The document summarizes the calibration of a long travel stage using machine metrology techniques. It describes the stage's positioning capabilities and measurement systems, including displacement measuring interferometers. Calibration involved a Fizeau interferometer to measure angular drift and a straightedge to monitor straightness. Analysis found sub-nanometer repeatability but cyclic errors combined with angular drift affected straightness measurements. Automatic cyclic error compensation was implemented to improve results. In conclusion, classical machine metrology provided high-precision calibration of the stage's straightness and angular motions.
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INTRODUCTION
• Lithography is a critical infrastructural technology demanding nanometer level
positioning uncertainties over macroscopic displacements
• Machine coordinate systems can be adapted to the part coordinate system to ensure
that feature overlay targets are met
• This approach is not possible for a variety of manufacturing and metrology tools
• In these cases it has long been the practice to design highly repeatable machine
systems which can subsequently be calibrated to correct for repeatable errors
• As target positioning uncertainties continue to decrease, the requirements for
repeatability, displacement metrology, and calibration all become more difficult
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MACHINE METROLOGY
• The measuring machine under development has a working
volume (X,Y,Z) of 1 x 1 x 500 mm3, with angular
adjustments (rx, ry, rz) of +/-1 mrad
• The system, located in a metrology laboratory with
temperature control to +/- 0.0l 0
C, operates in a coarse
vacuum (5 mBar)
• Stage position is measured using two different
configurations of displacement measuring interferometers
• A rotary table provides for discrete part rotation of +/-
1850
• A conventional Cartesian metrology frame required, at
minimum, two 500 mm long straightedges integrated into
the machine
• In addition to the six moving DMls, the machine is
equipped with 3 double pass, zero shear interferometers
• Three sets of DMls are arranged symmetrically around the
metrology frame, each fed by a separate delivery module Figure 1 Metrology frame concept
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• A retroreflector for the vertical interferometer is
carried on a mount attached to the part stage
• Beam delivery and steering optics, the inclined
straightedge, and the zeroshear interferometer and
its return flat are all attached to the metrology
frame
• The additional independent measurements may be
considered a counter balance to the loss of
resolution in the XY plane resulting from inclining
the straightedges (to 300
)
• The system designer has to choose between a
number of possible transformations between the 9
measurement signals and the 6 degrees of freedom -
a choice that affects both machine performance and
calibration
• The transformation described qualitatively as:
– 3 vertical DMI measurements give z, rx (pitch) and ry
(Yaw) ;
– differences between selected pairs of moving DMls
give x and y;
– difference between "clockwise" and "anti-clockwise''
moving DMls gives rz (roll) Figure 3 Calibration straightedge in situ
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CALIBRATION
• Two additional measurement systems are used to provide calibration data
• First, a Fizeau interferometer configured to provide a collimated beam approximately
parallel to the Z axis of the machine
• The Fizeau cavity comprises a transmission flat located in the metrology frame and a return
flat mounted in the stage
• The second calibration system comprises a four-sided Zerodur straightedge, the displacement
of which is monitored by 4 high stability plane mirror interferometers
• Straightedge is used for straightness and XY squareness
• In this case, we could not create a large enough through hole in the part mount (rotary table)
to achieve the required dynamic performance from the straightedge
• Since we directly measure angular error motions, we chose to mount the straightedge in the
moving stage (and for the straightedge)
• Use of opposed DMls and straightedge reversal gives two solutions for machine straightness
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ANGULAR ERROR MOTIONS
• The machine can be programmed to
autonull the Fizeau interferometer and
record the resulting tip and tilt (rx, ry)
• This drift(-9.6 nanorad/h (rx) and -6
nanorad/h (ry)) decreased with further time
after pump down
• Residuals from autonulling are of order 10
nanorad
• The difference between the data taken
moving "up" vs "down" is consistent with
the previously observed drift and the time
between measurements
Figure 5 Machine pitch and yaw
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STRAIGHTNESS
• Initial straightness measurements were made
before final DMI alignment; data were taken
at 1 mm increments over the full 500 mm
stage travel
• The two calculations for machine x-
straightness (after compensation for angular
error motion) are shown in Figures 6 and 7
• The sub-nm repeatability ripple with a spatial
period of approximately 3 mm and the
modulation envelope observed in the upper
portions of Figures 6 and 7 result from the
combination of:
– Different amplitude cyclic errors in the 3 z-axis
DMls
– Different cosine errors in the z-axis DMls
– Aliassing
Figure 7 Central portion of the data of Figure 6
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CYCLIC ERROR CORRECTION
• These errors can be minimized by DMI system
design and by careful alignment of tilt-tuned
waveplate
• Cyclic error compensation differentiates
between desired component of heterodyne
interferometer signal and undesired components
based on their frequency characteristics
• Desired component at a frequency = Reference
frequency of heterodyne interferometer light
source + Doppler shift
• Undesired components are located at unshifted
reference frequency and at reference frequency
minus Doppler shift
• Compensation is performed by measuring
undesired components
• Coefficients derived from these measurements
are digitally generated and signals subtracted
that are equal to cyclic error signals
• Coefficients are retained during periods when
interferometer is at or near rest and continue to
correctly compensate for cyclic error terms even
though signal components are not measured at
rest
Figure 8 Difference of straightness measurements
with and without cyclic error compensation
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SIMPLE STRAIGHTNESS MODEL
• Stage pitch and yaw are derived from the
3 vertical (Z) DMls
• It is apparent that cyclic errors and cosine
errors will cause stage angular motions
which will affect the output of the
"straightness" DMls
• This effect can be simply modeled and
sampled measurements of mixing in the
machine just before acquisition of the
data of Figures 6 and 7 were used to
estimate cyclic errors in the three Z DMls
• The qualitative similarity is striking
• Clearly all these plots are simply sampled
from an envelope which passes through
zero at z=100 mm, the control point for
the system
Figure 11 Multiple (44) measurements of straightness
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STRAIGHTNESS REPEATABILITY
• Straightness repeatability was evaluated by taking multiple measurement runs over
approximately 24 hours in the "forward" and "reversed" positions, in each case
starting data acquisition with 20 minutes after pump down
• Figure 11 shows the resulting 44 computations of the machine x-straightness
(before correction for angular errors)
• Standard deviations of each of the calibration DMls at each point is less than 0.5
nm
• Slopes removed from the data changed by less than 0.08 microradians over the
entire data set
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CONCLUSIONS
• This paper has presented results from the calibration of straightness and angular
error motions using classical machine metrology techniques
• High stability plane mirror interferometers provide sub-nanometer straightness
uncertainties
• Results from a Fizeau interferometer used in a "nulling" mode as an autocollimator
are limited at the 0.02 microradian level by residual machine drift
• Selection of a moving straightedge configuration results in a sensitivity to a
combination of cosine errors, Z-axis cyclic errors, and aliasing
• Automatic cyclic error compensation has been implemented
