Efficient Solution of the Wigner–Poisson Equations for Modeling Resonant Tunneling Diodes

A more efficient and accurate discretization of the Wigner-Poisson model for double barrier resonant tunneling diodes is presented. This new implementation uses nonuniform grids and higher order numerical methods to improve the accuracy of the solutions at a significantly lower computational cost. Using the new implementation, devices with short and long contact regions are analyzed as well as the effect of a correlation length parameter that defines the degree of nonlocality effects. The results show that devices with longer contact regions reduce numerical inconsistencies present when modeling shorter devices, and that longer correlation lengths generally improve the correspondence of the numerical solutions with those typically expected from experimental measurement. These new numerical simulation tools will enable researchers to successfully apply the Wigner-Poisson model to describe electron transport in nanoscale semiconductor tunneling devices. More specifically, the computationally more efficient numerical algorithms presented will be shown to allow for the quantum-based studies of resonant tunneling devices useful as sources and detectors at very high frequencies (e.g., THz regime). These types of devices are very important for use in sensors and sensing systems where very long wavelength characterization capabilities are important (e.g., interrogation of chemical and biological systems) as well as an array of other electronics applications.