Generalized Ellipsometry Using a Rotating Sample
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Generalized Ellipsometry Using a Rotating Sample Weiliang Xu*, Lowell T. Wood, and Terry D. Golding** Department of Physics, University of Houston, Houston, Texas 77204-5506, U.S.A. ABSTRACT We propose a generalized ellipsometric technique using a rotating sample. The ellipsometer consists of a polarizer, a rotatable sample holder, an analyzer, and a detector. Fourier coefficients are measured and used to extract the system’s dielectric tensors and film thicknesses. The main advantage of the technique is that all parts of the ellipsometer are fixed except the sample, whose azimuth angle can be modulated. We show calculated responses to isotropic and anisotropic materials as well as superlattices. Potential applications for characterizations of anisotropic nanostructures are discussed.
I. INTRODUCTION In a conventional rotating element ellipsometer, only one variable, i.e., the azimuth angle of the rotating element, is changed in the characterization of an isotropic material. In current generalized ellipsometers for characterizing anisotropic systems, however, either additional variables [1], e.g., the angle of incidence and the azimuth angles of the polarizer (or analyzer) and of the sample, are changed, or components not commonly found in a conventional rotating element ellipsometer are needed [2,3]. Even in the simplest case of uniaxial materials, two variables, i.e., the azimuth angles of the polarizer and analyzer, are required if sets of Ψ and ∆ are measured to determine the dielectric tensors of the materials [4]. Optimization of ellipsometric setups with fewer variables involved in measurements is highly desirable in situations where measurements are remotely controlled, since the reliability of the controls and the accuracy of the measured data are improved. One such situation is the characterization of samples grown in space. In this paper we present a theoretical development and show that changing only the sample’s azimuth angle is sufficient to determine dielectric tensors and film thicknesses of arbitrarily anisotropic systems. Instead of Ψ and ∆, the intensity dependence on the sample’s azimuth angle is measured. Two approaches for analysis are proposed to determine the dielectric tensors and film thicknesses from the measured intensities. Popular conventional ellipsometer setups, e.g., polarizer-compensator-sample-analyzer (PCSA) or polarizer-sampleanalyzer (PSA), can use this approach to characterize anisotropic systems by keeping all components fixed except the sample.
II. THEORY In this section, we study the dependence of intensity on αS, the sample’s azimuth angle, to permit extraction of the dielectric tensors and film thicknesses. For an n-layer anisotropic *
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C4.42.1
system, following the same procedure and coordinates setup as in Refs. [4,5], the Jones matrix (r) for reflection ellipsometry is rpp =
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