In order to check performance of Fuzzy APC vs. WA APC simulation of the system performed (Labview). Dose values were taken as input variables, also Focus values are present, but not used in simulation. Membership function were created as well as for Dose and Focus variables. Rules includes Dose and Focus impact, but feedback loop updates just Dose performance (close simulation for FAB Litho tool activity). Actual simulation not included any translation of Dose values to CD values for given Focus, it assumes that any inconsistencies are added as WN or trend in the final measurement. WA APC simulated as 5 tag window with 0.35/0.25/0.2/0.14/0.06 weights accordingly which is effectively matched NSO exponential weights average approach.

1. Introduction to Fuzzy Logic systems
and Fuzzy logic APC simulator
By LV Tailoring Software

2. Fuzzy Logic - background
• Western cultures adopted binary logic long time ago as they dealt with the yes
or no, guilty or not guilty – vocabulary of the binary Aristotelian logic
world.
• Eastern cultures easily accommodate the concept of Fuzziness due to
historical background – not the “certain answer” is the just way to express the
view of experienced person observing the world.
• In 1965 Prof. Lotfi A. Zadeh introduced fuzzy sets, where many degrees of
membership are allowed, and indicated with a number between 0 and 1. The
point of departure for fuzzy sets is simply the generalization of the valuation
set from the pair of numbers {0,1} to all the numbers in [0,1]. This is called a
membership function.
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3. Fuzzy Logic - background
• Mitsubishi manufactures a fuzzy air conditioner. While conventional air conditioners use on/off controllers that
work and stop working based on a range of temperatures, the Mitsubishi machine takes advantage of fuzzy rules; the
machine operates smoother as a result. The machine becomes less mistreated by sudden changes of state, more
consistent room temperatures are achieved, and less energy is consumed. These were first released in 1989.
• Sanyo, Panasonic, and Canon make fuzzy video cameras. These have a digital image stabilizer to remove hand jitter,
and the video camera can determine the best focus and lightning. Fuzzy decision making is used to control these
actions. The present image is compared with the previous frame in memory, stationary objects are detected, and its
shift coordinates are computed. This shift is subtracted from the image to compensate for the hand jitter.
• Fujitec and Toshiba have a fuzzy scheme that evaluates the passenger traffic and the elevator variables to determine
car announcement and stopping time. This helps reduce the waiting time and improves the efficiency and reliability
of the systems.
• The automotive industry has also taken advantage of the theory. Nissan has had an anti-lock braking system since
1997 that senses wheel speed, road conditions, and driving pattern, and the fuzzy ABS determines the braking action,
with skid control.
• Since 1988 Hitachi has turned over the control of the Sendai subway system to a fuzzy system. It has reduced the
judgment on errors in acceleration and braking by 70%. The Ministry of International Trade and Industry estimates
that in 1992 Japan produced about $2 billion worth of fuzzy products. US and European companies still lag far
behind. The market of products is enormous, ranging from fuzzy toasters to fuzzy golf diagnostic systems..
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4. Fuzzy Logic - background
• Example of Fuzzy logic reasoning:
• Everyone who is 60 to 70 years old is old, but very old if 71 years old or above;
everyone who is 20 to 39 is young but very young if 19 years old or below.
• Given - Hiram is 70 years old and Miriam is 39 years old.
• 3. Hiram is old but not very old; Miriam is young but not very young.
• This is an example of approximate reasoning; in order to deal with an
imprecise inference, fuzzy logic can be employed. It allows imprecise
linguistic terms such as:
• • Fuzzy predicates: rare, expensive, fast, high
• • Fuzzy quantifiers: few, usually, much, little
• • Fuzzy truth values: true, unlikely true, false, and mostly false.
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5. Fuzzy Logic - background
• Fuzzy set where the right part is singleton
• Example
• For Logic set - it is union of numbers
• For Fuzzy set – each number has it “degree of belonging” or certainty, some
could treat it as probability – but better way to express it as possibility.
• Often Fuzzy logic theory refers as the theory of possibility - analogous and yet
conceptually different from the theory of probability. Probability is a measure
of frequency of occurrence of an event, which has a physical event basis. Thus,
probabilities have a physical event basis and are related to statistical
experiments; they are primarily used for quantifying how frequently a sample
occurs in a population.
• Possibility theory attempts to quantify how accurately a sample resembles a
stereotype element of a population. This stereotype is a prototypical class of
the population and is known as a fuzzy set. This theory focuses more on the
imprecision intrinsic in the language, while probability theory focuses more on
the uncertainty of events, in the sense of its randomness in nature.
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6. Fuzzy Logic - background
• Fuzzy variables
• First step in build up of Fuzzy control system – creation of membership
function for all related variables (input and output).
• If we are going to use graph for representation of Fuzzy logic set we coming to
detention of the membership function.
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7. Fuzzy Logic - background
• Main Fuzzy logic mathematical operation – similar to binary.
• Union
• Intersection
• Negation
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8. Fuzzy Logic - background
• We just defined membership function for input data we need to operate on.
• We need to apply input data on certain function which in turn will be in turn
the fuzzy function – what is the rules of conversion?
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9. Fuzzy Logic - background
• Fuzzy rules
• It is possible that Fuzzy system we want to build has some input variable,
each of them represented by it’s own membership function.
• Inner relationship of this variables is not defined strictly by mathematical
rules, they should not be mutually independed, they just need to be relevant
to our application.
• Increasing number of the input variables has better definition of the system,
but could in turn complicate creation of the behavioral rules.
• Second step in build up of Fuzzy control system – creation of Fuzzy
Linguistic Descriptions or Fuzzy rules.
• IF (a set of conditions is satisfied) THEN (a set of consequences can be
inferred)
• A general fuzzy IF–THEN rule has the form:
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10. Fuzzy Logic - background
• Simplest Fuzzy logic controller
• What is Defuzzification?
• Simplest system – one input one output
• Center of Mass formula
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11. Fuzzy Logic –vehicle example
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12. Simulation of Fuzzy and WA APC
system
• In order to check performance of Fuzzy APC vs. WA APC simulation of the
system performed (Labview).
• Dose values were taken as input variables, also Focus values are present, but
not used in simulation.
• Membership function were created as well as for Dose and Focus variables.
• Rules includes Dose and Focus impact, but feedback loop updates just Dose
performance (close simulation for FAB Litho tool activity).
• Actual simulation not included any translation of Dose values to CD values for
given Focus, it assumes that any inconsistencies are added as WN or trend in
the final measurement.
• WA APC simulated as 5 tag window with 0.35/0.25/0.2/0.14/0.06 weights
accordingly which is effectively matched NSO exponential weights average
approach.
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13. 140.0
145.0
150.0
155.0
160.0
165.0
170.0
175.0
180.0
185.0
Focus steps
CD's
Focus
FE
Dose0
Dose2
Dose3
Dose5
Dose6
Regular FE
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14. 140.0
145.0
150.0
155.0
160.0
165.0
170.0
175.0
180.0
185.0
Focus steps
CD's
Focus
FE
Dose0
Dose2
Dose3
Dose5
Dose6
Area CD division Fuzzy APC controller -
Dose
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15. Membership function of Fuzzy APC
controller - Dose
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16. 140.0
145.0
150.0
155.0
160.0
165.0
170.0
175.0
180.0
185.0
Focus steps
CD's
Focus
FE
Dose0
Dose2
Dose3
Dose5
Dose6
Area CD division of Fuzzy APC controller -
Focus
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17. Membership function of Fuzzy APC
controller - Focus
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18. Rules of Fuzzy APC controller
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19. Test Surface Fuzzy APC controller
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20. Schematic Labview presentation of
Fuzzy APC controller
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21. GUI Labview presentation of Fuzzy vs.
Weighted average APC controllers
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22. Brief conclusions:
• Fuzzy APC operation depends just on current sample,
no history sample required to perform noise
reduction
• WA APC need historical sample to perform, which
could be irrelevant for RT operation sequence.
• Fuzzy APC better performed as WN cancellator,
reducing noise power significantly compared to WA
APC (~factor of 2)
• WA APC has better signal trend tracking.
• In Fuzzy APC signal trend contaminated noise
cancellation ability.
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23. Thank you for your attention
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