Fundamental Study on Calibration of Space Charge Distribution by Frequency-resolved Analysis

In the measurement of space charge by the pulsed electrostatic stress method acoustic signal as a result of the interaction between charge and pulse electric field represents charge distribution. As the signal is influenced by the transfer function of the measurement system, it should be calibrated using a reference signal that represents the impulse response of the system. The signal originated from the charge induced by a bias voltage can be applied as the impulse response, however, when the sample contains space charge, the signal from the space charge is superimposed and leads to an error. We propose a frequency-resolved analysis as one of the solutions to obtain a reference signal while avoiding the influence of space charge. By correlating the time variations of the bias voltage and the response signal via Fourier transform, the time variation of the signal component, whose source is the charge induced in the electrode by the bias voltage, is exactly proportional to the time variation of the bias voltage at all frequencies, and is in phase with the bias voltage. Since the signal due to stable space charge does not change with the bias voltage, its corresponding spectrum obtained by Fourier transform is zero including the DC component. The signal component due to unstable space charge, which varies with a finite delay time relative to the bias voltage, has an imaginary component in the spectrum because of the phase delay. The spectrum in such a frequency band should be discarded for calibration. Thus the frequency components with DC and imaginary components are excluded from the normalized spectrum, and the signal component whose source is the induced charge on the electrode due to the bias voltage is extracted and used as the reference waveform. Its validity was proved through experiment and simulation.