quantum lithography

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)

Â = 2kxsinµ

¢ xmin » ¸2


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


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


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)


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


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.


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


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


Effect of an N-Photon Absorber

→ As N increases, visibility improves, but no improvement in resolution.


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)


Classical Nonlinear Lithography

Linear absorbing medium:

TPA medium:

EL A = 12(1+ cosÂ)

ET P A =14(1+cosÂ)2

=14

µ32

+ 2cosÂ +cos2Â¶

“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

¢



N=1

N=2no averaging

N=2averaging

Proof-of-Principle Experiment

Bentley and Boyd, Opt. Exp. 12, 5735 (2004)


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.


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)



Substrate (Glass)

Phase retarder

PMMA

Developing

Path length difference /2

Interference pattern shifted by /4

/2

/4


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


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


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


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!


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.


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


Non-sinusoidal Patterns

For example if N=10, M=5…

Fit coefficients with an optimization routine.

Transverse dimension

Dos

age

Am

ount


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


Conclusions

• Optical parametric amplifiers offer a realistic approach to implementing quantum lithography.

• Classically simulated quantum lithography is a viable alternative.


Acknowledgements

Dr. Annabel A. Muenter Dr. Samyon Papernov &

Supported by - the US Army Research Office through a MURI grant


THANK YOU!www.optics.rochester.edu/workgroups/boyd/nonlinear.html

quantum lithography

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