1. Quantum Lithography Presented at SPIE, August 14th, 2006
Robert Boyd, Sean Bentley*, Hye-Jeong Chang, Heedeuk Shin, Malcolm O’Sullivan-Hale and Kam Wai Chan
Institute of Optics, University of Rochester, Rochester, NY
*Department of Physics, Adelphi University, Garden City, NY
Girish Agarwal
Department of Physics, Oklahoma State University, Stillwater, OK Hugo Cable, Jonathan Dowling
Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA
Presented at SPIE, August 14th, 2006

2. Quantum Lithography: Introduction
Two classical beams of light interfere… I = 1 2 ( + c o s  ) k x i n 2 s i n 2 x m i n 2
SPIE: Aug. 14th, 2006

3. Original Quantum Lithography Proposalj 1 ; i j 2 ; i +
Entangled photons produced in SPDC can increase resolution of an interferometric lithography system by factor of 2 (Boto et al., 2000)
N-fold enhancement possible when N photons are entangled
Boto et al., PRL 85, 2733 (2000)
SPIE: Aug. 14th, 2006

4. Experimental Challenges
Inconsistency?
Need strong enough light to excite two-photon absorption
Need weak enough light so that the statistics are those of individual photon pairs
Develop a multi-photon absorber
Nth harmonic generation/coincidence circuitry
Polymethylmethacrylate (PMMA)
Multi-photon absorber at visible wavelengths
e-beam resist
SPIE: Aug. 14th, 2006

5. Quantum Lithography with an OPA
Replace parametric down-converter with high gain optical parametric amplifier (OPA)
Can be very intense
Possesses strong quantum features
Agarwal, Boyd, Nagasko, Bentley, PRL 86, 1389 (2001)
SPIE: Aug. 14th, 2006

6. Quantum Lithography with an OPA
OPA Relations ^ a 1 = ( c o s h G ) i e Á n b y g j E p L
Two-photon Output R ( 2 ) / D ^ a y 3 E = + e i  b
Beamsplitter Relations ^ a 2 = 1 p ( + i b )
SPIE: Aug. 14th, 2006

7. Two-Photon Excitation Rate
For light from an OPA, both linear and quadratic dependence are present.
Cross-over point: I = 1 3 p h o t n s / m d e G : 5
For cases of practical interest, the rate scales quadratically with I.
SPIE: Aug. 14th, 2006

8. Visibility using an OPA and TPA
Visibility versus Gain V = c o s h 2 G + 4 i n V = R ( 2 ) m a x i n +
Visibility never falls below 20%
SPIE: Aug. 14th, 2006

9. Effect of an N-Photon Absorber
Replace TPA with an N-photon absorber. R ( N ) = D ^ a y 3 E
We can find an analytic solution: R ( N ) / = 2 X n P s i h G c o Â
with P N = p ! 2 n ( + 1 )
SPIE: Aug. 14th, 2006

10. Effect of an N-Photon Absorber
→ As N increases, visibility improves, but no improvement in resolution.
SPIE: Aug. 14th, 2006

11. Summary of OPA Results
For most cases, two-photon excitation rate scales as I2.
OPA + TPA produces fringes with visibility greater than 20%
OPA + N-photon absorber produces fringes with even greater visibility (but with no greater resolution)
SPIE: Aug. 14th, 2006

12. Classical Nonlinear Lithography
Linear absorbing medium: E L A = 1 2 ( + c o s  ) E T P A = 1 4 ( + c o s  ) 2 3
TPA medium:
“Non-quantum Quantum Lithography”:
Average 2 shots with phases c and c+p E = 1 4 3 2 + c o s Â
In general, use an N-photon absorber and average N shots
with the kth shot having phase 2pk/N.
SPIE: Aug. 14th, 2006

13. Classical Nonlinear Lithography
Proof-of-Principle Experiment
N=1
N=2
no averaging
N=2
averaging
Bentley and Boyd, Opt. Exp. 12, 5735 (2004)
SPIE: Aug. 14th, 2006

14. PMMA
Polymethylmethacrylate (PMMA) is a positive photo-resist that is transparent in the visible region.
800 nm can break chemical bonds, and the affected regions can be removed in the development process.
UV absorption spectrum of PMMA
PMMA is 3-photon 800 nm. Problem: Self-healing means multiple bonds must be broken.
800 nm
SPIE: Aug. 14th, 2006

15. Experimental Setup with regenerative amplifcation
120 fs, 1 W, 1 kHz, at 800 nm
(Spectra-Physics)
WP: half-wave plate; Pol.: polarizer; M1,M2,M3: mirrors; BS: beamsplitter; f1,f2: lenses; PR: phase retarder (Babinet-Soleil compensator)
SPIE: Aug. 14th, 2006

16. Classical Nonlinear Lithography
Interference pattern shifted by
l/4
Path length difference
l/2
Developing
l/2
Phase retarder
l/4
PMMA
Substrate (Glass)
SPIE: Aug. 14th, 2006

17. PMMA Preparation Sample Development
PMMA (120,000 MW) + Toluene Solution (20% solids by weight)
PMMA is spin-coated on a glass substrate
rpm, 20 sec
dried for 3 min
repeated 3 times → 1-mm-thick film
Development
Developer: 10 sec in 1:1 methyl isobutyl ketone (MIBK) to isopropyl alcohol
Rinse: 10 sec in DI water
Air blow dried
SPIE: Aug. 14th, 2006

18. Fringes on PMMA AFM images of PMMA surface Surface Cross-Section q
Recording wavelength: 800 nm
Pulse energy: 130 mJ/beam
Pulse duration: 120 fs
Recording Angle q: 70o
Period: 425 nm
AFM images of PMMA surface
Surface Cross-Section
SPIE: Aug. 14th, 2006

19. Sub-Rayleigh Fringes on PMMA
Two pulses with p phase-shift
Recording wavelength: 800 nm
Pulse energy: 90 mJ/beam
Pulse duration: 120 fs
Recording Angle q: 70o
Period: 213 nm
AFM image of PMMA surface
SPIE: Aug. 14th, 2006

20. Further Enhancement? 1/6 the recording wavelength!
PMMA is a 800 nm, so further enhancement should be possible.
Illuminate with two pulses with a 2p/3 phase-shift.
141 nm
1/6 the recording wavelength!
SPIE: Aug. 14th, 2006

21. Importance of PMMA Result
Demonstrates sub-Rayleigh resolution on a real material using the phase-shifted grating method.
Shows that PMMA is a N-photon absorber with adequate resolution for use in true quantum lithography.
SPIE: Aug. 14th, 2006

22. Non-sinusoidal Patterns
In principle, Fourier’s Theorem can be applied to generate arbitrary patterns.
Can only remove material
Visibility???
Alternatively, we can generalize method… E N ; M = X k 1 I I = 1 + A k e i  2 M
where
New term: Allow different amplitudes on each shot
SPIE: Aug. 14th, 2006

23. Non-sinusoidal Patterns
Fit coefficients with an optimization routine.
For example if N=10, M=5…
Dosage Amount
Transverse dimension
SPIE: Aug. 14th, 2006

24. Two-dimensional Patterns
Method can be extended into two dimensions using four recording beams.
For example,
N=10, M=5
FWHM of wall is l/10
SPIE: Aug. 14th, 2006

25. Conclusions
Optical parametric amplifiers offer a realistic approach to implementing quantum lithography.
Classically simulated quantum lithography is a viable alternative.
SPIE: Aug. 14th, 2006

26. Acknowledgements & Supported by
Dr. Annabel A. Muenter
Dr. Samyon Papernov
&
Supported by
- the US Army Research Office through a MURI grant
SPIE: Aug. 14th, 2006

27. THANK YOU! www.optics.rochester.edu/workgroups/boyd/nonlinear.html
SPIE: Aug. 14th, 2006