Quantum LithographyRobert 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
SPIE: Aug. 14th, 2006
Quantum Lithography: Introduction
Two classical beams of light interfere…
2µ¸
2sin µ
I = 12(1+cosÂ)
 = 2kxsinµ
¢ xmin » ¸2
SPIE: Aug. 14th, 2006
Original Quantum Lithography Proposal
SPDC
50/50 TPA
• 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)
j2;0i + j0;2ij1;1i
SPIE: Aug. 14th, 2006
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
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
Quantum Lithography with an OPA
OPA Relations
Beamsplitter Relationsa2 = 1p
2(¡ a1 + ib1)
b2 = 1p2(ia1 ¡ b1)
a1 = (coshG)a0 ¡ (ieiÁ sinhG)by0
b1 = (coshG)b0 ¡ (ieiÁ sinhG)ay0
G = gjEpjLTwo-photon Output
R(2) /Day
32a2
3
E
a3 = a2 + eiÂb2
SPIE: Aug. 14th, 2006
Two-Photon Excitation Rate
• For light from an OPA, both linear and quadratic dependence are present.
• Cross-over point:I = 1
3 photons/ modeG = 0:55
For cases of practical interest, the rate scales quadratically with I.
SPIE: Aug. 14th, 2006
Visibility using an OPA and TPA
V =R (2)
m ax ¡ R (2)m i n
R (2)m ax +R (2)
m i n
Visibility never fallsbelow 20%
Visibility versus GainV = cosh2 G
cosh2 G+4sinh2 G
SPIE: Aug. 14th, 2006
Effect of an N-Photon Absorber
Replace TPA with an N-photon absorber.
R(N ) = ¾(N )Day
3N aN
3
E
We can find an analytic solution:
withP N
N =p
N!
P NN ¡ 2n = 2
p(N ¡ 2n +1)P N ¡ 1
N ¡ 2n+1 +p
(N ¡ 2n)P N ¡ 1N ¡ 2n¡ 1
R(N ) /N=2X
n=0
2N ¡ 2n¯P N
N ¡ 2n
¯2 (sinhG)2(N ¡ n)(coshG)2n cos2n Â
SPIE: Aug. 14th, 2006
Effect of an N-Photon Absorber
→ As N increases, visibility improves, but no improvement in resolution.
SPIE: Aug. 14th, 2006
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
Classical Nonlinear Lithography
Linear absorbing medium:
TPA medium:
EL A = 12(1+ cosÂ)
ET P A =14(1+cosÂ)2
=14
µ32
+ 2cos +cos2¶
“Non-quantum Quantum Lithography”:
Average 2 shots with phases and
In general, use an N-photon absorber and average N shotswith the kth shot having phase 2k/N.
E = 14
¡32 + cos2Â
¢
SPIE: Aug. 14th, 2006
Classical Nonlinear Lithography
N=1
N=2no averaging
N=2averaging
Proof-of-Principle Experiment
Bentley and Boyd, Opt. Exp. 12, 5735 (2004)
SPIE: Aug. 14th, 2006
PMMA
•Polymethylmethacrylate (PMMA) is a positive photo-resist that is transparent in the visible region.
•3PA @ 800 nm can break chemical bonds, and the affected regions can be removed in the development process.
UV absorption spectrum of PMMA
800 nm
PMMA is 3-photon absorber @ 800 nm.
Problem: Self-healing means multiple bonds must be broken.
SPIE: Aug. 14th, 2006
Experimental Setup
Ti:sapphire fs-laser
f1M1
f2M2
PMMA
BS
M3Pol.WP
PR
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
Classical Nonlinear Lithography
Substrate (Glass)
Phase retarder
PMMA
Developing
Path length difference /2
Interference pattern shifted by /4
/2
/4
SPIE: Aug. 14th, 2006
PMMA Preparation
• Sample– PMMA (120,000 MW) + Toluene Solution (20% solids by weight)– PMMA is spin-coated on a glass substrate
• spin-coated @ 1000 rpm, 20 sec• dried for 3 min• repeated 3 times
→ 1-m-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
Recording wavelength: 800 nmPulse energy: 130 J/beamPulse duration: 120 fsRecording Angle 70o
Period: 425 nm
Fringes on PMMA
AFM images of PMMA surface
Surface Cross-Section
SPIE: Aug. 14th, 2006
Sub-Rayleigh Fringes on PMMA
Two pulses with phase-shiftRecording wavelength: 800 nmPulse energy: 90 J/beamPulse duration: 120 fsRecording Angle 70o
Period: 213 nm
AFM image of PMMA surface
SPIE: Aug. 14th, 2006
Further Enhancement?
PMMA is a 3PA @ 800 nm, so further enhancement should be possible.
• Illuminate with two pulses with a 2phase-shift.
141 nm
1/6 the recording wavelength!
SPIE: Aug. 14th, 2006
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
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…
I =¯¯1+ AkeiÂei2¼k=M
¯¯¯2
EN ;M =MX
k=1
I Nk where
New term: Allow different amplitudes on each shot
SPIE: Aug. 14th, 2006
Non-sinusoidal Patterns
For example if N=10, M=5…
Fit coefficients with an optimization routine.
Transverse dimension
Dos
age
Am
ount
SPIE: Aug. 14th, 2006
Two-dimensional Patterns
• Method can be extended into two dimensions using four recording beams.
For example,N=10, M=5
FWHM of wall is /10
SPIE: Aug. 14th, 2006
Conclusions
• Optical parametric amplifiers offer a realistic approach to implementing quantum lithography.
• Classically simulated quantum lithography is a viable alternative.
SPIE: Aug. 14th, 2006
Acknowledgements
Dr. Annabel A. Muenter Dr. Samyon Papernov &
Supported by - the US Army Research Office through a MURI grant
SPIE: Aug. 14th, 2006
THANK YOU!www.optics.rochester.edu/workgroups/boyd/nonlinear.html
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