Zhu Jueyong, Negahban Mehrdad, Xu Jie, Xia Rongyu, Li Zheng
Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China.
Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588, USA.
Micromachines (Basel). 2023 Nov 29;14(12):2174. doi: 10.3390/mi14122174.
Piezoelectric semiconductors, being materials with both piezoelectric and semiconducting properties, are of particular interest for use in multi-functional devices and naturally result in multi-physics analysis. This study provides analytical solutions for thick piezoelectric semiconductor plates with periodic boundary conditions and includes an investigation of electromechanical coupling effects. Using the linearization of the drift-diffusion equations for both electrons and holes for small carrier concentration perturbations, the governing equations are solved by the extended Stroh formalism, which is a method for solving the eigenvalues and eigenvectors of a problem. The solution, obtained in the form of a series expansion with an unknown coefficient, is solved by matching Fourier series expansions of the boundary conditions. The distributions of electromechanical fields and the concentrations of electrons and holes under four-point bending and three-point bending loads are calculated theoretically. The effects of changing the period length and steady-state carrier concentrations are covered in the discussion, which also reflects the extent of coupling in multi-physics interactions. The results provide a theoretical method for understanding and designing with piezoelectric semiconductor materials.
压电半导体作为兼具压电和半导体特性的材料，在多功能器件中具有特殊的应用价值，自然也会引发多物理场分析。本研究为具有周期性边界条件的厚压电半导体板提供了解析解，并对机电耦合效应进行了研究。通过对电子和空穴的漂移扩散方程在小载流子浓度扰动下进行线性化，利用扩展的斯托罗方法求解控制方程，该方法是一种求解问题特征值和特征向量的方法。以具有未知系数的级数展开形式得到的解，通过匹配边界条件的傅里叶级数展开来求解。理论上计算了四点弯曲和三点弯曲载荷下机电场的分布以及电子和空穴的浓度。讨论中涵盖了改变周期长度和稳态载流子浓度的影响，这也反映了多物理场相互作用中的耦合程度。研究结果为理解和设计压电半导体材料提供了一种理论方法。
