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Approximate Solution of Coupled Schrödinger and Poisson Equation in Inversion Layer Problem: An Approach Based on Homotopy Perturbations

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2019
Authors
Kevkić, Tijana
Stojanović, Vladica
Article (Published version)
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Abstract
In this paper, the homotopy perturbation method (HPM) is applied to the coupled set of Schrödinger-Poisson (SP) equations in inversion layer problem for obtaining the approximate analytical solution. Inversion layer of n-type is considered, and the electric quantum limit is assumed. By introducing some dimensionless quantities, the SP system has been turned into one which can be solved along the infinite interval. After some appropriate transformations, the infinite interval has been reduced to finite one (0,1)$(0,1)$, and recurrence series of the HPM approximate solutions of the coupled SP system have been obtained. The existence and convergence of obtained HPM approximate solutions have been formally proved. Moreover, these solutions show relative simple mathematical form, as well as high degree of accuracy what is desirable for semiconductor device modelling.
Keywords:
Approximation / Coupled SP Equations / Homotopy Perturbations / Inversion Layer
Source:
Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences, 2019

DOI: 10.1515/zna-2018-0495

ISSN: 0932-0784

WoS: 000471601100001

Scopus: 2-s2.0-85061697354
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URI
http://jakov.kpu.edu.rs/handle/123456789/869
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