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Abstract <p>This study presents an integrated sensitivity analysis framework combining classical mathematical methods with modern machine learning techniques to investigate Rayleigh wave propagation in rotating semiconductor solids. We examine six critical thermo-physical parameters rotational velocity (Ω) photogenerated carrier lifetime (τ), three-phase-lag times <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\left( {{{\tau }_{q}},~{{\tau }_{{v}}},~{{\tau }_{T}}} \right)\)</EquationSource> <!--MechSol2560550Khan-m1--> </InlineEquation>, and fractional order parameter (α) through a three-tiered analytical approach. Local sensitivity analysis (LSA) provides efficient parameter screening (1.7 s computation time), while global sensitivity analysis (GSA) using Sobol’s method delivers comprehensive interaction analysis at higher computational cost (111 min for 5000 samples). To bridge this efficiency gap, we develop a physics-informed neural network surrogate model achieving exceptional accuracy <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(({{R}^{2}} &gt; 0.99)\)</EquationSource> <!--MechSol2560550Khan-m2--> </InlineEquation> while enabling real-time predictions (0.01 s/sample). Our results demonstrate that rotational effects dominate phase velocity variance (79% contribution), while three-phase lag parameters exhibit strong nonlinear coupling in wave attenuation characteristics. The hybrid methodology establishes a practical workflow from initial LSA screening through detailed GSA validation to DL-enabled large-scale parametric studies, offering significant improvements in computational efficiency (four orders of magnitude faster than pure GSA) without sacrificing analytical rigor. These advances provide both fundamental insights into thermoelastic wave phenomena and practical tools for semiconductor device characterization and nondestructive evaluation applications.</p>

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Hybrid Sensitivity Analysis of Thermoelastic Rayleigh Waves in Semiconductors: Integrating Sobol’s Indices with Deep Learning Surrogates

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • Maaz Ali Khan,
  • Emad E. Mahmoud,
  • Adnan Jahangir,
  • Usman Riaz,
  • Raheem Gul

摘要

Abstract

This study presents an integrated sensitivity analysis framework combining classical mathematical methods with modern machine learning techniques to investigate Rayleigh wave propagation in rotating semiconductor solids. We examine six critical thermo-physical parameters rotational velocity (Ω) photogenerated carrier lifetime (τ), three-phase-lag times \(\left( {{{\tau }_{q}},~{{\tau }_{{v}}},~{{\tau }_{T}}} \right)\) , and fractional order parameter (α) through a three-tiered analytical approach. Local sensitivity analysis (LSA) provides efficient parameter screening (1.7 s computation time), while global sensitivity analysis (GSA) using Sobol’s method delivers comprehensive interaction analysis at higher computational cost (111 min for 5000 samples). To bridge this efficiency gap, we develop a physics-informed neural network surrogate model achieving exceptional accuracy \(({{R}^{2}} > 0.99)\) while enabling real-time predictions (0.01 s/sample). Our results demonstrate that rotational effects dominate phase velocity variance (79% contribution), while three-phase lag parameters exhibit strong nonlinear coupling in wave attenuation characteristics. The hybrid methodology establishes a practical workflow from initial LSA screening through detailed GSA validation to DL-enabled large-scale parametric studies, offering significant improvements in computational efficiency (four orders of magnitude faster than pure GSA) without sacrificing analytical rigor. These advances provide both fundamental insights into thermoelastic wave phenomena and practical tools for semiconductor device characterization and nondestructive evaluation applications.