Poster
Correlation of temperature dependent vibrations, structure and optical response of Si(100) surface from first principles
1University of Ontario Institute of Technology, Oshawa, ON, L1H 7L7
2Sigma Software, Toronto, ON. http://www.sigmasoft.ca/
Vibrational and optical spectroscopy combined with theoretical modeling is the tools of choice to accurately and non-invasively characterise various surface processes in-situ. Because Si(100) is one of the most fundamentally and technologically important semiconductor surfaces, its microscopic understanding is needed to enhance microelectronics device performance. A connection between dynamics and c(4×2) / p(2×2) reconstructions of the clean Si(100) surface at room temperature conditions with apparent (2×1) phase was established two decades ago through molecular dynamics (MD) simulations [1]. Surface vibrational spectra have also been calculated [1-2] and confirmed experimentally (see [3] and refs. therein). However, due to dimer flipping at Si(100), the dynamical processes at the surface are highly anharmonic. This phenomenon has not sufficiently been addressed theoretically. In addition to being responsible for c(4×2) → (2×1) order-disorder transition near room temperature, the anharmonicity of surface vibrations substantially influences high temperature behaviour of Si(100) [4-5]). Temperature induced modification of the Si(100) optical response [6] clearly indicates the strong contribution of the dimer vibrational anharmonicity to atomic structure, electron bands and optical transitions between them.
Here we combine the formalisms of [1] and [2] to calculate temperature-dependent vibrational spectra of the clean Si(100) surface, and then calculate its temperature dependent reflectance anisotropy (RAS). When modeling surface vibrations, two different first principles techniques are used: (i) highly accurate density-functional perturbation theory (DFPT) [2] that, however, is inherently harmonic; and (ii) postprocessing of temperature dependent MD trajectories through the Fourier transform of the velocity discrete correlation function. The second method includes anharmonicity implicitly, which is evident from our calculated spectra. To extract the vibrational density of states (VDOS), finite temperature Car-Parrinello Molecular Dynamics (CPMD) runs were carried out in a wide temperature range from 250K to 1000K to provide temperature-dependent atomic structural input. When calculating the optical response at nonzero temperature, the vibrational anharmonicity was included through averaging for several representative temperature-perturbed atomic configurations (snapshots). Agreement with experimental results [6] is demonstrated, including a temperature-induced shift of both surface and bulk optical peak to lower energy and broadening, while the temperature induced effects are more pronounced for the surface atoms than for the Si bulk atoms. This conclusion is even better illustrated when the layer-by-layer formalism uses to efficiently decouple the bulk and surface contributions to temperature dependent both vibrational and optical responses.
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[6] A. I. Shkrebtii, J. Heron, J. L. Cabellos, et al., MRS Online Proceedings Library 1370, 1039 (2011)