Epitaxial Growth of Silicon Films on SiO₂ Patterned Si(100) Substrates by Atmospheric Pressure Chemical Vapor Deposition

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.

APCVD Deposition of Si Film on SiO₂ Patterned Si (111) Substrates for Solar Cells

“…Comparing circular patterns and triangular prisms appearing in the Si films, it has been found that the size of a triangular prisms approximately equals to the sum of a circular diameter and a circular distance on the pretreated substrates. Epitaxial Si films grown on SiO 2 patterned Si (100) substrates showed different surface morphologies, and pyramid array appeared in the Si film surface on substrates with similar circular patterns [16].…”