Grown-in microdefects of a slowly grown Czochralski (CZ) silicon crystal were studied by short wavelength synchrotron radiation topography and successfully visualized. It was shown that the microdefects had spherical strain fields, by comparing the defect images in the two topographs taken with the Bragg reflections perpendicular and parallel to the growth direction. The radial distributions of the microdefect size and density were measured from the defect images in the topographs. The misfit volume of the microdefects was approximately 1 ×10-12 cm3 at the central axis region of the crystal ingot, and decreased monotonically toward the peripheral region of the crystal. The density of the microdefects was approximately 300/cm3 at the center of the crystal, increased toward the periphery and then decreased rapidly to almost zero in the very peripheral region approximately 7 mm from the surface of the crystal ingot. These radial distributions are discussed in connection with the self-interstitial atoms of silicon crystals.
Lattice defects induced by laser irradiation and their thermal stability during subsequent oxidation were studied by transmission electron microscopy, x‐ray topography, and preferential etching. High power laser pulses above 20 J/cm2 produced dislocation lines and dislocation clusters. Laser pulses of about 15 J/cm2 also generated dislocation clusters and pseudo‐swirl defects in the irradiated region. All of these defects were thermally stable. However, thermally stable defects were not observed when laser pulses of less than 15 J/cm2 were used, although unstable dislocations were generated. The suppression of defect formation by laser damage gettering was examined using Sirtl etching. It was found that thermally stable dislocations and pseudo‐swirl defects acted as sinks for point defects and prevented the formation of precipitates during a subsequent oxidation. Laser damage gettering was used to improve generation lifetime in metal‐oxide‐semiconductor (MOS) capacitors with the result that generation lifetime in the gettered area was improved by two orders of magnitude over that in the ungettered area.
Grown-in microdefects of a Czochralski (CZ) silicon crystal grown at a slow growth rate were studied by section topography using high energy synchrotron radiation. Images of the microdefects in the section topographs were analyzed quantitatively using computer simulation based on the Takagi-Taupin type dynamical diffraction theory of X-rays, and reproduced successfully by the simulation when the microdefects were assumed to be spherical strain centers. Sizes and positions of the microdefects were able to be determined by detailed comparison between the experiments and the computer simulations. The validity of the computer simulation in an analysis of the section topographs is discussed.
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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