Design and Fabrication of Computer-Generated Holograms for Fresnel Domain Lithography

José A. Domínguez-Caballero,1 Satoshi Takahashi,1 Sung Jin Lee,2 George Barbastathis1,31Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

2Samsung Electronics Co. Ltd., Suwon 442-600, South Korea3Singapore-MIT Alliance for Research and Technology (SMART) Centre, Singapore 117543

AbstractAn optimization algorithm for the design of Fresnel domain computer-generated holograms for lithographic applications is presented. The holograms are fabricated experimentally and their performance characterized. A sensitivity analysis is performed to estimate potential fabrication errors.

Motivation• Need of the semiconductor industry to fabricate ever smaller, faster and lower power consumption devices• Explore novel lithographic techniques• Computer Generated Holography (CGH) is a competitive alternative• Main advantages: - High-resolution (large effective NA) - Parallel, non-contact method for mass production - Optimize diffraction efficiency and uniformity - Simplified system - Robust to manufacture errors (encode redundant information)

CGH Design• Lithographic implementation in the Fresnel domain

z

CGH

Desired intensity

Probing wave

Photoresist

Substrate

After Development

• CGH phase map optimized using the Modified Error-Reduction (MER) algorithm• Three geometries are studied: in-line, off-axis, and TIR

Initial Guess Binarize?

Binary Constraint

X

Remove Undesirable

Orders

Forward Fresnel

Propagation

Inverse Fresnel

Propagation

Estimated Intensity

Error Metrics

Amplitude Constraint

Max Iter?Stop

Zero Absorption Constraint

X

P

P-1

Off-axis and TIR Geometries

Hologram Domain Photoresist Domain

Yes

No

Yes

No

1. Diffracted field2. Simulated optically recorded hologram3. Random4. Continuous phase5. Simulated optical diffuser

1. MSE2. L1 3. NCC4. Diffraction Efficiency5. Uniformity

Fabrication ProcessOptimization Results• Example of in-line CGH: λ = 532nm, d = 250μm, δ = 200nm, Initial guess: 1. Diffracted field, 2. Simulated optical diffuserOptimized In-line Binary CGH (Phase Map) Reconstruction Field Amplitude

1

2

Error Metrics: 1. Diffracted field Error Metrics: 2. Simulated Optical Diffuser

Err

or M

etric

s

Err

or M

etric

s

Sensitivity Analysis• Simulate potential manufacture errors: CGHs fabricated using electron-beam lithography• Studied errors: 1. Over dose, 2. Under dose, 3. Proximity effect, 4. Stitching error, 5. Phase error

Example of Dilation Analysis to Simulate E-Beam Over Dose

E-beam field size = 200µmx200µm

Example of Stitching Error Analysis

CGH Characterization

Experimental Results

• CGHs written on electron-beam sensitive resist: Hydrogen Silsesquioxane (HSQ)