Impedance Analysis of Semiconductor Electrodes Biased in the Accumulation Regime for Fuels Evolution

Abstract

This work explores the theory and experimental use of impedance analyses of semiconductor electrodes in the accumulation regime of semiconductor electrodes under bias. It contrasts with the established practice of measuring capacitance of the semiconductor-electrolyte biased in the depletion region to obtain semiconductor doping densities and flatband potentials (Ufb). The goal is to establish Ufb and the solution Helmholtz capacitance for an electrode in the working bias region where research is done on semiconductor electrodes for CO2 reduction and H2 evolution.The technique of measuring the capacitance of semiconductor electrodes when polarized in the depletion region was introduced by DeWald1 and is based upon the work of Garrett and Brattain2 where mathematical expressions were derived for the electric field of a semiconductor space charge region. A significant assumption in that work was that a Boltzmann expression could be used to determine the population of the majority charge carriers in the bands created through ionization of dopant. Research in this area is extensive and has been summarized.3 However, for degenerate semiconductors or for bias potentials of the semiconductor where the fermi level at the electrode surface equals the energy of the band edges, a full fermi function must be employed to describe population statistics in the solid. This is the condition commonly found in systems for fuels production at semiconductor electrodes. The solid state physics theory for this situation is known4 and describes the electric field in a semiconductor space charge region. However, it was put aside during the development of impedance evaluations in semiconductor electrochemistry because its mathematical complexity was too tedious to evaluate at that time. Only limits and simplifications were explored.5 With modern computational software, this theory has become straightforward to calculate and it becomes possible to apply it to experimental systems in a description of behavior over the entire range of doping and polarization. The nature of this full theoretical description will be discussed and illustrated through experimental measurements of Si and InP semiconductor electrodes.