Spatiotemporal Analysis of Coupled Thermo–Photoelastic Fields in Anisotropic Fiber-Reinforced Silicon Using an Eigenvalue Method

Summary

This study analyzes coupled thermo–photoelastic fields in anisotropic fiber-reinforced silicon using a normal mode and eigenvalue method. Results show spatial decay and time-dependent field evolution, with strong sensitivity to anisotropy. Heatmaps illustrate field distribution and localization.

Abstract

This study investigates a coupled thermo–photoelastic system in an anisotropic fiber-reinforced silicon semiconductor medium, aiming to capture the interaction between thermal, carrier, and mechanical fields. Such anisotropic fiber-reinforced materials play a crucial role in modern engineering applications, including microelectronic and optoelectronic devices, laser-based technologies, sensors, and advanced composite structures, where directional properties and enhanced mechanical performance are required. They are particularly important in the design of semiconductor components subjected to thermal and optical loading, where accurate prediction of coupled field behavior is essential for reliability and performance optimization. The governing equations are formulated based on the coupled physical model and subsequently transformed into a dimensionless form to simplify the analysis and highlight the relative influence of the involved parameters. The problem is solved using a normal mode technique and reduced to a first-order vector-matrix differential system, followed by an eigenvalue approach to obtain analytical solutions satisfying the imposed boundary conditions within a semi-infinite domain. Numerical analysis is carried out to examine the effect of time variation on all physical fields, revealing strong spatial attenuation and coupled behavior governed by anisotropy and fiber reinforcement. Spatiotemporal heatmap representations are used to visualize the evolution and localization of the fields, providing physical insight into the multiphysical interactions and demonstrating the effectiveness of the analytical approach.

Introduction

Thermo–photoelasticity has emerged as an important multidisciplinary field that describes the interaction between thermal, mechanical, and optical effects in semiconductor materials under photothermal excitation. The coupling between these fields becomes particularly notable in modern applications involving laser heating and optical excitation. For instance, Saeed¹ investigated thermo–photoelastic interactions in semiconductors using hyperbolic two-temperature models, demonstrating the importance of thermal relaxation effects in accurately predicting system behavior. The thermomechanical response of fiber-reinforced composites has a....

Protocol

This study is based entirely on theoretical modeling and numerical simulations and does not involve human participants, animal subjects, or biological specimens. Therefore, ethical approval and informed consent were not required.

Mathematical Formulation of Photo-Thermoelasticity in Fiber-Reinforced Anisotropic Media
The present study considered a 2D fiber-reinforced anisotropic semiconductor half-space subjected to surface optical excitation. The medium occupied the region x ≥ 0, where the boundary at x = 0 represents the exposed surface. The coordinate system was defined such that the x-axis....

Results

Numerical Results
In this section, numerical computations were performed to analyze the behavior of the coupled thermo–photoelastic-carrier system in an anisotropic fiber-reinforced semiconductor medium. The material considered was silicon (Si), and its physical and material parameters are listed in Table 1. These material constants were directly substituted into the governing equations and implemented in the numerical computations to evaluate the field variables. All parameters were.......

Discussion

The obtained results provide clear physical insight into the coupled thermo–photoelastic behavior in anisotropic fiber-reinforced semiconductor media. The present study proposes an eigenvalue-based analytical framework for investigating the interaction between thermal loading, carrier generation, and elastic deformation in such media. The observed response is fundamentally governed by the strong coupling between these physical processes. The absorption of optical energy at the boundary leads to localized heating an.......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Computational software (symbolic and numerical analysis)	Wolfram Research	Wolfram Mathematica (Version 12.0) was used	Used for eigenvalue computation, analytical solution implementation, and numerical evaluation
Data visualization tools (contour and heatmap generation)	Wolfram Research	Wolfram Mathematica (Version 12.0) was used for generating 2D contour plots and spatiotemporal heatmaps	Used for generating 2D contour plots and spatiotemporal heatmaps
Material parameter dataset (silicon semiconductor properties)	Various literature sources	N/A	Physical constants (elastic, thermal, carrier-related) used in computations (Table 1)
Personal computer/workstation	HP	N/A	Computations were performed on a standard personal computer running Windows OS with sufficient memory for numerical simulations
Equation editor	Microsoft  Word and MathType	N/A	Used for formatting and presenting mathematical expressions in the manuscript
Reference management software	Elsevier	N/A	Used for managing references and formatting citations (Vancouver style)