Theoretical Calculations of the Nonlinear Dielectric Function of Inhomogeneous thin Films
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THEORETICAL CALCULATIONS OF THE NONLINEAR DIELECTRIC FUNCTION OF INHOMOGENEOUS THIN FILMS STEVEN M. RISSER AND KIM F. FERRIS Pacific Northwest Laboratories, Materials and Chemical Sciences Center, Richland, WA ABSTRACT The dielectric function of inhomogeneous materials is composed of linear and nonlinear responses which are sensitive to the film microstructure as well as the intrinsic properties of the materials. We have developed a method to self-consistently determine the linear and non-linear contributions to the dielectric function of films with random microstructure. This method is based upon a numerical solution of the general electrostatic equations and is applicable to arbitrary shapes and orientations of model defects. This method provides near exact solutions to the linear response of the dielectric function. We have shown that the nonlinear part of the dielectric function is extremely sensitive to the void shape and void fraction. INTRODUCTION Dielectric films having identical chemical composition can exhibit substantial variation in their optical properties, which may be significantly different from those intrinsic to the bulk crystalline materials. The film deposition technique plays a large role in determining these variations, due to the large differences in the microstructure observed for the different preparation methods. The dielectric properties of the films are sensitive to the parameters of the microstructure, such as void and particle shape and size. Quasi-static and effective medium methods [1,2] have been developed to model the real part of the dielectric function in the long wavelength limit. These methods include varying degrees of information about the microstructure of the film. Dynamic corrections to these models can include a rough degree of microstructural information for conditions where the wavelength of light approaches the particle size. However, all these methods contain implicit assumptions about the extent and randomness of the microstructure and do not treat the nonlinear optical properties of the media. Because of the complex nature of the boundary conditions imposed on solutions of Maxwell's equations for a film composed of many particles of varying shapes, analytic solutions to determine the optical properties are not feasible. Such restrictions can be eliminated by computational approaches to the governing electrostatic equations. By modelling material microstructure by a series of finite elements, self-consistent methods can provide effective solutions to the polarizability. In this paper, we present numerical solutions of Maxwell's equations to determine the effects of microstructure on the nonlinear part of the dielectric function of inhomogeneous media.
METHODS The macroscopic dielectric response of a body in the long wavelength limit is given by:
D = F0E + P where E is the macroscopic electric field, P is the macroscopic polarization, D is the electric displacement and e is the dielectric function. Microscopically, the local polarization is given by:
Mat. Res. Soc.
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