Sherief H, Naim Anwar M, Abd El-Latief A, Fayik M, Tawfik A M
Department of Mathematics and Computer Sciences, Faculty of Sciences, Alexandria University, Alexandria, Egypt.
Department of Basic Sciences, Faculty of Engineering, Pharos University, Alexandria, Egypt.
Sci Rep. 2024 Jun 16;14(1):13876. doi: 10.1038/s41598-024-63554-2.
This study presents a new mathematical framework for analyzing the behavior of semiconductor elastic materials subjected to an external magnetic field. The framework encompasses the interaction between plasma, thermal, and elastic waves. A novel, fully coupled mathematical model that describes the plasma thermoelastic behavior of semiconductor materials is derived. Our new model is applied to obtain the solution to Danilovskaya's problem, which is formed from an isotropic homogeneous semiconductor material. The Laplace transform is utilized to get the solution in the frequency domain using a direct approach. Numerical methods are employed to calculate the inverse Laplace transform, enabling the determination of the solution in the physical domain. Graphical representations are utilized to depict the numerical outcomes of many physical fields, including temperature, stress, displacement, chemical potential, carrier density, and current carrier distributions. These representations are generated for different values of time and depth of the semiconductor material. Ultimately, we receive a comparison between our model and several earlier fundamental models, which is then graphically represented.
本研究提出了一种新的数学框架，用于分析受到外部磁场作用的半导体弹性材料的行为。该框架涵盖了等离子体、热和弹性波之间的相互作用。推导了一个描述半导体材料等离子体热弹性行为的全新全耦合数学模型。我们的新模型被应用于求解由各向同性均匀半导体材料构成的达尼洛娃问题。利用拉普拉斯变换，通过直接方法在频域中得到解。采用数值方法计算拉普拉斯逆变换，从而在物理域中确定解。利用图形表示法来描绘包括温度、应力、位移、化学势、载流子密度和电流载流子分布在内的多个物理场的数值结果。这些表示是针对半导体材料不同的时间值和深度生成的。最终，我们将我们的模型与几个早期的基础模型进行了比较，然后以图形方式呈现出来。
