1. Iterative Methods for Precision Motion Control with Application to a Wafer Scanner System
Hoday Stearns
Advisor: Professor Masayoshi Tomizuka
PhD Seminar Presentation
1/42

2. Semiconductor manufacturing
Photolithography
Courtesy of ASML
Advances in Photolithography
Resolution
Wavelength
Numerical aperture
Semiconductors have become a ubiquitous part of the modern world, found in many products and electronics we use every day.
Moore’s law describes the trend over the last few decades of the doubling of the density of transistors per chip every 2 years. This has made semiconductors much more cheaper and readily available to integrate into our lives, and sped up processing speeds.
The major driving force behind the extension of Moore’s law is advances in photolithography technology. Photolithography is the process of using light to print circuit patterns onto silicon wafers. Photolithography process involves several subporcesses: preparing wafer, coating with resist, pattern transfer, etching, and removing resist.
The exposure part of the process is done by an optomechanical device called a wafer scanner (point to fig). The process of wafer exposure is described by this figure (point to fig). An excimer laser is used to transfer the pattern from a photo mask to the resist; the exposed areas will harden to make a circuit. The light passes through the mask / reticle, then through projection lens to focus and reduce the pattern size, and then makes the pattern for one die on the wafer. The process is repeated many times using different masks to make many layers or complex circuits. Also, the same pattern is repeated many times on a single wafer in each die.
To be able to repeat the pattern on different dies on different locations of the wafer, the wafer is placed on a movable stage (“wafer stage”), which is capable of moving in the x and y directions. In “scanner” machines, during the exposure of one die, the light is passed through a slit, and the wafer stage is moved at a constant velocity in one direction, while the reticle stage is moved in the other direction at 4x the velocity, due to the reduction of the projection lens. Then, to expose the next die, the wafer stage “steps” over to the next one. This is why it is called a “step and scan” motion.
Advances in photolithography come mainly through improvements in achievable resolution by 1. decreasing wavelength (new light source), and 2. increasing numerical aperture of reducer system (lens, immersion lithography). Currently we are at 22nm node – this means 22 nm half-pitch. The resolution improvement is what allows smaller and smaller features to be printed on a wafer.
There are several challenges in the photolithography process: CD control (width of features), overlay control (overlay means aligning circuit layers), and lowering total-cost-of-ownership (related to scanning a high number of wafers-per-hour)..
Photolithography process may be improved through many ways (chemical, process, design, etc.)… Control is one of them.
Because the feature sizes on the wafer are so small, as higher resolution technologies are developed in the future, it is necessary for the stage motion control accuracy to keep up. Control requirements for the stage are: extremeley high precision positioning, at fast scan velocities.
2/42

3. Semiconductor manufacturing
Courtesy of IEEE Spectrum
22 nm Half-pitch
0.55 nm Inter-atom spacing in silicon
Improvements in photolithography process can be made in many ways (chemical, process, etc.), but one of the advances that has been responsible for enabling finer and finer feature sizes is the increase in achievable resolution. Increase in resolution can be attained by: Decrease of wavelength of the light source (recently EUV…), and increase of numerical aperture  (lens, immersion lithography). Currently the 22 nm node is the 2011 target.
Because the feature sizes on the wafer are so small, as higher resolution technologies are developed in the future, it is necessary for the stage motion control accuracy to keep up. It is easy to see that since such small features are being created, the wafer and reticle stages must be controlled so that their positions can be controlled to nanometer-level accuracy. Advanced control schemes are necessary for this. Control requirements for the stages are: extremely high positioning accuracy, at the same time as high velocity scans and accelerations .
Wafer stage motion control
Ultra-high positioning precision
High velocities
Synchronization
Advanced control schemes
3/42

4. Wafer stage test system
A wafer stage testbed system was developed to test all control algorithms developed. It is meant to simulate a single axis of an industrial wafer stage.
The stage has two movable parts: a single-axis linear stage, and a countermass. The purpose of the countermass is to balance the momentum; when the stage moves in one direction, the countermass moves in the other; the in a distance ratio porportional to their mass ratios. As a result, the overall center of gravity of the system remains the same, and no force is transmitted to the base structure, avoiding excitation of vibrations. The stage is supported by an air bearing, so that friction is extremeley low. The countermass is mounted on roller bearings.
4/42

5. Overall experimental setup
Prototype wafer stage
Interferometer
Linear motor
PCI axis board
This figure shows the overall experimental setup – hardware in the feedback control loop.
The position is sensed by a laser interferometer position measurement system. The complete system consists of a laser source, beam directing optics (including adjustable periscope mirrors, and beam splitter, and also reflection mirrors mounted on the stage), measurement optics (interferometer or half-mirror), optical receiver, and axis electronics. The entire optics system is mounted on a vibration isolation table. The system is capable of sensing displacement down to sub-nanometer precision.
The position information is input to the controller. The digital controller has two main subsystems: FPGA and real-time controller. FPGA handles the interfacing to all sensors and motors. The RT target is where the feedback controller is implemented, along with initialization of the position sensors, motor commutation, and reading and writing data files. All devices were programmed with LabVIEW.
The stage is moved by a linear motor; this consists of the stator, which is a permanent magnet rail, and the mover, which is the motor coils attached under the stage. LPMMs are popular for high-precision high-speed applications because of low inertia, low friction, and mechanical simplicity, which allow for fast and smooth movements.
Motor driver
FPGA 7831R
RT Target
5/42

6. Challenges in precision tracking
error
measure
position
Decrease
tracking
error
Reference
Command
Error while accelerating
disturbances
vibrations
Here I show data of the stage. This is the scan trajectory… constant velocity scan in one direction, hold, then return in the other direction.
The baseline tracking performance is shown here, when the stage is run with the baseline PID controller on the standard scan trajectory. The resulting tracking error is shown here. The driving thrust of the following research is to lower this tracking error as much as possible.
From this tracking error profile, we can identify several challenges in improving the tracking accuracy. We notice several features of the error signal:
The first is the large peak error that happens during stage accelerations; this is error due to setpoint changes in the reference trajectory; this happens because of poor response at high frequencies of the plant.
Other components of error are caused by external disturbances. This includes force ripple, cable forces, and vibrations. Force ripple happens because of an uneven motor gain due to misalignment or irregularities in the permanent magnet spacing or the motor coils. The cables connected to the stage (motor power cables, pressurized air tubes for the air bearing, encoder signal cables) also exert a disturbance force on the stage. The stage is also subjected to vibrations through the base.
Sensor noise also causes error of small magnitude.
Vibrations from the structure.
1 and 2 were addressed through feedforward control methods, 3 through feedback control, and 4 through upgrading the sensor.
Mainly the first two error sources are addressed in this research.
sensor noise
6/42

7. Baseline controller design
Feedback control …
Feedforward control …
Feedforward control …
Uses a-priori information
Improves transient response
Trajectory dependent
a-causal
Uses sensor measurements
Increases robustness
Trajectory independent
Limited to being causal
Feedback Controller
Feedforward
Controller
Plant
reference
error
measurement + -
Feedforward control design
Good feedback controller design is necessary for stabilizing systems, improving tracking, making robust to disturbances. However, it is limited to being reactive. On the other hand, feedforward controllers use a-priori known information about the traj and plant to predict the necessary control action. For high-precision motion control applications, both well-designed feedback and feedforward controllers are needed.
The control loop structure is shown here. For the feedback controller, a PID controller is used. For the feedforward controller, a model-inverse controller structure is used. In the remainder of this thesis, the PID controller was fixed; the other features such as feedforward control and ILC are implemented as an “add-on” feature. Most of the research in this thesis focuses on the design of the feedforward control.
7/42

8. Repetitive processes wafer die 8/42
How can we design good feedforward control? Recall that it is common to use a feedforward controller equal to the inverse of the plant model, however this is inadequate because the model is incomplete and simplified. Here we will discuss how we can use the repetitive nature of the step and scan motion trajectory to get a better feedforward control. Back to talking about the photolithography process, there is much repetition in the step and scan process, both on a die-to-die level and wafer-to-wafer level. The repetition can be exploited to improve the performance of the system. Information from past runs can be used to improve future runs. This is very similar to how humans learn from practice or repetition: for example, when we learn to shoot a basketball, we must practice many times, and watch what went wrong each time and adjust the way we throw based on this.
. Some main strategies for repetitive processes are:
Iterative learning control (ILC) – for systems that perform the same task, and stop and restart between tasks. The feedforward signal is incrementally adjusted with each trial to reduce the error.
Repetitive control (RC) – also for systems that perform the same task, but continuously (not restarted).
Iterative feedback tuning (IFT) – The controller parameters (rather than feedforward signal) are incrementally adjusted with each trial to reduce error.
8/42

9. Repetitive processes Iterative learning control (ILC)
wafer
Information from past runs is used to improve future runs
Iteratively update a feedforward signal
Iterative learning control (ILC)
Iteratively update a controller parameters
Iterative feedback tuning (IFT)
die
ILC is a control method for improving the perf of systems performing a repetitive task. ILC is based on the idea that the performance of a system executing a repetitive task can be improved by learning from previous executions. The learning aspect of ILC is similar to how humans learn to perfect a task through practice and repetition.
9/42

10. Iterative learning control
Improves performance of systems that operate repetitively over a fixed time interval
Updates a feedforward signal iteratively based on the tracking error signal of previous runs.
L: learning filter
ILC update law
In P-type ILC, L = scalar
Q: Q filter
Low-pass filter
Zero-phase
Q ≈ 1 : turn learning on
Q ≈ 0: turn learning off
For a motion control system, the goal of ILC is to synthesize the best input signal to the system to drive the tracking error to zero. This is done by repetitively adjusting the control signal each iteration based on the measured plant output of previous iterations. In this way, information learned from previous runs is used to incrementally improve system performance each run.
ILC is an attractive option due to:
-ILC is simple to design, implement, and analyze.
Requires little plant or disturbance knowledge.
Achieves a very high degree of tracking precision.
Works by adding a feedforward signal. Does not change the feedback loop so does not upset stability.
The basic ILC algorithm is captured in this update law:
ILC is highly effective for reducing errors due to repetitive factors i.e. factors that are the same from run to run, which are repetitive disturbances, and the trajectory.
10/42

11. Iterative learning control
Advantages:
Simple to implement
Effective
Data-driven method
Does not change feedback loop
ILC is effective at reducing error due to :
Repetitive disturbances
Trajectory
disturbances
sensor noise
Error while accelerating
vibrations
For a motion control system, the goal of ILC is to synthesize the best input signal to the system to drive the tracking error to zero. This is done by repetitively adjusting the control signal each iteration based on the measured plant output of previous iterations. In this way, information learned from previous runs is used to incrementally improve system performance each run.
ILC is an attractive option due to:
-ILC is simple to design, implement, and analyze.
Requires little plant or disturbance knowledge.
Achieves a very high degree of tracking precision.
Works by adding a feedforward signal. Does not change the feedback loop so does not upset stability.
The basic ILC algorithm is captured in this update law:
ILC is highly effective for reducing errors due to repetitive factors i.e. factors that are the same from run to run, which are repetitive disturbances, and the trajectory.
11/42

12. ILC example
Here I will show a simple example of how it works. Here is the error in the first iteration. Simple P-type ILC is applied for 5 iterations; we can see how fast the tracking error decreases, both from the peak error (caused by reference traj) and the repetitive disturbances (force ripple). Also here is a plot of the decrease in RMS error during the trajectory vs. iterations; this ILC scheme steadily decreased the error and appears to converge to a lower value of error  .  
12/42

13. ILC considerations
ILC design should satisfy the following considerations:
Stability
Asymptotic performance
Transient performance
Designing an ILC scheme means designing the ILC update law, which in the linear ILC update law case, boils down to choosing the learning filters and Q filters.
Considerations to be made in the designing of an ILC scheme are:
Stability (it is desired for tracking error not to blow up during learning iterations)
Monotonic convergence (it is desired for error to decrease in each iteration, never increase.)
Performance (It is desired that the final level of tracking error after the learning has converged be very low).
Robustneess (it is desired that the Q and L filters be designed so that the above three considerations are met even with uncertainty in the plant model).
- There are mathematical conditions for all of these.
Robustness
13/42

14. ILC design for systems with vibrations
ILC challenges
Vibrations
ILC design for systems with vibrations #1
We have just seen the motivation / application of precision control for wafer stages for photolithography. We have also seen some of the challenges in achieving this (high accelerations, force ripple disturbances, vibrations, noise….) which show up in the error profile. We have also explained how the repetitive trials of the scan process can help to improve the control signal to learn. It was also seen that ILC is very effective to reduce the errors due to repetitive components.
However, there are still some challenges to overcome in the use of ILC. One is when applying ILC to systems with vibrations. Often vibrations are different from iteration to iteration (different phase), but ILC is only effective for reducing repetitive errors. Also, even when vibrations are repetitive, they often occur at high frequencies. It is difficult to design ILC schemes that are effective up to high frequencies because of plant uncertainties in high frequencies.
A second challenge is that the results of ILC tuning are only applicable to one trajectory, the same trajectory used for training. When the trajectory is changed, the learning must be redone. We wanted to come up with a way so that the results of learning are applicable to other trajectories as well. One method that is proposed is to develop a method to generalize ILC results to a class of scan trajectories. We proposed a method to use ILC as a training method for feedforward signal patterns; the feedforward signals are then recombined to form feedforward signals for other trajectories.
A second way is to use the repetitive trials to tune feedforward controllers, rather than to tune feedforward signals. Then the tuned controllers will be applicable with any other trajectory, as well as the training trajectory. The IFT method was chosen as the iterative controller tuning method and applied to the wafer stage system. The structures of the controllers to be tuned are determined by knowledge of the plant model structure and disturbance model structure. We proposed feedforward controller structures for reducing error from accelerations and force ripple disturbances, and used IFT to identify the optimal controller parameters.
These three areas are the ones I will talk about in the remainder of this presentation. They represent the main contributions of this dissertation.
Nonrepetitive
High frequency
ILC can only compensate for repetitive disturbances
Difficult to design ILC algorithms with robust performance at high frequencies
14/42

15. Feedforward controller iterative tuning
ILC challenges
New Trajectories
Trajectory 1
Tracking error
ILC signal
Trajectory 2 ?
Apply
ILC
When trajectory changes, learning must be restarted from scratch
We have just seen the motivation / application of precision control for wafer stages for photolithography. We have also seen some of the challenges in achieving this (high accelerations, force ripple disturbances, vibrations, noise….) which show up in the error profile. We have also explained how the repetitive trials of the scan process can help to improve the control signal to learn. It was also seen that ILC is very effective to reduce the errors due to repetitive components.
However, there are still some challenges to overcome in the use of ILC. One is when applying ILC to systems with vibrations. Often vibrations are different from iteration to iteration (different phase), but ILC is only effective for reducing repetitive errors. Also, even when vibrations are repetitive, they often occur at high frequencies. It is difficult to design ILC schemes that are effective up to high frequencies because of plant uncertainties in high frequencies.
A second challenge is that the results of ILC tuning are only applicable to one trajectory, the same trajectory used for training. When the trajectory is changed, the learning must be redone. We wanted to come up with a way so that the results of learning are applicable to other trajectories as well. One method that is proposed is to develop a method to generalize ILC results to a class of scan trajectories. We proposed a method to use ILC as a training method for feedforward signal patterns; the feedforward signals are then recombined to form feedforward signals for other trajectories.
A second way is to use the repetitive trials to tune feedforward controllers, rather than to tune feedforward signals. Then the tuned controllers will be applicable with any other trajectory, as well as the training trajectory. The IFT method was chosen as the iterative controller tuning method and applied to the wafer stage system. The structures of the controllers to be tuned are determined by knowledge of the plant model structure and disturbance model structure. We proposed feedforward controller structures for reducing error from accelerations and force ripple disturbances, and used IFT to identify the optimal controller parameters.
These three areas are the ones I will talk about in the remainder of this presentation. They represent the main contributions of this dissertation.
Feedforward signal
recalculation method
Feedforward controller iterative tuning #2 #3
15/42

16. ILC design for systems with vibrations#1
ILC design for systems with vibrations
16/42

17. Error sources categorization
DOB and ILC
The first area of the thesis is in applying ILC for systems with vibrations. Vibrations, and also other disturbances, can be divided into repetitive vs. nonrepetitive, and also high frequency vs. low frequency, as shown in this chart. The first category: repetitive and low freq., includes force ripple dist. This is the easiest to compensate for, because ILC may be applied because it is repetitive, and the closed-loop freq. response is well known in low freq. ranges (approx equal to 1). Simple P-type ILC does well to compensate for the force ripple. The next category is nonrepetitive and low freq. , this includes an 18 Hz structural vibration, transmitted from the table base. The phase of this vibration changes with each run. This causes a problem for ILC; sometimes the ILC control effort will serve to reduce the 18 Hz vibration effect on the error, but sometimes it will make it worse. The proposed solution is to use a disturbance observer t o cancel out this vibration. The next category is repetitive and high-frequency; there is a 150 Hz vibration present that is repetitive with each run, and shows up after sharp accelerations only; therefore it is thought to be caused by some unmodeled plant dynamics, in particular we suspect the springs in the adjustable mirror on the stage. Because this vibration is repetitive from iteration to iteration, it was thought that ILC can compensate for it easily, but because it is of high frequency, it is difficult. The system freq. response is not known well at this frequency.
Repetitive
Non-repetitive
Low frequency
Force ripple (< 20 Hz)
Table vibration (18 Hz)
High frequency
Vibration modes of plant (150 Hz)
Sensor noise
DOB
filtering
Special ILC design
17/42

18. First try: P-type ILC P-type ILC, Q filter with 250 Hz cutoff
Q filter function:
Learning turned on in frequency bands where Q ≈ 1
Learning turned off in frequency bands where Q ≈ 0
We tried a simple P-type ILC, and here are the results. First, we set the cutoff frequency of the Q filter to ABOVE 150 Hz so that we can try to reduce the 150 Hz vibration (we set to 250). But here are the results… the 150 Hz vibration was amplified. So we tried lowering the Q filter cutoff to BELOW 150 (set to 100) to avoid this problem; but this low cutoff means that learning only happens to 100 Hz, so the peak errors during acceleration are not reduced as much as they could have been. So here there is a tradeoff between the vibration reduction ability of ILC, and the reduction of error in the acceleration phase. We want to try to design ILC schemes to work around this tradeoff.
Large learning transient
18/42

19. First try: P-type ILC P-type ILC, Q filter with 250 Hz cutoff
We tried a simple P-type ILC, and here are the results. First, we set the cutoff frequency of the Q filter to ABOVE 150 Hz so that we can try to reduce the 150 Hz vibration (we set to 250). But here are the results… the 150 Hz vibration was amplified. So we tried lowering the Q filter cutoff to BELOW 150 (set to 100) to avoid this problem; but this low cutoff means that learning only happens to 100 Hz, so the peak errors during acceleration are not reduced as much as they could have been. So here there is a tradeoff between the vibration reduction ability of ILC, and the reduction of error in the acceleration phase. We want to try to design ILC schemes to work around this tradeoff.
Transient eliminated
Worse peak error
19/42

20. P-type ILC with notch Q filter
P-type ILC, Q filter with 250 Hz cutoff
P-type ILC, Q filter with 250 Hz cutoff and notch at 150 Hz
Transient eliminated
P-type ILC, Q filter with 250 Hz cutoff and dynamic notch
20/42

21. Notch L filter P-type ILC, Q filter with 250 Hz cutoff
Notch L filter, Q filter with 250 Hz cutoff
Dynamic notch L filter, Q filter with 250 Hz cutoff
21/42

22. Frequency shaped L filter
P-type ILC, Q filter with 250 Hz cutoff
Frequency-shaped L filter, Q filter with 250 Hz cutoff
L filter shape
Notch L
Frequency shaped L
22/42

23. Model-inverse L filter
Model-inverse L, Q filter with 250 Hz cutoff
23/42

24. Overall comparison - experiment
Here is a comparison of the reduction of the RMS error over iterations, and also the reduction of max error over iterations. We included the 100 hz and 250 hz cutoff P-type ILCs as comparison. In total we tested 8 different ILCs. It is seen that the f-shaped method is the best. In both metrics. It was also very easy to design (heuristic in nature), and low-order filter so easy for implementation.
Frequency shaped L filter gives 42.2% improvement over P-type 250 Hz cutoff
Time-varying filters (Q and L) can give better performance than fixed filters
For L, choosing a filter can give better performance than choosing a scalar
Conclusions
Dynamic notch L filter gives 28.3% improvement over P-type 250 Hz cutoff
24/42

25. Stability of designed ILC
P-type 100 Hz cutoff
P-type 250 Hz cutoff
Frequency shaped L
The lowest is ILC with frequency- shaped L
Here is a comparison of the reduction of the RMS error over iterations, and also the reduction of max error over iterations. We included the 100 hz and 250 hz cutoff P-type ILCs as comparison. In total we tested 8 different ILCs. It is seen that the f-shaped method is the best. In both metrics. It was also very easy to design (heuristic in nature), and low-order filter so easy for implementation.
Stability condition
25/42

26. Performance of designed ILC
P-type 100 Hz cutoff
P-type 250 Hz cutoff
Frequency shaped L
The lowest is ILC with frequency- shaped L
Here is a comparison of the reduction of the RMS error over iterations, and also the reduction of max error over iterations. We included the 100 hz and 250 hz cutoff P-type ILCs as comparison. In total we tested 8 different ILCs. It is seen that the f-shaped method is the best. In both metrics. It was also very easy to design (heuristic in nature), and low-order filter so easy for implementation.
Asymptotic error equation
26/42

27. #2
Feedforward signal generation
for new trajectories via ILC
27/42

28. ILC for feedforward signal generation
A learned ILC signal is limited to a single trajectory.
If trajectory is changed, ILC signal must be relearned.
Trajectory 1
Tracking error
ILC signal
Trajectory 2 ?
Apply
ILC
The second part of the thesis was generalizing ILC results to different trajectories. The wafer stage is always doing step-and-scan motions, so we limited our consideration to a class of step-and-scan
Develop a method for generalizing ILC results to other scan trajectories
28/42

29. Construction of a scan trajectory
Scanning at constant velocity
Position
Constant acceleration
Specify
scan length,
velocity limit,
acceleration limit
Time-optimal trajectory
Polynomial spline
Velocity
First I will describe the design of a scan trajectory. When designing a scan trajectory, we can first specify the desired scan velocity and scan length, and specify limits on the acceleration. We can also specify limits on the jerk (derive of acc) and snap (double-deriv of acc). Then the time-optimal trajectory is uniquely determined; it is a polynomial spline. Here, we consider trajs that have up to only acc limits (no jerk or snap limits), because they are the simplest. When these limits are fixed, the trajectory is analytically determined in continuous time; the traj is determined by the acceleration start and stop times.
Acceleration
29/42

30. Construction of a Scan Trajectory+
Notice that acceleration is superposition of 4 shifted and scaled step signals
30/42

31. Feedforward signal analysis
ILC feedforward input signal is also a superposition
(assume no disturbances) + =
ILC input for Traj 1
decomposition
Learned signal
Base feedforward signal
Then we can notice that the acceleration is the addition of four shifted and scaled step inputs; this means that the reference traj. Is the double integral of these inputs, also the error and converged ILC inputs are also superpositions of some signal. So we can write this about the converged ILC input: (show the eq.) it is the superposition of a time-shifted and scaled “base feedforward signal”. We can easily calculate the base feedforward signal from the ILC input for the training traj. Then, when we are presented with a new trajectory, we can use the base ff signal to construct the appropriate ff input for the new trajectory , based on knowledge of the times t1 t2 t3 and t4 of the new trajectory. Here we show an example:
acausal
part
31/42

32. Feedforward signal synthesis
Synthesize ILC input
New scan trajectory
Then, test it in the system:
32/42

33. Experimental Results RMS error is 33.5% lower than with FF controller
The proposed method achieves performance that is:
Similar to ILC, but without need to repeat learning iterations
Better than feedforward controller
Advantages of proposed method
Doesn’t require model
Doesn’t require redoing learning iterations
Achieves low tracking error
33/42

34. Iterative tuning of feedforward controllers#3
Iterative tuning of feedforward controllers
34/42

35. Feedforward signal vs. controller
ILC
feedforward
signal +
reference
error
Feedback Controller +
Plant
measurement + -
Inverse plant structure
Feedback Controller
Feedforward
Controller
Plant
reference
error
measurement + -
Disturbance model structure
35/42

36. Iterative Controller Tuning
Iterative Feedback Tuning
IFT is an iterative method of tuning controller parameters
Minimizes a cost function
Descent algorithm search
Gradient direction estimated from experimental data
No model of the plant is needed for optimization
ρ= controller parameters to be tuned
= scalar to control step size
k = iteration #
R = positive definite matrix
36/42

37. Feedforward controller 1
Inverse model structure
For reducing error due to trajectory
Peak error decreased 95%
37/42

38. Force ripple
Force Ripple is a periodic disturbance that arises in linear permanent magnet motors due to imperfections
Force Ripple
38/42

39. Feedforward controller 2
Force ripple compensator
For reducing error due to force ripple disturbance
tune
tune
Feedforward signals
39/42

40. Comparison of ILC and IFT
Most effective
Simpler computation
No assumptions of model structures
Time plot of error
IFT:
Applicable for new trajectories
Performance can be improved by increasing controller complexity
40/42

41. Conclusion Iterative methods for high precision position control
ILC design for systems with vibration
ILC feedforward computation for scan trajectories
Iterative feedforward controller tuning
41/42

42. Precision motion control group
Thank you
MSC Lab
Professor Tomizuka
Precision motion control group
42/22

43. Repetitive Processes Silicon wafer 300mm diameter Die
Recall that the wafer stage performs a step-and-scan motion. There is much repetition, both on the die-to-die and wafer-to-wafer level. In fact, repetition is common in many robotic manufacturing applications. The repetitive nature of the scanning motion may be exploited to achieve higher accuracy in control. Information collected from past runs of the process, or “iterations”, can be used to improve the performance in future runs. Some main strategies for repetitive processes are:
Iterative learning control (ILC) – for systems that perform the same task, and stop and restart between tasks. The feedforward signal is incrementally adjusted with each trial to reduce the error.
Repetitive control (RC) – also for systems that perform the same task, but continuously (not restarted).
Iterative feedback tuning (IFT) – The controller parameters (rather than feedforward signal) are incrementally adjusted with each trial to reduce error.
Changing every year
43/22

44. Repetitive Processes Silicon wafer
300mm diameter
International Technology Roadmap for Semiconductors
Die
Translates to:
high tracking precision (error <1nm)
high repeatability
high scanning speeds
Changing every year
44/22

45. Modelling
The wafer stage was modeled as a simple mass with viscous damping system: (point to the TF). This represents the TF from the voltage sent t to the motor amplifier, to the position of the stage in meters. Here, m is the mass, b damping coefficient, and k is the amplifier and motor gain.
Sinesweep experiments were performed to verify the model.
The parameters were identified in a sinesweep experiment. The experimental data of the frequency response is shown in the Fig. The closed-loop frequency response is shown here. It can be seen that there are dynamics at high frequencies, which are due to the adjustable mirrors (containing springs). The stage model was augmented to be the same TF as shown above, multiplied by two notch filters to approximate the adjustable mirror dynamics.
45/22

46. Trajectory Design
46/22

47. Construction of a scan trajectory
Scanning at constant velocity
Position
Constant acceleration
Specify
scan length,
velocity limit,
acceleration limit
Time-optimal trajectory is unique
It is polynomial spline
The continuous-time trajectory is determined analytically then sampled
Velocity
Acceleration

48. Thesis contributions
Applying ILC for high precision control of systems with vibrations
Making ILC tuning results applicable to multiple trajectories
Compensating for force ripple disturbance through IFT.
We have just seen the motivation / application of precision control for wafer stages for photolithography. We have also seen some of the challenges in achieving this (high accelerations, force ripple disturbances, vibrations, noise….) which show up in the error profile. We have also explained how the repetitive trials of the scan process can help to improve the control signal to learn. It was also seen that ILC is very effective to reduce the errors due to repetitive components.
However, there are still some challenges to overcome in the use of ILC. One is when applying ILC to systems with vibrations. Often vibrations are different from iteration to iteration (different phase), but ILC is only effective for reducing repetitive errors. Also, even when vibrations are repetitive, they often occur at high frequencies. It is difficult to design ILC schemes that are effective up to high frequencies because of plant uncertainties in high frequencies.
A second challenge is that the results of ILC tuning are only applicable to one trajectory, the same trajectory used for training. When the trajectory is changed, the learning must be redone. We wanted to come up with a way so that the results of learning are applicable to other trajectories as well. One method that is proposed is to develop a method to generalize ILC results to a class of scan trajectories. We proposed a method to use ILC as a training method for feedforward signal patterns; the feedforward signals are then recombined to form feedforward signals for other trajectories.
A second way is to use the repetitive trials to tune feedforward controllers, rather than to tune feedforward signals. Then the tuned controllers will be applicable with any other trajectory, as well as the training trajectory. The IFT method was chosen as the iterative controller tuning method and applied to the wafer stage system. The structures of the controllers to be tuned are determined by knowledge of the plant model structure and disturbance model structure. We proposed feedforward controller structures for reducing error from accelerations and force ripple disturbances, and used IFT to identify the optimal controller parameters.
These three areas are the ones I will talk about in the remainder of this presentation. They represent the main contributions of this dissertation.

49. Experiment One complication: force ripple
Force ripple is NOT LTI so it cannot be scaled and time-shifted.
Nor is force ripple disturbance always the same : it depends on the reference trajectory

50. DOB Design Solution: Use a disturbance observer
DOB compensates the force ripple
And ILC feedforward signal compensates error due to the trajectory

51. Gradient estimate Cost function: Cost function gradient:
The relation of error to the controller is known, so
Assume SISO
r[n]
e[n] C P -
51/22

52. Controller Tuning Algorithm
Minimize a cost function:
ρ= controller parameters to be tuned
e = tracking error
u = control effort
Using a gradient-based iterative search
k = iteration #
= scalar to control step size
R = positive definite matrix
52/22

53. Gradient estimate Although are known,
are unknown/uncertain because involves plant
Gradient can be obtained by passing reference through system twice
r[n]
e[n] C P C P - -
53/22

54. Experiment Results
tune
tune
54/42

55. Experiment Results
tune
tune
55/42

56. Tuning Results
Norm of error
Evolution of ρ1, ρ2
56/42

57. Semiconductor manufacturing
Moore’s law
Photolithography
Transistor dimension vs. year
Courtesy of Intel
Semiconductors have become a ubiquitous part of the modern world, found in many products and electronics we use every day.
Moore’s law describes the trend over the last few decades of the doubling of the density of transistors per chip every 2 years. This has made semiconductors much more cheaper and readily available to integrate into our lives, and sped up processing speeds.
The major driving force behind the extension of Moore’s law is advances in photolithography technology. Photolithography is the process of using light to print circuit patterns onto silicon wafers. Photolithography process involves several subporcesses: preparing wafer, coating with resist, pattern transfer, etching, and removing resist.
The exposure part of the process is done by an optomechanical device called a wafer scanner (point to fig). The process of wafer exposure is described by this figure (point to fig). An excimer laser is used to transfer the pattern from a photo mask to the resist; the exposed areas will harden to make a circuit. The light passes through the mask / reticle, then through projection lens to focus and reduce the pattern size, and then makes the pattern for one die on the wafer. The process is repeated many times using different masks to make many layers or complex circuits. Also, the same pattern is repeated many times on a single wafer in each die.
To be able to repeat the pattern on different dies on different locations of the wafer, the wafer is placed on a movable stage (“wafer stage”), which is capable of moving in the x and y directions. In “scanner” machines, during the exposure of one die, the light is passed through a slit, and the wafer stage is moved at a constant velocity in one direction, while the reticle stage is moved in the other direction at 4x the velocity, due to the reduction of the projection lens. Then, to expose the next die, the wafer stage “steps” over to the next one. This is why it is called a “step and scan” motion.
Advances in photolithography come mainly through improvements in achievable resolution by 1. decreasing wavelength (new light source), and 2. increasing numerical aperture of reducer system (lens, immersion lithography). Currently we are at 22nm node – this means 22 nm half-pitch. The resolution improvement is what allows smaller and smaller features to be printed on a wafer.
There are several challenges in the photolithography process: CD control (width of features), overlay control (overlay means aligning circuit layers), and lowering total-cost-of-ownership (related to scanning a high number of wafers-per-hour)..
Photolithography process may be improved through many ways (chemical, process, design, etc.)… Control is one of them.
Because the feature sizes on the wafer are so small, as higher resolution technologies are developed in the future, it is necessary for the stage motion control accuracy to keep up. Control requirements for the stage are: extremeley high precision positioning, at fast scan velocities.
Courtesy of ASML
57/42

58. Semiconductor manufacturing
Photolithography
Advances in Photolithography
Resolution
Wavelength
Numerical aperture
Improvements in photolithography process can be made in many ways (chemical, process, etc.), but one of the advances that has been responsible for enabling finer and finer feature sizes is the increase in achievable resolution. Increase in resolution can be attained by: Decrease of wavelength of the light source (recently EUV…), and increase of numerical aperture  (lens, immersion lithography). Currently the 22 nm node is the 2011 target.
Because the feature sizes on the wafer are so small, as higher resolution technologies are developed in the future, it is necessary for the stage motion control accuracy to keep up. It is easy to see that since such small features are being created, the wafer and reticle stages must be controlled so that their positions can be controlled to nanometer-level accuracy. Advanced control schemes are necessary for this. Control requirements for the stages are: extremely high positioning accuracy, at the same time as high velocity scans and accelerations .
58/42

59. Semiconductor manufacturing
Advances in Photolithography
Resolution
Wavelength
Numerical aperture
22 nm Half-pitch
0.55 nm Inter-atom spacing in silicon
Improvements in photolithography process can be made in many ways (chemical, process, etc.), but one of the advances that has been responsible for enabling finer and finer feature sizes is the increase in achievable resolution. Increase in resolution can be attained by: Decrease of wavelength of the light source (recently EUV…), and increase of numerical aperture  (lens, immersion lithography). Currently the 22 nm node is the 2011 target.
Because the feature sizes on the wafer are so small, as higher resolution technologies are developed in the future, it is necessary for the stage motion control accuracy to keep up. It is easy to see that since such small features are being created, the wafer and reticle stages must be controlled so that their positions can be controlled to nanometer-level accuracy. Advanced control schemes are necessary for this. Control requirements for the stages are: extremely high positioning accuracy, at the same time as high velocity scans and accelerations .
Wafer stage motion control
Ultra-high positioning precision
High velocities
Synchronization
Advanced control schemes
59/42