Mechanical Analysis and Measurement of Scanning Probe Microscope Performance

Euler beam theory and Lagrangian mechanical analysis have been applied to the beetle-style scanning probe microscope (SPM) system to predict the natural frequencies for two significant vibrational modes. In the first mode, the three piezoelectric legs vibrate transversely and the scan head moves from side to side, and in the second, the legs bend tangentially and the scan head twists about its center. The closed-form solutions presented allow the designer to make quantitative comparisons when choosing the materials and dimensions used in the SPM design. The two modes have comparable natural frequencies in the 1-2 kHz range. The frequencies found experimentally are in good agreement with the predictions although other modes are also present. In addition, we find that different materials used in the leg-ramp system may substantially reduce vibrations.