Modeling the Elastic Fields in Epitaxially Grown Multilayers
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P2.10.1
Modeling the Elastic Fields in Epitaxially Grown Multilayers Ganesh Vanamu1, Tariq A. Khraishi2, Abhaya K. Datye1 and Saleem H. Zaidi3 Department of Chemical and Nuclear Engineering, University of New Mexico, Albuquerque, NM-87131, U.S.A. 2 Mechanical Engineering Department, University of New Mexico, Albuquerque, NM87131, U.S.A. 3 Gratings, Inc., 2700 B Broadbent Pkwy NE, Albuquerque, NM 87107. 1
ABSTRACT A model was developed to calculate the elastic fields, including strain energy density, in multilayers grown epitaxially on a planar substrate. This model works well for compliant and non-compliant substrates. In particular we illustrate the model for four layer heterostructure and apply it for graded Ge (SixGe1-x) grown on a planar silicon substrate. Using the equations for static equilibrium and Hooke’s law for isotropic materials under a plane stress condition, the elastic fields associated with each layer were calculated. The strain partitioning in this model reduces to the limiting case of a twolayer structure available in the literature. As it turns out here, strain partitioning is a function of the bulk unstrained lattice parameters, elastic constants and thicknesses of the layers. The model was qualitatively verified by comparing the strain energy density with the dislocation density away from a relatively thick substrate. This model helps shed some light on the factors important in achieving defect free multilayers for optoelectronic devices.
INTRODUCTION In recent years there has been great interest in the study of multilayer epitaxial structures (such as Si-Ge alloys) with varying composition (compositionally graded buffer layers). Graded buffer-layer composition has offered significant improvement in the epilayer quality [1] and hence was used for many advanced electronic and optoelectronic applications [2-5]. These different applications have different defect density tolerances. Although many applications can be explored with moderate defect density material, the ultimate implementation of these materials into products requires the threading dislocation densities to be lower than some critical amount in order to integrate III/V devices on silicon. In the case of field effect transistors (FETs) on silicon utilizing SiGe alloy buffers, the defect density tolerance is on the order of 5×105-107 cm-2. In the case of light-emitting diodes (LEDs) and photovoltaics on silicon, the defect densities need to be on the order of 105- 106 cm-2, whereas for monolithic lasers, photodetectors and solar cells on silicon, the densities should not exceed 104 cm-2. In principle the dislocations would be formed when the strain energy density exceeds a certain critical amount equal to the energy of formation of a single dislocation [6]. This last reference modeled a two-layer only heterostructure in which the authors calculated the film critical thickness based on strain energy considerations. The ultimate problem is thus to calculate the strain energy per unit volume in each layer.
P2.10.2
A model of strain pa
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