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Jiao, Yong-Chang; Dang, Chuangyin; Hao, Yue

The solution of the one-dimensional nonlinear Poisson’s equations by the decomposition method. (English) Zbl 1051.65079

Comput. Math. Appl. 46, No. 10-11, 1645-1656 (2003).
Summary: The decomposition method is a nonnumerical method for solving strongly nonlinear differential equations. In this paper, the method is adapted for the solution of the one-dimensional nonlinear Poisson’s equations governing the linearly graded \(p - n\) junctions in semiconductor devices, and the error analysis for the approximate analytic solutions obtained by the decomposition method is carried out. The simulation results show that the solutions obtained by the method are accurate and reliable, and that the quantitative analysis of the linearly graded \(p - n\) junctions can be conducted. This work indicates that the decomposition method has some advantages, which opens up a new way for the numerical analysis of semiconductor devices.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
82D37 Statistical mechanics of semiconductors
65L70 Error bounds for numerical methods for ordinary differential equations

Keywords:

Decomposition method; One-dimensional nonlinear Poisson’s equation; Approximate analytic solutions; Linearly graded \(p-n\) junctions; numerical examples; semiconductor devices; error analysis
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References:

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