(Invited) Schematic Description of the Internal Stress Distribution Responsible for Defect Generation in Larger-Diameter PVT-Grown 4H-SiC Single Crystals
Authors: Fujimoto Tatsuo , Nakabayashi Masashi , Ushio Shohji , Tani Komomo , Katsuno Masakazu , Sato Shinya , Tsuge Hiroshi 
Published: February 2020

Accurate control of the growth conditions, specifically in view of the temperature field, is more important as the diameter of SiC single crystals becomes larger. The temperature field during the physical vapor transport (PVT) growth inevitably induces the residual internal stresses depending on its actual temperature distribution profile, and the strength of the residual stress will become more significant for larger diameter SiC crystals, probably affecting on the crystal quality such as the dislocation density. Such views has, therefore, been well-accepted so-far as an essential key issue for realizing SiC crystals with lower levels of the dislocation density as well as the appropriately-controlled mechanical properties suitable for device productions such as BOW, and a number of literatures regarding numerical calculations of the stress distribution inside the crystals have hence been performed worldwide [1].
For PVT-growths of 4H-SiC with higher crystallinity applicable to power device applications, it is important to establish first the stabilization of 4H-SiC single polytype growth, and then realize the minimization of residual internal stress levels inside the crystal. However, these guiding principles usually lead to results in contradiction; for example, an appropriate convex shape of the grown crystal surface is necessary for single 4H-SiC polytype crystal growths, but in principle such growth conditions give rise to unwanted generation of the internal stress inside the crystal [2], and therefore a compromise has to be required for careful optimization of designing the growth conditions.
In our last presentation at ECS conference in 2012, we have demonstrated that the PVT process of SiC can be described successfully in terms of the phase transition between equilibrium phases in Si-C binary system [3]. In this presentation, we first discuss our model, in particular, in the viewpoint of microscopic elementary reaction processes which are ignored in the original representation scheme despite of its crucial importance for stabilization of 4H-SiC crystal growth. Upon the macroscopic growth stability described above, intense descriptions for possible emergence of thermoelastic inertia forces inside the SiC crystal will be developed by introducing a schematic representation of stress distributions in terms of the thermodynamic formulations [4]. The discussions are concentrated mainly on the shear stress component, σrz, and based upon the results obtained from the representation, the effect of the growth parameters on the SiC crystal quality will be discussed in order to obtain larger-diameter 4H-SiC single crystals with properties of importance for applications, optimized in views of both crystallinity and mechanical characteristics.

References
[1] For example, see, R. Ma, et al., Crystal Growth & Design, 2 (2002) p.213.
[2] S. Ha, et al., Material Science Forum, 338-342 (2000) p.67.
[3] T. Fujimoto, et al., ECS Journal of Solid State Science and Technology, 2 (2013) p.N3018.
[4] B. A. Burney, and J. H. Weiner, “Theory of thermal stresses”, John Wiley & Sons, Inc. 1960.