stochastic resist simulation for euv · stochastic resist model with poisson statistics ......
TRANSCRIPT
Outline
� What is Stochastic Resist Modeling?
� Stochastic Resist Model with Poisson Statistics – ArF Example
� Description of the Stochastic Model
� Calibration
� Validation of Model with CDU data
� Stochastic Resist Model for EUV Exposure
� Photoelectron Exposure Model
� EUV calibration
� CDU predictions and Comparison to ArF results
� CDU Predictions for 22nm Node
� Summary and Conclusions
3
What is Stochastic Resist Modeling?
Lithographic modeling strategies to date have mostly followed the continuum approximation, or the use of continuous mathematics to describe the average or mean-field behavior.
However,
1 – Photon shot noise gives dose fluctuations
2 – Resist reactants are discrete molecules
When describing behavior at the length scale of tens of nanometers, an alternate approach is to build the quantization of light and matter directly into the models.
This is stochastic modeling
Images from James Schombert, Dept. of Physics, Univ. of Oregon website @ ABYSS.UOREGON.EDU
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Computationally inexpensive way to study interesting lithographic behavior
1. Photon Counting Statistics
• Effects of photon shot noise
2. Resist formulary vs. behavior
• Effects of reactant loadings
• Quantum efficiency of bright and ‘dark’ exposure mechanisms
3. Resist line-edge roughness, line-width roughness, CD variability and failure mechanisms
• Statistical fluctuations in the placement of the resist edge
• Statistical fluctuations in the resist width
• Scumming and bridging phenomena
Why Consider a Stochastic Model?
Stochastic Model for Direct Photon Absorption at Ar FFluctuations from Formulation and Photon Shot Noise
Formulation Model
� PAG and quencher placed randomly throughout resist volume based on loading and Poisson statistics
Exposure Model
� Poisson statistics for photons
� Monte Carlo model for probability that PAG absorbs a photon, and for probability of conversion to acid
( )1
*
*
≤=
Φ=→→
hotonsnAbsorbedP
nAcidsYieldAcid
AcidPAGprob
PAGPAG hυ
1 nm3
Calibration Process
� Calibration Data� 3 Focus-Exposure Matrix wafers exposed under identical conditions
1. 50nm Line, 100nm Pitch
2. 80nm Line, 200nm Pitch
3. 110nm Line, 700nm Pitch
� Data processing for calibration� CDSEM images were reviewed and points where bridging, scumming or pattern collapse
was observed were excluded.
� Average CD and standard deviation where valid CD was obtained for all wafers.
� LWR values were determined for each site using SUMMIT (EUVL Technology Corp).
� Calibration Process� Absolute PAG and quencher loadings fixed to formulation values
� Resist optical parameters fixed to values measured with an ellipsometer
� Nonlinear least-squares fitting of exposure, development, and PEB parameters to minimize root-mean-square error for FEM CDs and LWR values.
Reference:Robertson, Biafore, Smith, Reilly, and Wandell, ”Predictive linewidth roughness and CDU simulation using a calibrated physical stochastic resist model”, Proc SPIE 7639 (2010)
Process Conditions
� BARC: 19 nm Dow AR124 over
79 nm Dow ARC26N
� Resist: Dow EPIC2013
� Resist Process: 130 nm Resist
100°/ 60” SB
100°/ 60” PEB
12” GP Nozzle development – Dow MF-26A with FIRM process
� Topcoat: 90nm JSR TCX04190°/ 60” Cure
� Mask: 6% AttPSM
� Exposure Conditions: 1.35NA Immersion, ASML/1900i0.90σo/0.60σi Annular (X/Y Polarization)
Experimental CD Vs Simulation (3 Trial Mean) Optimized Stochastic Model Parameters
50nm Line, 100nm Pitch FEM
30
35
40
45
50
55
60
-0.05 0 0.05 0.1 0.15 0.2
Focus ( µm)
CD
(nm
)
80nm Line, 200nm Pitch FEM
30
35
40
45
50
55
60
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Focus ( µm)
CD
(nm
)
110nm Line, 700nm Pitch FEM
50
55
60
65
70
75
80
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Focus ( µm)
CD
(nm
)
34.8mJcm-2 Expt
34.8mJcm-2 Sim
36.0mJcm-2 Expt
36.0mJcm-2 Sim
37.2mJcm-2 Expt
37.2mJcm-2 Sim
38.4mJcm-2 Expt
38.4mJcm-2 Sim
39.4mJcm-2 Expt
39.6mJcm-2 Sim
40.8mJcm-2 Expt
40.8mJcm-2 Sim
Average 3 σ LWR – Experimental Vs SimulationOptimized Model Parameters
0
1
2
3
4
5
6
7
8
9
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Defocus ( µm)
3 σ L
WR
(nm
)
100nm Pitch Expt
100nm Pitch Sim
200nm Pitch Expt
200nm Pitch Sim
700nm Pitch Expt
700nm Pitch Sim
Resist Profiles – Experimental Vs SimulationOptimized Model Parameters
50nm Line100nm Pitch
80nm Line200nm Pitch
110nm Line700nm Pitch
Verification data for ArF Resist Model
� Collected CDU data for line-space and for line-end shortening structures.� 50nm lines on 100nm pitch with different gap widths.
� Same scanner and process settings as calibration dataset.
� Experiment designed to minimize any non-resist contributions to CDU� All structures in the same position within the field
� Only one stage used on scanner
� Only a single flow through the track (same spin bowl, PEB hotplate, etc.)
� Only a single scan direction
Experiment Model
CDU – 50 nm Line, 100 nm Pitch (155 Sites)36 mJ/cm 2, 0.05 µm Focus (Best Focus)
CDFIT EXPT = 45.3 nmσFIT EXPT = 0.47 nm
CDFIT SIM = 46.0 nmσFIT SIM = 0.40 nm
43 43.5 44 44.5 45 45.5 46 46.5 47 47.5 480
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Data
Den
sity
Best Focus Experiment
Experiment FitBest Focus Simulated
Simulation Fit
CDU – Line End Shortening Pattern (155 Sites) 100 nm Gap [36mJ/cm 2 – Best Focus]
CDFIT EXPT = 166.3 nm CDFIT SIM = 165.7 nmσFIT EXPT = 3.2 nm σFIT SIM = 3.7 nm
155 160 165 170 1750
0.05
0.1
0.15
Data
Den
sity
100nm Gap Experiment
Experimental Fit100nm Gap Simulation
fit 8Simulation Fit
Mask
Wafer
Model
PAG conversion by electron kinetic energy
Probable exposure mechanism at EUV
Acid yields at EUV are not explained by direct photolysis of PAG. Acid generation at EUV is hypothesized to be similar to that found in e-beam resists: via ionization and electron scattering
Stochastic Model for EUV – Secondary ElectronsFluctuations from Formulation, Photon Shot Noise, a nd Secondary Electrons
( )larger?or1
2
*
*
>=
Φ=→+→++→++→
−−
+−−
−+
hotonsnAbsorbedP
nAcidsYieldAcid
AcidPAGprob
PAGePAGe
MeMe
eMM hυ
elastic mean-free path
inelastic mean-free path
stopping power
, scattering angles
el
inel
dE
dS
λλ
θ φ
=
=
=
=
-2-1
01
2
-2-1
01
2
-2
-1
0
1
2
nmnm
nm
10
20
30
40
50
60
70
80
Simulation Parameters:
Resist Atomic Density = 100 atoms per nm3
Average atomic number = (8*6 + 8*1)^(1/3)
PAG loading = 0.1 / nm3
PAG reaction radius = 2.7 nm
PAG Eact = 2.0 eV
Ionization potential = 8 eV
1 primary photoelectron
2 secondary electrons
Acid yield = 2
Energy, eV
PAG
acid
acid
PAG
electron trajectories
Acid yield and electron scattering from one EUV ionization event
Calibration Data – Process Conditions
� Resist: Shin Etsu SEVR40
� Resist Process: 70 nm Resist
100°/ 60” SB
100°/ 60” PEB
12” GP Nozzle development – Dow MF-26A with FIRM process
� Mask: 77nm absorber stack
32nm lines on 65nm, 75nm and 95nm pitches
Both horizontal and vertical
� Exposure Conditions: ASML ADT
0.25 NA, 0.5 partial coherence
Reference: Biafore, Smith, van Setten, Wallow, Naulleau, Blankenship, Robertson, and Deng “Resist pattern prediction at EUV”, Proc SPIE 7636 (2010)
-0.05 0 0.05 0.1 0.152
4
6
8
1032L75PH RMS LWR= 1.1 nm
focus, um
LWR
, nm
-0.05 0 0.05 0.1 0.152
4
6
8
1032L95PV RMS LWR= 0.7 nm
focus, um
LWR
, nm
-0.05 0 0.05 0.1 0.152
4
6
8
1032L95PH RMS LWR= 0.8 nm
focus, um
LWR
, nm
Global RMS Error = 1 nm, Max Err = 5 nm
Reasonable quantitative agreement between model and average CD, LWR
-0.05 0 0.05 0.1 0.1525
30
35
4032L75PH RMS CD= 0.8 nm
focus, um
CD
, nm
-0.05 0 0.05 0.1 0.1525
30
35
4032L95PV RMS CD= 0.5 nm
focus, um
CD
, nm
-0.05 0 0.05 0.1 0.1525
30
35
4032L95PH RMS CD= 0.3 nm
focus, um
CD
, nm
<CD>
Lines = model
LWR
Circles = model
Examples of fit to mean CD and LWR
28 nm V lines on 65 nm pitch, CDSEM 28 nm V lines on 56 nm pitch, simulation
Reasonable qualitative agreement between simulation and experiment
Comparison of Resist Profiles 28nm vertical lines on 56nm pitch
Comparison between ArF and EUV100nm Gap Line-end Shortening
CDFIT EXPT = 166.3 nm
σFIT EXPT = 3.2 nm
CDFIT SIM = 165.7 nmσFIT SIM = 3.7 nm
155 160 165 170 1750
0.05
0.1
0.15
Data
Den
sity
100nm Gap Experiment
Experimental Fit100nm Gap Simulation fit 8Simulation Fit
ArF Result
Experiment = ???
CDFIT SIM = 96.3 nmσFIT SIM = 1.7 nm
EUV Result
EUV predicted to require minimal OPC, and have bett er CDU control!
Extrapolation to Smaller Gap Sizes
Gap CD does not hit target for gaps smaller than 70nm. Pattern failure for 50nm pitch.
35L-70P 70 Gap
nm
nmGAP
27.2
1.74
=
=
σ
30L-60P 60 Gap
nm
nmGAP
46.2
8.69
=
=
σ
25L-50P 50 Gap
nm
nmGAP
40.2
2.68
=
=
σ
Summary and Conclusions
� We have presented a Stochastic Resist Model describes the fluctuations naturally present when imaging small features
� Photon shot noise
� Concentration fluctuations in PAG and Quencher
� Scattering of secondary electrons and reaction with PAG
� We have calibrated this model to CD and LWR data for both ArF and EUV exposures, and achieved good fits to these datasets.
� CDU prediction with ArF model agreed well with experimental data.
� Extrapolation to EUV shows broadening of CDU as features shrink
� Even with current EUV resists, gap CDU is still better than ArF result.
� Pattern ultimately fails on dense lines, not gap.
The PROLITH team
� Stewart Robertson
� David Blankenship
� Dale Legband
� Pat Lee
� Sanjay Kapasi
� Trey Graves
� Chris Walker
� Greg Floyd
� Heather Spears
� Dan Grubbs
ASML
� Eelco van Setten
� Anita Fumar-Pici
� Steve Hansen
References:
� Robertson, Biafore, Smith, Reilly, and Wandell, ”Predictive linewidth roughness and CDU simulation using a calibrated physical stochastic resist model”, Proc SPIE 7639 (2010)
� Biafore, Smith, van Setten, Wallow, Naulleau, Blankenship, Robertson, and Deng “Resist pattern prediction at EUV”, Proc SPIE 7636 (2010)
Acknowledgements
Lawrence Berkeley National Lab
� Patrick Naulleau
� Lorie-Mae Blaclea-an
Dow Electronic Materials
� Michael Reilly
� Jerome Wandell
GLOBALFOUNDRIES
� Tom Wallow
� Yunfei Deng