Numerical analysis of single-point spectroscopy curves used in photo-carrier dynamics measurements by Kelvin probe force microscopy under frequency-modulated excitation

In recent years, the investigation of the complex interplay between the nanostructure and photo-transport mechanisms has become of crucial importance for the development of many emerging photovoltaic technologies. In this context, Kelvin probe force microscopy under frequency-modulated excitation has emerged as a useful technique for probing photo-carrier dynamics and gaining access to carrier lifetime at the nanoscale in a wide range of photovoltaic materials. However, some aspects about the data interpretation of techniques based on this approach are still the subject of debate, for example, the plausible presence of capacitance artifacts. Special attention shall also be given to the mathematical model used in the data-fitting process as it constitutes a determining aspect in the calculation of time constants. Here, we propose and demonstrate an automatic numerical simulation routine that enables to predict the behavior of spectroscopy curves of the average surface photovoltage as a function of a frequency-modulated excitation source in photovoltaic materials, enabling to compare simulations and experimental results. We describe the general aspects of this simulation routine and we compare it against experimental results previously obtained using single-point Kelvin probe force microscopy under frequency-modulated excitation over a silicon nanocrystal solar cell, as well as against results obtained by intensity-modulated scanning Kelvin probe microscopy over a polymer/fullerene bulk heterojunction device. Moreover, we show how this simulation routine can complement experimental results as additional information about the photo-carrier dynamics of the sample can be gained via the numerical analysis.