Abstract
An easy-to-use and physically meaningful analytical predictive model is developed, using two-dimensional (plane-stress) theory-of-elasticity approximation, for the evaluation the lattice-misfit stresses in a GaN semiconductor film grown on a circular substrate (wafer). The addressed stresses include (1) the interfacial shearing stress, “responsible” for the occurrence and growth of dislocations, for possible delaminations, and for the cohesive strength of the buffering material, if any; and (2) the normal radial and circumferential (tangential) stresses acting in the film cross-sections and affecting its short- and long-term strength.
Highlights
GaN is a binary III/V direct bandgap semiconductor commonly used in bright light-emitting diodes
Sagar et al [4] have demonstrated that a reduction in dislocation density from about 1010 – 1012 cm-2 in a template prepared using molecular beam epitaxy (MBE) could be reduced to about 2.5×109 cm-2, if a porous SiC substrate is employed
It was determined that even if a reasonably good lattice match takes place and, in addition, the temperature change was significant, the thermal stresses were still considerably lower than the lattice-misfit stresses
Summary
GaN is a binary III/V direct bandgap semiconductor commonly used in bright light-emitting diodes. The elevated lattice-misfit and thermal-mismatch stresses in GaN films are the major limitations for obtaining high-quality GaN systems on technologically important substrates, such as, e.g., Si, SiC, AlN, or diamond (C). The relative level of the latticemisfit and thermal-mismatch stresses in bi-material GaN assemblies was recently addressed, based on analytical (mathematical) predictive modeling, with an objective to evaluate and to compare these two types of stresses [5]. It was determined that even if a reasonably good lattice match takes place (as, e.g., in the case of a GaN film fabricated on a SiC substrate, when the mismatch strain is only about 3%) and, in addition, the temperature change (from the fabrication temperature to the operation temperature) was significant (as high as 1000 ̊C), the thermal stresses were still considerably lower than the lattice-misfit stresses. Our intent is to evaluate, using the developed model, the applicability and accuracy of the SMA (that addresses a bi-material elongated strip as a more or less suitable substitute for an actual circular assembly)
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