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**Harvard**

Berland, K. (2011) *A general solution to the Schrodinger-Poisson equation for a charged hard wall: Application to potential profile of an AlN/GaN barrier structure*.

** BibTeX **

@article{

Berland2011,

author={Berland, Kristian},

title={A general solution to the Schrodinger-Poisson equation for a charged hard wall: Application to potential profile of an AlN/GaN barrier structure},

journal={Superlattices and Microstructures},

issn={0749-6036},

volume={50},

issue={4},

pages={411-418},

abstract={A general, system-independent, formulation of the parabolic Schrodinger-Poisson equation is presented for a charged hard wall in the limit of complete screening by the ground state. It is solved numerically using iteration and asymptotic boundary conditions. The solution gives a simple relation between the band bending and sheet charge density at an interface. Approximative analytical expressions for the potential profile and wave function are developed based on properties of the exact solution. Specific tests of the validity of the assumptions leading to the general solution are made. The assumption of complete screening by the ground state is found be a limitation; however, the general solution provides a fair approximate account of the potential profile when the bulk is doped. The general solution is further used in a simple model for the potential profile of an AlN/GaN barrier structure. The result compares well with the solution of the full Schrodinger-Poisson equation. },

year={2011},

keywords={Schrodinger-Poisson equation, Two-dimensional electron gas, Interfaces, Surface states, AlN/GaN heterostructures, Band bending, electric quantum limit, surface, semiconductor, field },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 148347

A1 Berland, Kristian

T1 A general solution to the Schrodinger-Poisson equation for a charged hard wall: Application to potential profile of an AlN/GaN barrier structure

YR 2011

JF Superlattices and Microstructures

SN 0749-6036

VO 50

IS 4

SP 411

OP 418

AB A general, system-independent, formulation of the parabolic Schrodinger-Poisson equation is presented for a charged hard wall in the limit of complete screening by the ground state. It is solved numerically using iteration and asymptotic boundary conditions. The solution gives a simple relation between the band bending and sheet charge density at an interface. Approximative analytical expressions for the potential profile and wave function are developed based on properties of the exact solution. Specific tests of the validity of the assumptions leading to the general solution are made. The assumption of complete screening by the ground state is found be a limitation; however, the general solution provides a fair approximate account of the potential profile when the bulk is doped. The general solution is further used in a simple model for the potential profile of an AlN/GaN barrier structure. The result compares well with the solution of the full Schrodinger-Poisson equation.

LA eng

DO 10.1016/j.spmi.2011.08.003

LK http://dx.doi.org/10.1016/j.spmi.2011.08.003

OL 30