Analysis of Basal Plane Bending and Basal Plane Dislocations in 4H-SiC Single Crystals

Abstract

We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdős-Rényi (E-R) random graph is determined by the average degree k and p(s) undergoes a dramatic change when k is varied around the critical point of the percolation transition, k = 1. When k 1, the p(s) is described by the statistics of the Gaussian orthogonal ensemble (GOE), one of the major statistical ensembles in Random Matrix Theory, whereas at k = 1 it follows the Poisson level spacing distribution. Closely above the critical point, p(s) can be described in terms of an intermediate distribution between Poisson and the GOE, the Brodydistribution. Furthermore, below the critical point p(s) can be given with the help of the regularized Gamma-function. Motivated by these results, we analyse the behaviour of p(s) in real networks such as the internet, a word association network and a protein-protein interaction network as well. When the giant component of these networks is destroyed in a node deletion process simulating the networks subjected to intentional attack, their level spacing distribution undergoes a similar transition to that of the E-R graph.

(Invited) Toward the Reduction of Performance-Limiting Defects in SiC Epitaxial Substrates

“…The observed basal plane bending of the crystal is reasonably understood in terms of the temperature distribution in SiC crystals during the PVT growth process [2,3]. In the PVT growth process, crystal growth is primarily driven by the temperature gradient along the c-axis, and thus large shear stresses are imposed on the crystal during growth.…”

“…3, where the densities of BPDs and TSDs show a positive correlation; crystals that contain more TSDs generally exhibit a larger density of BPDs [3]. This correlation stems from the multiplication process of BPDs in SiC crystals and is indicative of the relevance of the TSD reduction to the implementation of SiC substrates with a lower BPD density.…”

Polytype inclusions and polytype stability in silicon-carbide crystals

“…The possible causes of their appearance were considered previously [31][32][33][34][35][36][37] and can be related to the adsorption of an impurity [34,35], a difference between the energy parameters of various double Si-C layers within the polytype structure [33,36], a difference in the configuration of elementary steps [33,36,37], and so on.…”

Present Status and Prospects of Large Diameter SiC Single Crystal Substrates

“…Fig. 8 X-ray rocking curve relative peak position as a function of the beam position across the diameter of two-inch diameter 4H SiC crystals grown under diŠerent thermoelastic stress conditions; (a) crystal grown under a low thermoelastic stress condition and (b) crystal grown under a high stress condition 37) . Fig.…”