}_{\mathit{c}}$\ensuremath{\lesssim}5 and ${\mathit{mv}}_{\mathit{c}}^{2}$\ensuremath{\tau}/\ensuremath{\Elzxh}\ensuremath{\gtrsim}max{1, ${\mathrm{v}}_{\mathrm{d}}$/${\mathrm{v}}_{\mathrm{c}}$}.