Comparison of force sensors for atomic force microscopy based on quartz tuning forks and length-extensional resonators

The force sensor is key to the performance of atomic force microscopy (AFM). Nowadays, most atomic force microscopes use micromachined force sensors made from silicon, but piezoelectric quartz sensors are being applied at an increasing rate, mainly in vacuum. These self-sensing force sensors allow a relatively easy upgrade of a scanning tunneling microscope to a combined scanning tunneling/atomic force microscope. Two fundamentally different types of quartz sensors have achieved atomic resolution: the "needle sensor," which is based on a length-extensional resonator, and the "qPlus sensor," which is based on a tuning fork. Here, we calculate and measure the noise characteristics of these sensors. We find four noise sources: deflection detector noise, thermal noise, oscillator noise, and thermal drift noise. We calculate the effect of these noise sources as a factor of sensor stiffness, bandwidth, and oscillation amplitude. We find that for self-sensing quartz sensors, the deflection detector noise is independent of sensor stiffness, while the remaining three noise sources increase strongly with sensor stiffness. Deflection detector noise increases with bandwidth to the power of 1.5, while thermal noise and oscillator noise are proportional to the square root of the bandwidth. Thermal drift noise, however, is inversely proportional to bandwidth. The first three noise sources are inversely proportional to amplitude while thermal drift noise is independent of the amplitude. Thus, we show that the earlier finding that quoted an optimal signal-to-noise ratio for oscillation amplitudes similar to the range of the forces is still correct when considering all four frequency noise contributions. Finally, we suggest how the signal-to-noise ratio of the sensors can be improved further, we briefly discuss the challenges of mounting tips, and we compare the noise performance of self-sensing quartz sensors and optically detected Si cantilevers.