Theory of electric force microscopy in the parametric amplification regime

We propose to use a parametric amplification regime for small charge or potential difference detection in electric force microscopy. First we give a simple method to accurately estimate the instability domains of the oscillating system. Then we establish general and fully analytical expressions of the parametric amplification gain, and discuss the optimal parameter values which must be used for voltage or charge detection. We show that even in conventional Kelvin probe force microscopy the parametric effect should be taken into account.