reliability modeling of soldered interconnections

1046 IEEE TRANSACTIONS ON COMPONENTS, HYBRIDS, AND MANUFACTURING TECHNOLOGY, VOL. 15, NO. 6, DECEMBER 1992

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Reliability Modeling of Soldered Interconnections James F. Prosser and Nicholas T. Panousis, Fellow, IEEE

Abstract-This paper describes the results of work to determine the minimum solder height that would produce a satisfactory joint in an electronic assembly used in IBM disk drives. Solder pads with heights ranging from 20 to 160 pm were produced by varying the solder deposition process. After joints were made using the standard soldering process, the joint strengths were measured by pulling the wire at an angle of 45" and measuring the force required to either break the wire (wire breaks) or pull the wire out of the solder (wire peels). A figure of merit for the solder process is defined as the fraction of wire peels. A key part in this paper is the use of a generalized regression model to correlate this figure of merit to solder height. This allows interpolation of the data, calculation of confidence intervals, and a check of the validity of process control plans. The model is used to determine the minimum solder height, and to establish a sampling plan to monitor production.

I. INTRODUCTION N THE manufacture of electronic assemblies used in IBM I San Jose disk drives, solder joints are made to solder pads

on flexible cables. Soldering is done by pressing the wire into a solder bump on the cable with a heated thermode. The height of this solder bump is an important parameter; if the bump is too high, bridging occurs between adjacent bumps; if the bump is too low, the solder joint is weak and may be a reliability problem.

Experiments were done to determine the minimum solder height that would produce a satisfactory joint. Joints were made to solder pads with heights ranging from 20 to 160 pm. The height of each bump was measured by Tally step prior to forming the joint. The strength of the joint was determined by pulling the wire at a 45" angle and recording the force necessary to either break the wire, called a wire break, or to pull the wire out of the solder, called wire peel.

A figure of merit for the joint strength was selected as the ratio of the number of wire peels to the sum of the wire breaks plus wire peels. A regression model was used to determine this figure of merit as a function of solder height. The techniques of generalized linear models (GLM's) were used to do this. By using an appropriate transformation and iterative weighed regression, the problems associated with regression analyses in which the dependent variable is constrained to be between 0 and 1 are circumvented. These problems are nonnormality of errors, nonconstant variance, and finite data range.

Manuscript received February 3, 1992; revised August 7, 1992. This paper was presented at the 42nd Electronic Components and Technology Conference, San Diego, CA, May 18-20, 1992.

J. F. Prosser is with the Storage Systems Products Division, IBM Corpora- tion, San Jose, CA 95193.

N. T. Panousis is with Pacific Communication Sciences, Inc., San Diego, CA 92121.

IEEE Log Number 9203943.

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SOLDER HEIGHT IN MICRONS

Fig. 1. Distribution of solder heights.

This paper describes the results of the experiments, the analysis, and modeling of the data. The recommendations for a minimum solder height value, and a sampling plan for the quality control of the manufacturing line are given.

11. RESULTS

For each joint, the solder height, the breaking force, and the failure mode were recorded. Initially, four failure modes were recorded. However, for analysis, the data were grouped into two modes: 1) a wire peel and 2) a wire break. Heel breaks, nugget breaks, and wire breaks are all variations of wire breaks so these three modes are combined into the wire break mode.

Fig. 1 shows the distribution of solder heights in the experiment. Two representations are used to display the distribution: the empirical density function (left axis) and the empirical cumulative function (right axis). It can be seen that the range of solder heights was quite large, 18-160 pm. There is a gap in the range between 85 and 100 pm. A key part of this paper is the development of a linear model to allow interpolation in that missing region.

Table I is a summary of the pull strength failure mode results. It shows the fraction of joints failing as wire breaks and wire peels and also includes the fraction of joint strengths <2 g (all wire peels), as a function of solder height. At higher values of solder height, mainly wire breaks occur. This suggests that the intrinsic strength of the wire-to-solder bond is larger than the tensile strength of the wire. The solder height groupings in Table I were chosen to obtain an initial general view of the data. In a later section, when the linear model is developed, a much finer grouping of solder heights will be used.

0148-641 1/92$03.OO 0 1992 IEEE

PROSSER AND PANOUSIS: RELlABlLlTY MODELING OF SOLDERED INTERCONNECTIONS 1047

TABLE I SUMMARY OF PULL TEST FAILURE MODE RFSULTS

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Solder Heights (pm) Wire Breaks Wire Peels Joints with Strength < 2 g. All were wire peels

25-40 27/38 (71%) 11/38 (29%) 8/38 (21%)

56-70 182/191 (95%) 9/191 (5%) 0/191 (0%) 71-85 124/127 (98%) 3/127 (2%) 0/127 (0%) 86-100 25/25 (100%) 0/25 (0%) 0/25 (0%)

101+ 236/236 (100%) 0/236 (0%) 0/236 (0%)

41-55 125/138 (91%) 13/138 (9%) 1/121 (0.8%)

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45’ PULL STRENGTH (GRAMS)

Fig. 2. Distribution of wire peels only. Distribution is for the complete range of solder heights.

111. ANALYSIS

The first step in the analysis is to consider the total of all 755 individual pull test values as a single, overall, multimode distribution spanning the complete solder height range. The goal is to deconvolve (separate) this overall multimode distribution into its two constituent distributions; one for wire peels only, and the other for wire breaks only. The approach taken was that of Kaplan and Meier [l], often called the product limit method.

Fig. 2 shows the result for wire peels only plotted on log normal probability paper. The asterisks show the distribution of joints that were wire peels. The x’s displayed along the bottom of the graph represent the joints in which the values of the wire peels are masked by wire breaks. It can be seen in Fig. 2 that the range in wire peel strength is quite large: from 2 g (the lower resolution of the instrument) to 28 g. As noted earlier, still higher values of wire peel strengths are not detected in this weak link type of pull test. This is because the intrinsic wire-to-solder joint strength is larger than the tensile strength of the wire (about 28 g in this case), so the wire breaks leave the intrinsic strength of the wire-to-solder bond undetected. Fig. 3 is the complement of Fig. 2 and shows the distribution of wire breaks. This time the x’s along the bottom represent the solder joints which fail as wire peels.

LOGNORMAL PROBABILITY PLOT

45’ PULL STRENGTH (GRAMS)

Fig. 3. Distribution of wire breaks only. Distribution is for the complete range of solder heights.

The next step in the analysis is to consider the distribution of peel strengths as a function of solder height. These are shown in Fig. 4(a)-(d). As was seen in Table I the fraction of wire peels decreases as the solder height increases. Fig. 4 also shows that the strength of the wire peels, at a given percentile, increases as the solder height increases. The variance or spread also decreases with increasing solder height. So, for larger solder heights, not only are there a smaller fraction of wire peels, but the joints that do peel are stronger and more tightly distributed. Based on this, it was decided to define the fraction of peels as a figure of merit for joint strength.

IV. MODEL The intention is to express the fraction of peels as a function

of solder height. A method of doing this is generalized regression. The usual method of ordinary least squares (Om’s) regression is not appropriate for this situation for the following reasons: 1) the dependent variable (fraction peels) is binomial and varies from 0 to 1. In OLS, the dependent variable varies from -cc to 00; and 2) for binomial data, the variance is not constant over the range of the data.

The methods of generalized regression were developed to handle this situation. To take care of reason l), a transformation is made to the dependent variable. A common transformation for this case is Y = In( P/ 1 - P ) where P =


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(4 (d 1 Fig. 4. Distribution of wire peels only. Distribution is for the solder height ranges indicated

TABLE I1 SUMMARY OF GLM METHOD

NORMAL REGRESSION NOT APPROPRIATE BECAUSE: DATA BOUNDED BETWEEN 0 1 VARIANCE NOT CONSTANT OVER DATA RANGE

TRANSFORM DATA Y = ln(P/( l - P ) ) X = ln(SH) (lb)

GLM METHOD: (la)

USE WEIGHTED REGRESSION: WI = NI X PI X (1 - PI) SOLVE ITERATIVELY: Y = A + B X UPDATE W, WITH MOST RECENT VALUE OF PI CALCULATE CONFIDENCE INTERVALS:

( A + B r X - Y)/VAR*0.5 < li (2a) VAR = VAR(A) + 2rXrCOV(A, B) = X t 2xVARB

CHECK FOR OVER DISPERSION (2b)

fraction of peels. Since solder height (SH) varies from 0 to 00, a log transformation is used: X = ln(SH) to make it vary from -00 to 00. To address reason 2), iterative weighed least squares are used [2].

A good discussion of this method is contained in [3]. In addition to explaining the concepts, it contains the details necessary to perform the calculations using only a least squares regression program, Otherwise, special programs are required. However, the text in [3] contains an error. The appendix of our paper explains the error and gives the correct technique. Table I1 is a summary of this method. Table 111 gives the data used in the regression and Table IV gives the results. Fig. 5 shows the results of the model compared to the data.

From the model ((1) in Table IV), we can now produce Table V which shows the fraction of peels at various solder heights. To determine a satisfactory value for the figure of merit, consider Fig. 4. The distribution of joint strengths in Fig. 4(c) is such that values of wire peels < 2 g would not be expected. That leads to the conclusion that 3/127 or 0.02362 (-0.02) peels is an objective for the product. Based on our model and (2) in Table 11, we calculate that at 90% confidence to obtain 0.020 fraction peels, the SH will be between 71.4 and 96.0 pm.

Before we leave this analysis, a check for over-dispersion should be made. As the authors in [2] point out, in practice, there is a strong possibility that the variance in the Y variable (11(P/1 - P ) ) exceeds the variance that was assumed in generating the model (the binomial variance: mp(1-p)). If this is the case, the confidence limits will have to be recalculated, and it will not be appropriate to use standard methods for attribute control charts. A test for over-dispersion is

If O2 N 1, there is no over-dispersion. In our case, O2 = 1.12 indicating that, for this situation, over-dispersion is not a problem.

1049 PROSSER AND PANOUSIS: RELIABILITY MODELING OF SOLDERED INTERCONNECTIONS

TABLE Ill DATA USED FOR GLM

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Solder Heights Number Peels Number Joints

25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175

3 2 5 1 2 2 9 3 5 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

5 11 11 11 25 36 77 51 79 61 69 24 34 10 10 5

10 12 26 29 24 38 30 29 10 15 8 2 1 1 1

TABLE IV RESULTS OF GLM

ln(P/ l - P) = A + B x ln(SH) (1) il B Cov Matrix

TABLE V FRACTION PEEL VERSUS SOLDER HEIGHT DETERMINED FROM GLM

Solder Height (pms) Fraction Peel

50 0.094 60 0.052 70 0.032 80 0.020 90 0.013

100 0.009 110 0.008 120 0.005

To have a 0.02 fraction peel, the solder height is 80 pm. The confidence interval is: 71-96 pm.

SHEWHART OC CURVE - PROPORTION DEFECTIVE 'h N = 69. UCL = 0.0417

r I I I I I I I l ' I 0.02 0.04 0.06 0.08 0.10

PROCESS PROPORnON DEFECTM

SHEWHART ARL CURVE - PROPORTION DEFECTIVE N = 60, UCL = 0.0417

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PROCESS PROPORnON OEFECTM

11.32 -3.47 4.2841 - 1.0772 -1.0772 0.2729

Fig. 6. Sampling plan for process control.

SOLDER HEIGHT IN MICRONS

Fig. 5. Fit of generalized regression model to solder heights.

v. MONITORING THE PROCESS

To monitor the manufacturing process, it was decided to sample production on a daily basis and test the joints by pulling the wires as described earlier. The fraction of wire peels and their strengths were noted. A convenient sample size of 60 joints was chosen. Fig. 6 shows the average runlength (ARL) and operating characteristic (OC) curves for a sample size of 60. Since a very low value of peel strength usually indicates a processing problem irrespective of fraction failed, a minimum allowable value of peel strength was also added to the acceptance criteria.


VI. CONCLUSIONS

We have described the results of work to determine the minimum solder height that would produce a satisfactory joint. Based on distributional analysis, a figure of merit for the solder process is defined as the fraction of wire peels. Then a model was made correlating the figure of merit to solder height using a generalized regression analysis. Based on this model, a minimum solder height was determined, and a confidence interval was calculated for the minimum solder height. A check for over-dispersion was made and it was not found to be a problem. A sampling plan was developed to monitor the manufacturing process.

REFERENCES

[ 11 E. L. Kaplan and P. Meier, “Nonparametric estimation from incomplete observations,” J. Amer. Statist. Assoc., vol. 53, pp. 457-481, 1958.

(21 P. McCullagh and J. Nelder, Generalized Linear Models (2nd Edition). London, U.K.: Chapman and Hall, 1989.

[3] S. Weisberg, Applied Linear Regression (2nd Edition). New York: Wiley, 1985, pp. 267-270.

APPENDIX

In Weisberg [3, p 2691 shows how to use iterative weighted least squares regression to analyze binom51 regre_ssion data. The weights, he recommends, w, = nz/d,(l - d,), are not correct. These weights are the inverse of the variance of yz/n,. The appropriate weights should be the inverse of the variance of the logit (yz/n2), since logit (yz/nz) is used in the regression model, not (y,/n,). In the first edition of Analysis of Binary Data by D.R. Cox (Chapman & Hall, 1970), the asymptotic variance of logit (yz/nz) is given as l/O,(l - d,)n,. Hence, the YeightsJw,) given in [3, pp. 269-2701 of his book should be dZ(1 - 4)n,.

of 40 technical papers.

ACKNOWLEDGMENT

The authors thank Allan Greenberg for designing and exe- cuting the experiment and Armie Mesa for her tireless and diligent work.

James F. Prosser received the B.S. degree in physics from the University of Delaware and the M.S. degree in physics from Michigan State University.

In 1968 he joined IBM in East Fishkill, NY, where he worked in device and reliability physics of field effect transistors. Currently, he is at IBM’s San Jose facility where he works in the application of statistics to problems in reliability and quality control.

Nicholas T. Panousis (M’74-SM’82-F’92) is a Senior Reliability Engineer with Pacific Communi- cations Sciences Inc., San Diego, CA. Prior to that, he was a Senior Scientist with IBM in San Jose, CA, where his main interests were the design, development, and manufacturing of thin film magnetic recording heads for use in data storage systems. Before joining IBM he spent most of his earlier career with Bell Telephone Labs, in Allentown, PA, where he was involved with thin and thick film diffusion phenomena. He has published in excess

Dr. Panousis has served on the Technical Program Committee of the Electronic Components and Technology Conference for the past 17 years. He received the Award for the Best Paper of the 1978 ECTC. He has served as Editor of the IEEE Transactions on Components, Hybrids, and Manufacturing Technology for three years. In 1988 he received the CHMT Society’s Contribution Award.

reliability modeling of soldered interconnections

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