Efficient numerical simulation of electron states in quantum wires

Abstract

We present a new algorithm for the numerical simulation of electrons in a quantum wire as described by a two-dimensional eigenvalue problem for Schrödinger’s equation coupled with Poisson’s equation. Initially, the algorithm employs an underrelaxed fixed point iteration to generate an approximation which is reasonably close to the solution. Subsequently, this approximate solution is employed as an initial guess for a Jacobian-free implementation of an approximate Newton method. In this manner the nonlinearity in the model is dealt with effectively. We demonstrate the effectiveness of our approach in a set of numerical experiments which study the electron states on the cross section of a quantum wire structure based on III-V semiconductors at 4.2 and 77 K.

Numerical modeling of silicon quantum dots

“…In the last two decades, several computer-simulation programs have been written with the aim of finding the potential and mobile charge density distribution in conventional devices [2][3][4][5][6], Ravailoli et al [7] and Kerkhoven et al [8,9] have reported self-consistent computations of the electronic states of a quantum wire while Kumar et al [10][11][12] have presented self-consistent numerical solutions of the Poisson and Schrödinger equations for a GaAs-Al x Ga 1−x As quantum dot. Kerkhoven et al [8,9] work is for two-dimensional (2D) devices.…”

“…Kerkhoven et al [8,9] work is for two-dimensional (2D) devices. Kumar et al [11], working in three dimensions (3D), use a Newton loop for the Poisson equation with a polynomial preconditioned conjugate gradient method or the Lanczos method for the solution of the Hermitian matrix system.…”

A fast and stable Poisson-Schrödinger solver for the analysis of carbon nanotube transistors

“…Successive iteration continues until a convergence criterion is satisfied. In this work an adaptive damping factor was used [13]. The damping factor is initially set to α = 1.…”

Component mode synthesis approaches for quantum mechanical electrostatic analysis of nanoscale devices

“…Various computational models and approaches [9][10][11][12][13][14][15][16][17][18] have been developed to analyze these properties including the quantum effects in nanostructures and devices in the past few decades. Among these computational models, the Schrödinger-Poisson model [14][15][16][17][18] has been widely adopted for quantum mechanical electrostatic analysis of nanostructures and devices such as quantum wires, MOSFETs and nanoelectromechanical systems (NEMS). The numerical results allow for evaluations of the electrical properties such as charge concentration and potential profile in these structures.…”