Fundamentals of Package Manufacturing

1. Fundamentals of Package Manufacturing Ideen Taeb Noopur Singh

2. What is Manufacturing? Process by which raw material are converted into finished products In electronic Input material: Metals, polymers, ICs Output: dual-in-line packages, ball grid arrays, multichip modules, PWB Type of process in electronic packaging: coating, photolithography, planarization, soldering, bonding, encapsulation, …

3. Manufacturing System

4. Goals of Manufacturing Low Cost Yield High Quality Stable and well-controlled manufacturing High Reliability Minimization of manufacturing faults

5. System-level View of Packaging Technologies

6. Fundamentals of Manufacturing Discrete part manufacturing Assembly of distinct pieces to yield a final product: IC-> PWB Continuous flow manufacturing Processing operations which do not involve assembly of discrete parts Example: process which printed boards are produced prior to chip attachment

7. Statistical Fundamentals Quality characteristics are elements which collectively describe packaging products’ fitness for use. Variation: No 2 products are identical. 2 thin metal films Small vs. large Variation Quality improvement Statistics to describe variation

8. Statistic Fundamentals Sample Average( ) Sample Variance( )

9. Review of Statistical Fundamentals Probability Distribution Mathematical model that relates the value of a random variable with its probability of occurrence. Discrete vs. Continuous Discrete Distributions Binomial Distribution, Poisson Distribution

10. Binomial Distribution Process of only 2 possible outcomes: “success” or “failure”

11. Poisson Distribution It is defined as below Where x is an integer, and is a constant >0. Used to model the number of defects that occur as a single product

12. Continuous Distribution Normal distribution, exponential distribution

13. Normal Distribution Most important and well-known probability. Cumulative distribution

14. Exponential Distribution Widely used in reliability engineering as a model for the time to failure of a component or system

15. Random Sampling Any sampling method which lacks systematic direction or bias Allows every sample an equal likelihood of being selected

16. Chi-Square Sampling Distribution • Originates from normal distribution • If x1, x2 ,…. xn are normally distributed random variables with mean zero and variance one, then the random variable: • is distributed as chi-square with n degrees of freedom.

17. Chi-square Cont. • Probability density function of • Where is the gamma function

18. The t Distribution • Based on normal distribution • If x and are standard normal and chi-square random variables, then the random variable: • Is distributed as t with k degrees of freedom

19. The t distribution • The probability density function of t is

20. The t distribution

21. The F Distribution • Based on chi-square distribution • If and are chi-square random variables with u and v degrees of freedom, then the ratio:

22. The F Distribution • The probability density function of F is:

23. Estimation of Distribution Parameters • Challenge is to find the mean and the variance • Point estimator provides a single numerical value to estimate the unknown parameter • Interval estimator provides a random interval in which the true value of parameter being estimated falls within some probability. • Intervals are called confidence intervals.

24. Confidence Interval for the Mean with Known Variance • Where is the value of the N(0,1) distribution such that P{z>= }=a/2

25. Confidence Interval for the Mean with Unknown Variance Where is the value of t distribution with n-1 degrees of freedom P{tn-1>=ta/2,n-1}=a/2

26. Confidence Interval for the Difference between Two Means, Variances Known • Consider 2 normal random variables from two different populations, Confidence interval on the difference between the means of these two populations is defined as:

27. Confidence Interval for the Difference between Two Means, Variances Known • Pooled estimate of common variance

28. Hypothesis Testing • An evaluation of the validity of the hypothesis according to some criterion. • Expressed in the following manner: • H0 is called null hypothesis and H1 is called alternative hypothesis

29. Hypothesis testing • Two types of errors may result when performing such a test. • If the null hypothesis is rejected when it is actually true, the a Type I error has occurred. • If the null hypothesis is accepted when it is actually false, the a Type II error has occurred. • Probability for each error:

30. Hypothesis Testing • Statistical Power • Power represents the probability of correctly rejecting

31. Process Control • Controls to minimize variation in manufacturing • Statistical Process Control (SPC): tools to achieve process stability and reduce variability • Example: Control Chart-> Developed by Dr. Shewhart

32. Control Chart • Graphical display of a quality characteristic that has been measured from a sample versus the sample number or time

33. Control Chart • Represents continuous series of tests of the hypothesis that the process is under control • Points inside the limit-> accepting hypothesis • Points outside the limit-> rejecting hypothesis

34. Control Chart for Attributes • Attributes are quality characteristics that can not be represented by numerical values: Defective, Confirming • Three commonly used control charts for attributes: • Fraction nonconforming chart (p-chart) • The defect chart (c-chart) • The defect density chart (u-chart)

35. Control Chart for Fraction Nonconforming • Defined as number of nonconforming items in a population by total number of items in the population. • Where p is probability that any of the product will not confirm, D is number of nonconforming products • Sample fraction nonconforming is defined as

36. Defect Chart • Charts that represent total number of defects • Where x is the number of defect, c>0 is the parameter of poisson distribution

37. Defect Density Chart • Chart to show average number of defects over a sample size of n.

38. Process Capability • Quantifies what a process can accomplish when in control • PCR: Process Capability ratio: • A PCR>1 implies that natural tolerance limits are well inside the specification limits, therefore low number of nonconforming lines being produced

39. Statistical Experimental Design • Statistical Experimental design: Is an efficient approach for mathematically varying the controllable process variables in an experiment and ultimately determining their impact on process/product quality. • Benefits: • Improved Yield • Reduced Variability • Reduced development Time • Reduced cost • Enhanced Manufacturability • Enhanced Performance • Product Reliability

40. Comparing Distribution

41. Comparing Distributions • Statistical hypothesis test: • Calculate test statistic (to=0.88) • Calculate variances for each sample • (Sa=3.30, Sb=3.65) • Calculate pooled estimate of common variance (Sp=3.30) The likelihood of computing a test statistic with v=Na+Nb-2=18 degrees of freedom equal to 0.88 is 0.195. Statistical significance of the test is 0.195. Therefore, there is only a 19.5% chance that the difference in mean yields is due to pure chance. There is a 80.5% confidence that Method B is really superior to Method A

42. Analysis of Variance (ANOVA) • Used to compare two or more distributions simultaneously • To determine which process conditions have significant impact on process quality • To determine whether a given treatment or process results in a significant variation in quality

43. Analysis of Variance (ANOVA) • Through ANOVA we will determine whether the discrepancies between recipes or treatments are truly greater than the variation of the via diameters within the individual groups of vias processed with the same recipe.

44. Analysis of Variance (ANOVA) • Key parameters to perform ANOVA: Sum of squares to quantify deviations within and between different treatments ANOVA table

45. Analysis of Variance (ANOVA) • For the via example, the significance level of F ratio with vt and vr degrees of freedom if 0.000046. This means that we can be 99.9954% sure that real differences exist among the four different processes used to form vias in the example.

46. Factorial Designs • Factorial experimental designs used in manufacturing applications • Need to select • Set of factors (or variables) to be varied in the experiment • Range or levels over which variation will take place (maximum, minimum, center levels) • Two-level Factorials • Use max and min levels of each factor • For n factors (or variables) 2^n experimental runs

47. Two-level factorials • 2^3 factorial experiment for CVD process

48. Two-level factorials • We can determine • Effect of single variable on the response (deposition rate) called the Main effect • Interaction of two or more factors • Main effect = y+ - y- • P = dp+ - dp- (effect of pressure) • PxT = dpt+ - dpt- (variation of pressure effect with temperature) where d is the average deposition rate

49. Yates algorithm • Quicker and less tedious than the Factorial method • An experimental design matrix is arranged in standard order, • First column with alternating plus and minus signs • Second column of successive pairs of minus and plus signs • Third column of four minus signs and four plus signs (for the CVD example)

50. Yates algorithm