Charge-state dynamics in electrostatic force spectroscopy

We present a numerical model that allows us to study the response of an oscillating probe in electrostatic force spectroscopy to 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 when measuring a temporarily charged quantum dot on a surface. Namely, we analyze the dependence of the frequency shift, the dissipated energy, and their fluctuations on the resonance frequency of the tip and on the electron tunneling rates across the tip-quantum dot and quantum dot-sample junctions. 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.