Nonlinear Transient Finite Element Analysis of the Relaxation Mechanisms in Strained Silicon Grown on SiGe Virtual Subst
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Nonlinear Transient Finite Element Analysis of the Relaxation Mechanisms in Strained Silicon Grown on SiGe Virtual Substrate F. Sahtout Karoui,1 A. Karoui,2 G. Rozgonyi1 1
: Materials Science and Engineering Department, North Carolina State University, Raleigh, NC 27695-7916, USA. 2 : Nanoscience and Nanotechnology Research Center, Shaw University ABSTRACT Strained-silicon (ε-Si) is essential for future nanoscale MOSFET devices. In this paper we report on the dynamics of strain relaxation in Si/SiGe heterostructures, investigated by transient nonlinear finite element analysis. The contribution to total misfit strain is found largely plastic in the graded SiGe layer and the top of the Si substrate, while it is mainly elastic in the strained Si layer and part of the SiGe constant layer. The calculated lattice parameter for the strained Si layer is about 5.47Å for 5 -2 Si0.8Ge0.2 and 5.52 Å for Si0.6Ge0.4. Calculated threading dislocation density was about 5.6x10 cm for 6 -2 x=0.20 and 2.17x10 cm for x=0.40. A plastic strain rate of 8.4x10-3 s-1 for Si0.8Ge0.2 and 4.1x10-2 s-1 for 9 -2 10 -2 Si0.6Ge0.4 leading to a density of moving dislocations of ~2.2x10 cm and ~ 10 cm , respectively, have been obtained. The elastic strain in the strained-Si layer appeared to increase with increasing the cooling rate, while plastic work was found to be independent of cooling rates. INTRODUCTION Biaxial tensile strain is introduced in Si thin films grown on Si1-xGex “virtual substrate” to enhance carrier transport properties. Indeed, SiGe alloys have larger lattice constant than Si, due to the ~ 4% lattice mismatch between Si and Ge [1]. The reliability of devices made on the strained layer, depends on the stability of the latter as well as on the strain amount, and hence on the misfit dislocation density at the strained-layer interfaces. The ability to consistently predict the level of dislocation and resulting strain relaxation is critical in such devices. Currently, one of the more successful techniques for reducing threading dislocation density in the strained thin Si layer (15 nm in our case) is to grow the strained layer on top of relaxed graded SiGe buffer layer. The self-equilibrated residual stresses, which occur during relaxation in the deposited layers are generally the result of the elastic and/or plastic deformation when inhomogeneously distributed over the volume. They systematically occur during layer growth with variation of material composition. These stresses originate from lattice mismatch of contacting layers, but also from differences in thermal-expansion coefficients and exchange of point defects at the interfaces. For instance during cooling from growth to room temperature, the thermal expansion coefficient α Si of Si varies from 4.9 × 10-6 to 2.57 × 10-6 K-1, and α Ge of Ge varies from 8.55 × 10-6 to 5.9 × 10-6 K-1 [2]. When these stresses exceed the yield stress, at growth time, they lead to the onset of plastic deformation. In this paper, we have investigated the dynamics of strained-Si/Si0.8Ge0.2/S
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