Effect of Time and Pressure on Ultrasonic Bonding Strength of Flexible Printed Circuit Board to Glass with Nonconductive Film

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.

Evaluation of Die-Attach Bonding Using High-Frequency Ultrasonic Energy for High-Temperature Application

“…Low shear strength at low bonding force is caused by insufficient frictional heat generation and irregular movement of the ultrasonic horn. 7 To investigate the effect of the ultrasonic bonding time on the die-attach bonding, the ultrasonic power and bonding force parameters were set at 32 W and 20 MPa, which gave the highest shear strength previously. The ultrasonic bonding time was then varied from 0.5 s to 1.5 s. Figure 5 presents the results showing the effect of bonding time on shear strength.…”