Equivalent Circuit Analysis of the Impedance Response of Semiconductor/Electrolyte/Counterelectrode Cells

A method to determine the equivalent circuit of a semiconductor/electrolyte/counterelectrode cell is presented. The electrical analog of the phenomenon leading to frequency dependent behavior has been taken to be a resistor in series with a capacitor. The case where a large number of RC elements are present has been determined in the following way. The values of the capacitances and time constants of these elements have been assumed to be distributed exponentially. For this distribution it follows that the equivalent circuit can be represented as a frequency dependent resistor in parallel with a frequency dependent capacitor. Expressions for the frequency dependent resistance and capacitance have been derived. The impedance and admittance responses of a large number of circuits have been simulated. The circuit which best represented an cell was determined by comparing the simulated responses with the measured responses. Various equivalent circuit parameters have been determined. The simulated response of the representative circuit compares well with the experimental results, both in the impedance and admittance planes. The donor density and the flatband potential of the electrode were determined from a plot of the Mott‐Schottky relation.