Failure Probability Estimation of Anisotropic Conductive Film Packages With Asymmetric Upper-to-Lower Pad Size and Misalignment Offsets
Anisotropic conductive films (ACFs) are widely used in the packaging of flat panel displays and liquid crystal displays and for attaching bare chips to both flexible and rigid substrates. This paper utilizes the V-shaped curve method to analyze the failure probability of ACF packages with an asymmetric upper/lower pad size and misalignment offsets. In the proposed method, the probability of opening failures is modeled using a Poisson function, modified to take into account the effects of the pad-width difference and misalignment offset on the effective conductive area between opposing pads. Meanwhile, the probability of bridging failures is evaluated using an enhanced bridging model based on the distance between the neighboring pad pairs in the array. The failure probability of the pad array is evaluated as a function of both the difference in width of the upper and lower pads and the degree of misalignment between the opposing pads in the array. The results show that the V-shaped curve method provides the means to predict the ACF volume fraction which minimizes the failure probability of the ACF assembly given a knowledge of the pad-width difference and the misalignment offset. In addition, it is shown that when the misalignment offset is greater than the pad-width difference, the minimum failure probability reduces as the pad-width difference increases due to the corresponding increase in the effective conductive area between opposing pads. Conversely, when the misalignment offset is less than the pad-width difference, the minimum failure probability increases with an increasing pad-width difference due to the corresponding reduction in the effective conductive area between the pads.
Effects of Pad Array Dimensions and Misalignment Offsets on Optimal Fraction of Conductive Particles in Anisotropic Conductive Film Packages
The failure probability of anisotropic conductive film (ACF) packages is critically dependent on the volume fraction of conductive particles within the adhesive resin. In this study, the V-shaped curve method is used to determine the optimal volume fraction of conductive particles as a function of the bonding geometric parameters, the pad array dimension, and the misalignment offset between the upper and lower pads. In evaluating the corresponding failure probability of the ACF package, the probability of an opening failure is determined in accordance with a Poisson function model, while the probability of a bridging failure is derived using a box model. In computing the opening and bridging probabilities, the two models are modified to take account of the effects of package misalignments on the effective conductive area between opposing pads and the bridging path length between neighboring pairs of opposing pads, respectively. The opening and bridging probabilities are then combined using probability theory to establish the overall failure probability of the ACF package. In general, the results show that, for given bonding geometric parameters and misalignment offset, the optimal volume fraction of conductive particles remains approximately constant as the pad array dimension is increased. However, for given bonding geometric parameters and pad array dimension, the optimal volume fraction of conductive particles increases with an increasing misalignment error. Overall, the results show that, for any given values of the bonding geometric parameters, pad array dimension, and misalignment offset, the failure probability of the ACF package can be minimized by setting the volume fraction of conductive particles equal to the value corresponding to the tip of the V-shaped curve.
Numerical tools applied to power reactor noise analysis
In order to be able to calculate the space- and frequency-dependent neutron noise in real inhomogeneous systems in two-group theory, a code was developed for the calculation of the Green's function (dynamic transfer function) of such systems. This paper reports on the development as well as the test and application of the numerical tools employed. The code that was developed yields the space-dependence of the fluctuations of the neutron flux induced by fluctuating properties of the medium in the two-group diffusion approximation and in a two-dimensional representation of heterogeneous systems, for both critical systems and non-critical systems with an external source. Some applications of these tools to power reactor noise analysis are then described, including the unfolding of the parameters of the noise source from the induced neutron noise, measured at a few discrete locations throughout the core. Other concrete applications concern the study of the space-dependence of the Decay Ratio in Boiling Water Reactors, the noise-based estimation of the Moderator Temperature Coefficient of reactivity in Pressurized Water Reactors, the modeling of the beam- and shell-mode core-barrel vibrations in Pressurized Water Reactors, and the investigation of the validity of the point-kinetic approximation in subcritical systems driven by an external source. In most of these applications, calculations performed using the code are compared with at-power plant measurements. Power reactor noise analysis applications of the above type, i.e. core monitoring without disturbing plant operation, is of particular interest in the framework of the extensive program of power uprates worldwide.