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The formation of basal plane stacking faults in heavily nitrogen-doped 4H-SiC crystals was theoretically investigated. A novel theoretical model based on the so-called quantum well action mechanism was proposed; the model considers several factors, which were overlooked in a previously proposed model, and provides a detailed explanation of the annealing-induced formation of double layer Shockley-type stacking faults in heavily nitrogen-doped 4H-SiC crystals. We further revised the model to consider the carrier distribution in the depletion regions adjacent to the stacking fault and successfully explained the shrinkage of stacking faults during annealing at even higher temperatures. The model also succeeded in accounting for the aluminum co-doping effect in heavily nitrogen-doped 4H-SiC crystals, in that the stacking fault formation is suppressed when aluminum acceptors are co-doped in the crystals.

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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.

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