Transient quantum transport simulation based on the statistical density matrix

Abstract

A new quantum device simulation technology has been developed based on the statistical density matrix theory. By introducing the Hartree self-consistent-field model for electron-electron interactions and the relaxation time approximation for scattering processes, the one-dimensional time-dependent Liouville-von Neumann equation for the electron density matrix has been solved. The density matrix is a wavefunction-wavefunction correlation function with its off-diagonal elements directly measuring the phase coherence of wavefunctions in quantum mechanical devices. The authors report a numerical model for the transient density matrix, calculated initially in thermal equilibrium by self-consistently solving the Schrodinger equation and Poisson's equation. The present simulation technology is applied to the simple AlGaAs/GaAs resonant tunnelling diode and the femtosecond time evolution of the density matrix under an applied field is demonstrated. Remarkable oscillatory behaviour observed in the off-diagonal elements reveals the existence of long. range phase correlations of the electron wave in the resonance state. Intrinsic bistability and switching characteristics of the device are investigated from the viewpoint of charge accumulation in the quantum well, and the peak-to-valley current ratio is discussed in terms of phase coherence degradation of electron waves due to scattering.