fundamentals of package manufacturing ideen taeb noopur singh
TRANSCRIPT
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?