A Modified ZnO Film Model for Calculating Elastic and Piezoelectric Properties

Abstract

Abstmct-A modified ZnO film model to calculate the elastic and pi- ezoelectric constants and the SAW velocities of ZnO film (c-axis ori- ented) substrate layer structure is proposed. The influences of the ran- dom orientation and lattice distortion have been taken into account. Compared to the traditional single crystal model, the theoretical results of the modified model fit better with the experimental values of a laser- probe measuring system. minor effect on the SAW properties of the ZnO substrate layer structure when it is not larger than 3 O. In the present case the mean is less than l"; therefore, for simplicity it is assumed to be zero, and only the effect of U (o is equal to 3" from the X-ray diffraction pattern) is taken into ac- count. In our model, the ZnO film is treated as a collec- tion of many monocrystal columns. The orientation 7 of the c-axis of each crystal column has the value within ( -T/ 2, 7r/2) on both the y-z and x-z planes. The material pa- rameters of the monocrystal column with the c-axis ori- entation of 17 can be calculated by assuming that 17 follows the normal distribution Since all the monocrystal columns with c-axis orientations contribute to the material parameters, their mathematical expectation can be taken as the material parameters of ZnO film. The average can be obtained by integrating with respect to 7 twice, first in the x-z plane and then in the y- z plane. Since 7 is a two-dimensional variable, the first integration process in the x-y plane can be stated as fol- lows :