NCAFM2023 Programme Booklet

Tuesday 0920 - 0940

QUANTITATIVE CAPACITANCE AND CARRIER DENSITY MEASUREMENTS ON SEMICONDUCTOR BY ELECTROSTATIC FORCE MICROSCOPY

Ryota Fukuzawa 1,2 and Takuji Takahashi 2,3

1 Dept. of Electrical Engineering and Information Systems, The University of Tokyo, 113-8656 Japan, 2 Institute of Industrial Science/ 3Institute for Nano Quantum Information Electronics,

The University of Tokyo, 153-8505 Japan Email: fukuzawa@ntech.t.u-tokyo.ac.jp

An electrostatic force between a tip and a semiconductor is strongly related with electrical properties, such as surface potential, capacitance, and charge density, of a semiconductor, and frequency modulation electrostatic force microscopy (FM-EFM) with direct current (DC) and/or alternating current (AC) bias application enables local characterization of the semiconductor through the electrostatic force detection between a tip-apex and a sample. Although a frequency shift of the cantilever resonance induced by the electrostatic force is measured in a typical FM-EFM, quantitative estimation of the tip-sample capacitance from the measured frequency shift is difficult when the capacitance includes a surface depletion capacitance of the semiconductor because a straightforward formulation considering the dependence of the surface depletion on the external bias voltages is not well established. On the other hand, S. Hudlet et al. indicated that the electrostatic force F^ele between the tip and the semiconductor sample could be expressed to be proportional to square of charge using virtual work method [1]. Based on it, in this study, we have formulated the frequency shift induced by the electrostatic force under linear approximation of the charge response with the changes in tip-sample distance and voltage, and we also have performed quantitative capacitance-voltage (C-V) measurements on p- and n-type Si substrates by FM-EFM. For variable AC frequency measurements in FM-EFM, we applied dual AC voltages and DC voltage V dc +V 1 sin ω t+V 2 sin( ω + ω d )t between the tip and the sample, and the capacitance was calculated from the ω d ( << ω ) component of the frequency shift ------- using Eq. (1) brought from our formulation [2], where ω 0 /2π and k are a resonant frequency (~300 kHz) and a spring constant (~ 40 N) of the cantilever in free oscillation, and ϵ 0 and S are the dielectric constant of vacuum and equivalent area of the tip-sample capacitor, respectively. The value of S was evaluated from F ele -z characteristic at the voltage condition for accumulation, where the surface depletion capacitance could be neglected, and it is considered that the tip-sample capacitance is dominated by the series capacitance of the air gap and oxide film capacitances. Figure 1 shows C-V characteristic on the p-type Si substrate evaluated by applying Eq. (1) to the ------- values measured at 1 MHz and around 300 kHz. We found that the capacitance gradually decreased in the direction toward negative DC bias voltage where the surface was more depleted, and values of capacitance around atto-farad are considered reasonable for the tip-sample capacitance. Furthermore, we evaluated the charrier density from maximum depletion layer width which was estimated from the C-V characteristic obtained by FM-EFM. The evaluated carrier density was 2.0×10 17 cm -3 , which agrees well with a value of 2.4×10 17 cm -3 obtained by conventional hall effect measurements. Similar consistency was also obtained on the n-type substrate. These results support the validity of our quantitative analytical method.

Fig. 1 Capacitance-voltage characteristics on a p-Si substrate using Eq (1) under AC voltage modulation at 1 MHz .

References [1] S. Hudlet, et al., J. Appl. Phys., 77 , 3308 (1995). [2] R. Fukuzawa et al., Jpn. J. Appl. Phys., 61 SL1005 (2022).

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