New method for electrostatic force gradient microscopy observations and Kelvin measurements under vacuum.

It is shown that both dc and ac electrostatic force gradients can be observed under secondary vacuum by means of phase shifts under amplitude-controlled AFM and a double-pass method. Different flexure mode orders and electrical frequencies have been explored. A theoretical model based on the linear behaviour of the mechanical oscillator allows one to explain the experimental phase shifts and to deduce the key points governing such experiments and the expected performances. As a result, it is shown that surface voltage or Kelvin imaging becomes possible in parallel with morphology with an rms noise in the millivolt range.