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.