Temperature Dependent Optical Response of Si(100): Theory vs . Experiment
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Temperature Dependent Optical Response of Si(100): Theory vs. Experiment A.I. Shkrebtii1,2, J. Heron1, J.L. Cabellos2, N. Witkowski3, O. Pluchery3, B.S. Mendoza2 and Y. Borensztein3 1
University of Ontario Institute of Technology, Oshawa, ON, L1H 7L7, Canada Centro de Investigaciones en Optica, A. C., León, Guanajuato, 37150, México 3 Université Pierre et Marie Curie - Paris 6, Paris F-75005, France 2
ABSTRACT We investigate theoretically and experimentally the temperature-dependent linear optical properties of the clean c(4×2) reconstructed Si(100) surface for a wide range of temperatures. We combine two theoretical formalisms: the first one incorporates the contribution of temperature-dependent atomic motion to the surface optical response and, the second uses a dielectric function layer-by-layer separation method. Using these formalisms, we model temperaturedependent reflectance anisotropy (RA) of this surface for the first time: finite temperature abinitio Car-Parrinello Molecular Dynamics (CPMD) at different temperatures up to 1000 K provide temperature-dependent atomic structural inputs for optical calculations and subsequent average of dielectric functions. Experimentally, one-domain c(4x2) Si(100) surface was prepared and characterised by Reflectance Anisotropy Spectroscopy (RAS) in a temperature range between 300 K and 800 K. Good agreement between experiment and theory is demonstrated, including a temperature-induced red shift of both the surface and bulk optical peaks. Theoretical results indicate that the temperature-induced modification of the optical response is substantially more pronounced for the surface than for the bulk. INTRODUCTION A deeper understanding of the Si(100) surface, a cornerstone material of microelectronics, is necessary to enhance device performance. Optical techniques combined with theoretical modeling are the tools of choice to accurately characterize various surface processes (see [1] and references therein). Although the optical response is often measured at high temperatures and demonstrates significant temperature-induced changes an efficient formalism for calculating temperature-dependent linear dielectric functions of bulk semiconductors has only recently been developed [2-5]. For semiconductor surfaces, the temperature induced modification of the optical response should be even more pronounced due to the top atom reduced coordination, symmetry change, reconstruction phenomena and foreign atom adsorption. This was demonstrated more than a decade ago by measuring and theoretically interpreting temperature-dependent High Resolution Electron Energy Loss spectra of the clean Si(100) surface [6]. However, no systematic theoretical interpretation of the contribution of surface atom dynamics to the optical response of surfaces, nor detailed experimental measurements in a wide temperature range were available. Our theoretical approach for calculating the temperature-dependent optical properties of the Si(100) clean surface follows the formalism of [2]: the linear dielectric funct
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