Constitutive Modeling for CdTe Single Crystals
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INTRODUCTION
THE compound semiconductor cadmium telluride (CdTe) derives its technological importance primarily from use as a substrate material for the epitaxial growth of HgCdTe used in infrared radiation detectors. It is also used in devices for the detection of other types of radiation such as X-ray and gamma-ray spectrometers. The thermomechanical behavior of the solid state plays an important role in the final defect density and, consequently, optoelectronic performance and crystalline yield of CdTe single crystals grown by directional solidification. As-grown dislocation density is controlled, to a large extent, by the distribution of stress during the growth and the subsequent cooling of crystals. These stresses arise mainly by virtue of the temperature distributions which occur and by thermal expansion mismatch between the growth container and an adhering solid crystal. To control these factors, a better understanding of the role of thermomechanical stress in the process is needed. Thus, models of the development of stress (using, for example, the finite element method) during growth and the subsequent cooldown process are sought. These models must involve the coupling between thermomechanical stress, inelastic deformation, and dislocation density. Consequently, constitutive equations for the single-crystal behavior of these materials at small strain are needed. Several experimental studies have explored the mechanical behavior of CdTe and related compounds.[l-15.24] In recent years, these have included high-temperature behavior.V.4.~5.241 Typically, these studies have not focused on the small strain regime important for confined thermal J.C. MOOSBRUGGER, Associate Professor, is with the Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699-5729. A. LEVY, Principal Engineer, is with the Advanced Technology and Development Center, Northrup-Grumman Corporation MSA0126, Bethpage, NY 11714. This article is based on a presentation made in the symposium entitled "Microgravity Solidification, Theory and Experimental Results" as a part of the 1993 TMS Fall meeting, October 17-21, 1993, Pittsburgh, PA, under the auspices of the TMS Solidification Committee. METALLURGICALAND MATERIALS TRANSACTIONS A
stress problems. Some of these data, however, can be useful in the development of a small strain constitutive model. The results of these studies, which are relevant for the construction of a model, are highlighted in this article. A framework developed by Alexander and Haasentt6] was developed to model the coupling between dislocation density and inelastic deformation in semiconductor materials and provides a suitable basis for constitutive equations. This model was developed mainly around the elemental semiconductors, Si and Ge, and has been successfully used to predict isothermal, quasistatic displacement-controlled tests and creep tests including the correlation of dislocation density and inelastic strain. No explicit provisions for hightemperature recovery mechanisms wer
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