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<p>Despite advancements in classical photothermal models for semiconductors, significant gaps persist in capturing memory-dependent dynamics, nonlocal spatio-temporal effects, and fractional-order behaviors under complex loading, resulting in inaccurate predictions of coupled thermoelastic-plasma interactions. This study introduces a novel fractional photothermal model based on the Moore-Gibson-Thompson (MGT) thermoelastic framework, incorporating tempered Caputo fractional derivatives to account for regulated memory effects and the Klein-Gordon operator to capture concurrent spatial and temporal nonlocality, alongside single-phase-lag heat conduction. Key innovations include governing equations derived via fractional calculus for thermoelasticity, heat conduction, and carrier density in an unbounded semiconductor with a spherical cavity under dynamic thermal loads. Analytical solutions are obtained using Laplace transforms with numerical inversion, evaluating interactions across Caputo, Atangana-Baleanu, and tempered Caputo operators. Results show distinct field evolutions: tempered Caputo derivatives promote rapid stabilization, while others enhance long-term memory capture, emphasizing the role of memory and nonlocality in model accuracy. This advanced framework enables precise prediction of complex semiconductor behaviors, facilitating predictive design of photonic sensors, transistors, lasers, and optoelectronic systems where intertwined thermal, mechanical, and electromagnetic phenomena dominate.</p>

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Advanced nonlocal thermal size-dependent MGT photothermal modeling with fractional derivatives for unbounded semiconductor materials

  • 期刊论文

  • 发表日期：

    2026年4月3日

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  • Mohammed Aldandani,
  • Ahmed E. Abouelregal

摘要

Despite advancements in classical photothermal models for semiconductors, significant gaps persist in capturing memory-dependent dynamics, nonlocal spatio-temporal effects, and fractional-order behaviors under complex loading, resulting in inaccurate predictions of coupled thermoelastic-plasma interactions. This study introduces a novel fractional photothermal model based on the Moore-Gibson-Thompson (MGT) thermoelastic framework, incorporating tempered Caputo fractional derivatives to account for regulated memory effects and the Klein-Gordon operator to capture concurrent spatial and temporal nonlocality, alongside single-phase-lag heat conduction. Key innovations include governing equations derived via fractional calculus for thermoelasticity, heat conduction, and carrier density in an unbounded semiconductor with a spherical cavity under dynamic thermal loads. Analytical solutions are obtained using Laplace transforms with numerical inversion, evaluating interactions across Caputo, Atangana-Baleanu, and tempered Caputo operators. Results show distinct field evolutions: tempered Caputo derivatives promote rapid stabilization, while others enhance long-term memory capture, emphasizing the role of memory and nonlocality in model accuracy. This advanced framework enables precise prediction of complex semiconductor behaviors, facilitating predictive design of photonic sensors, transistors, lasers, and optoelectronic systems where intertwined thermal, mechanical, and electromagnetic phenomena dominate.