Frequency dispersion in the impedance of Schottky Barriers

Abstract

Surface impedance measurements in the dark have been obtained by use of a computer controlled continuous recording impedance analyzer over the frequency range from 5 Hz to 100 kHz on Nb-doped TiO 2 surfaces. Continuous recording allows rapid determination of, for example, Mott-Schottky plots over the frequency range. Thus, impedance changes that occur after immersion of the sample into the electrolyte, after light exposure, or after chemical surface treatment can be observed. The data contain a richness of behavior that has not heretofore been reported. In particular, a broad frequency dispersion occurs in the Mott-Schottky plots for all TiO 2 surfaces investigated. Depending on the distribution and magnitude of the surface states, the reciprocal square of the surface capacitance will vary approximately linearly or change abruptly as the Fermi level changes with applied surface potential at each measuring frequency. The slope is strongly frequency dependent, casting serious doubt on the common practice of obtaining the impurity density from the slope. Second, the intercept on the voltage axis is frequency dependent, and flat band potential can not be extracted simply by extrapolation to the voltage axis. A theory of the frequency dispersion of the surface impedance based on solution of the diffusion equation and Poisson's equation for the majority carriers in a Schottky-type surface barrier is also presented.