Two-fluid mobility model from coupled hydrodynamic equations for simulating laser-driven semiconductor switches

Abstract

We introduce a two-fluid mobility model incorporating fundamental aspects of electron-hole (e-h) scattering such as momentum conservation for simulating laser-driven semiconductor switches (LDSSs). Compared to previous works that use Matthiessen's rule, the two-fluid mobility model predicts distinct AC responses of e-h plasmas in semiconductors. Based on the two-fluid mobility model, we develop a theory with very few adjustable parameters for simulating the switching performance of LDSSs based on high-purity indirect-gap semiconductors such as silicon (Si). As a prototypical application, we successfully reproduce experimentally measured reflectance at around 320 GHz in a laser-driven Si switch. By injecting e-h plasmas with densities up to $10^{20}\,\rm cm^{-3}$, we reveal the importance of carrier-screening effects in e-h scattering and Auger recombination for carrier densities above the critical carrier density for exciton-plasma Mott transition. Our results also suggest a way to characterize the intrinsic momentum-relaxation mechanism, e-h scattering, and the intrinsic e-h recombination mechanism in indirect-gap semiconductors, Auger recombination. We reassess the ambipolar Auger coefficient of high-purity Si with high injection levels of e-h plasmas up to $10^{20}\,\rm cm^{-3}$ and find a minimal value of $1.8\times10^{-41}\,{\rm cm^6/ns}$. The value is more than one order of magnitude smaller than the ambipolar Auger coefficient widely used for simulating LDSSs, $3.8\times10^{-40}\,{\rm cm^6/ns}$, which was deduced from minority-carrier lifetime in highly doped silicon more than four decades ago.