Three-Dimensional Finite Element Calculations of Thermal Stresses in Patterned GaAs / Si
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THREE-DIMENSIONAL FINITE ELEMENT CALCULATIONS OF THERMAL STRESSES IN PATTERNED GaAs / Si E. H. LINGUNIS N. M. HAEGEL* AND N. H . KARAM* * Department of Materials Science and Engineering, University of California, Los Angeles, CA 90024 ** Spire Corporation, Patriots Park, Bedford, MA 01730
ABSTRACT Three-dimensional elastic finite element analysis was used to investigate the stress state in patterned GaAs/Si squares with different width to thickness ratios. Quantitative results for stress relief close to free edges were obtained. Features not revealed by previous twodimensional calculations show the necessity of the threedimensional treatment. For large areas the calculations give an approximately uniform biaxial stress everywhere, with reduced magnitude close to free edges. This allows for straightforward interpretation of high spatial resolution luminescence spectra and precise stress measurement. Experimental results from low temperature photoluminescence show good agreement with the calculated stresses. Finally, the effects of adjacent layers of different materials on the stress in epitaxial semiconductor thin films is investigated (particularly the case of InP/GaAs/Si) and discussed in conjunction with previous results.
INTRODUCTION Patterned GaAs/Si is attractive for the fabrication of cost-effective optoelectronic devices such as laser diodes. The material quality of GaAs/Si is compromised by large differences in lattice constant and thermal expansion coefficient between GaAs and Si. The lattice mismatch (4.1 %) is largely accomodated by misfit dislocations at the GaAs/Si interface. On cooling from the growth temperature to room temperature, stresses (tensile in GaAs) develop due to thermal expansion mismatch. While unpatterned GaAs/Si is under uniform biaxial tension, the stress in patterned GaAs/Si is complicated by the presence of free edges. Several studies [1],[2],[3) have shown that relief of the stress component perpendicular to free edges or microcracks occurs in the vicinity of those boundaries, while both components are relieved in the vicinity of corners or crack intersections. While some analytical [4],[5] and numerical [6] (finite element) calculations of thermal stresses in a thin infinite stripe on a thick substrate exist in the literature, the specific case of a square has not been reported to date. The purpose of this work is to describe quantitatively the stresses in square-patterned GaAs/Si (100) by 3-dimensional elastic finite element analysis. Mat. Res. Soc. Symp. Proc. Vol. 239. ©1992 Materials Research Society
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In this study the substrate and epilayer were assumed stress free at 800 K and thermal stresses were calculated at 4 K (at 300 K the stress is smaller by about 1/3). The SAP 9 0TM finite element code (Computers and Structures Inc.) was used on the structure shown in Fig. 1. Fig. 1(a) is the top view of a GaAs/Si square with vertical sidewalls, serving as a model for selectively etched GaAs/Si squares or selectively grown ones after removal of the masking layer [3]. Due to
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