Numerical Simulation of Quantum Transport in Semiconductor Devices

量子半导体器件（如共振隧道二极管、超晶格、HEMT和MODFET晶体管）中的电子传播可以建模为在异质结势垒处具有不连续跳变的连续带电量子气体的流动。量子流体动力学方程可以通过假设气体接近热平衡来推导，但期望更普遍有效。研究者和他的同事专注于基于“光滑”量子流体动力学模型和量子动力学方程（包括Bloch方程和Wigner-Boltzmann方程）的量子半导体器件中一维和二维空间电子流的理论建模、模拟和分析。强调了在高性能计算机上模拟这些方程的现代逆风数值方法的发展。依赖于量子隧道效应的半导体器件，如共振隧道二极管和晶体管，在先进的微电子应用中发挥着越来越重要的作用，包括多态逻辑和存储器件以及高频振荡器。研究人员利用量子流体动力学和量子动力学方程处理电子流动，建立了量子半导体器件的行为模型。模型和数值方法在高性能工业计算机程序中实现，可用于半导体制造业。通过这种方式，半导体设计工程师可以在实际制造半导体器件之前，在计算机上有效地探索各种器件材料和结构的行为。

Gardner 9706792 The propagation of electrons in quantum semiconductor devices (e.g. resonant tunneling diodes, superlattices, and HEMT and MODFET transistors) can be modeled as the flow of a continuous charged quantum gas in a potential that has discontinuous jumps at heterojunction barriers. Quantum fluid dynamical equations can be derived by assuming the gas is near thermal equilibrium, but are expected to be more generally valid. The investigator and his colleague focus on theoretical modeling, simulation, and analysis of the flow of electrons in one and two spatial dimensions in quantum semiconductor devices based on the ``smooth'' quantum hydrodynamic model and quantum kinetic equations (including the Bloch equation and the Wigner-Boltzmann equation). The development of modern upwind numerical methods for simulating these equations on high performance computers is emphasized. Semiconductor devices --- like resonant tunneling diodes and transistors --- that rely on quantum tunneling are playing an increasingly important role in advanced microelectronic applications, including multiple-state logic and memory devices and high frequency oscillators. The investigators model the behavior of quantum semiconductor devices by treating electron flow by means of quantum hydrodynamic and quantum kinetic equations. The models and numerical methods are implemented in a high-performance industrial computer program that can be used by the semiconductor manufacturing industry. In this way, semiconductor design engineers can efficiently explore the behavior of various device materials and structures on the computer before actually fabricating the semiconductor device.