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Reflection of thermo-elastic wave in semiconductor nanostructures nonlocal porous medium

热弹性波在半导体纳米结构非局部多孔介质中的反射

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Abstract

The current work is an extension of the nonlocal elasticity theory to fractional order thermo-elasticity in semiconducting nanostructure medium with voids. The analysis is made on the reflection phenomena in context of three-phase-lag thermo-elastic model. It is observed that, four-coupled longitudinal waves and an independent shear vertical wave exist in the medium which is dispersive in nature. It is seen that longitudinal waves are damped, and shear wave is un-damped when angular frequency is less than the cut-off frequency. The voids, thermal and non-local parameter affect the dilatational waves whereas shear wave is only depending upon non-local parameter. It is found that reflection coefficients are affected by nonlocal and fractional order parameters. Reflection coefficients are calculated analytically and computed numerically for a material, silicon and discussed graphically in details. The results for local (classical) theory are obtained as a special case. The study may be useful in semiconductor nanostructure, geology and seismology in addition to semiconductor nanostructure devices.

摘要

本文的工作是在含空洞的半导体纳米结构介质中将非局部弹性理论推广到分数阶热弹性理论, 并对三相滞后热弹性模型中的反射现象进行了分析。研究表明, 介质中存在四个耦合的纵向波和一个 独立的纵向剪切波。当角频率小于截止频率时, 纵波衰减, 横波无衰减。膨胀波受空洞、热和非局域 参数的影响, 而横波只受非局部参数的影响。结果表明, 反射系数受非局部参数和分数阶参数的影响。 对硅材料的反射系数进行了解析计算和数值计算, 并用图形进行详细讨论。作为特例, 本研究得到了 局部(经典)理论的结果。本研究除可应用于半导体纳米结构器件外, 还可应用于地质学及地震学。

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Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, 44000, Islamabad, Pakistan

    Ali Hashmat & Khan Aftab

  2. Department of Mathematics, COMSATS University Islamabad, Wah Campus, 47040, Islamabad, Pakistan

    Jahangir Adnan

Authors
  1. Ali Hashmat
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  2. Jahangir Adnan
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  3. Khan Aftab
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Contributions

HASHMAT Ali provided the concept and edited the draft of manuscript. ADNAN Jahangir conducted the literature review and wrote the first draft of the manuscript. AFTAB Khan edited the draft of manuscript.

Corresponding author

Correspondence to Jahangir Adnan.

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Conflict of interest

HASHMAT Ali, ADNAN Jahangir and AFTAB Khan declare that they have no conflict of interest.

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Hashmat, A., Adnan, J. & Aftab, K. Reflection of thermo-elastic wave in semiconductor nanostructures nonlocal porous medium. J. Cent. South Univ. 27, 3188–3201 (2020). https://doi.org/10.1007/s11771-020-4472-1

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  • DOI: https://doi.org/10.1007/s11771-020-4472-1

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