Scholarlink

<p>Analysis of coupled Poisson–Schrödinger equations is of substantial research interest in nano-scale semiconductor device modeling as it effectively captures the interdependence of quantum mechanical effects of charge carriers and electrostatic potential. In this article, we present an iterative mixed numerical scheme with a unified approach of finite difference—finite element method on layer-adapted meshes to comply with the singularly perturbed nature of Schrödinger equation. The latter being a singularly perturbed reaction-diffusion equation with non-homogeneous Neumann boundary conditions, the coupled equation is subjected to an extensive numerical analysis employing the proposed iteratively coupled scheme using the singular perturbation approach. The framing of a novel scheme that befits the singularly perturbed nature of the Schrödinger equation and executing an unprecedented singular perturbation analysis of an iterative scheme that decouples a singularly perturbed reaction diffusion equation with an ordinary differential equation demonstrates the novelty of the study. The errors associated with the proposed scheme are estimated and validated by comparing the results of computational works on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(MoS_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mi>o</mi> <msub> <mi>S</mi> <mn>2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> transistors of channel length of 20 nm. Also, the mixed numerical scheme is illustrated for two-dimensional coupled Poisson-Schrödinger equations subject to appropriate boundary conditions, and the computational results are presented.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Iterative mixed numerical scheme for one-dimensional coupled Poisson–Schrödinger equations in nano-scale semiconductor device modeling

  • 期刊论文

  • 发表日期：

    2026年4月2日

查看全文
  • S. Anila,
  • A. Ramesh Babu

摘要

Analysis of coupled Poisson–Schrödinger equations is of substantial research interest in nano-scale semiconductor device modeling as it effectively captures the interdependence of quantum mechanical effects of charge carriers and electrostatic potential. In this article, we present an iterative mixed numerical scheme with a unified approach of finite difference—finite element method on layer-adapted meshes to comply with the singularly perturbed nature of Schrödinger equation. The latter being a singularly perturbed reaction-diffusion equation with non-homogeneous Neumann boundary conditions, the coupled equation is subjected to an extensive numerical analysis employing the proposed iteratively coupled scheme using the singular perturbation approach. The framing of a novel scheme that befits the singularly perturbed nature of the Schrödinger equation and executing an unprecedented singular perturbation analysis of an iterative scheme that decouples a singularly perturbed reaction diffusion equation with an ordinary differential equation demonstrates the novelty of the study. The errors associated with the proposed scheme are estimated and validated by comparing the results of computational works on \(MoS_{2}\) M o S 2 transistors of channel length of 20 nm. Also, the mixed numerical scheme is illustrated for two-dimensional coupled Poisson-Schrödinger equations subject to appropriate boundary conditions, and the computational results are presented.