Charged-state dynamics in Kelvin probe force microscopy

TL;DR

This paper introduces a numerical model to analyze the charge state dynamics in Kelvin probe force microscopy, providing insights into frequency shift and energy dissipation related to quantum dot charge switching across different time scales.

Contribution

The study develops a comprehensive numerical model and analytical formulas to understand charge dynamics in Kelvin probe microscopy, including stochastic and deterministic approaches.

Findings

Frequency shift depends on tip resonance and tunneling rates.

Dissipated energy correlates with charge fluctuation dynamics.

Analytic formulas accurately describe small amplitude charge interactions.

Abstract

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.