Influence of the Schottky Junction on the Propagation Characteristics of Shear Horizontal Waves in a Piezoelectric Semiconductor Semi-Infinite Medium

Abstract

In this paper, a theoretical model of the propagation of a shear horizontal wave in a piezoelectric semiconductor semi-infinite medium is established using the optimized spectral method. First, the basic equations of the piezoelectric semiconductor semi-infinite medium are derived with the consideration of biased electric fields. Then, considering the propagation of a shear horizontal wave in the piezoelectric semiconductor semi-infinite medium, two equivalent mathematical models are established. In the first mathematical model, the Schottky junction is theoretically treated as an electrically imperfect interface, and an interface characteristic length is utilized to describe the interface effect of the Schottky junction. To legitimately confirm the interface characteristic length, a second mathematical model is established, in which the Schottky junction is theoretically treated as an electrical gradient layer. Finally, the dispersion and attenuation curves of shear horizontal waves are numerically calculated using these two mathematical models to discuss the influence of the Schottky junction on the dispersion and attenuation characteristics of shear horizontal waves. Utilizing the equivalence of these two mathematical models and the above numerical results, the numerical value of the interface characteristic length is reliably legitimately confirmed; this value is independent of the thickness of the upper metal layer, the doping concentration of the lower n-type piezoelectric semiconductor substrate, and biasing electric fields. Only the biasing electric field parallel to the Schottky junction can provide an evident influence on the attenuation characteristics of shear horizontal waves and enhance the interface effect of the Schottky junction. Since the second mathematical model is also a validation of our previous mathematical model established through the state transfer equation method, some numerical results calculated using these two mathematical models are compared with those obtained using the previous method to verify the correctness and superiority of the research work presented in this paper. Since these two mathematical models can better calculate the dispersion and attenuation curves of high-frequency waves in micro- and nano-scale piezoelectric semiconductor materials, the establishment of mathematical models and the revelation of physical mechanisms are fundamental to the analysis and optimization of micro-scale resonators, energy harvesters, and amplifications.

Influence of Homo- and Hetero-Junctions on the Propagation Characteristics of Love Waves in a Piezoelectric Semiconductor Semi-Infinite Medium

“…The influence of homo-and hetero-junctions on the dispersion and attenuation characteristics of Love waves in a PSC semi-infinite medium is the primary concern of the present work. According to the Gurtin-Murdoch theory [23][24][25], a new mathematical model of the interface effect originating from homo-and hetero-junctions is established through the spectral method [28][29][30][31], which includes four interface characteristic lengths to describe the electrical imperfect characteristics of homo-and hetero-junctions. To legitimately confirm these four interface characteristic lengths, another mathematical model is established, which is used to calculate the dispersion and attenuation curves of Love waves that can be compared.…”

“…where k U and ω U are the apparent wave number component and angular frequency of the upper PSC layer, respectively, and k L and ω L are the apparent wave number component and angular frequency of the lower PSC substrate, respectively. Based on the spectral method [28][29][30][31], the Legendre polynomials are used to expand the three undetermined amplitudes U U z , U ϕ , and U U c in the upper PSC layer…”

“…Two biasing electric fields are further considered in the basic equations of the lower n-type PSC substrate, which provides evident influence on the physical properties of the Schottky junction. Then, based on the Gurtin-Murdoch theory [24][25][26] and through the spectral method [28][29][30][31], two equivalent mathematical models are established to investigate the dispersion and attenuation characteristics of Love waves. Finally, based on the above two equivalent mathematical models, the numerical results of the dispersion and attenuation curves of shear horizontal waves are provided in Section 5.…”