多層壓電結構表面聲波元件的參數萃取與邊界波之特性分析

Parameters Extraction and Characteristics of the Boundary Wave in the Surface Acoustic Wave Device of Multilayer Piezoelectric Structure

王泰翔(Tai-Xiang Wang)

指導教授 ： 羅如燕

義守大學/電機資訊學院/電機工程學系/碩士(2014年)

https://doi.org/10.6343/ISU.2014.00230

摘要

本論文探討如何使用K-K定理萃取單埠共振器之等效電路參數，其中單埠共振器為AlN/Diamond結構且中心頻率約為4.3GHz，單埠共振器之等效電路是由諧振電路並聯電容再串聯電阻所組成，其中包括Rs、C0、R1、L1以及C1等參數，Rs以及C0為量測時所造成的寄生效應，R1、L1以及C1分為諧振電路上的電阻、電感以及電容的值，K-K定理為介電函數實部和虛部之間的關係式。當導納曲線在無寄生效應時，導納實部以及導納虛部會符合K-K定理。當實際量測Y值扣除適切的Rs以及C0時，導納曲線與K-K定理曲線會符合最小誤差條件。接著再利用諧振電路之輸入導納公式萃取單埠共振器之等效電路參數中的R1、L1以及C1，在最小誤差條件下求解適切的R1、L1以及C1。
在本論文另一重點，探討如何使用有限元素法分析邊界波的傳播模式，其中我們分析的多層壓電結構為AlN/ZnO/Diamond以及Diamond/ZnO/Diamond兩種。藉由改變薄膜厚度來找尋是否有邊界波，並計算等效速度以及機電耦合係數。藉由位移能量圖證明AlN/ZnO/Diamond以及Diamond/ZnO/Diamond兩種結構有邊界波的存在，且求解其傳播模式的最佳機電耦合係數下的最小薄膜厚度。

關鍵字

K-K 定理 ； 單埠共振器 ； 等效電路 ； 邊界波

並列摘要

This study discusses how to use the Kramers-Kronig (K-K) relations to retract the equivalent circuit parameters for a one-port surface acoustic wave (SAW) resonator, which was fabricated upon the AlN/diamond structure with a center frequency around 4.3 GHz. The equivalent circuits for the one-port SAW resonator includes three parameters, R1, L1 and C1, for the series resonant circuit and two parasitic parameters, Rs and C0. The real and imaginary parts of the admittance of the resonant circuit comply with the K-K relations, which imply that the K-K relations in addition to the least-square-error technique can be applied to retract the corresponding parameters from the measuring admittance of the one-port SAW resonator.
The use of the finite element method (FEM) to determine the propagation characteristics of piezoelectric boundary acoustic wave in layered structures such as AlN/ZnO/Diamond and Diamond/ZnO/Diamond is also investigated in this study. The effects of the thicknesses of films on phase velocities and coupling coefficients are demonstrated.

並列關鍵字

Kramers-Kronig relations ； one-port resonator ； Equivalent circuit ； Boundary Acoustic Wave

參考文獻

[22]陳昭昌 (1989)。有限元素法─工程上之應用。台南：復文書局。

[1]Rayleigh, L. (1885). On Waves Propagated along the Plane Surface of an Elastic Solid. Proceedings of the London Mathematical Society, 1(1), 4-11.

[2]White, R. M., & Voltmer, F. W. (1965). Direct piezoelectric coupling to surface elastic waves. Applied Physics Letters, 7(12), 314-316.

[3]Chauvin, D., Coussat, E., & Dieulesaint, E. (1971). Acoustic-surface-wave television filters. Electronics Letters, 7(17), 491-492.

[4]Special issue on surface acoustic wave devices and applications. (1976). Proc. IEEE, 64(5), 557-832.