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<p>This study presents a comprehensive analytical–numerical investigation of acoustic wave dispersion, attenuation, and energy dissipation in piezoelectric–semiconductor heterostructures composed of Si–PZT–Si and Ge–PZT–Ge layers. The governing electromechanical–diffusive equations for the coupled media are formulated with full continuity conditions, leading to a cubic characteristic equation solved using a hybrid irreducible Cardano method and functional iteration scheme. A detailed convergence analysis demonstrates stable, monotonic residual decay for both symmetric and asymmetric modes, confirming the robustness of the adopted solver. Numerical results reveal strong sensitivity of phase velocity, attenuation, and specific loss to wave number, semiconductor mobility, convergence and carrier concentration. Ge–PZT–Ge consistently exhibits higher phase velocity, reduced attenuation, and lower dissipative losses than Si–PZT–Si, primarily due to the higher carrier mobility and weaker acoustoelectric drag in Ge. Additional parametric plots highlight the influence of semiconductor quality and PZT layer thickness on acoustic energy confinement. The findings provide actionable design guidelines for optimizing SAW-based filters, delay lines, sensors, and signal-processing devices, where low loss, high velocity, and efficient energy trapping are critical.</p>

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Mathematical modelling and mechanics of acoustic waves in piezoelectric layers between n-type semiconductor plates: an irreducible Cardano method coupled with a functional iteration scheme

  • 期刊论文

  • 发表日期：

    2026年2月19日

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  • Seema,
  • G. V. Radhakrishnan,
  • Abdulkafi Mohammed Saeed,
  • Dyuti Banerjee,
  • Sheela Hundekari,
  • Anjali Chaudhary

摘要

This study presents a comprehensive analytical–numerical investigation of acoustic wave dispersion, attenuation, and energy dissipation in piezoelectric–semiconductor heterostructures composed of Si–PZT–Si and Ge–PZT–Ge layers. The governing electromechanical–diffusive equations for the coupled media are formulated with full continuity conditions, leading to a cubic characteristic equation solved using a hybrid irreducible Cardano method and functional iteration scheme. A detailed convergence analysis demonstrates stable, monotonic residual decay for both symmetric and asymmetric modes, confirming the robustness of the adopted solver. Numerical results reveal strong sensitivity of phase velocity, attenuation, and specific loss to wave number, semiconductor mobility, convergence and carrier concentration. Ge–PZT–Ge consistently exhibits higher phase velocity, reduced attenuation, and lower dissipative losses than Si–PZT–Si, primarily due to the higher carrier mobility and weaker acoustoelectric drag in Ge. Additional parametric plots highlight the influence of semiconductor quality and PZT layer thickness on acoustic energy confinement. The findings provide actionable design guidelines for optimizing SAW-based filters, delay lines, sensors, and signal-processing devices, where low loss, high velocity, and efficient energy trapping are critical.