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Stage Metrology Concepts: Application Specific ... - Owens Design

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<strong>Stage</strong> <strong>Metrology</strong> <strong>Concepts</strong>:<br />

<strong>Application</strong> <strong>Specific</strong> Testing<br />

Hans Hansen<br />

Sr. Systems <strong>Design</strong> Engineer<br />

BSME, MSE<br />

2/28/2008


Topics<br />

• Review of <strong>Stage</strong> Error Definitions<br />

• Setting <strong>Stage</strong> <strong>Specific</strong>ations for <strong>Application</strong>s<br />

• <strong>Application</strong>-<strong>Specific</strong> Ways of Providing <strong>Stage</strong><br />

<strong>Specific</strong>ations


Basic Definitions<br />

• Accuracy- the degree to which a system produces the<br />

correct result compared to a standard reference<br />

• Repeatability- the degree to which a system produces<br />

the same result from run to run<br />

By definition, accuracy can not be better than<br />

repeatability, but repeatability can be better than<br />

accuracy.<br />

• Precision- the resolution/”fineness” to which a system<br />

can position.


<strong>Stage</strong> Errors – Single Axis<br />

• Degrees of Freedom<br />

– Translation <strong>Stage</strong><br />

• 3 Translations : 2 fixed, 1 free<br />

• 3 Rotations : All fixed<br />

– Rotary <strong>Stage</strong><br />

• 3 Translations : All fixed<br />

• 3 Rotations : 2 fixed, 1 free<br />

• Errors<br />

– Motions that are supposed to be fixed, but aren’t<br />

– Motions that are supposed to be free but are inaccurate<br />

– Both have repeatable and non-repeatable terms


Accuracy, Repeatability & Resolution<br />

Low Accuracy<br />

Low Repeatability<br />

Low Accuracy<br />

High Repeatability<br />

High Accuracy<br />

High Repeatability<br />

Fine Resolution<br />

Coarse Resolution


Linear <strong>Stage</strong> Definitions<br />

• X Direction – Free: Positioning Accuracy &<br />

Repeatability<br />

• Y Direction – Fixed: Horizontal Straightness Error,<br />

Repeatable and Non-repeatable<br />

• Z Direction – Fixed: Vertical Straightness, Repeatable<br />

and Non-repeatable<br />

• Ө x – Fixed: Roll Error<br />

• Ө y – Fixed: Pitch Error<br />

• Ө z – Fixed: Yaw Error


<strong>Stage</strong> Errors - Linear


<strong>Stage</strong> Errors - Angular


Abbe’ Error<br />

• Linear Errors are affected by rotation errors an<br />

amount that depends upon where the error is<br />

measured.<br />

• Horizontal Straightness Measured at A Given<br />

Height is the sum of the straightness at the center<br />

of roll + product of the roll and the height from the<br />

roll center to the point of measurement<br />

• Height– Abbe’ distance<br />

• Error Component from roll – Abbe’ error


Abbe’ Error


Bidirectional vs. Unidirectional<br />

Positioning Repeatability<br />

• Unidirectional- target always approached from<br />

one direction<br />

• Bidirectional- target approached from both<br />

directions.<br />

• Applies to both linear and rotary systems


Unidirectional Repeatability


Bidirectional Repeatability


Squareness<br />

• Arises when we combine axes<br />

• Example: Squareness of XY <strong>Stage</strong> System<br />

– Measured using a square and indicator<br />

– Need to take measure at appropriate height<br />

– Combines rotation and linear errors


Fixed vs. Moving Sensitive Direction<br />

• Affects appropriate orientation of indicator and<br />

reference surface when measuring straightness<br />

• Example- Single axis microscope<br />

– Sample Fixed<br />

– Sample Moving<br />

– Indicator should always be mounted where the<br />

objective is mounted.


Rotary <strong>Stage</strong> Definitions<br />

• X Direction – Fixed: Radial Motion, Repeatable and<br />

Non-repeatable<br />

• Y Direction – Fixed: Radial Motion, Repeatable and<br />

Non-repeatable<br />

• Z Direction – Fixed: Axial, Repeatable and Nonrepeatable<br />

• Ө x – Fixed: Tilt Error in XZ plane<br />

• Ө y – Fixed: Tilt Error in YZ plane<br />

• Ө z – Free: Positioning Accuracy and Repeatability


Rotary <strong>Stage</strong> Errors<br />

Axial Radial Tilt/Wobble


Error Correction- Mapping<br />

• Errors measured and stored in computer as a<br />

lookup table or function<br />

• Mapping data must travel with stage<br />

• Only as accurate as repeatability of system as<br />

measured and in use.<br />

• Meaningful only if done at appropriate Abbe’<br />

height


2D Accuracy<br />

• Renishaw lasers used with an<br />

optical square to calibrate out<br />

accuracy, straightness, yaw,<br />

and orthogonality in one test<br />

• Laser outputs are read into<br />

two free encoder inputs of an<br />

A3200 system. Need to do<br />

this to synchronize the<br />

encoder and laser information<br />

• Matlab is used to post process<br />

the results and generate 2D<br />

calibration files<br />

Courtesy of Aerotech


Difficulty in Specifying <strong>Stage</strong>s Given<br />

All The Error Terms<br />

• <strong>Stage</strong>s typically specified in terms of the<br />

classical individual stage errors.<br />

• Performance we are interested in result from the<br />

combination of these errors


Proposal<br />

• Define performance in terms of applicationspecific<br />

tests<br />

• Specify individual errors only as necessary


Example – Simple 1 Axis System<br />

• Requirement to Position Sample Under<br />

Objective in X,Y & Z to <strong>Specific</strong> Accuracy &<br />

Repeatability<br />

• Specify X Positioning<br />

• Specify Y&Z Straightness<br />

• Both need to be at height of sample and take<br />

into consideration moving vs. stationary<br />

objective


Example – 2 Axis XY System<br />

• Requirement to Position Sample Under<br />

Objective in X,Y & Z to <strong>Specific</strong> Accuracy &<br />

Repeatability<br />

• Specify X&Y Positioning Test<br />

• Specify Combined Z Straightness Test<br />

• Both need to be at height of sample and take<br />

into consideration moving vs. stationary<br />

objective


4 Axis System<br />

Brushless DC Drives, 20 nm Resolution


Example – 3 Axis RӨZ System<br />

• Requirement to Position Sample Under<br />

Objective in R,Ө & Z to <strong>Specific</strong> Accuracy &<br />

Repeatability<br />

• Specify R,Ө Positioning Test<br />

• Specify Combined Z Straightness Test<br />

• Both need to be at height of sample and take<br />

into consideration moving vs. stationary<br />

objective


3 Axis RӨZ System (nanomotion motors)


Conclusion<br />

• Defining stage specifications in terms of<br />

individual stage errors can be cumbersome.<br />

• Consider defining your own specifications that<br />

are unique to your application


Backup


Linear vs. Mechanical Bearings<br />

Parameter<br />

Units<br />

Linear Motors<br />

Linear Bearings<br />

Linear Motors<br />

Air Bearings<br />

accuracy<br />

microns<br />

±5<br />

±0.5<br />

accuracy, mapped<br />

microns<br />

±1<br />

±0.25<br />

repeatibility, bi-directional<br />

microns<br />

±0.5<br />

±0.2<br />

positional stability<br />

microns<br />

+/-0.04<br />

+/-0.04<br />

encoder resolution<br />

microns<br />

0.01-1<br />

0.01-1<br />

straightness and flatness<br />

microns<br />

6-12<br />

2<br />

roll,pitch,yaw<br />

arc-sec<br />

10<br />

2<br />

speed, no load<br />

mm/sec<br />

1000-2000<br />

500<br />

acceleration, no load<br />

mm/sec^2<br />

30000<br />

10000<br />

settling time<br />

sec<br />


Measurement Techniques<br />

Straightedge Reversal Technique<br />

• Place straightedge on the carriage, parallel to the axis that is being tested<br />

• Mount gage on a stationary part of the tool, with the sensitive contact<br />

positioned against the straightedge and scan axis of interest<br />

• Repeat scan with the straightedge flipped 180 degrees around its long axis,<br />

and the gage head repositioned on the opposite side of the machine scanning<br />

the same surface.<br />

• The gage head's direction of motion is reversed, so that a "bump" on the<br />

straightedge should read as a positive number on both trials.<br />

• The results of one trace are subtracted from the other. Because the gage head<br />

was reversed, carriage errors cancel each other out, so any remaining<br />

deviation from zero reflects error in the straightedge. (assumes that carriage<br />

errors are repeatable.)<br />

• The results can be used as correction factors for all future uses of the<br />

straightedge.


Reversal- Setup 1


Reversal – Setup 2


Reversal- Math<br />

T 1 (Z) = P(Z) + S(Z)<br />

T 2 (Z) = P(Z) - S(Z)<br />

T= Indicator Reading<br />

P= <strong>Stage</strong> Straightness Error<br />

S= Straightedge Straightness Error

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