A fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schrödinger’s and Poisson’s equations is presented. Using quantum mechanical perturbation theory, a simple expression describing the dependence of the quantum electron density on the electrostatic potential is derived. This expression is then used to implement an iteration scheme, based on a predictor-corrector type approach, for the solution of the coupled system of differential equations. We find that this iteration approach simplifies the software implementation of the nonlinear problem, and provides excellent convergence speed and stability. We demonstrate the approach by presenting an example for the calculation of the two-dimensional bound electron states within the cross section of a GaAs-AlGaAs based quantum wire. For this example, the convergence is six times faster by applying our predictor-corrector approach compared to a corresponding underrelaxation algorithm.

A quasi-three-dimensional (3D) simulation of a quantum waveguide coupler has been performed, computing the self-consistent transverse potential along the electron waveguides and then solving the transport problem with a modified recursive Green's-function method. Results have been obtained for the tunneling conductance between the two waveguides as a function of coupling length and gate biases. A clear structure of conductance peaks is observed, strongly dependent on both the drain and the source biases. Such dependence has been investigated in greater detail for an idealized model, allowing a fast numerical simulation. A ridgelike conductance pattern has been obtained, which can be interpreted as a characteristic signature to be looked for when searching for the evidence of 113-to-1D tunneling in experimental data.

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.

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We discuss in this paper some of the methods for 2-D self-consistent simulation of semiconductor quantum well lasers. First, the electronic and optical parts are each treated separately, and then the coupling of the two problems is addressed. We briefly dicuss the evolution of self-consistent laser simulation up to its present level, and afterwards some of the electronic transport concerns are discussed in greater detail. Transport in bulk regions and at heterojunctions, and the coupling of classical and quantum regions are each presented separately. Then, we review the approaches to the solution of the eigenvalue problem for the optical field. Finally, to illustrate the issues involved in coupling electronic and optical solutions, we introduce a model laser structure in which the optical field is poorly confined in the lateral direction, and the different confinement mechanisms are discussed. We then present calculations showing how gain can contribute to the lateral confinement of the fundamental cavity mode.

Maintaining cladding layer material composition uniformity is inherently difficult during high temperature MBE growth of GaAs/AlGaAs laser structures. These non-uniformities can lead to asymmetrical waveguiding structures with distorted optical output characteristics of the laser. Distortions in optical characteristics can greatly affect the alignment and the coupling efficiency between laser diodes and optical fiber or other electro-optical systems in integrated opto-electronic applications. A two-dimensional dielectric waveguide simulator has been used to analyze the optical properties of GRINSCII GaAs/A1GaAs lasers with asymmetrical cladding structures. Through this analysis, we have demonstrated an optimal laser device structure which has the desired optical characteristics and is less sensitive to cladding composition asymmetries arising in typical growth conditions.

We present a fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schrödinger's and Poisson's equations in quantum structures. A simple expression describing the dependence of the quantum electron density on the electrostatic potential is used to implement a predictor – corrector type iteration scheme for the solution of the coupled system of differential equations. This approach simplifies the software implementation of the nonlinear problem, and provides excellent convergence speed and stability. We demonstrate the algorithm by presenting an example for the calculation ofthe two-dimensional bound electron states within the cross-section of a GaAs-AlGaAs based quantum wire. For this example, six times fewer iterations are needed when our predictor – corrector approach is applied, compared to a corresponding underrelaxation algorithm.