* AIT-4: Aberrations. Copyright 2006, Regents of University of California

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1 Advanced Issues and Technology (AIT) Modules Purpose: Explain the top advanced issues and concepts in optical projection printing and electron-beam lithography. AIT-: LER and Chemically Amplified Resists AIT-: Resolution Enhancement and PSM AIT-3: Small Features and Defects * AIT-4: Aberrations AIT-5: Maskless, High-NA, Immersion, EUV, Imprint AIT-6: Electron Beam Lithography Each module is a 0-5 min presentation of about a dozen slides. Suggested reading: Griffin: Plummer, Deal and Chapter 5 Sheats and Smith: 88-96, 4-33, 48-5, 8-88,, 4-3 Wong: 3-45, 55-58, 7-90, Fig 4., Fig. 4.0

2 Mask Lens Wafer Optical System as Fourier Optics Relationship for electric fields The lens is in the far field of the mask and sees the Fraunhoffer diffraction electric field which is the Fourier transform of the electric field emerging gfrom the mask. The lens passes only rays with wave angles inside the NA circle and is thus a D low pass filter. The lens re-phases the remaining emerging rays so that t they reconverge at the wafer with the same relative phases which is equivalent to the inverse Fourier transform.

3 (Sinθ x, Sinθ x ) wave accounting system σna Sinθ Y NA Renormalize e so that this point is.0 Lens Pupil Sinθ MAX = NA.0 Sinθ X Lens Illumination Sinθ MAX = σna Location (Sinθ x, Sinθ x ) corresponds to a ray making angles θ x and θ Y with the downward z-axis

4 Pupil position accounting system Divide by NA Sinθ Y /NA New variables r = {0,} α ={0, π} σ r α Lens Pupil Sinθ MAX / NA =.0 Sinθ X /NA Lens Illumination Sinθ MAX / NA = σ Location (Sinθ x /NA, Sinθ x /NA) corresponds to a ray making angles θ x and θ Y with the downward z-axis

5 Optical Path Difference The optical path difference (OPD) is the phase error over the pupil between rays for the actual lens and those for a perfect diffraction limited lens. The OPD is usually normalized to wavelengths. The OPD contributes an additional phase factor of e j(π/λ)opd in the integration of the rays in computing the electric field at the image. Born and Wolf 7 th ed, Ch 9 For primary aberrations like tilt, defocus, spherical, coma, and astigmatism a power series is used Φ = A n, m n ρ cos m θ Zernike introduced the so called circle polynomials that are orthonormal on the unit circle to describe aberrations. n m Φ = A00 + An 0Rn ( ρ) + AnmRn ( ρ) cos mθ n= n= m= ±mm R n () = Primary Coma => orthogonal components => tilt + balanced coma

6 Expansion of Zernike The Zernike polynomials are individual functional variations in radius r and angle α in an orthonormal expansion over the lens pupil normalized to radius. Z Tilt in x is r cos(α) Z7 is Coma in x with Tilt removed or so called balanced coma. Sheats and Smith, pp. 4

7 Strehl Ratio The peak value of the point spread function decreases proportionally to the square of the RMS value of the aberrations present. The Strehl Ratio is defined as the ratio of the peak value with aberrations to the peak value without aberrations. RMS OPD = (P-V OPD)/3.5 The Strehl Ratio is approximately - 4π (RMS OPD) Sheats and Smith pp 55

8 Strehl Ratio vs. Peak-to-Valley OPC New projection printers have Strehl Ratios over => aberrations of 0.05 RMS or 0.09 PV The human eye works best in bright light when the pupil is small and typically has a Strehl ratio of 0.6.

9 Mathematics of Aberrations and OPD The electric field produce by the convergence of the cone of plane waves from the pupil at any point x on the wafer is given by integrating ti the waves over the pupil. E( x) = Pupil When OPD is small E( x) π π π 00 Spectrum E( r, α) e e jkopd jkopd( r, α ) Optical Path Difference e jkopd jk x = E( r, α)[ jkopd( r, α) ] e π 0 0 rδrδα Kernel Green s Function jk x rδrδα Area element Unaberrated E-Field Aberration Ghost E-Field

10 Finding the Strehl Ratio E( x) = π π 0 0 E( r, α) e jk x e jkopd( r, α ) rδrδα To find the Strehl ratio (relative value the peak intensity in the presence of an aberration) we only need look at x = 0 and assume that E(r,a) is produced by a small pin hole and thus constant. This greatly simplifies ifi the integral to When the OPD is small E(0) = π r α e jkopd (, ) π 0 0 rδrδα π k k E(0) = [ jkopd( r, α) OPD ( r, α)] rδrδα = jkφ π 00 Where Φ is the average of OPD over the pupil The intensity is given by 4π Orthogonal for Zernike s k k E( 0) = jkφ Φ = Φ jkφ k Φ + k π ( Φ) = 4π Φ = 4π Φn, m = 4 n, m Φ Zero for Zernike s n, m A n, m

11 Simple Coma 0.0 Waves 3 space pattern Coma Unaberrated This bump suggests ways to monitor coma.

12 Aberration E-Field Point-Spread Functions n = 0 n = Each aberration has a characteristic e-field point spread function. Note that the sidelobe levels are as high (0.5) as those for the diffraction limited point-spread function and have maxima at various radii. Garth Robins and Kostas Adam

13 Programmed-Probe Aberration Targets 0.6 λ/na Line 0.5 λ/na 0.4 λ/na 80 o Sq. Defect Sidelobe The04l/NAby04λ/NA programmed 80 o phase defect provides an interferometric like reference electric field with magnitude 0.43 and phase of 80 o compared to the clear area field. Detect Sidelobe by over exposing.5x and using automatic wafer inspection Coma Sidelobe -0. wave => wave => wave => 0 0.

14 Defect-Probe Aberration Targets Probe Dark Field Patterns Grid is 0. λ/na Astigmatism Spherical at 90 o Trefoil Coma at 0 o at 80 o Lens aberrations cause lateral spillover of light in imaging in directions related to the aberration symmetry.

15 Pattern-and-Interferometric-Probe Aberration Monitors Garth Robins (λ/na) (λ/na) Defocus Spherical HO Spherical Mask phases yellow = 0 green = 90 red = 80 Defocus target Experiment on AIMS at low NA looks just like simulation! ity (00% CF) Coma Intens (λ/na) HO Coma (λ/na) (λ/na) Discovered through simulation Lead to a new theory Becoming a practical technology Probe Position x-position in field (pixels)

16 Phase Shift Mask Monitors Developed for: Polarization Monitoring Greg McIntyre Design Image (simulated) ) I (center) NA 0: : :0 Polarization Ratio (X:Y) Take advantage of high-na vector effects Illumination Monitoring PSM Performance Beam steering with 4- phase grating Mask Resist Proximity effect and beam steering Use orthogonality of phase and transmission errors

17 Interferometric Probe Monitors: Verification RZ3_055cr Annular.6/.0 PSM Monitors: Limits of Nature or Man? Thin Mask Thick Mask Experiment Peak Intensity (00% CF) RZ3055cr_all probe T (no probe, 80 inner ring) 0. Mask making T (70 probe, 80 inner ring) 0 EM effects T3 (90 probe, 80 inner ring) Pupil Shift probe. Orientation dependence. Feature size/depth error -RU 0 Focal Plane step = 0.45 RU +RU Garth Robins and Greg McIntyre

18 Projection Printer Examples Mask Wafer Stepper Mask Wafer Scanner Sheats and Smith

19 Impact of Aberrations: Magnitude ½ OPC 0.05 waves of RMS aberration Strehl Ratio = Adjust L Point of It Interestt Take Cutline Line End Cha ange L (λ λ/na) dx (λ/na A) Line end position change of a 0.6 λ/na line vs. linewidth of an adjacent line 0.05 σ = Width (L) in λ/na Linewidth L (λ/na) The effects of aberrations are typically half that of the proximity effect of an adjacent figure OPC Coma Spherical HO Coma

20 Basic Aberrations in Projection Printing These are simple aberrations that are not always orthogonal to each other (e.g. coma contains tilt.)