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

Abstract

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.

Imaging the Quantum Capacitance of Strained MoS2 Monolayers by Electrostatic Force Microscopy

“…Therefore, at sufficiently high probing frequency, the only contribution to c S is given by the quantum capacitance c Q . This approach has been previously used by Izumi et al 42 to measure the interface state capacitance (thus the interface state density) in a pn-patterned Si. By extracting c S from the df(V DC ) spectroscopy, in the two frequency limits f RF < < f c and f RF > > f c , and subtracting one from the other, the authors were able to decouple the bulk depletion contribution c D from the interface contribution c int to the total sample capacitance.…”

“…In the case of 2D materials, c Q and c SRH play the role of c D and c int , 42 respectively, so that, in the low frequency limit, eq 1 reproduces the DC case,…”

“…Middle: c T (black dashed line) and MoS 2 bubble c S (red plot) vs V DC (Main). Equivalent circuital configuration of the EFM experiment on MoS 2 bubble (Inset) (the same equivalent circuit is proposed by ref in HL-KPFM). Bottom: cantilever oscillation amplitude A vs V DC (Main).…”

“…When an AC bias voltage V RF cos (2 π f RF t ) is applied with f RF < f c , the DB will periodically fill and empty. , Conversely, for f RF ≫ f c , the contribution of the defects to c S is frozen out (i.e., c SRH goes to zero). Therefore, at sufficiently high probing frequency, the only contribution to c S is given by the quantum capacitance c Q .…”

“…In the case of 2D materials, c Q and c SRH play the role of c D and c int , respectively, so that, in the low frequency limit, eq reproduces the DC case, V normalT , 0 = c normalS c normalT + c normalS V (with c S = c Q + c SRH ) while in the limits of high frequency, V normalT , ∞ = c normalQ c normalT + c normalQ V . These equations are formally the same as derived by Izumi et al…”