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 (

k

2

eff

) versus the mode order is derived

and a unique mode with maximum

k

2

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

k

2

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

k

2

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.