Case Studies of Batch Processing Experiments

Diane K. MichelsonInternational Sematech Statistical Methods

May 21, 2003 Quality and Productivity Research Conference

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Abstract• Experimentation in the semiconductor

industry requires clever design and clever analysis.

• In this paper, we look at two recent experiments performed at ISMT.

• The first is a split plot design at a clean operation.

• The second is a strip plot design of 3 factors over 3 process steps.

• The importance of using the correct error terms in testing the model will be discussed.

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Split Plot Experiment

• An experiment was designed to optimize the performance of a wafer cleaning step.

• Factors were chemical supplier and three process factors (time, temp, concentration).

• A 24 full factorial (plus centerpoints) was first considered.

Ru

n 1

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-1-1-1-1

-1-1-1+1

-1-1+1-1

-1-1+1+1

-1+1-1-1

-1+1-1+1

-1+1+1-1

-1+1+1+1

+1-1-1-1

+1-1-1+1

+1-1+1-1

+1-1+1+1

+1+1-1-1

+1+1-1+1

+1+1+1-1

+1+1+1+1

ABCD

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Completely Randomized Design

• In the CRD, treatments are randomly assigned to experimental units.

• The CRD would require 16 bath changes, one for each run.

• This was not practical, since bath changes are expensive and time-consuming.

• Engineering wanted to run all treatment combinations using one supplier first in one bath, and all treatment combinations using the second supplier in another bath.

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What Engineering Wanted

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Multiple experimental units

• The split plot design has two (or more) experimental units.

• The experimental unit for the supplier variable is a bath (whole plot).

• The experimental unit for the process factors is a wafer (sub plot).

• Note that supplier is not a blocking factor.

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A=+1

A=-1

Visual Look

B=+1,C=+1 B=+1,C=+1

B=+1,C=+1

B=+1,C=+1

B=+1,C=-1

B=+1,C=-1

B=+1,C=-1B=+1,C=-1

B=-1,C=+1

B=-1,C=+1

B=-1,C=+1B=-1,C=+1

B=-1,C=-1

B=-1,C=-1

B=-1,C=-1

B=-1,C=-1

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Analysis

• The model is

• Parameter estimates are not affected by the split plot design

• The error term for testing effects is not necessarily the residual, since there are restrictions on randomization.

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μ

CDBDBCADACAB

DCBAy

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ANOVA

• The ANOVA table for an unreplicated split plot design shows that with just one “run” of each supplier, the supplier effect can not be tested.

Source dfdenominator forstatistical tests

1 A 1 reps(A)2 whole plot error (reps(A)) 0 residual3 B 1 residual4 C 1 residual5 D 1 residual6 A*B 1 residual7 A*C 1 residual8 A*D 1 residual9 B*C 1 residual

10 B*D 1 residual11 C*D 1 residual12 sub plot error (residual) 5

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Replicated Whole Plots

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ANOVA for replicated whole plots

• Replicating the supplier once gives this ANOVA table.

Source dfdenominator forstatistical tests

1 A 1 reps(A)2 whole plot error (reps(A)) 2 residual3 B 1 residual4 C 1 residual5 D 1 residual6 A*B 1 residual7 A*C 1 residual8 A*D 1 residual9 B*C 1 residual

10 B*D 1 residual11 C*D 1 residual12 sub plot error (residual) 19

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A cheaper option

• Another choice is to run a fractional factorial within each supplier run.

• Statistical software will not create this design, in general.

• It is typically easier to create these designs “by hand” in a spreadsheet package.

A B C D A_err1 -1 -1 -1 -1 12 +1 +1 -1 -1 23 +1 -1 +1 -1 24 -1 +1 +1 -1 15 +1 -1 -1 +1 26 -1 +1 -1 +1 17 -1 -1 +1 +1 18 +1 +1 +1 +1 29 -1 -1 -1 -1 3

10 +1 +1 -1 -1 411 +1 -1 +1 -1 412 -1 +1 +1 -1 313 +1 -1 -1 +1 414 -1 +1 -1 +1 315 -1 -1 +1 +1 316 +1 +1 +1 +1 4

B

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ANOVA for fractioned design

• ANOVA table for the fractioned design. Note the decrease in residual df.

• Adding 2 centerpoints per supplier run will add 4 df to the residual and allows for a test of curvature of the process factors.

Source dfdenominator forstatistical tests

1 A 1 reps(A)2 whole plot error (reps(A)) 2 residual3 B 1 residual4 C 1 residual5 D 1 residual6 A*B 1 residual7 A*C 1 residual8 A*D 1 residual9 B*C 1 residual

10 B*D 1 residual11 C*D 1 residual12 sub plot error (residual) 3

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Considerations

• CRD– very expensive, since one factor is hard to vary

• Split plot– cheaper, but not as much information on the supplier

effect as on the process effects

– must have replicates of whole plot factor

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Strip plot experiment

• Problem: yield issues on Interconnect baseline product

• Product is a short loop process of Metal 1, Via, Metal 2

• The failing electrical parameter was Via chain yield

• Yield was fine after M2 but bad after Final Test

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Yield drop between M2 and Final

Yield of 360k 0.25 um via chains RCON-CCE (CHE)Interconnect Oxide Baseline 800BSL000 (<1 ohm/via)

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Metal 2 probe Final probe

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Via chains

• Each measurement represents the resistance of a via chain as measured by forcing a current through the 360,000 via chain, and sensing a voltage.

• This generates a resistance value for the chain, which is divided by 360,000 to get the per-via resistance.

• The responses were yield and median resistance of a via in a chain of 360,000 vias. Yield was defined using a 1 ohm criterion for the .25m via diameter.

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Failure after passivation

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Process Flow / Factors19 Dep nit750/ox4k/nit750/ ox7k PECVD 41 Sputter M1 Ta250/Cu1.3k

20 Back of wafer clean (Cu) 42 Plate M1 Cu 7500 A

21 CMP oxide, remove 2kA 43 Anneal copper 150C 30'

22 Back of wafer clean (Cu) 44 CMP copper

23 Via Litho preinspection 45 Electrical test

24 Via Litho (0.25 um target) 46 Double sided brush scrub

25 Via:M1 Overlay measurement 47 Dep 1kA SiN, 2kA SiO2

26 Resist CDs 48 Back of wafer clean (Cu)

27 Via etch to SiN over M1 49 Pad open Litho preinspection

28 Ash resist 50 Pad open Litho (0.25 um target)

29 Back of wafer clean (Cu) 51 Pad etch to SiN under 2kA SiO2 mask

30 Final CDs for vias 52 Ash with no exposed Cu

31 M2 Litho preinspection 53 Etch SiN down to Cu

32 M2 Litho (0.25 um target) 54 BPD_LVL

33 M2:Via Overlay measurement 54 Sputter M1 TaN 400A

34 Resist CDs 55 Sputter 7.5kA Al-Cu

35 M2 etch to SiN under M2 56 Back of wafer clean (Cu)

36 Ash, remove BARC from via 57 Pad metal Litho preinspection

37 Etch nitride from via and trench bottom 58 Pad metal Litho (0.25 um target)

38 Wet clean vias 59 Pad metal etch

39 Back of wafer clean (Cu) 60 Solvent clean

40 Final CDs for M2 trench 61 380 C Forming gas anneal

62 Electrical test

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Design

• Three factors, each at 2 levels, plus centerpoints 23 full factorial.

• If run as a Completely Randomized Design, this experiment would use 10 wafers, and 10 runs.

• Wafers are not batched.

Run Ash TimeNitride

Etch TimeSputter

Etch Time

1 0 0 02 -1 -1 -13 -1 -1 14 -1 1 -15 -1 1 16 1 -1 -17 1 -1 18 1 1 -19 1 1 110 0 0 0

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Design

• Engineering wanted to batch wafers together at each step.

• Using just 10 wafers would mean 3 runs of each tool, one for each level of the factor.

• This leads to 0 error df, and untestable effects.

• Need to have multiple runs at each level.

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Factor A

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Design

• This design is a strip plot.

• Wafers are batched.

• Requires 20 wafers in 2 lots of 10, but only 6 runs of each tool.

Lot Wafer Ash TimeNitride

Etch TimeSputter

Etch Time

1 1 0 0 01 2 -1 1 -11 3 -1 1 11 4 -1 -1 11 5 1 -1 -11 6 1 -1 11 7 1 1 11 8 -1 -1 -11 9 1 1 -11 10 0 0 02 1 0 0 02 2 1 1 12 3 1 1 -12 4 1 -1 12 5 -1 1 12 6 -1 1 -12 7 -1 -1 12 8 -1 -1 -12 9 1 -1 -12 10 0 0 0

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Visual Look

A=-1

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Analysis

• The model is

• The strip plot design does not change effect calculations.

εμ BCACABCBAy

DOE results: M2 ash time, N2 etch time, sputter etch time before barrierAll chains are 360k M2 test results ---------------------------------------------------------------------------------------------------------------|

WaferAsh time

Nit etch time

Sput etch time

Yield: 225 nm

Yield: 250 nm

Yield: 275 nm

Yield: 300 nm

Yield rating

med R 225 nm

med R 250 nm

med R 275 nm

med R 300 nm

225 250 275 300 225 250 275 3001 60 60 6 82 91 91 100 87 1.02 0.57 0.48 0.432 50 70 3 95 100 95 100 97 0.99 0.57 0.47 0.43 50 70 9 82 91 100 100 89 1.1 0.57 0.49 0.454 50 50 9 64 91 95 100 81 1.17 0.57 0.5 0.455 70 50 3 50 100 91 100 78 1.12 0.62 0.48 0.436 70 50 9 55 86 95 91 75 1.15 0.57 0.49 0.437 70 70 9 59 100 86 100 81 1.14 0.56 0.49 0.458 50 50 3 68 100 100 91 87 1.14 0.62 0.46 0.469 70 70 3 59 95 100 95 82 1.09 0.58 0.49 0.41

10 60 60 6 55 100 95 100 81 1.12 0.55 0.49 0.4411 60 60 6 59 91 95 100 79 1.11 0.59 0.49 0.4412 70 70 9 59 82 77 91 72 1.09 0.56 0.5 0.4513 70 70 3 50 100 91 100 78 1.05 0.56 0.45 0.414 70 50 9 64 95 100 95 84 1.1 0.57 0.5 0.4515 50 70 9 59 100 100 100 84 1.16 0.56 0.5 0.4616 50 70 3 9 95 100 95 62 2.00E+05 0.64 0.47 0.4117 50 50 9 23 100 100 100 69 1.07E+05 0.55 0.48 0.4518 50 50 3 45 86 100 100 72 7.10E+05 0.61 0.49 0.4319 70 50 3 50 100 95 95 79 1.15 0.6 0.49 0.4320 60 60 6 50 95 100 95 78 1.05 0.57 0.49 0.43

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Testing effects

• In the CRD, the denominator of the F-statistic for testing the main effects and two factor interactions is the residual.

Source dfDenominator for statistical tests

1 Lot 1 complex2 A 1 A error3 A error (Lot*A) 14 B 1 B error5 B error (Lot*B) 16 C 1 C error7 C error (Lot*C) 18 A*B 1 residual9 A*C 1 residual

10 B*C 1 residual11 residual 10

• In the Strip Plot, there are restrictions on randomization, therefore, the error term for testing effects is not necessarily the residual.

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Testing effects

• The error term for testing all the effects at one process step is the LOT*EFFECT interaction.

• The error term for testing effects which cross process steps is the residual.

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Considerations• CRD

– more runs

– less wafers

– wafers should not be batched together

– textbook analysis

• Strip plot– less runs

– more wafers

– wafers can be batched

– more complex analysis

• Analyzing a strip plot as a CRD may lead to missing significant effects.

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General considerations• What about single wafer tools?

– Each wafer is a separate run.

– If the only thing defining a batch is the wafer handling, treat it as a single wafer tool.

– If the chamber needs to heat up or otherwise change before a batch is run, treat it as a batch tool.

• What about estimating variability from the past?

• R&D Engineers are looking for very large effects.– they want to see these effects each and every time a process

is run.

• What do you do when Things Go Horribly Wrong?– graphs…

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Conclusions

• Experimentation in the wafer fab requires consideration of– design structure

– execution structure

• Experiments with hard-to-vary factors are good candidates for split plot designs

• Experiments which cover multiple process steps are good candidates for strip plot designs