Calculation of two-dimensional quantum-confined structures using the finite element method

Abstract

The finite element method was used for calculating the wave functions and energy levels of electrons in arbitrarily shaped two-dimensional quantum-confined structures. The calculated results indicate the possibility of quasi-quantum wires by simply growing single quantum wells on corrugated substrates.

A study of the ground state of quantum wires using the finite difference method

“…In general this cannot be done analytically except for special geometries such as isotropic cylindrical QWRs [5] with infinite potential barrier height [6]. Several numerical methods have been used for the solution of the two-dimensional Schrödinger equation such as plane wave expansion [7], coordinate transformation with a variational procedure used only for V-shaped QWRs [8], finite element method [9][10][11] and finite difference methods [12][13][14][15]. Of these, perhaps, the most mature and successful methods to date have been the finite difference methods.…”

Stark Effect Dependence on Hydrogenic Impurities in GaAs Parabolic Quantum-Well Wires

“…[23−24] The analytical calculation of the eigenstates of QWWs is complicated or insoluble even due to the existence of the twodimensional confinement and Coulomb potential. In order to solve this problem, many authors adopted several numerical methods such as finite element method, [25] plane wave expansion, [26−27] variational method, [28−31] and finite difference method. [32−34] Recently, Bednarek et al [35] have proposed an analytical 1D formula for the effective interaction potential between confined charge carriers.…”

Simulation of electron states in quantum wires with mixed finite elements

“…A conventional approach to the solution of Schrödinger’s equation is to use the finite difference method[15]. Because the geometry of the device has very different scales, we think that the finite element method is more appropriate[16, 17]. However, the values of the parameters in the semi‐conductor equations have a very large range.…”