Spectroscopic Ellipsometry Analysis of InGaN/GaN and AlGaN/GaN Heterostructures Using a Parametric Dielectric Function M
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Spectroscopic Ellipsometry Analysis of InGaN/GaN and AlGaN/GaN Heterostructures Using a Parametric Dielectric Function Model J. Wagner, A. Ramakrishnan, H. Obloh, M. Kunzer, K. Köhler, and B. Johs1 Fraunhofer-Institut für Angewandte Festkörperphysik, Tullastrasse 72, D-79108 Freiburg, Germany, [email protected]; 1 J. A. Woollam Co., Inc., 645 ´M´ Street #102, Lincoln, Nebraska 68508 ABSTRACT Spectroscopic ellipsometry (SE) has been used for the characterization of AlGaN/GaN and InGaN/GaN heterostructures. The resulting pseudodielectric function spectra were analyzed using a multilayer approach, describing the dielectric functions of the individual layers by a parametric oscillator model. From this analysis, the dielectric function spectra of GaN, AlxGa1-xN (x≤0.16), and In0.13Ga0.87N were deduced. Further, the dependence of the AlxGa1-xN band gap energy on the Al mole fraction was derived and compared with photoluminescence data recorded on the same material. The SE band gap data are compatible with a bowing parameter close to 1 eV for the composition dependence of the AlxGa1-xN gap energy. Finally, the parametric dielectric functions have been used to model the pseudodielectric function spectrum of a complete GaN/AlGaN/InGaN LED structure. INTRODUCTION Reproducible growth of high-quality (AlGaIn)N heterostructures requires, because of the rather narrow growth parameter window, fast and efficient characterization of, e.g., layer thickness and composition. Spectroscopic ellipsometry (SE) is a nondestructive optical characterization technique which has been used successfully for the characterization of conventional III-V heterostructures [1-4]. For a quantitative analysis of SE data on group III-arsenide and -antimonide heterostructures, detailed modeling of the pseudodielectric function spectra has been performed employing a multilayer approach, incorporating parametric dielectric function models for the individual layers [2-4]. With respect to the group III-nitrides, SE data and model fits to the dielectric function spectra have been reported so far mostly for bulk-like GaN and AlGaN [5-10]. We have reported recently on the SE characterization of InxGa1-xN (x≤0.1) layers on GaN, but no modeling of the pseudodielectric function spectra has been performed to extract the dielectric function spectra of the individual layers [11]. The aim of the present investigation was to characterize hexagonal (AlGaIn)N heterostructures by variable angle SE and to analyze the resulting pseudodielectric function spectra within the framework of a multilayer model based on parametric dielectric functions. Parameterized dielectric function spectra have been derived for GaN, In0.13Ga0.87N, and AlxGa1-xN (x≤0.16), allowing a direct determination of the composition dependence of the AlxGa1-xN band gap energy EG(x). There is an ongoing controversy regarding the deviation of EG(x) from a linear dependence on x. Recent values for the bowing parameter b, which describes the magnitude of parabolic nonlinearity, range from 0, as derived from photo
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