AC IMPEDANCE INVESTIGATION OF TA2O5 FILM FOR USE AS A STORAGE CAPACITOR DIELECTRIC

The dielectric properties of anodically formed oxide layers of different thicknesses on tantalum in contact with electrolyte were analyzed by measuring the frequency dependence of the impedance from 0.25 to 25 kHz. It was found that the reciprocal capacitance is a linear function of the logarithm of frequency, and the resistance is a linear function of reciprocal frequency for all layer thicknesses in the frequency range from 0.35 to 10 kHz. Deviation from linearity occurs for the capacitance component above 10 kHz and for the resistance component below 0.35 kHz. This is in accordance with theoretical Young's relations which are valid in the range from zero to infinity. It is demonstrated that Young's equations are mutually dependent owing to the validity of the Kramers-Kronig (KK) relations which are in a mathematical sense the integral equations. The right-hand sides of these equations are improper integrals. Evaluation of improper integrals, of which the numerators of the integrands are Young's equations, were solved by applying Cauchy's residue theorem. The results are interpreted in terms of a model which proposes an exponential variation of resistivity through the oxide. The exponential variation of the resistivity may be associated with the existence of the exponential distribution of oxygen vacancies in the anodic oxide layer, which occurred during growth of the oxide layer.