Libor Švéda1, Martina Landová2, Martin Míka2, Ladislav Pína1, Radka Havlíková1, Veronika Semencová3

1) KFE FJFI ČVUT2) VŠCHT Praha3) Rigaku Innovative Technologies Europe s.r.o.

Glass thermal formation -

experiment vs. simulation

• Motivation• Glass forming process – brief description• Metrology• Simulations – theory• Simulations – initial results• Perspectives – metrology upgrades– simulation modifications

Motivation

• Thermal glass forming as a method how to obtain precise shapes• Precursor to Si wafer forming• Typical applications

– glass:• Space x-ray mirrors (large scale, low specific mass, good surface roughness)• Mirrors for catadioptric systems, like the HUD display (large, low cost)• Mirrors for condensors, like the sun heat sources, photomultiplyers etc. (large, low

cost)– Silicon

• Space x-ray mirrors (excellent surface quality)• Laboratory x-ray mirrors (diffraction imaging, excellent surface quality)

Glass forming process

Form defined shaping• Arbitrary shape• High temperature form / mandrel• Contact method – possible surface

contamination

„Freefall forming“• Shape given by physics• Efficient shape modification only by

temperature gradients• Non-contact method

FOven

G

Oven

Metrology - overview

• Low precision• In-situ• Process dynamics

• Very high precission• On the table• No process dynamics• Possible contamination• Effect of transportation

Metrology – in situprocess dynamics intro

Metrology – in situprocess dynamics curves

Form process parameters prediction

Metrology – in situprofile measurement

End of formation

After cool down

Metrology – on-the-table

Forming simulations - theory

• Heat-up process– Elastic material properties

• Forming process– Viscous liquid approximation at given temperature– Strong change of viscosity with temperature!!!– Problem of boundary conditions

• Cool-down process– Similar to forming process, except that changing temperature

according to the measured temperature decay

G

Temperature gradient?

Simulations – input parameters

DESAG D263 glass• density: 2.510 g/cm3

• Young modulus: 72.9 Mpa• Poisson ratio: 0.209• thermal coeff. of expansion: 7.2e-6 K-1

• strain point: 529°C• annealing point: 557°C• softening point: 736°C• sample size:• 75x25x0.7 mm• 100 x 100 x 0.4 mm

• temperatures used: 540-660°CDynamic viscosity used

Simulations – viscous liquid

Comsol Multiphysics simulations

• Viscous liquid at given temperature• Velocity fields at given time• Actual glass profile is obtained by

integrating the velocity curves

http://www.comsol.com/

Simulations vs. metrologyprocess dynamics

75x25x0.75 mm glassWhy?

Simulation vs. metrologyfixed edges

Form process predictions - simulation

Simulation vs. metrologycool down process

Known error sources

• Cool down during the image acquisition• Cool down process and corrections for that process• Temperature gradients• No definition of fixed points for forming• Image distortions during the in-situ measurements, no camera fixation• Lighting conditions not well defined• Non existent fast non-contact profilometry (no need to transport over large distances, time

gaps)

Perspectives – metrology upgradesin-situ

Ronald A. Petrozzo and Stuart W. Singer Schneider Optics Hauppauge, NY -- Test & Measurement World, 10/15/2001

Perspectives – metrology upgradeson-the-table I

www.stilsa.com

Chromatic aberration based method• Non-contact method• Precision vs. measuring range vs.

allowed surface slope• Typical values:

Measuring range 0.4 mm 4.0 mm 12.0 mmWorking distance 11.0 mm 16.4 mm 29.0 mmAxial resolution 22 nm 160 nm 400 nmAccuracy 80 nm 300 nm 900 nm

Perspectives – simulation upgrades

• Include temperature gradients– Measure actual temperature inside the oven– Apply the temperatures to the simulation

• Include cool down process as a standard point• Treat more precisely the glass/form interface

Conclusions

• First in-situ shaping measurements (full profile)• Discrepancy between simulations and experiment

– Experiment is non-linear x Simulation predict linear bending curve– Higher temperatures are preserved precisely (experiment)– Inoptimal metrology (experiment)– Boundary conditions not well defined (experiment + simulation)

• Experience gathered is used for developing new metrology methods for future experiments (including Silicon shaping)

Finito