Tuning of direct current bias-induced resonances in micromachined Ba0.3Sr0.7TiO3 thin-film capacitors

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Direct current (dc) bias-induced acoustic resonance phenomena have been observed in micromachined tunable thin-film capacitors based on paraelectric Ba0.3Sr0.7TiO3 thin films. Both resonance and antiresonance frequencies are dc bias dependent. The antiresonance frequency is only weakly dc bias dependent and shifts slightly down with increasing dc bias. The resonance frequency shows a much stronger dependence on the applied dc bias than the antiresonance frequency, and also shifts down to lower frequencies with increasing bias. The resonance frequency shifted by 2.0% for a frequency of about 3 GHz and an applied field of 730 KV/cm. At the same time the effective electromechanical coupling constant kt,eff2 increased up to 3.6%. The tuning of the resonance frequency depends on the tunability of the film permittivity and on the mechanical load on the piezoactive layer. The constitutive equations controlling the tuning of the resonance and antiresonance frequency were derived from the Landau theory using the P-expansion of its free energies. The theoretical predictions show that, in the considered system, the frequency of the first-order resonance (λ/2 resonance) will always shift down with increasing bias, whereas the antiresonance frequency might shift up or down with increasing bias. The sense of the shift of the antiresonance frequency depends on the sign and the magnitude of the corresponding coefficients of the tensors of linear and nonlinear electrostriction. The theoretical predictions corroborate the experimental observations very well.