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ARTICLE

A Semicontinuum Model for Si_xGe_{1 - x} Alloys: Calculation of Their Elastic Characteristics and the Strain Field at the Free Surface of a Semi-Infinite Alloy

by V.K. Tewary¹, M. D. Vaudin²

1 Materials Reliability Division, National Institute of Standards & Technology (NIST), Boulder, CO 80305, USA
2 Ceramics Division, National Institute of Standards & Technology (NIST), Gaithersburg, MD 20899, USA

Computers, Materials & Continua 2011, 25(3), 265-290. https://doi.org/10.3970/cmc.2011.025.265

Abstract

A semicontiuum Green's-function-based model is proposed for analysis of averaged mechanical characteristics of Si_xGe_{1 - x}. The atomistic forces in the model are distributed at discrete lattice sites, but the Green's function is approximated by the continuum GF in the far field and by the averaged lattice GF in the near field. Averaging is achieved by replacing Si and Ge atoms by identical hypothetical atoms that are x fraction Si and (1-x) fraction Ge. The parameters of the model are derived using the atomistic model from the interatomic potential between the hypothetical atoms. The interatomic potential is obtained from the radial embedded atom model proposed in an earlier paper. The parameters of the model potential are estimated partly by interpolation and partly by fitting the calculated and measured values of the cohesive energy and the lattice constant of Si_xGe_{1 - x} as functions of x. The model is applied to calculate the elastic constants of Si_xGe_{1 - x} and the displacement and the strain field at the free surface of a semi-infinite alloy for different values of x due to a buried point defect. The elastic constants predicted by the model are used to calculate the curvature of a single crystal of Si with a 49 nm epitaxial film of Si(0.846)Ge(0.154). The calculated value (312.8 m) of the radius of curvature is in excellent agreement with the recently measured value (314.5 m) at our laboratory.

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