Michael J. Varnau This article describes a reliability analysis of various process variations for aluminum wire bonds used in hybrid electronic modules. It illustrates the importance of selecting an appropriate distribution for data analysis based on an understanding of the real world factors driving the data and calculating the mathematical best fit to the distribution. Theoretical
Overview Background
One of the added process complexities is controlling the thickness of the solder joint under the bond pad. This is important since the effective coefficient of thermal expansion of the bond pad is significantly higher than the alumina oxide ceramic substrate. If the joint is too thin, the solder joint can crack in temperature cycling. If the joint is too thick, there is a strong tendency for the bond pad to tilt, which adversely impacts the quality of the bond of the aluminum wire to the bond pad. The electronics industry typically specifies the minimum average solder joint thickness for small devices such as these bond pads. However, one of the major customers for this product family specifies the absolute minimum acceptable solder joint thickness for all devices in their modules at a 4.5 sigma capability. The process in use exceeded the reliability requirements of all customers, but was not capable of meeting the minimum specified solder joint thickness and constraining the bond pad tilt within the wire bonding process requirements. The wire bonding process capability begins to deteriorate when the tilt exceeds 5 degrees and becomes unacceptable when the tilt exceeds 7 degrees.
Figure 1: Electronic ignition module subassembly, aluminum clad copper bond pad construction (side view) and illustration of solder thickness and tilt angle Process Development and
Data Analysis The Bond Pad Solder Thickness histogram (Figure 2) shows that the distribution of Bond Pad Solder Minimum Thickness is both peaked and skewed to the right. This visual observation is validated by statistical analysis. The data analysis indicates that the average 3 sigma value of the distribution is a negative number, which is physically impossible. The calculated Skew and Kurtosis values shown in Table 1 also validate that a Gaussian model is not a good fit to this data set. The values shown in red indicate that the distribution is nonGaussian.
Figure 2: Histograms of solder thickness and tilt
Table 1: Data Summary One of the features of Weibull++ is the ability to quickly determine an appropriate distribution for analysis of data using the Distribution Wizard. The results of the Distribution Wizard for one of the potential improved processes indicates that the best fit is a 3 parameter Weibull and the second best fit is a Lognormal distribution. Probability plots for both distributions are shown in Figures 3 and 4.
Figure 3: Probability plot for Weibull analysis
Figure 4: Probability plot for Lognormal analysis Both distributions have a mean value of 34.7 microns thickness. The 3parameter Weibull distribution has ρ = 0.9918 and the Lognormal has ρ = 0.9910 but they make very different predictions near the left tail of the distribution. While the 3parameter Weibull makes predictions that are closer to the customer expectations, its choice for this physical situation would be difficult to justify. Other experiments clearly show that it is possible to get minimum solder thicknesses much lower than the calculated γ value. There was no change of process parameter between Process 1 and Process 2 that inherently assures a minimum thickness condition. The other consideration is that the distributions of the other process variations in the experimental space are a better fit to the Lognormal distribution. The choice of the Lognormal distribution in this case allows the comparison of all the process variations on the same plot. This is otherwise not possible since the scales of the Lognormal and Weibull distribution plots are different. Many process variations were evaluated using Design of Experiment methodologies. Two of the most interesting process variations are shown along with the original process in Figure 5. The mean values of Processes 1, 2 and 3 are 8.3, 34.8 and 14.9 microns, respectively. However, the predicted values of mean 4.5 sigma are 2.5, 5.2 and 7.0 microns, respectively. Process 3 has a much lower mean value, but has much less variation, which is represented by a steeper slope in the plotted Lognormal distribution. The differences in process variation are highlighted in the contour plot comparing the three different distributions (Figure 6). The plot shows that the mean values of the distributions are significantly different. The plot highlights the difference in variation between processes and indicates that the amount of variation in Process 1 is not statistically significantly different than Processes 2 or 3. However, the amount of variation in Process 3 is statistically significantly lower than Process 2.
Figure 5: Multiple plot for solder thickness comparison
Figure 6: Contour plot for solder thickness Similar analyses can (and should) be made for the bond pad tilt for each process. The Distribution Wizard indicates that the best model for bond pad tilt is either a Normal or 2 parameter Weibull distribution, depending on the specific process variation being analyzed. On the whole, the 2parameter Weibull distribution was the best compromise across the experimental space. The multiple plot and contour plot for Processes 1, 2 and 3 are shown in Figures 7 and 8. The tilt evaluation of Process 3 is shown to be not as good as Process 2, but is acceptable. The plot format chosen here is the "Unreliability vs. Time." The plot has been relabeled to match its actual use. This format accommodates multiple distributions and gives the user a better feel for how the distribution will behave near the right tail than other plot formats. The contour plot for the tilt evaluation validates our conclusions from the previous plot. Again, Process 3 has more tilt than Process 2, but the mean value is less than Process 1. Figure 7: Multiple plot for tilt comparison
Figure 8: Contour plot for bond pad tilt Summary of Data Analysis
Summary of Analysis
Process The analysis described in this article was performed in ReliaSoft’s Weibull++ 6. If Weibull++ is installed on your computer, you can download the Data Folio from the Web by rightclicking the following link and selecting Save Target As: Weibull++ 6 Data Folio (*.rw6, 398 KB).
