Semiconductor nanodevice simulation by multidomain spectral method with Chebyshev, prolate spheroidal and Laguerre basis functions

Abstract

A new approach based on spectral method with efficient basis functions is proposed in the paper to simulate semiconductor nanodevice by solving the Schrödinger equation. The computational domain is partitioned at heterojunctions into a number of subdomains. The envelope functions in subdomains are expanded by various efficient basis functions and then patched by the BenDaniel–Duke boundary conditions to preserve exponential order of accuracy. Importantly, the consideration to choose the basis functions depends on the oscillatory characteristics of envelope functions. Three kinds of basis functions including prolate spheroidal wave functions, Chebyshev polynomials, and Laguerre–Gaussian functions are used according to the mathematical features in this work. In addition, the determinations of optimum values of scaling factor in Laguerre–Gaussian functions and bandwidth parameter in prolate spheroidal wave functions are also discussed in detail. Several quantum well examples are simulated to validate the effectiveness of the present scheme. The relative errors of energy levels achieve the order of 10 −12 requiring merely a few grid points.