Operating a phase-locked loop controlling a high-Q tuning fork sensor for scanning force microscopy

摘要

The implementation of a tuning fork sensor in a scanning force microscopeoperational at 300 mK is described and the harmonic oscillator model of thesensor is motivated. These sensors exhibit very high quality factors at lowtemperatures. The nested feedback comprising the sensor, a phase locked loopand a conventional $z$-feedback is analyzed in terms of linear control theoryand the dominant noise source of the system is identified. It is shown that thenested feedback has a low pass response and that the optimum feedbackparameters for the phase-locked loop and the $z$-feedback can be determinedfrom the knowledge of the tuning fork resonance alone regardless of the tipshape. The advantages of this system compared to pure phase control arediscussed.