Design, Optimization and Implementation of Fresnel Domain Computer Generated Holograms (CGHs) Diffraction optical elements: reconstruct semi-arbitrary 2D or 3D optical fields Numerical design: flexible encoding strategy high diffraction efficiency and uniformity Avoid complications from conventional optical recording process History: Detour (Brown, 1966), Kinoform (Lesem, 1969) Applications: beam shaping, optical trapping, communications, 3D television, optical testing 1 - Pure phase: binary*, multi-level - Fabrication method: electron-beam lithography

Motivation Increasing demand for smaller sized features, large working area semiconductor devices (e.g. LCD manufacture) need novel lithographic methods CGHs promising candidates for replacing conventional 2D or 3D lithographic techniques Key advantages: Processing In-line CGH Lithography Final Device - Non-contact - Parallel exposure - High resolution - Large working area - 2D or 3D patterning - Depth of focus control - Robust design - Standard fabrication - Simple optical setup - Cost effective 2

Problem Definition Performance of CGHs depends primarily on optimization algorithm and fabrication method Previous work: X-ray (Jacobsen, 1992), UV (Wyrowski, 2001), EUV (Isoyan, 2006) Local search methods: inefficient, sensitive to initial point, get trapped at local minima Current multi-search schemes: optimize small size CGHs 3 CGH Plane Reconstruction Plane Inverse Problem Encoding Free parameter Reconstruction Plane Back-propagation CGH Plane Desired Pattern

Problem Definition Performance of CGHs depends primarily on optimization algorithm and fabrication method Previous work: X-ray (Jacobsen, 1992), UV (Wyrowski, 2001), EUV (Isoyan, 2006) Local search methods: inefficient, sensitive to initial point, get trapped at local minima Current multi-search schemes: optimize small size CGHs 4 CGH: encoded signal Encoding Process CGH Plane Reconstruction Plane Inverse Problem Decoding CGH Plane Forward-propagation Reconstruction Plane Photoresist Exposure Final Pattern

Reduced Complexity Hybrid Optimization Algorithm (RCHOA) Efficient optimization of Fresnel binary and multi-level phase CGHs Reduce problem complexity by introducing: Local Diffuser Phase Elements (LDPE) and Local Negative Power Elliptical Phase Elements (LNPEPE) masks Optimize reduced subset of variables Key features: - Multi-point parallel search - Robust: insensitive to initial points - Flexible choice of encoding signal - Reduced complexity - Optical efficient results - Computationally efficient: GPU implementation 5

System Geometries In-Line Geometry*Off-Axis Geometry 6 TIR Geometry

Local Diffuser Phase Elements Mask Maximize information transfer: amplitude (reconstruction plane) to phase (CGH plane) Step 1: decompose desired pattern into N bp binary patterns Step 2: assign local diffuser phase element to each pattern Diffusivity of qth element controlled by: and LDPE mask: Mask Decomposition Binary function Random matrix Reduced number of DOF: 7 Phase Amplitude x Binary Phase CGH Multi-level LDPE Mask Desired Amplitude Mask Each element has different diffusivity Fresnel Back-Propagation Reconstruction Plane CGH Plane

Local Negative Power Elliptical Phase Elements Mask Maximize information transfer: amplitude (reconstruction plane) to phase (CGH plane) Step 1: decompose desired pattern into N bp binary patterns Step 2: apply LNPEPE to each pattern Controlled parameters: LNPEPE mask: Binary function Truncation window Reduced number of DOF: Binary pattern center coordinates 8 Phase Amplitude x LNPEPE Mask Desired Amplitude Mask Negative power elliptical phase Fresnel Back-Propagation Reconstruction PlaneCGH Plane

Genetic Algorithms Block Multi-point optimization scheme Inspired in biological evolution: “survival of the fittest” Reduced complexity allow optimizing large populations Individual: or Global minimum The MathWorks TM 9

MER Block Local search, iterative optimization method Refine solution: fast convergence Compare results with: diffracted field (DF) and simulated optically recorded hologram (SORH) encoding strategies 10

Error Metrics Four considered error metrics Choice of error metric is application dependent Photoresist Contrast Curve - Mean square error: bias estimator ( and ) - Additional metrics: L1 (bias) and normalized cross-correlation (similarity), hybrid dose - Diffraction efficiency Input power Signal Power Signal Power Inside H size Amplitude Constraint Effective efficiency inside pattern (G. Zhou, et al., 2000) 11

Optimization Results Optimization example: - binary phase CGH: resolution target - LDPE encoding strategy Wavelength532nmElite Children5 Working Distance150μmCrossover Fraction0.6 Pixel Size200nmGenerations100 CGH Size300μmPopulation Size100 Object Window180μmIterations400 Main Parameters: Desired Pattern Optimized LDPE Mask Phase Map: Optimized Binary CGH 12 Reconstruction from Multi-Level CGH at Photoresist Plane (Before Exposure) Intensity Reconstruction from Binary CGH at Photoresist Plane (Before Exposure) Intensity Convergence GA Block Convergence MER Block

Optimization Results Optimization example: - binary phase CGH: resolution target - LDPE encoding strategy 13 Comparison of Encoding Strategies After GAs Block: Multi-Level CGH Sensitivity Analysis: problem parameters (e.g. cross-over fraction, population size, etc.) Parallel implementation on graphic processing unit: speedup >180X - GPU computational time: 4.47 hours - CPU estimated time: days!

Error Comparison: Binary CGH Extending the Depth of Focus Extend DOF: tolerate potential axial misalignments during exposure process Modify RCHOA to impose constraints at multiple planes Regular DOF: Multiple Plane Constraint Extended DOF CGH Extended: 14

CGH Fabrication Fabrication Process Fabricated using electron-beam lithography Binary phase CGH Resist: Hydrogen Silsesquioxane (HSQ) 15 Scanning Electron Microscope Image of Fabricated Sample 50μm Fused Silica Aluminum HSQ E-beam Patterning Remove Aluminum & Develop HSQ

Characterization of Fabricated CGHs Implemented methods: evaluation algorithm*, optical characterization*, exposure test Evaluation algorithm: analyze fabricated CGH 2D error map (correct over/under dose) Block Diagram of Evaluation Algorithm Stitched Binarized Fabricated CGH2D Error Map 16

Characterization of Fabricated CGHs Implemented methods: evaluation algorithm*, optical characterization*, exposure test Optical characterization: measure reconstructed intensity Optical Setup: Coherent Illumination Measured Reconstructed Intensities Binary CGH: DF Encoding Strategy Binary CGH: Diffuser Encoding Strategy -Fabricated CGHs not fully optimized - Eliminate speckle using partial coherence illumination μm

Sensitivity Analysis Estimate and assist in the correction of potential fabrication errors Considered errors: e-beam over/under dose, proximity effect, uniform/nonuniform phase, stitching and positional errors Dilation Test: Over Dose ErrorStitching Error Analysis 18 MSE Offset Distance