Anomalous diffusion in nonmetals (origin and effects of internal electric fields)

Abstract

When electrically active impurities or defects diffuse in a material with a band gap ≳ 10kT, the changing concentration of these ions may result in internal electric fields which will significantly alter the diffusion process, and result in gross misinterpretation of diffusion experiments. Equations are derived which describe the diffusion of interstitial impurities in such a system, and which take proper account of compensating immobile impurities. A technique for numerical solution of these equations is described and the results of calculations for the case of H⁺ in TiO₂ are presented. These calculations predict a large enhancement of the over−all diffusion rate and a very distinctive concentration profile. The latter is of critical importance in identifying this effect, since our calculations show that a measurement of total impurity content vs time will appear to agree fairly well with Fick’s law; however, the apparent diffusion coefficient obtained in this way can be in error by a factor of 100 or more. Experimental results for the H⁺−TiO₂ system are presented, which agree quantitatively with our calculations.