<p>Understanding coupled thermo-photo-mechanical interactions in semiconductors remains a central challenge in modern micro- and nanotechnology, particularly when multiple physical processes operating on vastly different time scales must be reconciled within a single predictive framework. This work introduces, for the first time, a unified theoretical framework that integrates fractional-order Moore–Gibson–Thompson (MGT) heat conduction with Klein–Gordon-type (KG-type) spatiotemporal nonlocality to model photo-thermoelastic diffusion in rotating semiconductor cylinders. A key physical motivation that merits explicit emphasis concerns the apparent disparity between ultrafast photothermal excitation (picosecond to nanosecond scale) and slow moisture diffusion (millisecond to hour scale). The coupling is not based on instantaneous simultaneous dynamics; rather, it captures two essential sequential mechanisms: (i) repetitive or sustained photothermal loading cumulatively alters the local temperature field, which, in turn, modulates moisture diffusivity and solubility through Arrhenius-type dependencies—a history-dependent process naturally described by the fractional Caputo derivative; and (ii) the slowly evolving moisture concentration modifies the semiconductor’s thermal conductivity, elastic constants, and band structure, thereby continuously reshaping the thermoelastic and carrier recombination responses to subsequent optical pulses. The fractional-order and nonlocal operators bridge these disparate time scales without artificial scale separation. Unlike existing formulations, the proposed model simultaneously captures memory-dependent thermal transport through the Caputo fractional derivative, finite-speed heat propagation via the MGT paradigm, size-dependent behavior through KG nonlocal differential operators, carrier plasma dynamics, and moisture diffusion under rotational effects—all within a fully coupled system. The governing equations are solved semi-analytically using the Laplace transform combined with numerical inversion. Key findings reveal that fractional order, nonlocal parameters, and angular velocity exert pronounced and physically distinct influences on the thermomechanical and electronic responses, demonstrating that classical local models significantly underestimate field intensities near boundaries. These results have direct implications for the design and reliability assessment of rotating semiconductor components—such as turbomachinery sensors, centrifugal micro-sensors, rotating resonators, and optoelectronic devices—that operate under photothermal loading. In these applications, non-Fourier heat conduction, small-scale effects, and exposure to environmental moisture must be accurately predicted to prevent premature failure.</p>

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Photo-thermoelastic behavior of a rotating diffusive semiconductor material under the Klein–Gordon nonlocality based on a fractional MGT heat conduction model

  • Anouar Saidi,
  • Ahmed E. Abouelregal

摘要

Understanding coupled thermo-photo-mechanical interactions in semiconductors remains a central challenge in modern micro- and nanotechnology, particularly when multiple physical processes operating on vastly different time scales must be reconciled within a single predictive framework. This work introduces, for the first time, a unified theoretical framework that integrates fractional-order Moore–Gibson–Thompson (MGT) heat conduction with Klein–Gordon-type (KG-type) spatiotemporal nonlocality to model photo-thermoelastic diffusion in rotating semiconductor cylinders. A key physical motivation that merits explicit emphasis concerns the apparent disparity between ultrafast photothermal excitation (picosecond to nanosecond scale) and slow moisture diffusion (millisecond to hour scale). The coupling is not based on instantaneous simultaneous dynamics; rather, it captures two essential sequential mechanisms: (i) repetitive or sustained photothermal loading cumulatively alters the local temperature field, which, in turn, modulates moisture diffusivity and solubility through Arrhenius-type dependencies—a history-dependent process naturally described by the fractional Caputo derivative; and (ii) the slowly evolving moisture concentration modifies the semiconductor’s thermal conductivity, elastic constants, and band structure, thereby continuously reshaping the thermoelastic and carrier recombination responses to subsequent optical pulses. The fractional-order and nonlocal operators bridge these disparate time scales without artificial scale separation. Unlike existing formulations, the proposed model simultaneously captures memory-dependent thermal transport through the Caputo fractional derivative, finite-speed heat propagation via the MGT paradigm, size-dependent behavior through KG nonlocal differential operators, carrier plasma dynamics, and moisture diffusion under rotational effects—all within a fully coupled system. The governing equations are solved semi-analytically using the Laplace transform combined with numerical inversion. Key findings reveal that fractional order, nonlocal parameters, and angular velocity exert pronounced and physically distinct influences on the thermomechanical and electronic responses, demonstrating that classical local models significantly underestimate field intensities near boundaries. These results have direct implications for the design and reliability assessment of rotating semiconductor components—such as turbomachinery sensors, centrifugal micro-sensors, rotating resonators, and optoelectronic devices—that operate under photothermal loading. In these applications, non-Fourier heat conduction, small-scale effects, and exposure to environmental moisture must be accurately predicted to prevent premature failure.