Quantum Hydrodynamic Model for Semiconductor Devices: Theory and Computations

摘要

Quantum transport effects including electron or hole tunneling through potential barriers and buildup in quantum wells are important in predicting the performance of ultra-small semiconductor devices. These effects can be incorporated into the hydrodynamic description of charge propagation in the semiconductor device. A new extension of the classical hydrodynamic model to include quantum transport effects was derived. This 'smooth' quantum hydrodynamic (QHD) model is derived specifically to handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. The smooth QHD model makes the barriers partially transparent to the particle flow and provides the mechanism for particle tunneling in the QHD model. Smooth quantum hydrodynamic model simulations of the resonant tunneling diode were presented which exhibit enhanced negative differential resistance (NDR) when compared to simulations using the original QHD model. At both 300 K and 77 K, the smooth QHD simulations predict significant NDR even when the original QHD model simulations predict no NDR.