High–low Kelvin probe force spectroscopy for measuring the interface state density

The recently proposed high–low Kelvin probe force microscopy (KPFM) enables evaluation of the effects of semiconductor interface states with high spatial resolution using high and low AC bias frequencies compared with the cutoff frequency of the carrier transfer between the interface and bulk states. Information on the energy spectrum of the interface state density is important for actual semiconductor device evaluation, and there is a need to develop a method for obtaining such physical quantities. Here, we propose high–low Kelvin probe force spectroscopy (high–low KPFS), an electrostatic force spectroscopy method using high- and low-frequency AC bias voltages to measure the interface state density inside semiconductors. We derive an analytical expression for the electrostatic forces between a tip and a semiconductor sample in the accumulation, depletion, and inversion regions, taking into account the charge transfer between the bulk and interface states in semiconductors. We show that the analysis of electrostatic forces in the depletion region at high- and low-frequency AC bias voltages provides information about the interface state density in the semiconductor bandgap. As a preliminary experiment, high-low KPFS measurements were performed on ion-implanted silicon surfaces to confirm the dependence of the electrostatic force on the frequency of the AC bias voltage and obtain the interface state density.