Approximate Solution of Coupled Schrödinger and Poisson Equation in Inversion Layer Problem: An Approach Based on Homotopy Perturbations
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 LayerSource:
Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences, 2019, 74, 6, 457-467Publisher:
- Tübingen : Verlag der Zeitschrift für Naturforschung
DOI: 10.1515/zna-2018-0495
ISSN: 0932-0784
WoS: 000471601100001
Scopus: 2-s2.0-85061697354
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Institution/Community
JakovTY - JOUR AU - Kevkić, Tijana AU - Stojanović, Vladica PY - 2019 UR - http://jakov.kpu.edu.rs/handle/123456789/869 AB - 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. PB - Tübingen : Verlag der Zeitschrift für Naturforschung T2 - Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences T1 - Approximate Solution of Coupled Schrödinger and Poisson Equation in Inversion Layer Problem: An Approach Based on Homotopy Perturbations VL - 74 IS - 6 SP - 457 EP - 467 DO - 10.1515/zna-2018-0495 ER -
@article{ author = "Kevkić, Tijana and Stojanović, Vladica", year = "2019", 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.", publisher = "Tübingen : Verlag der Zeitschrift für Naturforschung", journal = "Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences", title = "Approximate Solution of Coupled Schrödinger and Poisson Equation in Inversion Layer Problem: An Approach Based on Homotopy Perturbations", volume = "74", number = "6", pages = "457-467", doi = "10.1515/zna-2018-0495" }
Kevkić, T.,& Stojanović, V.. (2019). Approximate Solution of Coupled Schrödinger and Poisson Equation in Inversion Layer Problem: An Approach Based on Homotopy Perturbations. in Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences Tübingen : Verlag der Zeitschrift für Naturforschung., 74(6), 457-467. https://doi.org/10.1515/zna-2018-0495
Kevkić T, Stojanović V. Approximate Solution of Coupled Schrödinger and Poisson Equation in Inversion Layer Problem: An Approach Based on Homotopy Perturbations. in Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences. 2019;74(6):457-467. doi:10.1515/zna-2018-0495 .
Kevkić, Tijana, Stojanović, Vladica, "Approximate Solution of Coupled Schrödinger and Poisson Equation in Inversion Layer Problem: An Approach Based on Homotopy Perturbations" in Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences, 74, no. 6 (2019):457-467, https://doi.org/10.1515/zna-2018-0495 . .