A generalized Ramo–Shockley theorem for classical to quantum transport at arbitrary frequencies

Abstract

We present a generalized Ramo–Shockley theorem to evaluate particle currents and energy currents at device contacts, in classical drift-diffusion or hydrodynamic simulation techniques as well as for semiclassical Monte Carlo and quantum mechanical transport simulation. In contrast to the Ramo–Shockley theorem, our technique (1) is derived for conditions of extreme time dependence in the charge carriers and forces (including particle-induced radiation), (2) explicitly accounts for particle generation and recombination processes such as photoexcitation, forward and inverse Auger processes, or Shockley–Read–Hall recombination, and (3) distinguishes clearly between the contributions of electrons, holes, and the displacement current. The resulting simple new formalism reduces to the standard Ramo–Shockley theorem as a special case.