# A self‐consistent solution of Schrödinger–Poisson equations using a nonuniform mesh

@article{Tan1990ASS, title={A self‐consistent solution of Schr{\"o}dinger–Poisson equations using a nonuniform mesh}, author={I. H. Tan and Gregory L. Snider and L. D. Chang and Evelyn L. Hu}, journal={Journal of Applied Physics}, year={1990}, volume={68}, pages={4071-4076} }

A self‐consistent, one‐dimensional solution of the Schrodinger and Poisson equations is obtained using the finite‐difference method with a nonuniform mesh size. The use of the proper matrix transformation allows preservation of the symmetry of the discretized Schrodinger equation, even with the use of a nonuniform mesh size, therefore reducing the computation time. This method is very efficient in finding eigenstates extending over relatively large spatial areas without loss of accuracy. For… Expand

#### 622 Citations

A one-dimensional, self-consistent numerical solution of Schrödinger and poisson equations

- Physics
- 1991

A self‐consistent, one‐dimensional, numerical solution of Schrodinger and Poisson equations has been obtained. To solve Schrodinger equation, instead of the conventional finite difference approach,… Expand

A new finite difference scheme adapted to the one-dimensional Schrödinger equation

- Mathematics
- 1993

We present a new discretisation scheme for the Schrödinger equation based on analytic solutions to local linearisations. The scheme generates the normalised eigenfunctions and eigenvalues… Expand

Application of an efficient algorithm for solving the one‐band effective mass equation self‐consistently in the modelling of some low‐dimensional structure devices

- Mathematics
- 1992

An efficient algorithm is presented for the self-consistent numerical solution of the single-band effective mass equation. This algorithm has a different form depending on whether the effective mass… Expand

A comparison between different numerical methods used to solve Poisson’s and Schroedinger’s equations in semiconductor heterostructures

- Physics
- 1993

A comparison between different numerical methods which are used to solve Poisson’s and Schroedinger’s equations in semiconductor heterostructures is presented. Considering Schroedinger’s equation,… Expand

Discretization techniques for the efficient solution of the eigenvalue problem in heterostructures

- Mathematics
- 2009

A systematic development of efficient discretization schemes for the numerical evaluation of the eigenvalues of the single-band effective mass equation that describes the motion of electrons in an… Expand

Spectral Element Method for the Schrödinger-Poisson System

- Mathematics
- 2004 Abstracts 10th International Workshop on Computational Electronics
- 2004

A novel fast Spectral Element Method (SEM) with spectral accuracy for the self-consistent solution of the Schrödinger-Poisson system has been developed for the simulation of semiconductor… Expand

Solution of the 1D Schrödinger equation in semiconductor heterostructures using the immersed interface method

- Mathematics, Computer Science
- J. Comput. Phys.
- 2012

A novel method simple enough to implement yet powerful enough to solve Schrodinger equation in semiconductor devices with high accuracy is presented herein. Expand

Analysis of MOS Device Capacitance-Voltage Characteristics Based on the Self-Consistent Solution of the Schrödinger and Poisson Equations

- Materials Science
- 1999

The one-dimensional Schridinger and Poisson equations have been numerically solved in metal-oxide-semiconductor devices using a three-point finite difference scheme with a non-uniform mesh size. The… Expand

Exact Artificial Boundary Condition for the Poisson Equation in the Simulation of the 2D Schrödinger-Poisson System

- Mathematics
- 2014

We study the computation of ground states and time dependent solutions of the Schrodinger-Poisson system (SPS) on a bounded domain in 2D (i.e. in two space dimensions). For a disc-shaped domain and… Expand

The self-consistent quantum-electrostatic problem in strongly non-linear regime

- Physics
- SciPost Physics
- 2019

The self-consistent quantum-electrostatic (also known as
Poisson-Schrödinger) problem is notoriously difficult in situations
where the density of states varies rapidly with energy. At low… Expand

#### References

SHOWING 1-10 OF 22 REFERENCES

Semiconductor heterostructure nonlinear Poisson equation

- Physics
- 1989

A nonlinear Poisson partial differential equation descriptive of heterostructure physics is presented for two‐dimensional device cross sections. The equation is solved using a hybrid nonlinear… Expand

Electron states in narrow gate-induced channels in Si

- Physics
- 1986

Self‐consistent numerical solutions of the Poisson and Schrodinger equations have been obtained for the states of electrons under a narrow gate or under a narrow slit in a metal‐oxide‐silicon… Expand

Electron states in mesa‐etched one‐dimensional quantum well wires

- Physics
- 1990

Two‐dimensional, self‐consistent solutions of the Schrodinger and Poisson equations are used to find the electron states in GaAs/AlGaAs quantum well wires. Both deep and shallow mesa structures are… Expand

MONTE: A Program to Simulate the Heterojunction Devices in Two Dimensions

- Computer Science, Materials Science
- IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
- 1986

This paper describes the two-dimensional heterojunction device simulator MONTE, and a heuristic approach has been devised for evaluating the mobility of electrons based on the quasi-Fermi level. Expand

Calculation of the electron wave function in a graded‐channel double‐heterojunction modulation‐doped field‐effect transistor

- Physics
- 1989

We investigate theoretically three double‐heterojunction modulation‐doped field‐effect transistor structures with different channel composition. All of these transistors have an InxGa1−xAs channel… Expand

Modeling for electron transport in AlGaAs/GaAs/AlGaAs double-heterojunction structures

- Physics
- 1989

Two-dimensionally quantized electron transport in modulation-doped double-heterojunction structures is investigated using a Monte Carlo simulation in which the energy quantization in a well is… Expand

One‐dimensional electronic systems in ultrafine mesa‐etched single and multiple quantum well wires

- Physics
- 1988

Ultrafine mesa‐etched structures with lateral geometrical dimensions of 250 to 550 nm have been prepared in modulation‐doped AlGaAs/GaAs heterostructures and multiple quantum well systems. From… Expand

Principles and procedures of numerical analysis

- Mathematics
- 1978

Preliminaries.- Approximation and Interpolation of Functions.- Numerical Differentiation and Integration.- General Theory for Iteration Methods.- Solution of Nonlinear Equations.- The Solution of… Expand

(AlAs)0.5(GaAs)0.5 fractional‐layer superlattices grown on (001) vicinal surfaces by metalorganic chemical vapor deposition

- Chemistry
- 1987

(AlAs)0.5(GaAs)0.5 fractional‐layer superlattices with a new periodicity perpendicular to the growth direction was successfully grown by metalorganic chemical vapor deposition on (001) GaAs… Expand

Molecular-beam epitaxy growth of tilted GaAs/AlAs superlattices by deposition of fractional monolayers on vicinal (001) substrates

- Materials Science, Chemistry
- 1988

We report the successful growth of GaAs/AlAs superlattices having interface planes tilted with respect to the substrate surface plane. The amount of tilt and the superlattice period may be controlled… Expand