Measurement of semiconductor local carrier concentration from displacement current-voltage curves with a scanning vibrating probe

A theoretical equation has been fitted to displacement current-voltage curves of semiconductor in order to obtain the local carrier concentration of the semiconductor. The distance between a semiconductor surface and a scanning probe is changed sinusoidally and is adjusted as small as a few nm at which tunneling current flows. Displacement current due to the change in electric flux from the semiconductor surface to the scanning probe flows periodically in accordance with the vibration of the scanning probe, and it is separated from tunneling current using a two-phase lock-in amplifier. The displacement current-probe voltage curve is analyzed by taking into account two-dimensional electric flux profile from the semiconductor surface. It is realized that the lateral resolution of the displacement current depends on the probe voltage and that it is between one-eighth and one-fifteenth smaller than the top radius of the probe since the depletion-layer width of the semiconductor is determined by the probe voltage, the distance, and the carrier concentration. The theoretical displacement current-voltage curves are in good agreement with the measurement in both voltage regions where the majority carriers are accumulated and depleted. The local carrier concentration can be determined by fitting the theoretical displacement current-voltage curve with the experimental results.