Debye–Hückel Screening on Bulk SH Waves at Flexoelectric Semiconductor–flexomagnetic Composite Interfaces

This work develops a rigorous framework for oblique incidence of bulk shear-horizontal (SH) waves at the interface between an n-type flexoelectric-piezoelectric semiconductor halfspace and a flexomagnetic-piezomagnetic halfspace. Conventionally, upon incidence, the SH wave splits into reflected and refracted components in respective media. A key novelty of the work lies in the incorporation of carrier-induced electrostatic screening through the well-known Debye-Hückel mechanism, which governs the redistribution of carriers and attenuates the electric field exponentially over a finite spatial region. Unlike conventional models, the electrical boundary conditions are reformulated as Robin-type mixed boundary conditions, explicitly incorporating the Debye screening length to ensure a physically consistent representation of interfacial electrostatics. An analytical formulation is developed to obtain closed-form expressions for scattered wave amplitudes and energy fractions. Numerical results reveal that Debye screening acts as an effective control parameter for wave manipulation. Larger screening lengths enhance energy transmission into the flexomagnetic medium, whereas smaller screening lengths suppress electric fields and promote reflection-dominated behavior, approaching total reflection under strong doping conditions. Additionally, flexoelectric and flexomagnetic effects increase impedance mismatch, further reducing transmission. Pronounced dependence of amplitudes on incidence conditions is observed, with grazing incidence leading to near-total reflection. The model is shown to recover classical results in the limiting cases of negligible screening and vanishing flexoelectric-flexomagnetic couplings, thereby validating the formulation. These findings highlight doping-induced Debye screening as a viable mechanism for tuning wave propagation characteristics, offering potential applications in semiconductor-based sensors and bulk acoustic wave (BAW) devices requiring precise control of signal transmission and reflection.