Uncertainty quantification of charge transfer through a nanowire resonant-tunneling diode with an ADHIE-FDTD method

The influence of barrier thickness variability on the charge transfer characteristics of an InP/InAs/InP nanowire resonant-tunneling diode is studied. The transmission probability through the diode is calculated by solving the time-dependent effective-mass Schrödinger equation with the Alternating-Direction Hybrid Implicit-Explicit (ADHIE) Finite-Difference Time-Domain (FDTD) method. This recently developed method is tailored towards multiscale problems and thus […]

Nonuniform and higher-order FDTD methods for the Schrödinger equation

Two Finite-Difference Time-Domain (FDTD) methods are developed for solving the Schrödinger equation on nonuniform tensor-product grids. The first is an extension of the standard second-order accurate spatial differencing scheme on uniform grids to nonuniform grids, whereas the second utilizes a higher-order accurate spatial scheme using an extended stencil. Based on discrete-time stability theory, an upper bound is […]

A perturbative stochastic Galerkin method for the uncertainty quantification of linear circuits

This paper presents an iterative and decoupled perturbative stochastic Galerkin (SG) method for the variability analysis of stochastic linear circuits with a large number of uncertain parameters. State-of-the-art implementations of polynomial chaos expansion and SG projection produce a large deterministic circuit that is fully coupled, thus becoming cumbersome to implement and inefficient to solve when […]

Scattering parameters characterization of periodically nonuniform transmission lines with a perturbative technique

In this article, a novel procedure for the frequency-domain solution of nonuniform transmission lines (NUTLs) is presented. The procedure is based on a recently proposed perturbative technique, which is proven to be computationally more efficient than standard solution approaches, which are based on line subdivision into uniform cascaded sections. With respect to the original perturbation […]

Machine-learning-based hybrid random-fuzzy uncertainty quantification for EMC and SI assessment

Modeling the effects of uncertainty is of crucial importance in the signal integrity and Electromagnetic Compatibility assessment of electronic products. In this article, a novel machine-learning-based approach for uncertainty quantification problems involving both random and epistemic variables is presented. The proposed methodology leverages evidence theory to represent probabilistic and epistemic uncertainties in a common framework. […]