Semiconductor Test

8/9/2019 Semiconductor Test

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IEE 572

Project Report

Electronic Copy

Submitted by :

Brian Benard

Navin Jeyacandran

!ari Ja"annatan Bala#ubramanian


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Reco"nition and #tatement o$ te Problem:

The system under consideration is shown above. In a semiconductor-manufacturing

environment, wafers have to be tested with the intention of getting repeated

measurements as a baseline of system performance, accuracy, and measurement

variability.

A series of device test structures is available for testing circuits built on wafers using 0.8-

micron technology. There are 3 sites measured on each wafer as shown in the figure, with

the sites in the lower left, right, lower right, center, and top sections of the wafer, with the

reference as the flat section of the wafer at the bottom. At each site specific electrical

parameters are measured and recorded. The recorded data is automatically uploaded to a

central factory server for storage after the whole wafer is tested. The normal routine is,

after a wafer is robotically loaded onto a vacuum chuc, for the operator to locate the

probe needles e!actly over the first set of test structures on the first site probed. At each


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site, "# sets of test structures are available. A program automatically moves the wafers

se$uentially through each of these sets, at which a pre-programmed number of electrical

tests are done and results, are measured. Then, the program automatically moves the

wafer to the second site, with no operator intervention, and the measurements are taen

on the same set of test structures. This repeats until the last site is tested, after which the

wafer is robotically removed and another wafer can be robotically loaded.

Two testers are available for this purpose. An operator is also present to conduct the tests.

%lectrical parameters measured give information about the design performance,

robustness, fabrication accuracyand variability. A set of response variables, which are

called &eithley electrical parameters, is chosen that best reflect the above-enumerated

issues 'in Italics(. )or deciding the response variables 'as there are many to choose from(

people from the design department, $uality assurance and the manufacturing department

are consulted.

The problem is to understand whether te#ter#, the operator#, and %a$er# produce

variability in results. *uccinctly stated, we need to find finite source of variation in

Keithley electrical parameters. +nce the e!periment is conducted and analyed, an e!act

test procedure can be suggested.

Coice o$ $actor#& level#& and ran"e#:

. 'e#ter# ( urrently there are two &eithley *ystems used for testing / this factor,

therefore, has two fi!ed levels and is a categorical factor. The variation would be due

to differences in calibration of current sources, voltmeters, and resistor networs to

traceable standards and noise factors such as 1probe-up capacitance1. )or e!ample,

the programmed value for this is treated as a system constant, at a value of 0.3# p)

'pico)arads(, but could affect parameters that rely on a measurement of capacitance,

such as film thicness 'one of the responses chosen(. Another effect due to tester, or

perhaps operator, is the incidence of 1bad 1 data points meaning points where the

probe needles did not mae low-resistance contact with the test structures. Three of the


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responses 'in varying degrees with the leaage parameter being the most sensitive(

could be potentially affected due to this source of variation. The number of these bad

data points may be added as a response variable as these points are typically passed to

the database as an obvious outlier value e.g. 2%2 value for data that normally falls

between 0 and 2 olts.

2. )perator# ( The intention is to perform the e!periment using two different operators

and see whether variability in the results can be caused if different operators perform

the test. This is a fi!ed factor due to small sample of trained operators for the testers.

3. *a$er#- 4afers of the same type and the same technology are used for testing. These

wafers can be used as blocs while the other factors are tested randomly within this

bloc. The original design was intending to select a set of wafers '5golden6 wafers( as

a fi!ed factor to be used in all the e!perimental cells, and run a typical gauge study. At

the time of this report, due to production constraints out of the control of the

e!perimenters, only half of the originally planned e!periment had been run, and the

data was unavailable. Instead, randomly selected wafers were used to generate the

e!perimental data. The wafers were of the same device type and technology, run at the

same time period through the factory, and were from the same batch of starting

material. Therefore we assume they are from the same normally distributed

population of samples, even though selected from different fabrication lots.

7. +ocation o$ te#t ( 3 points on the wafer are tested. The observations obtained at these

points are duplicates and the mean of the observations is taen as the response

variable. This factor could have been used as a nested factor within wafer 'the data is

automatically provided in this manner(, but was not. andomiing testing at all three

locations is a tedious tas posing a practical difficulty. The dispersion of the data

'variance of the wafer average response( can be analyed.


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#. The variation due to a different probe card on the same tester was considered. This

might have variation independent of the tester itself, and could be confounded with a

tester effect. 9owever, it was difficult to add as a factor for both testers, unless done

as a before:after change. The difficulty arises in the e!ecution of the e!periment,

where e!cessive setup time would be needed in a random order that varies the probe

card. Therefore this factor was notincluded.

Re#pon#e ,ariable#;

These responses were chosen as a cross-section of the different types of measurements

done in normal production testing, and of the different measurement sub-systems in the

tester The following is a list of responses that are most significant;

. *heet esistance of . It is sub?ect to all of the temperature variations in the

process.

2. *heet esistance of first layer of metal or width 3@, ohms ; The typical variation as a

percentage of the mean is 2>3. eaage urrent of capacitor with electrodes composed of the first and second metal

layers, amperes ; The typical variation as a percentage of the mean is 0 to 20>. The

leaage current can be sensitive to needle contact, therefore to system or operator.

The actual measurement is in the nA 'nanoampere( range, so coding or transformation

of the response may be appropriate.

7. Threshold voltage of large 4: n-channel transistor, volts ; The typical variation as a

percentage of the mean is to 2>.

#. +!ide thicness of dielectric between first and second metal layers, Angstroms; The

typical variation as a percentage of the mean is 3>. This response could be sensitive

to the 1probe-up capacitance6. It is a well-controlled process in the factory.


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Coice o$ -e#i"n;

There were practical difficulties associated with this e!periment, and the choice of design

was dictated more by the practical issues than anything else. If wafer were considered as

a factor, it would imply randomiing wafer order during the time e!periment was run,

leading to e!cessive handling that was deemed too risy to successful completion of the

e!periment. This, in terms of the e!periment, would have meant re-running all

combinations again, and also financial losses. 9ence, the wafer was to be considered as a

bloc and the treatment combinations were supposed to be run in a randomied fashion

on a wafer.

Another possible factor that was considered was the site-location / i.e. the point where

the wafer is tested. onsidering it as a factor would have meant randomiing the order of

points at which the wafer is tested. This implied changing the stepper program and having

different run orders for different wafers. *uch a modification, though possible, was hardly

feasible practically. A natural simplification would be considering only three points, and

maing the tas of randomiing easier. This aspect of the e!periment was considered but

after considering the set-up of the e!periment, it was decided that the observations were

actually duplicate observations. 9ence the mean of the observations at these points was to

be considered as the response. The analysis of the variability of the locations, or the

variance of the response by wafer 'dispersion effects( could be gained from this data.

The design suggested therefore seems tentative. %ach wafer was to be a bloc and

combinations of tester and operator are tested on each wafer. This meant four

combinations on each wafer, and the value of a particular response variable is the mean of

the observations at the three different sites.

Hence, the experiment under consideration for this project was a general factorial

design, with two factors - operator and tester at two levels. Blocing was to be done by

the third factor wafer, and there were supposed to be five blocs.

Number o$ Replicate#:


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The number of replicates was decided using a trial an error method on Besign %!pert.

There are fifteen replicates, which means there are three replicates per bloc. This gave

us a power of C".D> with at a significance level of #>.

Run )rder:

Std Run Block Tester Operator Std Run Block Tester Opera

47 1 wafer 1 t2 s2 52 31 wafer 3 t2 s2

48 2 wafer 1 t2 s2 7 32 wafer 3 t1 s1

16 3 wafer 1 t2 s1 54 33 wafer 3 t2 s2

18 4 wafer 1 t2 s1 37 34 wafer 3 t1 s2

46 5 wafer 1 t2 s2 9 35 wafer 3 t1 s1

33 6 wafer 1 t1 s2 8 36 wafer 3 t1 s1

31 7 wafer 1 t1 s2 57 37 wafer 4 t2 s2

1 8 wafer 1 t1 s1 40 38 wafer 4 t1 s2

2 9 wafer 1 t1 s1 42 39 wafer 4 t1 s2

32 10 wafer 1 t1 s2 27 40 wafer 4 t2 s1

3 11 wafer 1 t1 s1 55 41 wafer 4 t2 s2

17 12 wafer 1 t2 s1 11 42 wafer 4 t1 s1

50 13 wafer 2 t2 s2 10 43 wafer 4 t1 s1

34 14 wafer 2 t1 s2 25 44 wafer 4 t2 s1

19 15 wafer 2 t2 s1 41 45 wafer 4 t1 s2

49 16 wafer 2 t2 s2 12 46 wafer 4 t1 s1

4 17 wafer 2 t1 s1 56 47 wafer 4 t2 s2

35 18 wafer 2 t1 s2 26 48 wafer 4 t2 s1

6 19 wafer 2 t1 s1 15 49 wafer 5 t1 s1

21 20 wafer 2 t2 s1 43 50 wafer 5 t1 s2

51 21 wafer 2 t2 s2 45 51 wafer 5 t1 s2

5 22 wafer 2 t1 s1 30 52 wafer 5 t2 s1

20 23 wafer 2 t2 s1 14 53 wafer 5 t1 s1

36 24 wafer 2 t1 s2 59 54 wafer 5 t2 s2

53 25 wafer 3 t2 s2 28 55 wafer 5 t2 s1

23 26 wafer 3 t2 s1 60 56 wafer 5 t2 s2

22 27 wafer 3 t2 s1 29 57 wafer 5 t2 s1

39 28 wafer 3 t1 s2 58 58 wafer 5 t2 s2

38 29 wafer 3 t1 s2 44 59 wafer 5 t1 s2

24 30 wafer 3 t2 s1 13 60 wafer 5 t1 s1

Per$ormin" te e.periment:


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The design that was suggested in previous pro?ect proposals was eeping wafers,

operators and testers as fi!ed factors. 9owever, the e!periment was run in a different

manner. This was because of various factors that affect e!periments in industrial settings

lie availability of time and resources, and understanding of the personnel in-charge of

the e!periment. onse$uently, the e!perimental design had to be changed in accordance

with the way the e!periment was run. 4afers were made a random factor nested within

operators. The responses considered were the same. The ob?ective was still to find the

source of variation in the electrical parameters measured. 9owever, the e!periment would

now also tell us if any variability e!isted in the wafer population.

The revised design is shown below;

+perator +perator 24 42 43 47 4# 4" 4D 48 4 42 43 47 4# 4" 4D 48

Tester

Tester 2

!ight wafer levels representing the wafer population nested within operators were tested

with the two tester levels/ "ne replication was done with these eight levels. This

e!perimental design does not e!actly conform to the design initially considered and

planned, but it might still be a reasonable model to use in maing conclusions. The

wafers were selected randomly from the population for each cell of this revised design.

9owever, the conclusions cannot be taen for granted. )ollow up e!periments need to

be conducted to ensure that the results are the same as those predicted by this e!periment

e.g. the originally designed gauge study.

Stati#tical 0naly#i# o$ -ata:

The following represents


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n - *heet esistance of


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eaage urrent of capacitor with electrodes composed of the first and second

metal layers, amperes

Results for: Worksheet 2

ANOVA: leakage versus tester, operator, wafereaage urrent of capacitor with electrodes composed of the first and second

metal layers, amperes

Factor Type Levels Values

wafer(operator) random 8 1 2 3 4 5 6

8

tester f!"ed 2 1 2

operator f!"ed 2 1 2

#nalys!s of Var!ance for lea

$ource %F $$ &$ F '

wafer(operator) 14 181 13 316

tester*operator 1 141536 141536 238

tester 1 1446+4 1446+4 2442

operator 1 +1+ +

,rror 14 831 5+3

Total 31 31238+

$ource Var!ance ,rror ,"pected &ean $-uare for ,ac. Term

component term (us!n/ restr!cted model)

1 wafer(operator) 8+ 5 (5) 2(1)

2 tester*operator 5 (5) 82

3 tester 5 (5) 163

4 operator 1 (5) 2(1) 164

5 ,rror 5+3 (5)

A lo" tran#$ormationwas done on the original readings to mae the data conform to the

assumptions. The A


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ANOVA: 2sn versus tester, operator, wafer



8

tester f!"ed 2 1 2


#nalys!s of Var!ance for m2sn

$ource %F $$ &$ F '

wafer(operator) 14 51456 365 235 6

tester 1 21 21 13 25

operator 1 1484 1484 3832


,rror 14 2186 1561Total 31 24162



1 wafer(operator) 15 5 (5) 2(1)

2 tester 5 (5) 162

3 operator 1 (5) 2(1) 163


5 ,rror 1561 (5)

The A


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Re#po#n#e 5 teo#: +!ide thicness of dielectric between first and second metal

layers, Angstroms


ANOVA: teos versus tester, operator, wafer



8

tester f!"ed 2 1 2


#nalys!s of Var!ance for teos

$ource %F $$ &$ F '

wafer(operator) 14 5224 332 84 63tester 1 32 32 +3

operator 1 5645 5645 22


,rror 14 62564 446+

Total 31 16+6848



1 wafer(operator) 03685 5 (5) 2(1)

2 tester 5 (5) 162

3 operator 1 (5) 2(1) 163


5 ,rror 4468+ (5)

The operator and testFoperator interaction are shown as significant.


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The


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Appendi!

Re#idual "rap# $or Rn Seet Re#i#tance o$ N6 active area& om##8uare9

30252015105

0.15

0.10

0.05

0.00

-0.05

-0.10

-0.15

Observation Order

Residual

Residuals Versus te Order of te !ata

"res#onse is rn$

4.03.93.83.73.6

0.15

0.10

0.05

0.00

-0.05

-0.10

-0.15

%itted Value

Residual

Residuals Versus te %itted Values

"res#onse is rn$


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0.150.100.050.00-0.05-0.10-0.15

2

1

0

-1

-2

&or'al()ore

Residual

&or'al *robabilit+ *lot of te Residuals

"res#onse is rn$

2.01.51.0

4.1

4.0

3.9

3.8

3.7

3.6

o#erator

rn


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2.01.51.0

4.1

4.0

3.9

3.8

3.7

3.6

tester

rn

87654321

4.1

4.0

3.9

3.8

3.7

3.6

wafer

rn


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Re#idual "rap# $or ,tn 're#old volta"e o$ lar"e *+ n(cannel tran#i#tor& volt# 9

30252015105

0.003

0.002

0.001

0.000

-0.001

-0.002

-0.003

Observation Order

Residual


"res#onse is vtn$

0.910.900.890.880.870.86

0.003

0.002

0.001

0.000

-0.001

-0.002

-0.003

%itted Value

Residual


"res#onse is vtn$


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0.0030.0020.0010.000-0.001-0.002-0.003

2

1

0

-1

-2

&or'al()ore

Residual


"res#onse is vtn$

2.01.51.0

0.91

0.90

0.89

0.88

0.87

0.86

0.85

o#erator

vtn


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2.01.51.0

0.91

0.90

0.89

0.88

0.87

0.86

0.85

tester

vtn

87654321

0.91

0.90

0.89

0.88

0.87

0.86

0.85

wafer

vtn


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Re#idual "rap# $or +ea3a"e +ea3a"e Current o$ capacitor %it electrode#

compo#ed o$ te $ir#t and #econd metal layer#& ampere#9

30252015105

0.1

0.0

-0.1

Observation Order

Residual


"res#onse is lea,$

-8.5-8.6-8.7-8.8-8.9-9.0-9.1-9.2-9.3-9.4-9.5

0.1

0.0

-0.1

%itted Value

Residual


"res#onse is lea,$


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0.10.0-0.1

2

1

0

-1

-2

&or'al()ore

Residual


"res#onse is lea,$

2.01.51.0

-8.5

-8.6

-8.7-8.8

-8.9

-9.0

-9.1

-9.2

-9.3

-9.4

-9.5

o#erator

lea,


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2.01.51.0

-8.5

-8.6

-8.7

-8.8

-8.9

-9.0

-9.1

-9.2

-9.3

-9.4

-9.5

tester

lea,

87654321

-8.5

-8.6

-8.7

-8.8

-8.9

-9.0

-9.1

-9.2

-9.3

-9.4

-9.5

wafer

lea,


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Re#idual rap# $or ;2Sna3 Seet Re#i#tance o$ $ir#t layer o$ metal or %idt


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210-1-2

2

1

0

-1

-2

&or'al()ore

Residual


"res#onse is '2sn$

2.01.51.0

136

131

126

o#erator

'2sn


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2.01.51.0

136

131

126

tester

'2sn

87654321

136

131

126

wafer

'2sn


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Re#idual rap# $or 'eo# ).ide tic3ne## o$ dielectric bet%een $ir#t and #econd metal

layer#& 0n"#trom#9

5 10 15 20 25 30

-30

-20

-10

0

10

20

30

Observation Order

Residual


"res#onse is teos$

10100 10200 10300

-30

-20

-10

0

10

20

30

%itted Value

Residual


"res#onse is teos$


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-30 -20 -10 0 10 20 30

-2

-1

0

1

2

&or'al()ore

Residual


"res#onse is teos$

2.01.51.0

10350

10250

10150

o#erator

teos


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2.01.51.0

10350

10250

10150

tester

teos

87654321

10350

10250

10150

wafer

teos


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