Investigation of the electrical model parameters of quartz tuning forks from a low-frequency impedance analysis using a lock-in amplifier

Quartz tuning forks (QTFs) have been used as alternative force detection sensors in scanning probe microscopy due to their many favorable properties such as high quality factor, low cost, excellent mechanical stability, and wide availability. A QTF is usually modeled by using the Butterworth-Van Dyke equivalent circuit, and the relevant electrical parameters associated with the Butterworth-Van Dyke equivalent circuit can be calculated by analyzing the complex admittance measured with an impedance analyzer. However, an impedance analyzer is not a commonlyavailable laboratory instrument due to its high cost. It is also employed in radio-frequency (RF) and microwave measurements where the operating frequencies are outside the range of interest. Because the frequency range of interest for QTFs is usually less than 100 kHz, a relatively low-frequency impedance measurement setup involving a basic preamplifier and a lock-in amplifier can effectively replace an impedance analyzer. We present our implementation of such a setup and the measured electrical parameters. In addition, the measurement results obtained by using our low-frequency lock-in amplifier setup and those obtained by using a commercial precision impedance analyzer are compared to validate our approach.