Case Studies of Batch Processing Experiments

1
Case Studies of Batch Processing Experiments

• Diane K. Michelson
• International Sematech Statistical Methods

May 21, 2003 Quality and Productivity Research
Conference
2
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.

3
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.

Run 1
Run 2
Run 3
Run 4
Run 5
Run 6
Run 7
Run 8
Run 9
Run 10
Run 11
Run 12
Run 13
Run 14
Run 15
Run 16
4
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.

5
What Engineering Wanted
A -1
A 1
RUN 10
RUN 11
RUN 12
RUN 13
RUN 14
RUN 15
RUN 16
RUN 9
RUN 1
RUN 2
RUN 3
RUN 4
RUN 5
RUN 6
RUN 7
RUN 8
-1
1
-1
1
-1
1
-1
1
B
-1
-1
1
1
-1
1
1
-1
C
-1
-1
-1
-1
1
1
1
1
D
1
2
3
4
5
6
7
8
6
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.

7
Visual Look
8
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.

9
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.

10
Replicated Whole Plots
11
ANOVA for replicated whole plots

• Replicating the supplier once gives this ANOVA
  table.

12
A cheaper option
A
A
-1
1
1
2

• 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.

3
4
-1
1
-1
1
-1
1
-1
1
B
-1
-1
1
1
-1
-1
1
1
C
-1
-1
-1
-1
1
1
1
1
D
13
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.

14
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

15
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

16
Yield drop between M2 and Final
17
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 .25?m via
  diameter.

18
Failure after passivation
19
Process Flow / Factors
20
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.

21
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.

22
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.

23
Visual Look
B1
B-1
A1
A-1
A-1
A1
B1
B-1
24
Analysis

• The model is
• The strip plot design does not change effect
  calculations.

25
Testing effects

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

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

26
Testing effects

• The error term for testing all the effects at one
  process step is the LOTEFFECT interaction.
• The error term for testing effects which cross
  process steps is the residual.

27
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.

28
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?
• RD 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

29
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