An analytical model for predicting the underfill flow characteristics in flip-chip encapsulation

Dynamic Filling Characteristics of a Capillary Driven Underfill Process in Flip-Chip Packaging

“…Among these, accurate predictions of filling time and front position are very important to making the underfill process more efficient and controllable. Much research 6,8,14,15) has modeled the filling time on the basis of the Washburn model, 7) which assumes a Newtonian fluid with one-dimensional, fullydeveloped laminar flow. According to the Washburn model, the filling time is given by, …”

“…The original Washburn model has two critical limitations: it intrinsically does not consider non-Newtonian characteristics of the encapsulant, nor does it model the effects of solder bump resistance. Thus, we used the analytical solutions proposed by Wan et al 8) to reflect both the geometric effects of the solder ball arrangement and the non-Newtonian fluid characteristics and then compared these analytical solutions and numerical results with experimental data. According to the Wan et al model, 8) the filling time is given by…”

“…To resolve it, a more elaborate study should be conducted in order to obtain detailed information on the dynamic contact angle with respect to time during the encapsulation process. Figure 6 presents the transient behavior of the filled volume fraction for the cases listed in Table 2, and compares the numerical predictions and analytical solutions from Wan et al's model 8) with the experimental data. Agreement was quite good, although some deviation was evident in the later stage of injection in Case 1.…”

“…The simplest model, the Washburn model, 7) assumes that the capillary flow is a fully developed laminar flow of a Newtonian fluid between two parallel plates without solder bumps. Wan et al 8) modified the Washburn model to reflect the flow resistance due to solder bumps and used the power-law constitutive equation for describing the non-Newtonian fluid behavior. In a numerical simulation, Nguyen et al 9) ascertained the solder ball resistance of the underfill flow using the plastics integrated circuit encapsulation computer aided design (PLICE-CAD) and validated the results by comparison with experimental data.…”

“…From the captured images, we estimated the filling times, which can be affected by two important factors: bump arrangements and resin viscosities. In addition, we conducted a FVM (finite volume method)-based numerical simulation using commercial CFD code (Fluent v. 6.3.26), and compared its numerical results to both the experimental data and the analytical solutions given by the previous model described by Wan et al (2005). The numerical predictions and analytical solutions estimating filling time were in good agreement with the experimental data, and the increase in spatial density of solder bumps allowed the flow to fill more slowly due to the increase in flow resistance.…”