= n. Psin. Qualitative Explanation of image degradation by lens + 2. parallel optical beam. θ spatial frequency 1/P. grating with.

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1 Qualitative Explanation of image degradation by lens Mask + 2 lens wafer plane +1 φ 0 parallel optical beam -2-1 grating with θ spatial frequency 1/P Psin φ = n λ n = 0, ± 1, ± 2,... L S P l m P=2L sin φ < NA of lens Sheats and Smith 15

2 Bragg Condition P Incident ray with wave fronts L S Quartz P=L+S P sin n = nλ ϕ nλ φ n Transmitted ray Chrome Wavefronts Ray of Light Diffracted ray #3 The Bragg condition sets the diffraction angles 16

3 Pupil Wave Traffic: Partial Coherence #4 Lens is a low pass filter of mask diffraction at Bragg angles Sinθ Y NA Shifted by sinφ = λ/p Lens Pupil Sinθ MAX = NA Cone of Incident Light Some misses pupil Diffracted Orders from a mask with period P Sinθ X +2 Potential for entering the pupil 17

4 Electric Field: Sinusoids Binary Mask with period P and opening space s P When filtered to three waves (0, +1, and -1) E( x) = E + 2E1 s [ ( s )] 0 A sin nπ E P n = 2 [ ( s )] nπ 2πx cos P k x1 = 2π/P P When s = P/2 E( x) = cos π 2πx P Sheats and Smith 18

5 Intensity as Square of Electric Field The energy carried by a wave and the work done on a material are proportional to the time average of the square of the electric field. Thus the intensity is proportional to E 2 when the field is real and EE* when phasors are used and E is complex. Intensity = EE* gives I * ( x) = EE = E + 2E E cos( ) + 4E cos πx 2πx Since the Fourier transform converges to the average at a discontinuity, the electric field at the mask edge will be about 0.5, and the intensity at a mask edge will be about #5 The intensity at a mask edge is only 30% of the clear field intensity regardless of feature type and size. P 1 P 19

6 Intensity at the mask edge is about 0.30 for all feature types Mask Edge Space Dense L = S Sigma 0.5 Dense Line C DENSE = ( ) ( ) = 0.98 Convention: Line is a line in positive resist. Image Contrast C = (I max I min )/(I max + I min ) 20

7 #6 Superposition Fails for Images! (but superposition holds for Electric-Fields instead) 0.3λ/NA 0.5λ/NA 0.8λ/NA Much taller and wider. Peak intensity initially increases as the square of linewidth. Consequence of I = EE* This messes up fast OPC based on linear transforms!! 21

8 Mask Error Factor (MEF) Linewidth on Wafer Another Consequence of I = EE* (Linewidth on Mask)/M Expected Lines (2x slope) Contacts (4x slope) Effect is larger at k 1 < 0.6 CD PRINTED = MEF CD M MASK MEF = MEEF = Mask Error Enhancement Factor 22

9 Focus Behavior: Bossong Plot (SMILE) Dense Line = Space = 180 nm Line = 300 nm Exposure Exposure JSR M91Y resist, 248nm, NA = 0.63, 0.8/0.4 annular illumination C. Mack

10 Process Window: Exposure/Focus Percent Exposure Variation 60.0 Percent Exposure Latitude Line Focal Position (microns) Space Contour Map for 10% linewidth change Depth of Focus (microns) C. Mack

11 Standing Waves hv Incident Aerial Image Positive Photoresist substrate After development Positive Photoresist. substrate 25

12 Electric Field within Resist Air Resist n 1 n 2 Substrate n 3 5 waves match boundary conditions (or use signal flow analysis) use definition of τ D Downward wave Round trip propagation Upward wave E RESIST ( x, y, z) = E AIR _ INC τ ( x, y) 12 Transmission in Reflection at substrate ( jk ) 2z 2 + jk2z e + ρ τ e 1+ ρ 12 ρ τ D 2 D Round trip loop gain (loss) 26

13 Measured Dissolution vs. Dose i-line (Positive) DUV (Negative) DUV (Positive) S-shaped Corner-shaped Corner-shaped γ > 5 γ > 8 γ > 15 27

14 Dissolution Rate Models R(E) R R DILL ( M ) = e 2 ( E + E M + E M ) 1 ( M, z) f ( M, z) R ( M KIM = 2 3 BULK z f ( M, z) = 1 R MACK ( 1 ( R5 ( R5 R6 ) M )) 4 e R Dissolution rate R in µm/s as a function of energy E or photoactive generator M. ) 2 BULK ( a + 1)(1 M ) + ( 1 M ) n ( M ) RMAX R ( M ) = + R Ferguson ( ) MIN a ( M ) = R0 (1 CE / C0 n α ) ( ) M It = R = e 1 Me R ICt R 1 = e 1 M ) E Ct 1 + Me R 3 ( 3 R (1 M ) 2 28

15 Hands On Exploration 29

16 Basic Projection Printing Applet Sigma_in Dense Defocus 30

17 Annular Illumination: k 1 =0.4 Large DOF L = S = 0.4 σ IN = 0.5 σ OUT = 0.8 DOF = 2.0 Contrast =

18 LAVA Applet: Pattern and Aberration This applet is one of mask type choices in the interaction of defects with features applet. 32

19 Image Quality: Across Line k 1 = 0.6 Feature Slope: 2.5/(λ/NA) This 1D image slope is nearly doubled by I =EE*. Mask Opening This 1D image slope is nearly independent of feature size. Another Consequence of I = EE* 33

20 Image Quality: Line End k 1 = 0.6 Feature Slope: 1.8/(λ/NA) Mask Opening #7 The slope of the 2D image at the end of the line is only 72% as large. 34

21 Basic Aberrations in Projection Printing These are simple aberrations that are not always orthogonal to each other (e.g. coma contains tilt.) 35

22 Simple Coma 0.10 Waves 3 space pattern Coma Unaberrated This bump suggests ways to monitor coma. 36

23 SAMPLE2D Resist Line Edge Profile 75s 15s 30s 45s 60s Mack Model 120 mj/cm 2 #8A Interference in the resist produces standingwaves with a period = λ/2n RESIST 37

24 Simpl_display PC Layout Viewer for GDSII Frank Gennari 2004 SRC Right mouse click and drag to enlarge Then f key to return to fit to window Abacus Chip Example Download this code from the LAVA website 38

25 Simpl_display PC Layout View Manipulation Numbers on keyboard toggle mask levels: 1= poly, 2=con, 3=met Left poly con 3 => Right poly Con met Lower case s saves current view as jpg in an image file Stipple patterns are possible with 8 x8 fill pattern: NAME POLY RGB FILL