Schrödinger Equation Monte Carlo: Bridging the Gap From Quantum to Classical Transport

Schrödinger Equation and (based) Monte Carlo (SEMC), a simulation method designed to bridge the gap from quantum to classical transport, is described. This method provides a non-perturbative, current conserving quantum mechanical treatment of carriers, phonons, and their coupling, yet the SEMC algorithm is analogous to and compatible with that of semiclassical Monte Carlo (SMC). Indeed, SEMC allows carriers to be followed through a sequence of stochastically sampled scattering events. Phase breaking and energy dissipation for charge carriers within the Schrödinger-equation-based method are modeled via the exchange of probability among oscillator degrees of freedom, mimicing the true process of carrier-phonon scattering. Carrier-phonon coupling potentials for SEMC are obtained by Monte Carlo sampling of (the spatial correlation functions of) the true carrier-phonon coupling potentials. Illustrative results demonstrate SEMC's ability to provide both physically and quantitatively accurate modeling of, in particular, long-range polar-optical scattering, and to completely bridge the gap between phase-coherent and phase-incoherent transport.