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Membrane mask aero and thermoelastic control for proximity lithography
Microelectronic Engineering 83 (2006) 923–925 www.elsevier.com/locate/mee
Membrane mask aero and thermoelastic control for proximity lithography Dryver Huston a
a,*
, James Plumpton a, Brian Esser a, Dylan Burns a, Brent Boerger b, Robert Selzer b
Mechanical Engineering Department, University of Vermont, Burlington, VT 05405-0156, United States JMAR Systems, A Division of JMAR Technologies, Inc., South Burlington, VT 05403, United States
b
Available online 3 February 2006
Abstract Proximity lithography using thin membrane window structures to carry masking patterns during radiation exposure steps is reaching levels of such high precision that the process can benefit from active elastic control of membrane deformations. This paper discusses two methods of actively controlling membrane mask deformation. The first is the mitigation of unwanted out-of-plane aeroelastic effects caused by rapidly stepping between wafer exposure fields while maintaining a sub 100 lm gap. The second is an in-plane thermoelastic active deformation to improve overlay accuracy. 2006 Elsevier B.V. All rights reserved. Keywords: Membrane; Mask; Thermoelastic; Aeroelastic; Proximity; Lithography; Active; Control
1. Introduction Proximity lithography is a technique where a thin membrane mask is held in close proximity parallel to a substrate wafer with a small gap (usually sub 100 lm). Patterns on the mask are transferred to the wafer by selectively transmitting radiation to a photoresist with soft (1–2 nm) X-rays. The process can produce features at least as small as 50 nm. Attaining such levels of resolution places extremely tight mechanical performance requirements on the system. Additional demands arise due to the pressures of production that require rapid positioning and gap settling. Membrane mask windows typically have thicknesses of less than 2 lm, spans of up to 50 mm and are made of mechanically stable materials, such as silicon carbide. The lithographic operation sequence is to position the membrane mask to within close proximity of a flat wafer (5– 100 lm gap), with a lateral overlay accuracy of 5 nm; hold this position for radiation exposure; and step to a new expo-
sure field on the wafer for new positioning and control as quickly as possible. Attaining and sustaining the desired overlay and positional accuracies requires controlling deformations in the mask. Unwanted deformations in the mask arise due to a variety of loads including aerodynamic, mechanical and thermal. In many situations, aerodynamic loading due to stepping and positioning maneuvers can cause significant out-of-plane deformations. Mechanical and thermal loadings on the mask, as well as previous layer printing errors can cause in-plane overlay errors. Sustaining the desired position with an accuracy needed for sub 50 nm feature lithography is difficult with using only passive mechanical rigid body position control. Alternative, though more complex, means can supplement rigid body positioning. These include precise gap control and aerodynamic devices for the control of aeroelastic effects, and active in-plane mask deformation procedures to minimize overlay errors. 2. Aeroelastic effects and control
*
Corresponding author. Tel.: +1 802 656 1922; fax: +1 802 656 1929. E-mail addresses: [email protected], [email protected] (D. Huston). 0167-9317/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2006.01.042
Out-of-plane deformations caused by the interaction of fluids in the gap with lateral stepping motions can signifi-
924
D. Huston et al. / Microelectronic Engineering 83 (2006) 923–925
o op o op dh dh h3 h3 þ2 þ ¼ g 6U ox ox oy oy dx dt
Fig. 1. Aeroelastic deformations caused by lateral stepping.
cantly deflect and possibly damage the membrane, Fig. 1. Aerodynamic loads that deflect the mask, alter the gap dimensions and then alter the aerodynamic loads. The combination of aerodynamic and elastic effects in a feedback loop is often called an aeroelastic phenomenon [1]. The standard procedure for analyzing aeroelastic effects is to form separate models for the mechanics of the aerodynamic and elastic effects. Matching the displacement and pressure across the fluid-structure interface couples the aerodynamic and elastic models to form an aeroelastic model. The two principal aerodynamic loadings on the membrane are caused by gap closing and opening maneuvers, and by lateral stepping at gap. Both of these situations are examples of thin film fluid flows, with a low Reynolds number. Viscous forces and not inertial forces dominate these flows. As a result effects based on Bernoulli’s principle, such as the development of lift by fluid flow tangent to a surface, are negligible. The dimensions under consideration are sufficiently small to suggest that molecular effects may be important. The Knudsen number, Kn, is defined as the ratio of the mean free path/macro length scale-gap. When Kn < 103 or 102 classical Navier–Stokes models with no-slip boundary conditions can be used. For a 30 lm gap using air at 1 atm, Kn = 1.15 · 102. Smaller gaps and lower pressures may require consideration of slipping boundary conditions. Based on the above assumptions and a few more, such as neglecting gravity, Reynolds hydrodynamic lubrication equation can model the fluid forces [2]
ð1Þ
x and y are in-plane spatial coordinates. The gap distance as a function of x and y is h. The pressure normal to the gap surfaces as a function of x and y is p. The lateral stepping velocity and viscosity are U and g, respectively. An examination of Reynolds equation indicates that the maximum pressure is proportional to h3, the wedge angle dh/ dx, a lateral dimension D, and the stepping speed U. The membrane mask is assumed to deform as an elastic structure. Plate and shell mechanics nominally apply [3]. However, for thin structures with large in-plane tensions, such as a silicon carbide mask, it is possible to use simpler membrane mechanics with a pressure-displacement relation of the form p ð2Þ r2 w ¼ T The out-of-plane membrane deformation is w. The pressure applied to the membrane is p. T is the in-plane tension. Matching the pressure and displacement in (1) and (2) forms the aeroelastic model for this system. Based on these considerations, it can be determined that the out-of-plane aeroelastic effects are minimized when the gap is held at a 0 wedge angle. Detailed finite element models (FEMLAB Multiphysics) confirm this conclusion. Additionally aerodynamic breathing devices formed as perforations through the supporting wafer were modeled. The finite element results indicate that the breathing devices can significantly reduce pressures and membrane deflections, Fig. 2. Experiments to verify the predictions of the aeroelastic model were conducted on a test bed that simulated lateral stepping at gap maneuvers. A polished granite block sliding on air bearings in front of a membrane mask was the basis of the test bed. The results of the experiments were to confirm the predictions of the aeroelastic models. Fig. 3 shows membrane mask midspan deflections as a function of time and wedge angle for an oscillating lat-
Fig. 2. Aeroelastic pressure contours from finite element model.
Delta Y Position (nm)
D. Huston et al. / Microelectronic Engineering 83 (2006) 923–925
925
180 160 140 120 100 80 60 40 20 0 0
2
4
6
8
1
Delta Temp (Deg C) Fig. 5. Controlled thermoelastic displacement vs applied temperature in membrane mask.
Fig. 3. Measured membrane mask aeroelastic deflection as a function of wedge angle for oscillating lateral stepping at gap.
eral stepping motion. Reducing the wedge angle reduces the membrane deflection. Other experimental results confirm that minimal out-of-plane aeroelastic deformations occur if a neutral 0 wedge angle is maintained during stepping, but that maintaining very small gaps may suffer from electrostatic attractions between the mask and wafer. 3. Thermoelastic control Thermal distortions due to radiation heating, mask-towafer overlay distortions due to tooling and manufacturing imperfections cause overlay errors that are difficult to correct by rigid body positioning. Flexible-body mechanical control of the in-plane mask shape is a possible solution [4,5].
After considering several competing strategies for actively controlling in-plane motion, it was determined that possibly the most practical approach is a thermoelastic technique where thermoelectric actuators are placed on the mask-supporting wafer near to the mask perimeter and to use a multichannel control algorithm. The thermoelastic results are that a linear control scheme can be effective, but that modeling the thermoelastic behavior is complicated by uncertainties about boundary conditions. Fig. 4 shows the membrane mask with thermoelectric actuators and an ALX metrology system. Fig. 5 shows typical results of controlled thermoelastic deformations where the deformations are linear with applied temperature down to at least 20 nm. 4. Conclusions Process operations and tooling errors in manufacture inevitably cause overlay errors and mask deformations that cannot be completely eliminated by passive rigid body techniques. Physical models based on aeroelastic and thermoelastic control were developed, simulated and tested with prototype systems. The results of the prototype bench top tests were largely successful and indicate the potential viability of using these techniques in production. Acknowledgments This work has been supported by NAVAIR Contract #N00421-02-D-3189. The authors thank and acknowledge DARPA/MTO–Dr. Joseph Mangano and NAVAIR Mr. Charles Caposell and Mr. Glenn Marshall without whose support this program would not be possible. References
Fig. 4. Membrane mask with thermoelectric actuators and ALX metrology system.
[1] E. Dowell, A Modern Course in Aeroelasticity, Elsevier, 2004. [2] A. Cameron, Basic Lubrication Theory, second ed., Wiley, New York, 1977. [3] A. Ugural, Stresses in Plates and Shells, second ed., McGraw Hill, 1998. [4] D. Huston, W. Sauter, IEEE Trans. Semiconduc. Manufact. 13 (2001) 3. [5] M. Feldman, J. Vac. Sci. Technol. B 17 (1999).
Membrane mask aero and thermoelastic control for proximity lithography Dryver Huston a
a,*
, James Plumpton a, Brian Esser a, Dylan Burns a, Brent Boerger b, Robert Selzer b
Mechanical Engineering Department, University of Vermont, Burlington, VT 05405-0156, United States JMAR Systems, A Division of JMAR Technologies, Inc., South Burlington, VT 05403, United States
b
Available online 3 February 2006
Abstract Proximity lithography using thin membrane window structures to carry masking patterns during radiation exposure steps is reaching levels of such high precision that the process can benefit from active elastic control of membrane deformations. This paper discusses two methods of actively controlling membrane mask deformation. The first is the mitigation of unwanted out-of-plane aeroelastic effects caused by rapidly stepping between wafer exposure fields while maintaining a sub 100 lm gap. The second is an in-plane thermoelastic active deformation to improve overlay accuracy. 2006 Elsevier B.V. All rights reserved. Keywords: Membrane; Mask; Thermoelastic; Aeroelastic; Proximity; Lithography; Active; Control
1. Introduction Proximity lithography is a technique where a thin membrane mask is held in close proximity parallel to a substrate wafer with a small gap (usually sub 100 lm). Patterns on the mask are transferred to the wafer by selectively transmitting radiation to a photoresist with soft (1–2 nm) X-rays. The process can produce features at least as small as 50 nm. Attaining such levels of resolution places extremely tight mechanical performance requirements on the system. Additional demands arise due to the pressures of production that require rapid positioning and gap settling. Membrane mask windows typically have thicknesses of less than 2 lm, spans of up to 50 mm and are made of mechanically stable materials, such as silicon carbide. The lithographic operation sequence is to position the membrane mask to within close proximity of a flat wafer (5– 100 lm gap), with a lateral overlay accuracy of 5 nm; hold this position for radiation exposure; and step to a new expo-
sure field on the wafer for new positioning and control as quickly as possible. Attaining and sustaining the desired overlay and positional accuracies requires controlling deformations in the mask. Unwanted deformations in the mask arise due to a variety of loads including aerodynamic, mechanical and thermal. In many situations, aerodynamic loading due to stepping and positioning maneuvers can cause significant out-of-plane deformations. Mechanical and thermal loadings on the mask, as well as previous layer printing errors can cause in-plane overlay errors. Sustaining the desired position with an accuracy needed for sub 50 nm feature lithography is difficult with using only passive mechanical rigid body position control. Alternative, though more complex, means can supplement rigid body positioning. These include precise gap control and aerodynamic devices for the control of aeroelastic effects, and active in-plane mask deformation procedures to minimize overlay errors. 2. Aeroelastic effects and control
*
Corresponding author. Tel.: +1 802 656 1922; fax: +1 802 656 1929. E-mail addresses: [email protected], [email protected] (D. Huston). 0167-9317/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2006.01.042
Out-of-plane deformations caused by the interaction of fluids in the gap with lateral stepping motions can signifi-
924
D. Huston et al. / Microelectronic Engineering 83 (2006) 923–925
o op o op dh dh h3 h3 þ2 þ ¼ g 6U ox ox oy oy dx dt
Fig. 1. Aeroelastic deformations caused by lateral stepping.
cantly deflect and possibly damage the membrane, Fig. 1. Aerodynamic loads that deflect the mask, alter the gap dimensions and then alter the aerodynamic loads. The combination of aerodynamic and elastic effects in a feedback loop is often called an aeroelastic phenomenon [1]. The standard procedure for analyzing aeroelastic effects is to form separate models for the mechanics of the aerodynamic and elastic effects. Matching the displacement and pressure across the fluid-structure interface couples the aerodynamic and elastic models to form an aeroelastic model. The two principal aerodynamic loadings on the membrane are caused by gap closing and opening maneuvers, and by lateral stepping at gap. Both of these situations are examples of thin film fluid flows, with a low Reynolds number. Viscous forces and not inertial forces dominate these flows. As a result effects based on Bernoulli’s principle, such as the development of lift by fluid flow tangent to a surface, are negligible. The dimensions under consideration are sufficiently small to suggest that molecular effects may be important. The Knudsen number, Kn, is defined as the ratio of the mean free path/macro length scale-gap. When Kn < 103 or 102 classical Navier–Stokes models with no-slip boundary conditions can be used. For a 30 lm gap using air at 1 atm, Kn = 1.15 · 102. Smaller gaps and lower pressures may require consideration of slipping boundary conditions. Based on the above assumptions and a few more, such as neglecting gravity, Reynolds hydrodynamic lubrication equation can model the fluid forces [2]
ð1Þ
x and y are in-plane spatial coordinates. The gap distance as a function of x and y is h. The pressure normal to the gap surfaces as a function of x and y is p. The lateral stepping velocity and viscosity are U and g, respectively. An examination of Reynolds equation indicates that the maximum pressure is proportional to h3, the wedge angle dh/ dx, a lateral dimension D, and the stepping speed U. The membrane mask is assumed to deform as an elastic structure. Plate and shell mechanics nominally apply [3]. However, for thin structures with large in-plane tensions, such as a silicon carbide mask, it is possible to use simpler membrane mechanics with a pressure-displacement relation of the form p ð2Þ r2 w ¼ T The out-of-plane membrane deformation is w. The pressure applied to the membrane is p. T is the in-plane tension. Matching the pressure and displacement in (1) and (2) forms the aeroelastic model for this system. Based on these considerations, it can be determined that the out-of-plane aeroelastic effects are minimized when the gap is held at a 0 wedge angle. Detailed finite element models (FEMLAB Multiphysics) confirm this conclusion. Additionally aerodynamic breathing devices formed as perforations through the supporting wafer were modeled. The finite element results indicate that the breathing devices can significantly reduce pressures and membrane deflections, Fig. 2. Experiments to verify the predictions of the aeroelastic model were conducted on a test bed that simulated lateral stepping at gap maneuvers. A polished granite block sliding on air bearings in front of a membrane mask was the basis of the test bed. The results of the experiments were to confirm the predictions of the aeroelastic models. Fig. 3 shows membrane mask midspan deflections as a function of time and wedge angle for an oscillating lat-
Fig. 2. Aeroelastic pressure contours from finite element model.
Delta Y Position (nm)
D. Huston et al. / Microelectronic Engineering 83 (2006) 923–925
925
180 160 140 120 100 80 60 40 20 0 0
2
4
6
8
1
Delta Temp (Deg C) Fig. 5. Controlled thermoelastic displacement vs applied temperature in membrane mask.
Fig. 3. Measured membrane mask aeroelastic deflection as a function of wedge angle for oscillating lateral stepping at gap.
eral stepping motion. Reducing the wedge angle reduces the membrane deflection. Other experimental results confirm that minimal out-of-plane aeroelastic deformations occur if a neutral 0 wedge angle is maintained during stepping, but that maintaining very small gaps may suffer from electrostatic attractions between the mask and wafer. 3. Thermoelastic control Thermal distortions due to radiation heating, mask-towafer overlay distortions due to tooling and manufacturing imperfections cause overlay errors that are difficult to correct by rigid body positioning. Flexible-body mechanical control of the in-plane mask shape is a possible solution [4,5].
After considering several competing strategies for actively controlling in-plane motion, it was determined that possibly the most practical approach is a thermoelastic technique where thermoelectric actuators are placed on the mask-supporting wafer near to the mask perimeter and to use a multichannel control algorithm. The thermoelastic results are that a linear control scheme can be effective, but that modeling the thermoelastic behavior is complicated by uncertainties about boundary conditions. Fig. 4 shows the membrane mask with thermoelectric actuators and an ALX metrology system. Fig. 5 shows typical results of controlled thermoelastic deformations where the deformations are linear with applied temperature down to at least 20 nm. 4. Conclusions Process operations and tooling errors in manufacture inevitably cause overlay errors and mask deformations that cannot be completely eliminated by passive rigid body techniques. Physical models based on aeroelastic and thermoelastic control were developed, simulated and tested with prototype systems. The results of the prototype bench top tests were largely successful and indicate the potential viability of using these techniques in production. Acknowledgments This work has been supported by NAVAIR Contract #N00421-02-D-3189. The authors thank and acknowledge DARPA/MTO–Dr. Joseph Mangano and NAVAIR Mr. Charles Caposell and Mr. Glenn Marshall without whose support this program would not be possible. References
Fig. 4. Membrane mask with thermoelectric actuators and ALX metrology system.
[1] E. Dowell, A Modern Course in Aeroelasticity, Elsevier, 2004. [2] A. Cameron, Basic Lubrication Theory, second ed., Wiley, New York, 1977. [3] A. Ugural, Stresses in Plates and Shells, second ed., McGraw Hill, 1998. [4] D. Huston, W. Sauter, IEEE Trans. Semiconduc. Manufact. 13 (2001) 3. [5] M. Feldman, J. Vac. Sci. Technol. B 17 (1999).