Charged-state dynamics in Kelvin probe force microscopy

We present a numerical model which allows us to study the Kelvin force probe microscopy response to the charge switching in quantum dots at various time scales. The model provides more insight into the behavior of frequency shift and dissipated energy under different scanning conditions measuring a temporarily charged quantum dot on surface. Namely, we analyze the dependence of the frequency shift, its fluctuation and of the dissipated energy, on the resonance frequency of tip and electron tunneling rates between tip - quantum dot and quantum dot - sample. We discuss two complementary approaches to simulating the charge dynamics, a stochastic and a deterministic one. In addition, we derive analytic formulas valid for small amplitudes, describing relations between the frequency shift, dissipated energy, and the characteristic rates driving the charging and discharging processes.