Affiliation:
1. Department of Physics , Faculty of Sciences and Mathematics , Kosovska Mitrovica , Serbia
2. Department of Informatics , Academy of Criminalistic and Police Studies , Belgrade , Serbia
Abstract
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.
Subject
Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics
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