Quantitative capacitance measurements in frequency modulation electrostatic force microscopy

Abstract

We have proposed a method for quantitative capacitance measurements using frequency modulation electrostatic force microscopy (EFM) with a dual bias modulation method and demonstrated it on n- and p-type Si samples. First, we theoretically derived a conversion formula from a frequency shift of cantilever resonance in EFM into a capacitance value based on the parallel plate capacitor model, by which a pair of an EFM tip and a semiconductor sample is expected to be equivalently represented. Then the capacitance measurements were experimentally conducted on the n- and p-type Si substrates, and the acquired capacitance–voltage curves indicated that the obtained capacitance values were consistent with the expected ones and that the carrier densities evaluated from the depletion capacitances were also in good agreement with those evaluated by the conventional Hall effect measurements. From those results, the validity of our quantitative evaluation method has been well confirmed.