Flat-Band Potential of a Semiconductor: Using the Mott–Schottky Equation

Semiconductors are an important category of materials involved in many applications in modern society. One such application revolves around the search for efficient sustainable forms of energy, in this case the use of semiconductors to assist in the conversion of light to electrical energy. Related to a semiconductor's behavior in such an application is its flat-band potential. In this article we have described an experiment suitable for fourth-year undergraduate or graduate students that involves determination of the flat-band potential of a semiconductor using electrochemical impedance spectroscopy (EIS) and the Mott–Schottky equation, which relates semiconductor–electrolyte interfacial capacitance to voltage. To demonstrate this approach we used a polycrystalline ZnO electrode in an electrolyte of 7 x 10-4 M K3Fe(CN)6 (1 M KCl). EIS, with a suitable equivalent circuit, was used to extract interfacial capacitance data (C), which was then compared with the electrode voltage via the Mott–Schottky equation (C-2 versus V). From the x-axis intercept the flat-band potential was determined to be -0.316 ± 0.033 V versus SCE. For descriptive purposes, some fundamentals of band theory have been included in the Supplemental Material, as has the derivation of the Mott–Schottky equation.