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UCB-TCAD

Optical Projection Printing: Methtodologies, Modeling and Monitoring

UCB TCAD Overview Talk Spring 2004Andy Neureuther, Yunfei Deng, Lei Yuan, Frank Gennari,

Garth Robins, Michael Lam, Scott Hafeman, Greg McIntyre, Dan Ceperley, and Jacob Poppe

UC BerkeleySupported by the Lithography Network DARPA/SRCby industry through the State of California UC-SMART and UC-DiscoveryAdvanced Energy, ASML, Atmel Corp., Advanced Micro Devices, Applied Materials, Asyst Technologies Inc., Cadence, Canon, Cymer, DuPont, Ebara, EVG, Intel Corporation, KLA-TENCOR, Mentor Graphics, Mykrolis Corp., Nikon Research Corp., Novellus Systems Inc., Panoramic Technologies, Photronics, Synopsys, and Tokyo Electron,by Intel EUV Mask Simulation, andby JPL Terrestrial Planet Finding

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UCB-TCAD

Simulation Discovered Phenomena: Intensity Imbalance in Phase Shifting Masks

Discovered by simulation and verified experimentally, IEDM, 1992 Wong

∆

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Simulation Discovered Theory: InterferometricPattern-and-Probe Monitors

Defocus target

0 Aberration 0.05 waves Defocus 0.05 waves Spherical

Spherical targetsensitivityorthogonality

sensitivityorthogonality

(λ/NA)

(λ/NA)

• 0.4 λ/NA x 0.4 λ/NA probe; red = 180º, yellow = 0º, green = 90º

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UCB-TCAD

UCB TCAD Research Themes

• Fast EM Analysis methods to attain speeds required for EUV, OPC and die-to-database inspection

• Photomasks as precision instruments for monitoring projection printing

• Linking Process and EDA through multi-student test structure design, pattern-matching and experiment

• Physical models and algorithms for emerging tools and treatments

• Actively apply simulation to guide innovation and characterization

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Outline

• Methodologies (Slides 5-29)– Basic optical physical principles– Resolution enhancement

• Modeling (Slides 30-40)– Immersion as a two-for in a sea of waves– Resist modeling as the proverbial bottleneck– Rigorous EM as the sawmill for EUV and PSM– Fast EM analysis methods for OPC

• Monitoring (Slides 41-57)– Phase-shifting masks as precision instruments– Linking Process and Electronic Design

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Optical Projection Printing Parameters

Wavelength λ = 248 nm

Partial Coherence Factor σ = (NAc/NAo) = 0.3

Numerical Aperture NA = sin (θ) = 0.5

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Resolution in Projection Printing

NAdf

df λ

λλ 61.0

2

61.022.1 =

=

Minimum separation of a star to be visible.

f = focal distanced = lens diameter

Point spread function

Null position

PDG Fig. Ch 5

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Resolution ~ Transverse Variation

λ = 248 nm

λTRANS = λ/sinφ= 3.22λ = 800nm

φ

Wave graphic by OngiEnglander and Kien Lam

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Depth of Focus: Phase change on vertical axis

Plane of Best Focus

4.75λ

5.0λ

Plane of Rayleigh l/4 Defocus

Observe phase along a vertical line

Wave graphic by OngiEnglander and Kien Lam

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Normalized Parameters

NAkLLINEWIDTH

λ1=

( )22 2 NAkDOF λ

=

λ = 365, 248,193, 157, 13.4 nmNA = 0.167, 0.38, 0.5, 0.63, 0.7, 0.75, 0.80

Instead of recalculation for every new combination of λ and NA a universal catalog of image behavior can be utilized if we first determine the k1 and k2factors in the actual system for the linewidth and defocus and look up results in a data based based on λ = 0.5µm and NA =0.5.

mkmkNA

kLLINEWIDTH µµλ

111 5.05.0

===

( ) ( )mkmk

NAkDOF µ

µλ22222 5.02

5.02

===

For any wavelength λ and numerical aperture NA.

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Bragg Condition for Off-Axis Illumination

PP=L+S

L S

Chrome

Quartz

λ

φn Ray of Light

Wavefronts

φINC_R

λ

d2

d1

d1 + d2 = nλ

Psin(φINC_R) + Psin(φn) = nλ

sin(φn) = nλ/P − sin(φINC_R) for angles from the right

sin(φn) = nλ/P + sin(φINC_L) for angles from the left

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UCB-TCAD

(Sinθx, Sinθx) wave accounting system

SinθX

SinθY

1.0

Location (Sinθx, Sinθx)corresponds to a ray making angles θx and θY with the downward z-axis

NA

Lens PupilSinθMAX = NA

σNA

Lens IlluminationSinθMAX = σNA

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Pupil Wave Traffic: Partial Coherence

SinθX

SinθY

1.0

NA

Lens PupilSinθMAX = NA

Cone of Incident Light

Diffracted Orders from a mask with period P

+20-2 -1 +1

Some misses pupil

Potential for entering the pupil

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Electric Field and Intensity: Plane Waves

( ) ( ) ∑∑ ⋅−+− ==n

xkjn

n

znkxkjnTOTAL

nn eEeEE)()cossin( 00 θθ

zzxxx ˆˆ +=Spatial position vector

( ) ( )zkxkzkxkk nnzxn ˆcosˆsinˆˆ 00 θθ +=+=Propagation (k) vector

where k0 = (2π/P)

Genralizes to y-direction

( ) ( ) ( ) )cos22(1

)cos220(0

)cos22(1

101 zxPjzx

PjzxPj

TOTAL eEeEeEE +− +−+

+⋅−+−−− ++=

θλππ

θλππ

θλππ

Three wave case for on-axis illumination of mask with period P

( )2

1cos

−=Pn

nλ

θ( )n

nλ

θ =sin

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Illumination Controls Proximity EffectsTwo Pinholes in a mask

• Wafer• Tails of electric field overlap (spillover)• Relative phases depend on phase of illumination

2221

21 2 EEEEITOTAL ++= 2

22121 2 EEEEITOTAL +−=

0180Normal Off-axis

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Mutual Coherence Function: Top Hat

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Aerial Image Intensity for Knife Edge

σ = ∞

σ = 0.6

Toe

Slope

Overshoot

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Feature Type Effect with Defocus

Contrast for Dense = 0.75

Dense L = SSpace

Line

0.99

0.11 ( )( ) 80.0

11.098.011.098.0

=+−

=DENSEC

DOF = k2 = 1 µm

Isofocal points

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Superposition Failure for Partially Coherent Images! (add Electric-Field instead)

0.3λ/NA 0.8λ/NA0.5λ/NA

Mask linewidth percentage errors are twice as large on the wafer. Thus the mask enhancement factor (MEF) is due to partial coherence!

Much taller and wider.

Peak intensity initially increases as the square of linewidth.

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High-Fidelity Audio System Off-Axis Analogy

• The lateral spatial variation across a wafer of an off-axis light ray is analogous the temporal variation of a note in a Hi-Fi audio system.

• More rapid variations (spatial or temporal) from higher frequencies (spatial or temporal) allow sharper artifacts(spatial {lithography feature} or temporal {drum beat}) to be produced.

• Just as it is difficult to improve upon the pulse width times bandwidth product it is difficult to improve upon the feature size times NA product.

• BUT IN RESOLUTION ENHANCEMENT WE TRY TO GET A FACTOR OF TWO INCREASE ANYWAY.

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Frequency0 Frequency0

Frequency0

Frequency0

Frequency0

Frequency0

ModifiedIllumination

PhaseMask

In-LensFilter

ConventionalIllumination

BinaryMask

LensCapture

Resolution Enhancement Emphasizes High Frequencies

Resolution Enhancement Techniques

Bokor, Neureuther, Oldham, Circuits and Devices, 1996

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UCB-TCAD

Two Ray Infinite DOF

θ1 θ2

Ray # 1 Ray

# 2

TransversekPitchPeriod

∆==

π2

( )( )

NAPitch NA

2sin2sin λ

θλ θ →= =

( )θsin2 0kkTransverse =∆

When θ1 =θ2 the contributions from Ray #1 and Ray #2 track each exactly with axial distance and an INFINITE depth of focus is produced.

kx

ky

Doubled Resolution! With infinite DOF

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Strategy to improve both resolution and DOF

• Since the small features or edges are are most important emphasize the high-frequency off-axis ray to improve resolution.

• Since the change in the image with focus comes from the relative phase change among the rays with axial distance, utilize rays at similar azimuthal angles that track in phase with focus to improve DOF.

NAPitchSPOT ⋅=

λσ

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Illumination Schemes

• The k1 factor is inversely proportional to the lateral separation of the illumination k1 = 1/(2 x separation)

Top Hat – General Shapesk1 = 0.67k2 = 1.3

Annular – DOF, Contactsk1 = 0.55k2 = 1.7

Dipole – V lines, DOFk1 = 0.35k2 = 3.0

Quadruple – H,V lines, DOFk1 = 0.45k2 = 2.0 H lines and

contacts formed via a double exposure

1-1

1-1 1-1

1-1

Top Hat – General Shapesk1 = 0.67k2 = 1.3

Annular – DOF, Contactsk1 = 0.55k2 = 1.7

Dipole – V lines, DOFk1 = 0.35k2 = 3.0

Quadruple – H,V lines, DOFk1 = 0.45k2 = 2.0 H lines and

contacts formed via a double exposure

Pupil

Pupil Pupil

Pupil

σIN = 0.55

σOUT = 0.85

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Phase-Shifting Mask

Sheats and Smith

P P

P P/2

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Phase-Shifting Mask

Sheats and Smith

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Phase Defects May Print Worse Out of Focus

Wantanabe, et al.

Severity Factor [1-Mcos(φ)] becomes [2] when phase of defocus is included.

M = E field transmission

amplitude

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UCB-TCAD

Resolution Enhancement: In-Lens Filter

Fukuda JVST B Nov/Dec 91

( ) rjrj eer22 222 5.05.02cos πβπβπβ −+=

Defocus away and toward the lens.

• The cos(2πβr2) filter creates dual defocused images that are very effective in increasing the total focal range of contact patterns.

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Resolution and Focus Trends

k1 = 0.61

k2 = 1.0

Rayleighcriteria

Trend with modified illumination and resists

Trend with resolution enhancement techniques

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Vector Addition at High NAParallel Orientation Perpendicular Orientation

EtotalEtotal

M. Lam

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UCB-TCAD

SPLAT 6.0 for High-NA and Immersion• Uses vector or

scalar TCC• Models high-NA

and immersion• Exploits some

symmetry in vector TCC calculations

• In agreement with high-NA models by Flagello and Adam

t

Projection Optics

Mask Plane (m)

Entr. Pupil Plane (p)

Wafer Plane (w)

Image Plane in Resist (R)

Efield x, y orientations

Scattered Orders

Radial,SagittalPupil position

Location(subscript)

Variables

Aberrations

t||, ts, Ray tiltObliquity factor

StandingwaveExR, EyR, EzR

STE(Ow), STM(Ow)

E xR=

E yR=

E zR=

||tE rp

||tE rp

||tE rp

)( wTMS θ

)( wTMS θ

)( wTMS θ

Rθcos

Rθcos

Rθsin

pφcos

pφsin

)( wTES θ

)( wTES θ

pφsin

pφcos

⊥tE pφ

⊥tE pφ

-

+TM polarization problemLower maximumHigher minimum S. Hafeman

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UCB-TCAD

B.J. Lin Sept. 02

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B.J. Lin, 157 Workshop, Sept. 02

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Immersion Lithography

• Promise – Improve resolution of 193 to that of 157 using a

lower NA (0.9 => 0.77) and a slight increase (1.08) in DOF.

• Industry View – Gives 193 the punch of 157 without the

complications of 157 and cheaper to explore

• Issues– Liquid (optics), liquid (resist), liquid (machine)

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Comparison of Imaging for 193 nm Immersion and 157nm air

• Cut lines taken at 50 nm into the resist stack• 193 nm immersion shows better field coupling into resist

0.7 lambda/NA Contact,NAair=0.85, 300 nm resist film n=1.72

Air @157nm

0.00

0.20

0.40

0.60

0.80

-1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9 1.1Position (lambda/NA)

Inte

nsity

(A.U

.)

Scalar Vector

Water @193nm

0.00

0.20

0.40

0.60

0.80

1.00

-1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9 1.1Position (lambda/NA)

Inte

nsity

(A.U

.)

Scalar Vector

S. Hafeman

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UCB-TCAD

Simulation of Inhomogeneous Liquid Effects

• Several models for n(x,y,z) are algebraically tractable• PACIFIC: Add-on to SPLAT 6.0 that determines an

equivalent pupil map describing the fluid• Used to develop goals for liquid purity and fluid flow

CDF Simulation (Wisconsin) PACIFIC (Image Cone)

Pupil Map

S. Hafeman

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UCB-TCAD

Simulation Extraction of Resist Parameters in 2D

Reaction enhanced diffusion

Reaction reduced diffusion

The sequentially double exposed corner shape determines the type of acid diffusion and enables 2D pattern prediction. STORM simulation

Sequentially double exposed cross

L. Yuan

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UCB-TCAD

Fickean diffusion Enhanced non-Fickean

Reduced non-Fickean SEM of APEX-E

Deprotection level of one quarter double exposed cross (STORM simulation and SEM)

L. Yuan

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UCB-TCAD

Reaction Reduced Diffusion is best 2D Predictor for APEX-E and UV210

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.2 0.3 0.4 0.5 0.6 0.7

Designed trench width

Diag

onal

cro

ss s

pace

(u

m)

ExperimentalFickeanReducedEnhanced

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.5

0.5

0.5

0.5

0.5

0.5

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.5

Fickean

Reaction Reduced Diffusion

• Only Reaction Reduced Diffusion predicts corner-to-corner spacing correctly

• Only Reaction Reduced Diffusion predicts standing wave removal correctly

• Does Reaction Reduced Diffusion reduce line-edge roughness? L. Yuan

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UCB-TCAD

Electric Field Enhanced PEB vs. Standard:Improved Focus Latitude

5.3mJ, +0.6um defocus, 500/500nm L/S

Standard PEB, none of the trenches cleared

EFE-PEB, downward E-field of ~200,000 V/cm

•Apex-E resist with Shipley’s RTC top coat, an ASML KrF stepper, NA 0.5, σ 0.2, dose 4.5~5.5mJ/cm2, spin 3000rpm, SB 100oC, 60sec, PEB 90oC, 60sec, resist thickness 900nm.

J. Poppe

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UCB-TCAD

TEMPEST FDTD Simulator

Instantaneous Electric Fields

Maxwell’s Equations on a Staggered Grid

15 nodes/λ;

50 bytes/node;

30 cycles

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UCB-TCAD

n=1 n=1.563

λ=193nm

39.7o

Ey (TE)

ScatterningScatterning from the Phasefrom the Phase--Well CornerWell Corner

Front

Results in crosstalk between trenches. K. Adam

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UCB-TCAD

µm

µm

µm

µm

TE : Ey polarization

TM : Ex polarization

CDSB

x-axis

z-ax

is

Incident radiation

y-axis

CDtarget=130nmMag=4Xλ=193nm

|Ey|

|Ex|

Adam, SPIE 4000-72

With SB

Defocus

Aer

ial I

mag

e C

D

Scatterbarsimprove DOF

Scattering Bar Simulation with TEMPEST

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UCB-TCAD

TEMPEST EM simulation of EUV multilayer masksMultilayer reflecting bilayers, N: 20Multilayer e-Beam affected bilayers, N: 20Period 1 (0°, R~62%): 6.938nmPeriod 2 (540°, R~4%): 6.312nmEdge transition: slow, sigma=10nm,

sharp, sigma=1nm

e-Beam

Period 2

Period 1Phase Well Depth

Geometry for attPSM (540°, 0°, 540°, 0°, 540°)

X position on Mask (nm)

Z Z

Electrical Field Intensity distribution

X position on Mask (nm)

0 °

540 °0 °

540 °540 °Y. Deng

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UCB-TCAD

EUV Mask with 20,000,000 nodes as largest TEMPEST simulation to date

Coma target: center square at 180° (0.4*M*λ/NA), two rectangle sidebars at 0° & 180° (0.6*M*λ/NA) x (1.2*M*λ/NA)

Wavelength λ = 13.4nm, NA=0.25, M=4, σ=0.3Coma Target: Geometry X-Z cut-plane

X position on Mask (nm)

Z

Cr 100nm

0.6*M*λ/NA

1.2*M*λ/NA

0.4*M*λ/NA

X at wafer (nm)Yunfei Deng SPIE 2002

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UCB-TCAD

How can you “rigorously” simulate this pattern?

> ~ 10µm

> ~

10µm

157nm < λ < 248nm

4000 λ2 − 1600 λ2

~ 1µm height26,000 λ3 − 6,500 λ3 !!

~ 0.4 – 0.8 billion nodes!

~ 13-26Gb required memory

~ 32bytes/node

K. Adam

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Fast-CAD: Edge-by-Edge Decomposition of Phase-Shifting Masks•Any Manhattan mask geometry can be broken into a sum of its isolated edge diffractions, minus the background.• Libararies of pre-simulated rigorous 2D edge diffractions from all types of edges (phase, underetch, etc.) can be stored and accessed to synthesize the nearfields of an arbitrary 2D or 3D structure.

80nm Cr

180deg50nm

x

z

yEy

x

y

z .

80nm Cr

180deg

50nm

Ey

Lx

Ly

x

yz.

clear polygon

Ey

edge shadow regions

unaffected field through Cr-layer

edges subject to TE(//) polarization

edges subject to TM( ) polarization

When is this accurate enough for imaging?K. Adam and M. Lam

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Pattern-and-Interferometric-Probe Aberration Monitors

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200x-position in field (pixels)

Inte

nsity

(100

% C

F)

Probe Position

Discovered through simulation

Becoming a practical technologyLead to a new theory

Defocus targetExperiment on AIMS at low NA looks just like simulation!

Defocus Spherical HO Spherical

(λ/NA) (λ/NA)(λ/NA)

(λ/NA) (λ/NA)

Coma HO Coma

Mask phases• yellow = 0°• green = 90°• red = 180°

G. Robins

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Reading Strategy: Peak vs. Diameter

• Peak is easier to read• Trend across die is clear ~100nm• 25nm focus accuracy ~ 1/8 RU

Across die

∆X = 1800µm ∆f = 200nm ~ 1RU

λ = 248 nm, NA = 0.8

G. Robins

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UCB-TCAD

Coma Target Results

• Performance issuesDo not see the expected rings0° regions are significantly brighter than the 180° regions

• Possible reasonsMaxwell Demon at mask: electromagnetic intensity imbalanceVector addition Demon at image: high-NAMask making Demon: phase etch depth and tolerancesWafer Demon: wafer thickness variation

λ = 248 nm, NA = 0.70

0o

G. Robins

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UCB-TCAD

PSM as Precision Instruments for Illumination and Mask Making

Concentric spillover for measuring dipole imbalance

0.05

0.10

0.15

-20% -15% -10% -5% 0%

90 probe 0 probe

Transmission error of 180° region

Example Alt-PSM Target:Probe intensity vs. transmission

0° probe90° probeChrome

A(0°)

B(180°)

0.10

0.15

0.20

0 5 10

90 probe 0 probe

Phase error of 180° region (deg)

Example Alt-PSM Target:Probe intensity vs. phase error

Inte

nsity

(cle

ar fi

eld)

Inte

nsity

(cle

ar fi

eld)

Phase TransmissionG. McIntyre

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UCB-TCAD

Linking Process and EDAthrough Pattern Matchng

Zernike.txt

IFT

PatternMatcher

SPLAT

MaskLayout

Pattern(coma)

MatchLocation(s)

Aerial Image SimulatorRule-based speed at accuracy of

model based approaches Goal: real-time OPC and die-to-

database comparison for

Concept:Given a residual process effect find a test pattern with the maximal lateral impactThen identify worst-case impact locations in a layout using the degree of similarity of the local layout

http://cuervo.eecs.berkeley.edu/Volcano/F. Gennari

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UCB-TCAD

Layout Locations Impacted by Process Residuals

0/180 phase chip layout with top 100 matches for each of 12 patterns

Close-up of coma match location with match factor of 0.374

All locations along edges and corners of layout are searched fordegree of similarity to match patternPattern matching is faster than an OPC iterationMatch time is 1.5 hrs on 1GHz PIII for all edges and corners on417mm2 mask layout with 35 million shapes – 2.6 billion test points

3mm x 3mm400,000 rects1200 results

F. Gennari

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UCB-TCAD

Examples of Maximal Lateral Impact Functions

Aberrations

PSM

Reflective Notching

Reflection from Slope

Laser Assisted Thermal Processing

Thermal Conduction

Defects

Image

CMP Dishing

Procedural based on distances and density

Large Areas

Alignment

Multilayer

F. Gennari

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Test Mask: Self-Testing Phase and Intensity

Probe size: 1um

(A) 0-180,90 : 0-180 patterns with 90 probeG. McIntyre

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UCB-TCAD

Multi-Student Process-EDA Test-MaskEdward Hwang CMP Garth Robins AberrationGreg McIntyre Illumination, PSM phase error, plasma etch Jason Cain MetrologyJihong Choi CMPLing Wang CMP

• Point of Contact: Greg McIntyre, EECS, UC Berkeleyoffice (510)642-8897, gmc@eecs.berkeley.edu

• Mask info: All dimensions are for mask in um (unless otherwise noted) ; Wavelength = 248nm; 4 phase etches (0,90,180,270); Main field size = 105 x 105 mm (noted by border); Dark field mask; Alignment markers are for ASML PAS 5500/90 (our microlab stepper); Will also be used on ASML: 4x .63na , 4x .7na, & 4x .8na

G. McIntyre

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Future Devices: Mass Manufacturing Needs

Photonic Crystal WaveguideIssues: Performance, Tolerances, Inspection

Air background, εr=3.376, pitch=0.5 µm, r=0.1 µm, λ=1.55 µm, TE

TCAD => nano-CADRefractive Index Map of holes in silicon forming an optical stop-band.

Plane Wave excitationPath into and along which the light propagates.

D. Ceperley

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UCB-TCAD

Summary

The ability to model lithography tools and treatments is playing a very important role

• in guiding innovation in future lithography systems, • in application of automatic compensation to layout

designs, and • in creation of strategies for manufacturing control.

TCAD is important for many phases of advanced lithography and especially mask issues