计算了四层复合结构的薄膜体声波谐振器(FBAR)的输入阻抗谱,各层采用的材料分别是Al/AlN/Al/Si其尺寸为0.8μm/1.9μm/0.8μm/100μm,得出其有效机电耦合系数k²_eff随谐振模式的分布情况，从而得到最大k²_eff的独特谐振模式在1～2GHz为第40阶谐振模式。从理论上探讨了各层的尺寸及材料属性对该独特谐振模式及其频移的影响,以及串联谐振品质因数FOM等滤波器设计的主要性能参数在该模式下的分布情况。实验结果表明,工作在独特谐振模式下的FBAR的性能依赖于各层材料尺寸,当压电层厚度从0.2μm 变到4.3μm 时,特殊谐振模式频率从1.2GHz增加到4.8GHz;当基底厚度变厚时,有效机电耦合系数从3.2%变到0.8%，串联品质因数从2000变到700;而电极变厚后,有效机电耦合系数趋于一个稳定值.这些数据在实际设计过程中对滤波器的微调具有参考意义。

The spectra of input electric impedance for a four-layer (electrode/piezoelectric film/electrode/substrate) thin Film Bulk Acoustic Resonator (FBAR) with the materials of Al/AlN/Al/Si and the thickness of each layer of 0.8 μm/1.9 μm/0.8 μm/100 μm is researched by a transfer matrix method. The distribution of the effective coupling factor (k²_eff) versus the mode order is derived,and a unique mode with maximum k²_eff is obtained in the 40th mode from 1 GHz to 2 GHz in simulation. The effects of various electrodes and the substrates on the distribution of unique mode and the frequency shift are studied,and the quality factor at series resonant frequency and the Figure of Merit (FOM) which are the main parameters to indicate the features of the crystal resonator in a filter design are investigated.Experimental results show that the performance of the FBAR working in the unique mode relies greatly on the sizes and the materials of layers. The unique mode shifts in a higher frequency are from 1.2 GHz to 4.8 GHz when the film thicknesses come from 0.2 μm to 4.3 μm in simulation; the k²_eff and Q_s are from 3.2% to 0.8% and from 2 000 to 700 in simulation,respectively when the substrate becomes thicker and the k²_eff of the unique mode declines and tends to a stable value when the electrode becomes thicker.These conclusion gives some guidelines for the design of a proper FBAR.