Effective, easy-to-use and physically meaningful analytical predictive models are developed for the evaluation the lattice-misfit stresses (LMS) in a semiconductor film grown on a circular substrate (wafer). The two-dimensional (plane-stress) theory-of-elasticity approximation (TEA) is employed. First of all, the interfacial shearing stresses are evaluated. These stresses might lead to the occurrence and growth of dislocations, as well as to possible delaminations (adhesive strength of the assembly) and the elevated stress and strain in the buffering material, if any (cohesive strength of the assembly). Second of all, the normal radial and circumferential (tangential) stresses acting in the film cross-sections are determined. These stresses determine the short- and long-term strength (fracture toughness) of the film material. It is shown that while the normal stresses in the semiconductor film are independent of its thickness, the interfacial shearing stresses increase with an increase in the induced force (not stress!) acting in the film cross-sections, and that this force increases with an increase in the film thickness. This leads, for a thick enough film, to the occurrence, growth and propagation of dislocations. These start at the assembly ends and propagate, when the film thickness increases, inwards the structure. The TEA data are compared with the results obtained using a simplified strength-of-materials approach (SMA). This approach considers, instead of an actual circular assembly, an elongated bi-material rectangular strip of unit width and of finite length equal to the wafer diameter. The analysis, although applicable to any semiconductor crystal growth (SCG) technology is geared in this analysis to the Gallium-Nitride (GaN) technology. The numerical example is carried out 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 acting in the major mid-portion 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. This stress can be quite high at the circular boundary of the assembly. At the assembly edge the circumferential stress is as high as σθ = (2–ν1)σ1, i.e., by the factor of 2–ν1 higher than the normal stress, σ1, in the mid-portion of the film. In this formula, ν1 is Poisson’s ratio of the film material.
E. Suhir and S. Yi, "Predicted lattice-misfit stresses in a gallium-nitride (GaN) film," Proc. SPIE 10104, Gallium Nitride Materials and Devices XII, 1010408 (Presented at SPIE OPTO: January 30, 2017; Published: 16 February 2017); https://doi.org/10.1117/12.2246963.
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