Consequences of anisotropy in electrical charge storage: application to the characterization by the mirror method of TiO2 rutile

Abstract

This paper is devoted first, to anisotropic distributions of stored electric charges in isotropic materials and second, to charge trapping and induced electrostatic potential in anisotropic dielectrics.On the one hand, we examine the case of anisotropic trapped charge distributions in linear homogeneous isotropic insulators, obtained after an electron irradiation in a scanning electron microscope. This injection leads to the formation of a mirror image. We first establish the characteristics of the mirror image obtained from such anisotropic distribution by linking the mirror diameter to the curvature tensor of the equipotentials thanks to the geometric optics ansatz (GOA). Second, the equipotentials induced by the presence of an anisotropic charge distribution in such isotropic dielectrics have been determined in the case of homeoidal (ellipsoidal) distributions that generalize the classical spherical distributions. Then, for these homeoidal distributions in isotropic dielectrics, the features of the mirror image have been deduced from the previous GOA estimation. Elliptic mirrors can be obtained and calculated in the limit cases of such homeoidal distributions.On the other hand, we consider the non-trivial case of a point charge lying at the interface between the vacuum and a linear homogeneous orthotropic anisotropic dielectric and the determination of its corresponding potential seen from the vacuum. This problem has already been solved in the case of transversal isotropic dielectrics (εx = εy = εr, εr ≠ εz), but we extend in this paper the classical dielectric image problem to the more general case where εx ≠ εy ≠ εz. The equivalent charge and the induced electrostatic potential are evaluated. For these anisotropic insulators, the equipotentials created by a point charge at the interface are found to be ellipsoids and this leads to an elliptic mirror image. The ratio between the two main axis values of the elliptic mirror is proportional to the square root of the ratio of the permittivities values in the plane of the interface. Finally these calculations are used to explain the experimental results obtained by the mirror method on a TiO2 sample that is known to be an anisotropic dielectric.