Technical Briefs

Lattice-Misfit Stresses in a Circular Bi-Material Gallium-Nitride Assembly

[+] Author and Article Information
E. Suhir

Bell Laboratories,
Physical Sciences and Engineering Research Division,
Murray Hill, NJ 07974;
University of California,
Department of Electrical Engineering,
Santa Cruz, CA 95064;
University of Maryland,
Department of Mechanical Engineering,
College Park, MD 20742;
Technical University,
Department of Electronic Materials,
1040 Vienna, Austria;
ERS LLC Co., Los Altos, CA 94024
e-mail: suhire@aol.com

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 17, 2011; final manuscript received June 11, 2012; accepted manuscript posted July 6, 2012; published online November 19, 2012. Assoc. Editor: Pradeep Sharma.

J. Appl. Mech 80(1), 014505 (Nov 19, 2012) (12 pages) Paper No: JAM-11-1481; doi: 10.1115/1.4007104 History: Received December 17, 2011; Revised June 11, 2012; Accepted July 06, 2012

A simple and physically meaningful analytical (“mathematical”) predictive model is developed using two-dimensional (plane-stress) theory-of-elasticity approach (TEA) for the evaluation of the effect of the circular configuration of the substrate (wafer) on the elastic lattice-misfit (mismatch) stresses (LMS) in a semiconductor and particularly in a gallium nitride (GaN) film grown on such a substrate. The addressed stresses include (1) the interfacial shearing stress supposedly responsible for the occurrence and growth of dislocations, for possible delaminations, and for the cohesive strength of the intermediate strain buffering material, if any, as well as (2) normal radial and circumferential (tangential) stresses acting in the film cross-sections and responsible for the short- and long-term strength (fracture toughness) of the film. The TEA results are compared with the formulas obtained using strength-of-materials approach (SMA). This approach considers, instead of the actual circular substrate, an elongated bi-material rectangular strip of unit width and of finite length equal to the wafer diameter. The numerical example is carried out, as an illustration, for a GaN film grown on a silicon carbide (SiC) substrate. It is concluded that the SMA model is acceptable for understanding the physics of the state of stress and for the prediction of the normal stresses in the major midportion of the assembly. The SMA model underestimates, however, the maximum interfacial shearing stress at the assembly periphery and, because of the very nature of the SMA, is unable to address the circumferential stress. The developed TEA model can be used, along with the author's earlier publications and the (traditional and routine) finite-element analyses (FEA), to assess the merits and shortcomings of a particular semiconductor crystal growth (SCG) technology, as far as the level of the expected LMS are concerned, before the actual experimentation and/or fabrication is decided upon and conducted.

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