Recently, some researchers have studied the frequency characteristics of a quartz crystal resonator (QCR) covered with micropillars to measure the physical and geometric parameters of the micropillars. A recent study showed that the QCR-pillars device can greatly enhance the sensitivity when compared with conventional QCR sensors. In this research, we calculate the frequency and bandwidth shift of a QCR covered with micropillars based on the transmission line model with conductance analysis and small-load approximation, respectively. Numerical results showed that the frequency and bandwidth shift of QCR changed significantly when the height of the pillar approaches the critical height, which implies the coupled resonance. Two results fit very well except for the neighborhood of resonance point where the small-load approximation does not hold. The small-load approximation is quite simple and efficient as long as the frequency shift is small. The conductance analysis is relatively complicated but can deal with any case. The outcomes of this research are helpful for micro/nanowires characterization and further improvement of QCR-pillars devices for various applications such as biochemical sensors.

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