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@ -443,6 +443,9 @@ A nice way to have a 1dof flexure guiding with stiff frame is shown in Figure [[
[[file:./figs/z_stage_triangles.png]]
* Keynote: Mechatronic challenges in optical lithography :@hans_butler:
yt:DF8GrWlMwEE
** Introduction
*Question*: in chip manufacturing, how do developments in optical lithography impact the mechatronic design?
@ -605,6 +608,280 @@ The conclusions are:
- EUV: all-vacuum stages
- High-NA EUV: new optics, much larger accelerations
* Keynote: High precision mechatronic approaches for advanced nanopositioning and nanomeasuring technologies :@eberhard_manske:
yt:6hSWI1wtjfo
** Coordinate Measurement Machines (CMM)
Examples of Nano Coordinate Measuring Machines are shown in Figure [[fig:prec_cmm]].
#+name: fig:prec_cmm
#+caption: Example of Coordinate Measuring Machines
#+attr_latex: :width \linewidth
[[file:./figs/prec_cmm.png]]
** Difference between CMM and nano-CMM
With classical CMM, the Abbe-principle is not fulfilled in the x and y directions (Figure [[fig:prec_cmm_nano_cmm]]).
The Abbe error can be determined with:
\begin{equation}
\Delta l_{x,y,z} = l_{x,y,z} \sin \Delta \phi_{x,y,z}
\end{equation}
Even with the best spindle: $l_{x,y} = 100 mm$ and $\Delta \phi = 2 \text{arcsec}$, we obtain an error of:
\begin{equation}
\Delta l = 0.1 \mu m
\end{equation}
which is not compatible with nano-meter precisions.
Then, the classical CMM will not work for nano precision
#+name: fig:prec_cmm_nano_cmm
#+caption: Schematic of a CMM
#+attr_latex: :scale 0.5
[[file:./figs/prec_cmm_nano_cmm.png]]
** How to do nano-CMM
High precision mechatronic approaches are required for advanced nano-positionign and nano-measuring technologies:
- High precision measurement concept
- High precision measurement systems
- High precision nano-sensors
Combined with:
- Advanced automatic control
- Advanced measuring strategies
** Concept - Minimization of the Abbe Error
In order to minimize the Abbe error, the measuring "lines" should have a common point of intersection (Figure [[fig:prec_nano_cmm_concept]]).
The 3D-realization of Abbe-principle is as follows:
- 3 interferometers: cartesian coordinate system
- probe located as the intersection point of the interferometers
#+name: fig:prec_nano_cmm_concept
#+caption: Error minimal measuring principle
#+attr_latex: :scale 0.5
[[file:./figs/prec_nano_cmm_concept.png]]
** Minimization of residual Abbe error
Still some residual Abbe error can happen as shown in Figure [[fig:prec_abbe_min]] due to both a change of angle and change of position.
#+name: fig:prec_abbe_min
#+caption: Residual Abbe error
#+attr_latex: :width \linewidth
[[file:./figs/prec_abbe_min.png]]
** Compare of long travel guiding systems
In order to have the Abbe error compatible with nano-meter precision, the precision of the spindle should be less and one arcsec which is not easily feasible with air bearing of precision roller bearing technologies as shown in Figure [[fig:prec_comp_guid]].
#+name: fig:prec_comp_guid
#+caption: Characteristics of guidings
#+attr_latex: :scale 0.5
[[file:./figs/prec_comp_guid.png]]
** Extended 6 DoF Abbe comparator principle
The solution used was to measure in real time the angles of the frame using autocollimators as shown in Figure [[fig:prec_6dof_abbe]] and then to minimize this tilt by close loop operation with additional actuators.
The angular measurement error and control is less than $0.05 \text{arcses}$ which make the residual Abbe error:
\begin{equation}
\Delta l < 0.05\,nm
\end{equation}
Without an error-minimal approach, nano-meter precision cannot be achieved in large areas.
#+name: fig:prec_6dof_abbe
#+caption: Use of additional autocollimator and actuators for Abbe minimization
#+attr_latex: :width \linewidth
[[file:./figs/prec_6dof_abbe.png]]
** Practical Realisation
A practical realization of the Extended 6 DoF Abbe comparator principle is shown in Figure [[fig:prec_practical_6dof]].
#+name: fig:prec_practical_6dof
#+caption: Practical Realization of the
#+attr_latex: :width \linewidth
[[file:./figs/prec_practical_6dof.png]]
** Tilt Compensation
To measure compensate for any tilt, two solutions are proposed:
1. Use a zero point angular auto-collimator (Figure [[fig:prec_tilt_corection]])
- Resolution: 0.005 arcsec
- Stability (1h): < 0.05 arcsec
2. 6 DoF laser interferoemter (Figure [[fig:prec_tilt_corection_bis]])
- Resolution: 0.00002 arcsec
- Stability (1h): < 0.00005 arcsec
#+name: fig:prec_tilt_corection
#+caption: Auto-Collimator
#+attr_latex: :scale 0.5
[[file:./figs/prec_tilt_corection.png]]
#+name: fig:prec_tilt_corection_bis
#+caption: 6 Interferometers to measure tilts
#+attr_latex: :scale 0.5
[[file:./figs/prec_tilt_corection_bis.png]]
** Comparison of long travail guiding systems - Bis
Now, if we actively compensate the tilts are shown previously, we can fulfill the requirements as shown in Figure [[fig:prec_comp_guid_bis]].
*Measurement and control technology to minimize Abbe errors to achieve*:
- sub-nanometer precision
- smaller moving mass
- better dynamics
#+name: fig:prec_comp_guid_bis
#+caption: Characteristics of the tilt compensation system
#+attr_latex: :width \linewidth
[[file:./figs/prec_comp_guid_bis.png]]
** Drive concept
Usually, in order to achieve a large range over small resolution, each axis of motion is a combination of a coarse motion and a fine motion stage.
The coarse motion stage generally consist of a stepper motor while the fine motion is a piezoelectric actuator.
The approach here is to use an *homogenous drive concept for increase dynamics* (Figure [[fig:prec_drive_concept]]).
Only one linear voice coil actuator is used which with large moving range and sub-nanometer resolution can be achieve at one time.
#+name: fig:prec_drive_concept
#+caption: Voice Coil Actuator
#+attr_latex: :scale 0.5
[[file:./figs/prec_drive_concept.png]]
** NPMM-200 with extended measuring volume
The NPMM-200 machine can be seen in Figure [[fig:prec_mechanics]].
Characteristics:
- Measuring range: 200 mm x 200 mm x 25 mm
- Resolution: 20 pm
- Abbe comparator principle
- 6 laser interferometers
- Active angular compensation
- Position uncertainty < 4 nm
- Measuring uncertainty up to 30 nm
#+name: fig:prec_mechanics
#+caption: Picture of the NPMM-200
#+attr_latex: :width \linewidth
[[file:./figs/prec_mechanics.png]]
The NPMM-200 actually operates inside a Vacuum chamber as shown in Figure [[fig:prec_vacuum_cham]].
#+name: fig:prec_vacuum_cham
#+caption: Vacuum chamber used
#+attr_latex: :scale 0.5
[[file:./figs/prec_vacuum_cham.png]]
** measurement capability
Some step responses are shown in Figure [[fig:prec_results_meas]] and show the nano-metric precision of the machine.
#+name: fig:prec_results_meas
#+caption: Sub nano-meter position accuracy
#+attr_latex: :width \linewidth
[[file:./figs/prec_results_meas.png]]
Picometer steps can even be achieved as shown in Figure [[fig:prec_results_pico]].
#+name: fig:prec_results_pico
#+caption: Picometer level control
#+attr_latex: :width 0.6\linewidth
[[file:./figs/prec_results_pico.png]]
** Extension of the measuring range (700mm)
If the measuring range is to be increase, there are some limits of the moving stage principle:
- large moving masses (~300kg)
- powerful drive systems required
- nano-meter position capability problematic
- large heat dissipation in the system
- dynamics and dynamic deformation
The proposed solution is to use *inverse dynamic concept for minimization of moving masses*.
** Inverse kinematic concept - Tetrahedrical concept
The proposed concept is shown in Figure [[fig:prec_inverse_kin]]:
- mirrors and object to be measured are fixed
- probe and interferometer heads are moved
- laser beams virtually intersect in the probe tip
- Tetrahedrical measuring volume
This fulfills the Abbe principe but:
- large construction space
- difficult guide and drive concept
#+name: fig:prec_inverse_kin
#+caption: Tetrahedrical concept
#+attr_latex: :scale 0.5
[[file:./figs/prec_inverse_kin.png]]
** Inverse kinematic concept - Scanning probe principle
An other concept, the scanning probe principle is shown in Figure [[fig:prec_inverse_kin_scan]]:
- cuboidal measuring volume
- Fixed x-y-z mirrors
- moving measuring head
- guide and drive system outside measuring volume
#+name: fig:prec_inverse_kin_scan
#+caption: Scanning probe principle
#+attr_latex: :scale 0.5
[[file:./figs/prec_inverse_kin_scan.png]]
** Inverse kinematic concept - Compact measuring head
In order to minimize the moving mass, compact measuring heads have been developed.
The goal was to make a lightweight measuring head (<1kg)
The interferometer used are fiber coupled laser interferometers with a mass of 37g (Figure [[fig:prec_interferometers]]).
#+name: fig:prec_interferometers
#+caption: Micro Interferometers
#+attr_latex: :scale 0.5
[[file:./figs/prec_interferometers.png]]
The concept is shown in Figure [[fig:prec_inverse_meas_head]]:
- 6dof interferometers are used
- one micro-probe
- the total mass of the head is less than 1kg
There is some abbe offset between measurement axis of probe and of interferometer but *Abbe error compensation by closed loop control of angular deviations* is used.
#+name: fig:prec_inverse_meas_head
#+caption:
#+attr_latex: :scale 0.5
[[file:./figs/prec_inverse_meas_head.png]]
** Inverse kinematic concept - Scanning probe principle
As shown in Figure [[fig:prec_abbe_compensation]], the abbe error can be compensated from the two top interferometers as:
\[ \text{for } l_x = a: \quad \Delta l_{\text{Abbe}} = \Delta l_{\text{int}} \]
Thus the tilt and Abbe errors can be compensated for with sub-nm resolution.
#+name: fig:prec_abbe_compensation
#+caption: Use of the interferometers to compensate for the Abbe errors
#+attr_latex: :scale 0.5
[[file:./figs/prec_abbe_compensation.png]]
** Conclusion
Proposed approaches to push the nano-positioning and nano-measuring technology:
- Measurement and control technology to minimize Abbe errors
- Homogeneous drive concept for increased dynamics
- Inverse kinematic concept for minimization of moving mass
- Abbe-error compensation by closed loop control of angular deviations
* Designing anti-aliasing-filters for control loops of mechatronic systems regarding the rejection of aliased resonances :@ulrich_schonhoff:
** The phenomenon of aliasing of resonances
Weakly damped flexible modes of the mechanism can limit the performance of motion control systems.
@ -1164,277 +1441,6 @@ The RR proposed algorithm is giving the best results
- Computationally tractable design framework for large scale MIMO systems established
- Near global optimal quality achieved on wafer stage setup using RR algorithm
* Keynote: High precision mechatronic approaches for advanced nanopositioning and nanomeasuring technologies :@eberhard_manske:
** Coordinate Measurement Machines (CMM)
Examples of Nano Coordinate Measuring Machines are shown in Figure [[fig:prec_cmm]].
#+name: fig:prec_cmm
#+caption: Example of Coordinate Measuring Machines
#+attr_latex: :width \linewidth
[[file:./figs/prec_cmm.png]]
** Difference between CMM and nano-CMM
With classical CMM, the Abbe-principle is not fulfilled in the x and y directions (Figure [[fig:prec_cmm_nano_cmm]]).
The Abbe error can be determined with:
\begin{equation}
\Delta l_{x,y,z} = l_{x,y,z} \sin \Delta \phi_{x,y,z}
\end{equation}
Even with the best spindle: $l_{x,y} = 100 mm$ and $\Delta \phi = 2 \text{arcsec}$, we obtain an error of:
\begin{equation}
\Delta l = 0.1 \mu m
\end{equation}
which is not compatible with nano-meter precisions.
Then, the classical CMM will not work for nano precision
#+name: fig:prec_cmm_nano_cmm
#+caption: Schematic of a CMM
#+attr_latex: :scale 0.5
[[file:./figs/prec_cmm_nano_cmm.png]]
** How to do nano-CMM
High precision mechatronic approaches are required for advanced nano-positionign and nano-measuring technologies:
- High precision measurement concept
- High precision measurement systems
- High precision nano-sensors
Combined with:
- Advanced automatic control
- Advanced measuring strategies
** Concept - Minimization of the Abbe Error
In order to minimize the Abbe error, the measuring "lines" should have a common point of intersection (Figure [[fig:prec_nano_cmm_concept]]).
The 3D-realization of Abbe-principle is as follows:
- 3 interferometers: cartesian coordinate system
- probe located as the intersection point of the interferometers
#+name: fig:prec_nano_cmm_concept
#+caption: Error minimal measuring principle
#+attr_latex: :scale 0.5
[[file:./figs/prec_nano_cmm_concept.png]]
** Minimization of residual Abbe error
Still some residual Abbe error can happen as shown in Figure [[fig:prec_abbe_min]] due to both a change of angle and change of position.
#+name: fig:prec_abbe_min
#+caption: Residual Abbe error
#+attr_latex: :width \linewidth
[[file:./figs/prec_abbe_min.png]]
** Compare of long travel guiding systems
In order to have the Abbe error compatible with nano-meter precision, the precision of the spindle should be less and one arcsec which is not easily feasible with air bearing of precision roller bearing technologies as shown in Figure [[fig:prec_comp_guid]].
#+name: fig:prec_comp_guid
#+caption: Characteristics of guidings
#+attr_latex: :scale 0.5
[[file:./figs/prec_comp_guid.png]]
** Extended 6 DoF Abbe comparator principle
The solution used was to measure in real time the angles of the frame using autocollimators as shown in Figure [[fig:prec_6dof_abbe]] and then to minimize this tilt by close loop operation with additional actuators.
The angular measurement error and control is less than $0.05 \text{arcses}$ which make the residual Abbe error:
\begin{equation}
\Delta l < 0.05\,nm
\end{equation}
Without an error-minimal approach, nano-meter precision cannot be achieved in large areas.
#+name: fig:prec_6dof_abbe
#+caption: Use of additional autocollimator and actuators for Abbe minimization
#+attr_latex: :width \linewidth
[[file:./figs/prec_6dof_abbe.png]]
** Practical Realisation
A practical realization of the Extended 6 DoF Abbe comparator principle is shown in Figure [[fig:prec_practical_6dof]].
#+name: fig:prec_practical_6dof
#+caption: Practical Realization of the
#+attr_latex: :width \linewidth
[[file:./figs/prec_practical_6dof.png]]
** Tilt Compensation
To measure compensate for any tilt, two solutions are proposed:
1. Use a zero point angular auto-collimator (Figure [[fig:prec_tilt_corection]])
- Resolution: 0.005 arcsec
- Stability (1h): < 0.05 arcsec
2. 6 DoF laser interferoemter (Figure [[fig:prec_tilt_corection_bis]])
- Resolution: 0.00002 arcsec
- Stability (1h): < 0.00005 arcsec
#+name: fig:prec_tilt_corection
#+caption: Auto-Collimator
#+attr_latex: :scale 0.5
[[file:./figs/prec_tilt_corection.png]]
#+name: fig:prec_tilt_corection_bis
#+caption: 6 Interferometers to measure tilts
#+attr_latex: :scale 0.5
[[file:./figs/prec_tilt_corection_bis.png]]
** Comparison of long travail guiding systems - Bis
Now, if we actively compensate the tilts are shown previously, we can fulfill the requirements as shown in Figure [[fig:prec_comp_guid_bis]].
*Measurement and control technology to minimize Abbe errors to achieve*:
- sub-nanometer precision
- smaller moving mass
- better dynamics
#+name: fig:prec_comp_guid_bis
#+caption: Characteristics of the tilt compensation system
#+attr_latex: :width \linewidth
[[file:./figs/prec_comp_guid_bis.png]]
** Drive concept
Usually, in order to achieve a large range over small resolution, each axis of motion is a combination of a coarse motion and a fine motion stage.
The coarse motion stage generally consist of a stepper motor while the fine motion is a piezoelectric actuator.
The approach here is to use an *homogenous drive concept for increase dynamics* (Figure [[fig:prec_drive_concept]]).
Only one linear voice coil actuator is used which with large moving range and sub-nanometer resolution can be achieve at one time.
#+name: fig:prec_drive_concept
#+caption: Voice Coil Actuator
#+attr_latex: :scale 0.5
[[file:./figs/prec_drive_concept.png]]
** NPMM-200 with extended measuring volume
The NPMM-200 machine can be seen in Figure [[fig:prec_mechanics]].
Characteristics:
- Measuring range: 200 mm x 200 mm x 25 mm
- Resolution: 20 pm
- Abbe comparator principle
- 6 laser interferometers
- Active angular compensation
- Position uncertainty < 4 nm
- Measuring uncertainty up to 30 nm
#+name: fig:prec_mechanics
#+caption: Picture of the NPMM-200
#+attr_latex: :width \linewidth
[[file:./figs/prec_mechanics.png]]
The NPMM-200 actually operates inside a Vacuum chamber as shown in Figure [[fig:prec_vacuum_cham]].
#+name: fig:prec_vacuum_cham
#+caption: Vacuum chamber used
#+attr_latex: :scale 0.5
[[file:./figs/prec_vacuum_cham.png]]
** measurement capability
Some step responses are shown in Figure [[fig:prec_results_meas]] and show the nano-metric precision of the machine.
#+name: fig:prec_results_meas
#+caption: Sub nano-meter position accuracy
#+attr_latex: :width \linewidth
[[file:./figs/prec_results_meas.png]]
Picometer steps can even be achieved as shown in Figure [[fig:prec_results_pico]].
#+name: fig:prec_results_pico
#+caption: Picometer level control
#+attr_latex: :width 0.6\linewidth
[[file:./figs/prec_results_pico.png]]
** Extension of the measuring range (700mm)
If the measuring range is to be increase, there are some limits of the moving stage principle:
- large moving masses (~300kg)
- powerful drive systems required
- nano-meter position capability problematic
- large heat dissipation in the system
- dynamics and dynamic deformation
The proposed solution is to use *inverse dynamic concept for minimization of moving masses*.
** Inverse kinematic concept - Tetrahedrical concept
The proposed concept is shown in Figure [[fig:prec_inverse_kin]]:
- mirrors and object to be measured are fixed
- probe and interferometer heads are moved
- laser beams virtually intersect in the probe tip
- Tetrahedrical measuring volume
This fulfills the Abbe principe but:
- large construction space
- difficult guide and drive concept
#+name: fig:prec_inverse_kin
#+caption: Tetrahedrical concept
#+attr_latex: :scale 0.5
[[file:./figs/prec_inverse_kin.png]]
** Inverse kinematic concept - Scanning probe principle
An other concept, the scanning probe principle is shown in Figure [[fig:prec_inverse_kin_scan]]:
- cuboidal measuring volume
- Fixed x-y-z mirrors
- moving measuring head
- guide and drive system outside measuring volume
#+name: fig:prec_inverse_kin_scan
#+caption: Scanning probe principle
#+attr_latex: :scale 0.5
[[file:./figs/prec_inverse_kin_scan.png]]
** Inverse kinematic concept - Compact measuring head
In order to minimize the moving mass, compact measuring heads have been developed.
The goal was to make a lightweight measuring head (<1kg)
The interferometer used are fiber coupled laser interferometers with a mass of 37g (Figure [[fig:prec_interferometers]]).
#+name: fig:prec_interferometers
#+caption: Micro Interferometers
#+attr_latex: :scale 0.5
[[file:./figs/prec_interferometers.png]]
The concept is shown in Figure [[fig:prec_inverse_meas_head]]:
- 6dof interferometers are used
- one micro-probe
- the total mass of the head is less than 1kg
There is some abbe offset between measurement axis of probe and of interferometer but *Abbe error compensation by closed loop control of angular deviations* is used.
#+name: fig:prec_inverse_meas_head
#+caption:
#+attr_latex: :scale 0.5
[[file:./figs/prec_inverse_meas_head.png]]
** Inverse kinematic concept - Scanning probe principle
As shown in Figure [[fig:prec_abbe_compensation]], the abbe error can be compensated from the two top interferometers as:
\[ \text{for } l_x = a: \quad \Delta l_{\text{Abbe}} = \Delta l_{\text{int}} \]
Thus the tilt and Abbe errors can be compensated for with sub-nm resolution.
#+name: fig:prec_abbe_compensation
#+caption: Use of the interferometers to compensate for the Abbe errors
#+attr_latex: :scale 0.5
[[file:./figs/prec_abbe_compensation.png]]
** Conclusion
Proposed approaches to push the nano-positioning and nano-measuring technology:
- Measurement and control technology to minimize Abbe errors
- Homogeneous drive concept for increased dynamics
- Inverse kinematic concept for minimization of moving mass
- Abbe-error compensation by closed loop control of angular deviations
* Reducing control delay times to enhance dynamic stiffness of magnetic bearings :@jan_philipp_schmidtmann:
** Introduction
This projects focuses on reducing the control delay times of a magnetic bearing shown in Figure [[fig:magn_bear_intro]].