Abstract
Kelvin probe force microscopy (KPFM) has been used for the characterization of metals, insulators, and semiconducting materials on the nanometer scale. Especially in semiconductors, the charge dynamics are of high interest. Recently, several techniques for time-resolved measurements with time resolution down to picoseconds have been developed, many times using a modulated excitation signal, e.g., light modulation or bias modulation that induces changes in the charge carrier distribution. For fast modulation frequencies, the KPFM controller measures an average surface potential, which contains information about the involved charge carrier dynamics. Here, we show that such measurements are prone to artifacts due to frequency mixing, by performing numerical dynamics simulations of the cantilever oscillation in KPFM subjected to a bias-modulated signal. For square bias pulses, the resulting time-dependent electrostatic forces are very complex and result in intricate mixing of frequencies that may, in some cases, have a component at the detection frequency, leading to falsified KPFM measurements. Additionally, we performed fast Fourier transform (FFT) analyses that match the results of the numerical dynamics simulations. Small differences are observed that can be attributed to transients and higher-order Fourier components, as a consequence of the intricate nature of the cantilever driving forces. These results are corroborated by experimental measurements on a model system. In the experimental case, additional artifacts are observed due to constructive or destructive interference of the bias modulation with the cantilever oscillation. Also, in the case of light modulation, we demonstrate artifacts due to unwanted illumination of the photodetector of the beam deflection detection system. Finally, guidelines for avoiding such artifacts are given.
Highlights
Kelvin probe force microscopy (KPFM) [1] has been widely used for the characterization of metals, insulators, and semiconducting materials on the nanometer scale [2]
The cantilever tip dynamics are governed by the equation of motion: served, where the minimum is extracted, which corresponds to (1) the VCPD that will be measured with the applied modulated square voltage pulses
We note that the quality factors used in the presented simulation results are rather small, even smaller than typical values obtained for atomic force microscopy (AFM) operation in ambient air
Summary
Kelvin probe force microscopy (KPFM) [1] has been widely used for the characterization of metals, insulators, and semiconducting materials on the nanometer scale [2]. The imaging mechanism relies on the compensation of electrostatic forces by application of a bias voltage that corresponds to the local contact potential difference (CPD), the relative difference between the work function of the tip and that of the sample area below the tip. (i) Variations in the local surface structure, chemistry, or material can affect the CPD by means of a change in the surface dipole, the electron affinity, or the work function [3,4,5]. (iii) doping type and charge-carrier concentration in semiconductors will control the position of the Fermi level, affecting the work function, which is defined as the energy difference between the local vacuum level and the Fermi level [12]. Especially in semiconductors, and in view of points (ii) and (iii), the charge dynamics are of high interest in materials and device characterization, and knowledge of the nanoscale charge-carrier dynamics can provide valuable insight into device functionality and limitations in device performance
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