Fundamentals of Package Manufacturing

Ideen Taeb

Noopur Singh

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, …

Manufacturing System

Goals of Manufacturing

Low Cost– Yield

High Quality– Stable and well-controlled manufacturing

High Reliability– Minimization of manufacturing faults

System-level View of Packaging Technologies

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

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

Statistic Fundamentals

Sample Average( )

Sample Variance( )

n

xxxx n

...21

2

n

ii xx

ns

1

22 )(1

1

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

)( ii xpxxP

Binomial Distribution

Process of only 2 possible outcomes: “success” or “failure”

xnx ppx

nxp

)1()(

np

)1(2 pnp

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

!)(

x

exP

x

2

Continuous Distribution

Normal distribution, exponential distribution

Normal Distribution

Most important and well-known probability.

Cumulative distribution

                                            ])(2

1exp[

2

1)( 2

x

xf

adxxfaFaxP )()()(

Exponential Distribution

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

xexf )(

aeaF 1)(

22 /1

/1

Random Sampling

Any sampling method which lacks systematic direction or bias

Allows every sample an equal likelihood of being selected

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.

222

21

2 ... nn

Chi-square Cont.

Probability density function of

Where is the gamma function

2/21)2/(2

2/

2 )(

22

1)(

en

f n

n

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

2k

k

xt

k

k/2

The t distribution

The probability density function of t is

1

)2/(

]2/)1[()(

2

k

t

kk

ktf

The t distribution

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:

2u2

v

v

uF

v

uvu /

/2

2

,

The F Distribution

The probability density function of F is:

2/)(

12/

2/

1222

2)( vu

u

u

Fu

Fvuvuvu

Fg

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.

Confidence Interval for the Mean with Known Variance

Where is the value of the N(0,1) distribution such that P{z>= }=a/2

2/z2/z

nzx

nxx

2/2/

Confidence Interval for the Mean with Unknown Variance

n

stx

n

stx nn 1,2/1,2/

Where is the value of t distribution with n-1 degrees of freedom P{tn-1>=ta/2,n-1}=a/2

1,2/ nt

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:

2

22

1

21

2/21212

22

1

21

2/21 {)(}{nn

zxxnn

zxx

Confidence Interval for the Difference between Two Means, Variances Known

Pooled estimate of common variance

}11

{)(}11

{21

,2/212121

,2/21 nnstxx

nnstxx pvpv

2

)1()1(

21

222

211

nn

snsnsp

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

01

00

:

:

H

H

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:

)()__(

)()__(

00

00

falseHacceptHPerrorIItypeP

falseHrejectHPerrorItypeP

Hypothesis Testing

Statistical Power

Power represents the probability of correctly rejecting

)(1 00 falseHrejectHPPower

0H

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

Control Chart

Graphical display of a quality characteristic that has been measured from a sample versus the sample number or time

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

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)

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

n

Dp ˆ

xnx ppx

nxDP

)1()(

Defect Chart

Charts that represent total number of defects

Where x is the number of defect, c>0 is the parameter of poisson distribution

!)(

x

cexP

xc

Defect Density Chart

Chart to show average number of defects over a sample size of n.

n

cu

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

6LSLUSL

PCRC p

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

Comparing DistributionPWB Board Method A Yield(%)

(standard)

Method B Yield(%)

(modified)

1 89.7 84.7

2 81.4 86.1

3 84.5 83.2

4 84.8 91.9

5 87.3 86.3

6 79.7 79.3

7 85.1 86.2

8 81.7 89.1

9 83.7 83.7

10 84.5 86.5

Average 84.24 85.54

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

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

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.

Via diameters (um) for four different process recipes

Recipe 1 Recipe 2 Recipe 3 Recipe 4

62 63 68 56

60 67 66 62

63 71 71 60

59 64 67 61

65 68 63

66 68 64

63

59

Analysis of Variance (ANOVA)• Key parameters to perform ANOVA: Sum of squares to quantify

deviations within and between different treatments

ANOVA table

Source of variation

Sum of Squares

Degrees of freedom

Mean Square

F- Ratio

Between treatments

St vt=k-1 st^2 st^2/sr^2

Within treatments

Sr vr=N-k sr^2

Total Sd vd=N-1 sd^2

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.

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

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

Run Pressure P

Temperature T

Gas flow rate F

Deposition Rate, d (A/min)

1 - - - d1

2 + - - d2

3 - + - d3

4 + + - d4

5 - - + d5

6 + - + d6

7 - + + d7

8 + + + d8

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

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)

Yates algorithmP T F Y (1) (2) (3) Divis

orEffect ID

- - - 94.8 206.76 675.70 1543.0 8 192.87

Avg

+ - - 110.96 469.94 867.29 163.45 4 40.86 P

- + - 214.12 240.06 57.86 651.35 4 162.84

T

+ + - 255.82 627.23 105.59 27.57 4 6.89 PT

- - + 94.14 16.16 264.18 191.59 4 47.90 F

+ - + 145.92 41.70 387.17 47.73 4 11.93 PF

- + + 286.71 51.78 25.54 122.99 4 30.75 TF

+ + + 340.52 53.81 2.03 -23.51 4 -5.88 PTF

Yield Modeling

• Yield = % of devices that meet a nominal performance specification

• Functional Yield (hard yield) is caused by open circuits or short circuits caused by physical defects such as faults and particles

• Parametric Yield (soft yield) is when a fully functional product still fails to meet performance specifications for one or more parameters such as speed, noise level, or power consumption.

Functional Yield• Models to estimate functional yield help predict product

cost, determine optimum equipment utilization and identification of problematic products or processes.

• Functional yield impacted by presence of defects.

• Defects arise from:

– Contamination of equipment

– Process or handling

– Mask imperfections

– Airborne particles

• Defects include

– Shorts, opens, misalignment, photo resist splatters, flakes, holes, scratches

Functional Yield• Yield model Y=f(Ac, Do)

Function of average defects per unit area Do and critical area Ac

• Critical area is the area in which a defect occurring has a high probability of resulting in a fault

• The relationship between yield, defect density, and critical area is complex and depends on the circuit geometry, the density of photolithographic patterns, the number of photolithographic steps used in the manufacturing process and other factors

Poisson Model• There are C^M unique ways in which M defects

can be distributed on C circuits• If one circuit is removed i.e. found to contain no

defects then the no. of ways to distribute the M defects among remaining circuits is (C-1)^M

• Prob. That circuit will contain zero defects,(C-1)^M ------------ = (1 – 1/C)^M C^M

Where M=CAcDoYield is the number of circuits with zero defects Y =lim(C->infinity)( 1- 1/C)^M =exp(-AcDo)

Murphy’s Yield Model

• Yuniform = 1 – e^(-2DoAc) / 2DoAc

• Ytriangular = [1 – e^(-2DoAc) / DoAc]^2

(Gaussian distribution)

Triangular Murphy Yield Model is widely used in the industry to determine the effect of manufacturing process defect density

Parametric Yield• Monte Carlo Simulation is used to evaluate

parametric yield• Large number of pseudo-random sets of values

for circuit or system parameters are generated according to an assumed prob. Distribution based on sample means and standard deviations extracted from measured data

• For each set of parameters, a simulation is performed to obtain information about the predicted behavior of a circuit or system and the overall performance distribution is then extracted from the set of simulation results.

Parametric Yield

• For example using the monte carlo method we can estimate the parametric yield of microstrips produced by a given manufacturing process within a certain range of characteristic impedances by computing the value of Zo for every possible combination of d and W.

• Yield(microstrips with a<Zo<b) =[∫f(x) dx]a->b

QUESTIONS?