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Comment on "Fabrication of strained silicon on insulator by strain transfer process" [Appl. Phys. Lett. 87, 051921 (2005)]

R. L. Peterson, K. D. Hobart, F. J. Kub, J. C. Sturm

2006
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Applied Physics Letters
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In a recent letter, Jin et al. 1 demonstrated a new technique for achieving biaxially tensile strained silicon on insulator ͑SOI͒. An unstrained SOI film is capped with a commensurately strained SiGe layer and the sample is ion implanted with nitrogen. A postimplant anneal creates a superviscous interface between the silicon and the underlying oxide, which allows the strain to transfer from the SiGe into the silicon. An equation is given ͑derived in part from Ref. 2͒ for the final silicon and
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... Ge strains achieved by this strain equalization process. The purpose of this Comment is to point out inconsistencies in the given strain transfer equations. When an elastic thin film is subject to a biaxial in-plane strain, the strain energy density of the film, E, is given by 3,4 where h is the film thickness, ⑀ biaxial is the film's biaxial strain, and B = c 11 + c 12 −2c 12 2 / c 11 , where c 11 and c 12 are film elastic stiffness coefficients. For a bilayer of epitaxial SiGe and silicon, as in Refs. 1, 2, and 5, the silicon and SiGe layers have a coherent interface between them. The SiGe layer has an initial biaxial compressive strain of ⑀ o ͑for Si 0.8 Ge 0.2 , ⑀ o = −0.8%͒ and the silicon is unstrained. Coherency requires that the strained in-plane lattice constants of the two films be equal, that is, a r,SiGe ⌬⑀ SiGe = a r,Si ⌬⑀ Si , where a r is the relaxed cubic lattice constant of the film, and the strain is defined as ⑀ ϵ͑a strained, in-plane − a r ͒ / a r . Upon high temperature annealing, the silicon/oxide interface becomes viscous ͑using a variety of techniques 1,2,5 ͒, allowing the SiGe to partially relax and reduce its compressive strain, thereby stretching the underlying silicon so it becomes tensile. Strains in the two films are related by Note that even if the lattice constant factor is neglected, this differs from the equation given in Ref. 1, ⑀ o = ⑀ SiGe + ⑀ Si , that is said to be valid "since the alloy composition remains con-stant throughout the relaxation process" ͑where subscripts 1 and 2 in Ref. 1 represent Si and SiGe͒. If correct, this equation would imply that as one layer becomes more tensile, the other becomes more compressive. Obviously this is not physically possible for coherently linked layers. We now comment on the final equilibrium state of the bilayer films under the conditions that the two layers remain coherent and planar. Combining Eqs. ͑1͒ and ͑2͒, one can solve for the total energy of the strained bilayer,

doi:10.1063/1.2192641
fatcat:qywgdfd54jadfecctcgfbydfme