- Email: [email protected]
Initial wafer heating analysis for a SCALPEL lithography system
IVlZCI~EI.ZCTRONIC ENGmq'/DmlNG
ELSEVIER
Microelectronic Engineering 46 (1999) 235-238
Initial wafer heating analysis for a SCALPEL lithography system
Smart T. Stantona, J. Alexander Liddlea, Gregg M. Gallatina, Byungkyu Kimb, and Roxanne L. Engelstadu "Lucent Technologies - Bell Laboratories, Murray Hill, NJ 07974, USA bDept, of Mechanical Engineering, University of Wisconsin - Madison, Madison, WI 53706, USA
A high-throughput SCALPEL tool will employ a typical exposure current of 30 pA and electron column potential of 100 KV, delivering power up to -3 W through a 0.25 mm (wafer scale) square optical subfield. Electrons lose energy to form heat in the upper 60 gm of a wafer in vacuum during a sub-field exposure period of -200 microseconds, creating significant local wafer heating at the time of image formation. Our initial analysis indicates that expansion-induced pattern placement errors will require a sub-field position correction strategy.
1. INTRODUCTION A high-throughput SCALPEL (SCattering with Angular Limitation Projection Electron-beam Lithography) tool 1 is expected to employ an exposure current o f - 3 0 gA and a resist sensitivity of 6-10 gC/cm:. For electron column operation at 100 KV, the power delivered as heat to the wafer, for a clear mask area, is ~3 W minus 7% energy removed by electron back-scattering. This power is delivered through a 0.25 mm (wafer scale) square optical sub-field, illustrated in figure 1.
Figure 1: Beam heating of wafer.
Resist heating effects for shaped-beam or cell-projection electron-beam lithography tools have previously been seen and analyzed by others. 2 However, the SCALPEL case is distinguished by its use of projection imaging in a relatively large (0.25 ram) sub-field, rapidly scanned to afford a larger (3
mm) effective field3 which dwells in an exposure area for a longer time. During image formation, there is substantial diffusion of the temperature profile into the wafer depth and into a wide area (½ sub-field in the simplest writing strategy). Since the heat dose is delivered in the upper 60 gm of a wafer in vacuum, there is negligible heat dissipation during the exposure time period (-200 microseconds), despite downward diffusion of new heat doses toward the chuck. Further, the temperature and area are inadequate for substantial radiative cooling of the sub-field area. Therefore, significant local wafer heating, associated with time and space scales of one sub-field exposure, occurs at the time of image formation. We have extensively exercised semianalytical models approximating the wafer heat deposition and diffusion phenomenon. We have examined hot region expansion strains, constrained by cooler surrounding material, using a thermoelastic potential4 model. Linear superposition of sub-field responses enables us to simulate many variations in writing strategy and other parameters. For versatility and speed, the approximate models used simplified boundary conditions. Analysis was
0167-9317/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S0167-9317(99)00070-2
236
S.T. Stanton / Microelectronic Engineering 46 (1999) 235-238
2-dimensional in both heat transfer and elasticity, with the wafer edges at +/- infmity where they are fixed at ambient temperature and zero strain. It is most valid for moderate spatial scales, neither very near the hot sub-field position where the 3-D nature is important, nor near actual wafer edges. We have also initially exercised rigorous 3D finite-element analysis models of the same problems, with full boundary conditions. Of several types of error, the most important is the sub-field pattern placement error due to the thermal expansion shift of the wafer surface. In this work, we will discuss these initial results and basic concepts for correction to meet error budget requirements.l
Dynamic expansion blur effects or magnification and distortion effects have been shown to be - 1-2 nm for all-bright or severe bright-to-dark transitions of the sub-field pattern density. The common result of many writing strategy and pattern density variation case analyses is that pattern density detail below about one subfield size is not important, and the heat profile is diffused adequately during exposure to smooth any local strain profile. The remaining issue is position errors of the sub-field image center. The static, bright sub-field profile diffusion and constrained expansion results are illustrated in figure 2.
1"I
T
2. TYPES OF H E A T I N G ERRORS Briefly, the possible error types due to deposition of heat are:
100
~ ' ~ / 10o
•
Resist temperature and sensitivity change.
•
Added image blur due to dynamic expansion.
•
Magnification or distortion in the sub-field.
•
Sub-field center placement errors.
~'~V"
50tl/ /
/ /
/
s0 x or
100 yaxis,
microns
Figure 2: Sub-field responses. The simple diffusion-edge motion relationship, d = "~ kt, where k is the diffusivity of the material, indicates that the diffusion edge moves a distance d - half the sub-field width in the time of a sub-field exposure (t ~ 200 microseconds). This diffusion process is three dimensional, acting on a relatively deeply deposited heat profile, peaked 20 microns below the resist. Approximate models show that almost all the shape-detail of the heat dose image is blurred away in 10% of the exposure time. The high electron energy level used in SCALPEL requires a relatively large exposure dose. Most electrons pass through the resist, so the direct heating of the resist is weak. The underlying heat profile may cause -23 K surface temperature rise, as seen in both approximate and FEA models. This, along with a maximum 8 K background for 200mm wafers, is estimated to cause negligible resist sensitivity change for the high activation-energy chemically-amplified resists used by SCALPEL.
3. PATTERN P L A C E M E N T E R R O R S We have examined heat profiles for this sub-field as it is dynamically scanned over the effective field. 3 Figure 3 illustrates a sequence of sub-field scans with steps in the stage-scan direction to form the chip-length stripe. Extremely effective smoothing and peak-reduction can also be achieved using multiple mini-scans of the sub-field as it defmes the effective field. Exposure using ten cycles eliminates the local hot-spot at the sub-field, reducing the peak distortion by - 2X. The full chip image is an assembly of chiplength image stripes. After a stripe-scan length of about 10 mm, the heating profile is found to be steady, assuming constant average pattern density
S.T. Stanton / Microelectronic Engineering 46 (1999) 235-238 .
~te
1 Cycl e
4 Cycles . .
237
10 Cycles .
ask
==~B~ stage Figure 3: Effective field created by sub-field scans, showing heat profile change with multiple scan cycles.
(65 % clear example). The material moves forward of its cool position by ~ 8 nm, as prior heat doses accumulate behind the sub-field. While proximity of other stripes has some effect, diffusion makes them modest and slowly varying. The stripe itself is the most important writing element needing a predictable sub-field placement correction, since a correction scheme cannot rely on any alignment targets inside the chip area.
'° iiii
3.0
! ....
2.0
0.0
....
!
......... I _ _ ~ _ ~ i r ~ d t
.........................
,
-1.0
.......................... ~............................ T..........
-2.0
-3.0
,
4. INITIAL FINITE E L E M E N T RESULTS The main contrasts between the approximate models and the fmite element analysis (FEA) are: •
FEA is a full 3-D model, with true energy deposition profiles.
•
FEA provides rigorous boundary condition treatment for wafer surfaces and edges.
In general, one would expect FEA to show somewhat larger local strain near the hotspot, as measured at the surface. The most severe difference in result occurs near the hot-spot with no multi-cycling, since diffusion has not had time to flatten the depth profile and the depth-averaged analysis is inadequate. Simple comparison of approximate and FEA results for one sub-field dose, as in figure 4 compared to figure 2, show that strains very local to the hot sub-field are about 3.7 times larger in the FEA model. Similar results have been obtained for FEA models of sub-field scans, and an extensive FEA analysis of important writing and pattern variation cases is under way.
i
-0.2
~
,
,
,
i
,
~
,
. . . .
i
.
.
.
0,1
-0.1
.
.
. 0.2
X-axis position (cm)
F i g vu r e
4:
FEA Result for static sub-field.
5. C O R R E C T I O N S T R A T E G Y BASICS The placement of the imaging sub-field must be dynamically corrected to 1-2 nm precision locally, in response to the local average pattern density within the sub-field. This part of the correction can be predictive, since the pattern is completely known, along with key operating parameters of the tool. Global correction is a distinct, slowly-varying coordinate adjustment of the repeating chip-scale local correction scheme. SCALPEL's electron backscatter alignment sensor6 can rapidly provide updated mark position error information at selected sites in the scribe alleys, as well as extensive first-time image-motion response calibrations. It will be employed mainly on stripe or chip scales.
238
S.T. Stanton / Microelectronic Engineering 46 (1999) 235-238
The suggested combination of predictive and metrology-based position correction is similar to a Kalman filter7 approach, as utilized extensively in many control systems. The Kalman filter provides a continuous loop in which the optimal weighting of predictive/historical information and new measurement information is found, based on analysis of the error statistics (figure 5).
REFERENCES 1. 2. 3.
CONCLUSIONS
4.
Extensive approximate analyses of SCALPEL wafer-heating effects, supported by initial FEA models, indicate a significant sub-field position error, requiring correction. However, the low spatial order, semi-repetitive, and predictable nature of the error suggests the feasibility of correction using calibration and well-known optimal control algorithms. Efforts continue on complete modeling, experimental verification, and correction scheme development.
5.
I resp°nse
~
i:~
TIME UPDATE: Mode Predict next (pattern + %. estimated operating / position and error state)
/
covariance.
6. 7.
S.T. Stanton et al., SPIE Vol. 3331 (1998) p. 673. For example: S. Babin and I. Y. Kuzmin, SPIE Vol. 3048, (1997) p. 374. W. K. Waskiewicz et al., Proc. of the International Conf. of Micro and NanoEngineering '97 (Sept. 1997). S.P. Timoshenko and J. N. Goodier, Theory. of Elasticity, McGraw Hill, New York, 1987 S. Stanton et al., The 42 "d International Conf. on Electron, Ion, and Photon Beam Technol. (May 1998) R . C . Farrow et al., J. Vac. Sci. Technol. B 10(6), Nov/Dec 1992, p. 2780. A . V . Balakrishnan, Kalman Filtering Theory. Optimization Software, Inc., New York, 1984
This work was SEMA TECH.
supported
by
DARPA
I Initial I [position&|
MEASUREMENT / 1 UPDATE: Compute Kalman ./~lignment gain,measure to I ensor update position I ~ . & error estimates I ~1
Figure 5: Kalman filter methodology for sub-field position correction.
and
ELSEVIER
Microelectronic Engineering 46 (1999) 235-238
Initial wafer heating analysis for a SCALPEL lithography system
Smart T. Stantona, J. Alexander Liddlea, Gregg M. Gallatina, Byungkyu Kimb, and Roxanne L. Engelstadu "Lucent Technologies - Bell Laboratories, Murray Hill, NJ 07974, USA bDept, of Mechanical Engineering, University of Wisconsin - Madison, Madison, WI 53706, USA
A high-throughput SCALPEL tool will employ a typical exposure current of 30 pA and electron column potential of 100 KV, delivering power up to -3 W through a 0.25 mm (wafer scale) square optical subfield. Electrons lose energy to form heat in the upper 60 gm of a wafer in vacuum during a sub-field exposure period of -200 microseconds, creating significant local wafer heating at the time of image formation. Our initial analysis indicates that expansion-induced pattern placement errors will require a sub-field position correction strategy.
1. INTRODUCTION A high-throughput SCALPEL (SCattering with Angular Limitation Projection Electron-beam Lithography) tool 1 is expected to employ an exposure current o f - 3 0 gA and a resist sensitivity of 6-10 gC/cm:. For electron column operation at 100 KV, the power delivered as heat to the wafer, for a clear mask area, is ~3 W minus 7% energy removed by electron back-scattering. This power is delivered through a 0.25 mm (wafer scale) square optical sub-field, illustrated in figure 1.
Figure 1: Beam heating of wafer.
Resist heating effects for shaped-beam or cell-projection electron-beam lithography tools have previously been seen and analyzed by others. 2 However, the SCALPEL case is distinguished by its use of projection imaging in a relatively large (0.25 ram) sub-field, rapidly scanned to afford a larger (3
mm) effective field3 which dwells in an exposure area for a longer time. During image formation, there is substantial diffusion of the temperature profile into the wafer depth and into a wide area (½ sub-field in the simplest writing strategy). Since the heat dose is delivered in the upper 60 gm of a wafer in vacuum, there is negligible heat dissipation during the exposure time period (-200 microseconds), despite downward diffusion of new heat doses toward the chuck. Further, the temperature and area are inadequate for substantial radiative cooling of the sub-field area. Therefore, significant local wafer heating, associated with time and space scales of one sub-field exposure, occurs at the time of image formation. We have extensively exercised semianalytical models approximating the wafer heat deposition and diffusion phenomenon. We have examined hot region expansion strains, constrained by cooler surrounding material, using a thermoelastic potential4 model. Linear superposition of sub-field responses enables us to simulate many variations in writing strategy and other parameters. For versatility and speed, the approximate models used simplified boundary conditions. Analysis was
0167-9317/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S0167-9317(99)00070-2
236
S.T. Stanton / Microelectronic Engineering 46 (1999) 235-238
2-dimensional in both heat transfer and elasticity, with the wafer edges at +/- infmity where they are fixed at ambient temperature and zero strain. It is most valid for moderate spatial scales, neither very near the hot sub-field position where the 3-D nature is important, nor near actual wafer edges. We have also initially exercised rigorous 3D finite-element analysis models of the same problems, with full boundary conditions. Of several types of error, the most important is the sub-field pattern placement error due to the thermal expansion shift of the wafer surface. In this work, we will discuss these initial results and basic concepts for correction to meet error budget requirements.l
Dynamic expansion blur effects or magnification and distortion effects have been shown to be - 1-2 nm for all-bright or severe bright-to-dark transitions of the sub-field pattern density. The common result of many writing strategy and pattern density variation case analyses is that pattern density detail below about one subfield size is not important, and the heat profile is diffused adequately during exposure to smooth any local strain profile. The remaining issue is position errors of the sub-field image center. The static, bright sub-field profile diffusion and constrained expansion results are illustrated in figure 2.
1"I
T
2. TYPES OF H E A T I N G ERRORS Briefly, the possible error types due to deposition of heat are:
100
~ ' ~ / 10o
•
Resist temperature and sensitivity change.
•
Added image blur due to dynamic expansion.
•
Magnification or distortion in the sub-field.
•
Sub-field center placement errors.
~'~V"
50tl/ /
/ /
/
s0 x or
100 yaxis,
microns
Figure 2: Sub-field responses. The simple diffusion-edge motion relationship, d = "~ kt, where k is the diffusivity of the material, indicates that the diffusion edge moves a distance d - half the sub-field width in the time of a sub-field exposure (t ~ 200 microseconds). This diffusion process is three dimensional, acting on a relatively deeply deposited heat profile, peaked 20 microns below the resist. Approximate models show that almost all the shape-detail of the heat dose image is blurred away in 10% of the exposure time. The high electron energy level used in SCALPEL requires a relatively large exposure dose. Most electrons pass through the resist, so the direct heating of the resist is weak. The underlying heat profile may cause -23 K surface temperature rise, as seen in both approximate and FEA models. This, along with a maximum 8 K background for 200mm wafers, is estimated to cause negligible resist sensitivity change for the high activation-energy chemically-amplified resists used by SCALPEL.
3. PATTERN P L A C E M E N T E R R O R S We have examined heat profiles for this sub-field as it is dynamically scanned over the effective field. 3 Figure 3 illustrates a sequence of sub-field scans with steps in the stage-scan direction to form the chip-length stripe. Extremely effective smoothing and peak-reduction can also be achieved using multiple mini-scans of the sub-field as it defmes the effective field. Exposure using ten cycles eliminates the local hot-spot at the sub-field, reducing the peak distortion by - 2X. The full chip image is an assembly of chiplength image stripes. After a stripe-scan length of about 10 mm, the heating profile is found to be steady, assuming constant average pattern density
S.T. Stanton / Microelectronic Engineering 46 (1999) 235-238 .
~te
1 Cycl e
4 Cycles . .
237
10 Cycles .
ask
==~B~ stage Figure 3: Effective field created by sub-field scans, showing heat profile change with multiple scan cycles.
(65 % clear example). The material moves forward of its cool position by ~ 8 nm, as prior heat doses accumulate behind the sub-field. While proximity of other stripes has some effect, diffusion makes them modest and slowly varying. The stripe itself is the most important writing element needing a predictable sub-field placement correction, since a correction scheme cannot rely on any alignment targets inside the chip area.
'° iiii
3.0
! ....
2.0
0.0
....
!
......... I _ _ ~ _ ~ i r ~ d t
.........................
,
-1.0
.......................... ~............................ T..........
-2.0
-3.0
,
4. INITIAL FINITE E L E M E N T RESULTS The main contrasts between the approximate models and the fmite element analysis (FEA) are: •
FEA is a full 3-D model, with true energy deposition profiles.
•
FEA provides rigorous boundary condition treatment for wafer surfaces and edges.
In general, one would expect FEA to show somewhat larger local strain near the hotspot, as measured at the surface. The most severe difference in result occurs near the hot-spot with no multi-cycling, since diffusion has not had time to flatten the depth profile and the depth-averaged analysis is inadequate. Simple comparison of approximate and FEA results for one sub-field dose, as in figure 4 compared to figure 2, show that strains very local to the hot sub-field are about 3.7 times larger in the FEA model. Similar results have been obtained for FEA models of sub-field scans, and an extensive FEA analysis of important writing and pattern variation cases is under way.
i
-0.2
~
,
,
,
i
,
~
,
. . . .
i
.
.
.
0,1
-0.1
.
.
. 0.2
X-axis position (cm)
F i g vu r e
4:
FEA Result for static sub-field.
5. C O R R E C T I O N S T R A T E G Y BASICS The placement of the imaging sub-field must be dynamically corrected to 1-2 nm precision locally, in response to the local average pattern density within the sub-field. This part of the correction can be predictive, since the pattern is completely known, along with key operating parameters of the tool. Global correction is a distinct, slowly-varying coordinate adjustment of the repeating chip-scale local correction scheme. SCALPEL's electron backscatter alignment sensor6 can rapidly provide updated mark position error information at selected sites in the scribe alleys, as well as extensive first-time image-motion response calibrations. It will be employed mainly on stripe or chip scales.
238
S.T. Stanton / Microelectronic Engineering 46 (1999) 235-238
The suggested combination of predictive and metrology-based position correction is similar to a Kalman filter7 approach, as utilized extensively in many control systems. The Kalman filter provides a continuous loop in which the optimal weighting of predictive/historical information and new measurement information is found, based on analysis of the error statistics (figure 5).
REFERENCES 1. 2. 3.
CONCLUSIONS
4.
Extensive approximate analyses of SCALPEL wafer-heating effects, supported by initial FEA models, indicate a significant sub-field position error, requiring correction. However, the low spatial order, semi-repetitive, and predictable nature of the error suggests the feasibility of correction using calibration and well-known optimal control algorithms. Efforts continue on complete modeling, experimental verification, and correction scheme development.
5.
I resp°nse
~
i:~
TIME UPDATE: Mode Predict next (pattern + %. estimated operating / position and error state)
/
covariance.
6. 7.
S.T. Stanton et al., SPIE Vol. 3331 (1998) p. 673. For example: S. Babin and I. Y. Kuzmin, SPIE Vol. 3048, (1997) p. 374. W. K. Waskiewicz et al., Proc. of the International Conf. of Micro and NanoEngineering '97 (Sept. 1997). S.P. Timoshenko and J. N. Goodier, Theory. of Elasticity, McGraw Hill, New York, 1987 S. Stanton et al., The 42 "d International Conf. on Electron, Ion, and Photon Beam Technol. (May 1998) R . C . Farrow et al., J. Vac. Sci. Technol. B 10(6), Nov/Dec 1992, p. 2780. A . V . Balakrishnan, Kalman Filtering Theory. Optimization Software, Inc., New York, 1984
This work was SEMA TECH.
supported
by
DARPA
I Initial I [position&|
MEASUREMENT / 1 UPDATE: Compute Kalman ./~lignment gain,measure to I ensor update position I ~ . & error estimates I ~1
Figure 5: Kalman filter methodology for sub-field position correction.
and