# Transient Numerical Modelling of the Pin-in-Paste Technology
## 3 Results and Discussion
If connectors are oriented in parallel with the squeegee movement (due to design considerations), providing additional solder paste to the last holes (where a lower filling is expected) would be required, e.g., by utilizing pre-form (pre-shaped and fluxless) solders. The effect of hole shape on the hole-filling was also investigated. Oblong-shaped through-holes were analyzed by utilizing rectangular-shaped holes in the numerical model. Five different shapes were investigated, and the linear dimensions of the holes were varied at 1.0 \(\times\) 1.0, 1.0 \(\times\) 1.5, 1.0 \(\times\) 2, 1.0 \(\times\) 2.5, and 1.0 \(\times\) 3.0 mm (Figure 12). The holes with different shapes were also oriented in two directions: perpendicular to and in parallel with the travelling direction of the printing squeegee. Note that the dimension of the through-holes in \(z\)-direction was increased from 1.55 to 4 mm, since in the case of larger holes (e.g., 1.0 \(\times\) 2 mm), a filling larger than 1.55 mm was expected. The filling of rectangular-shaped through-holes was investigated at three different printing velocities (20, 70, and 120 mm/s). Similarly to the previous case, the size of the rectangular holes (1 \(\times\) 1 mm \(\ldots\) 1 \(\times\) 3 mm) did not affect the hole-filling significantly if the holes were oriented perpendicular to the travelling direction of the squeegee. However, a significant increase in the hole-filling was found, depending on the hole size, if the holes were oriented in parallel with the squeegee movement. The differences in the hole-filling between the smallest (1 \(\times\) 1 mm) and the largest (1 \(\times\) 3 mm) holes were 13%, 11%, and 10% for the printing velocities of 120, 70, and 20 mm/s, respectively (Figure 12). Figure 11: Comparing the cases utilizing a single hole or multiple holes in the printed wiring board (printing speed was 120 mm/s): (**a**) dynamic viscosity of the solder paste; (**b**) pressure along the line of the stencil. The dynamics of hole-filling were analyzed and compared between the cases of orienting a through-hole perpendicular to or in parallel with the travelling direction of the printing squeegee. It was found that the through-holes were filled almost linearly over time (Figure 13). However, the pressure on the solder paste increases exponentially as the squeegee travels over the through-hole [10,11]. The amount of solder paste also gradually increases in the hole, introducing resistance against the filling and resulting in almost linear fill-dynamics. This implies that the hole-filling depends mainly on time spent by the printing squeegee over the through-holes (considering identical process and material parameters). Therefore, larger hole-filling is expected if the rectangular- or oblong-shaped through-holes are oriented in parallel with the travelling direction of the squeegee. Similarly, gradually larger hole-filling is anticipated if the linear size of the holes is extending in parallel with the squeegee movement. The orientation of oblong-shaped through-holes can be designed according to the solder paste requirement for a specific component lead geometry. If the component leads are smaller for a particular oblong-shaped through-hole, thus requiring more solder paste to form appropriate solder joints, the respective through-holes should be oriented in a parallel direction with the squeegee movement. If the lead sizes are larger, the through-holes can be oriented perpendicular to the squeegee movement. Figure 12: Hole-filling as a function of rectangular-shaped through-holes at different printing speeds (note that the dimension of the holes in \(z\)-direction was 4 mm). Figure 13: Comparing the hole-filling of rectangular-shaped holes (1 \(\times\) 2 mm) oriented in parallel with or perpendicular to the travelling direction of the printing squeegee (printing speed was 120 mm/s).