Effects of charge accumulation and biasing on resonant tunneling energies and tunneling dynamics

摘要

We introduce charge accumulation in quantum wells through the use of a nonlinear Schrodinger equation. Looking first at infinite and finite square wells allows us to calculate the new energy spectrum including the separate effects of a biasing electric field and charge accumulation. This gives us insight into the new resonant tunneling energies that arise due to the quasibound states being shifted by either the external field or the reaction field built up through the accumulation of charge. Using a double barrier potential, we calculate the transmission coefficient with and without the external bias field and then with charge accumulation. To study the tunneling dynamics, we first start with a single barrier in an infinite well and discover a fractal- like character to the probability for finding an electron wavepacket in one side of the structure. Finally we numerically integrate the full time-dependent nonlinear Schrodinger equation with various barrier potentials to obtain the dynamics of a wavepacket incident on the structures.