Opening the Extreme UltraViolet Lithography Source Bottleneck : The development of a 13'5 nm plasma

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Opening the Extreme Ultra-Violet Lithography
Source Bottleneck The development of a 13.5 nm
plasma based source for the semiconductor
industry

• OEUVLSB

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In search of a clean, bright, narrow source
coming soon to a Sematech manufacturer
near you

• starring Robert Cowan, D. Colombant and G.F.
  Tonon
• special effects by CXRO
• and a cast of tens at UCD

debris-free, 3 efficient (with 75 Mo/Si
reflectivity), 13.5 nm 2005?, 2007?
SEmiconductor MAnufacturing TECHnology an
organizing cooperative of firms which share
developing semiconductor manufacturing
technology. Firms include AMD, Agere Systems, HP,
Infineon Technologies, IBM, Intel, Motorola,
Philips, TSMC, and Texas Instruments. Sematech
publishes the International Technology Roadmap
for Semiconductors (ITRS), which supplies the
metrics for next generation lithography (NGL)
development.
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0. Introduction

• Atomic physics oscillator strength Cowan
• Plasma physics ion density rate equations
  Colombant and Tonon
• Optics mirror reflectivity CXRO
• All together FOM UCD
• Plasmod a quick demo
• Whats next? (e.g., experimental spectra,
  time-dependent plasma modelling)

FOM ?z(?gf(z) ? f(z)) x R(?)
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1. Atomic physics Cowan input

• Robert Cowan in Los Alamos
• multi-configuration Hartree-Fock (MCHF)
• self-consistent iteration (start with an initial
  solution ? and perturb until change is lt eps)

e.g., Sn XI (Sn10)
2 -9 2 10 0.2 5.e-08 1.e-11-2 0150
1.0 0.65 0.0 1.0 -6 50 11sn
p64d4 4p6 4d4 50 11sn
p54d5 4p5 4d5 50 11sn
d34f1 4p6 4d3 4f1 50 11sn
d35p1 4p6 4d3 5p1 -1    g5inp
000 0.0000 00 7
9099909090 0.00 001104229 -1

• can include higher levels nd, nf, np
• more configurations ? more configuration
  interaction

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1. Atomic physics Cowan output

• Sn11.out36 ?
• Sn11.spec gf versus ? for each configuration
• Sn.wo gf versus ? (all configurations)

4p ? 4d 4d ? 4f
gf
4d ? 5p
? (nm)
Note any atom/ion can be theoretically
represented Sn XI with 3 configurations 7788
transitions (3245, 2825,1718) no theoretical
line width (convolute Doppler, Stark, Voight)
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1. Atomic physics Cowan notes

• results depend on configuration interaction (CI)

Sn XI 4 configurations (7788 transitions), 13
configurations (49,326 transitions)
of transitions
Small Large Large/Small Sn VII 1247
6763 5.4 Sn VIII 5009 29175
5.8 Sn IX 10432 64486 6.2
Sn X 11959 76500 6.4 Sn XI
7788 49326 6.3
Note wavelength is higher with more
configurations
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1. Atomic physics Cowan notes

• Cowan can calculate atomic parameters (?, ?) for
  any ion stage
• ? (ionisation potential), ? (number of outer
  shell electrons) such that ?Ez lt ?Ez1 for
  successive configurations (ion stages)
• ?, ? are important in ion density rate equations
  (later)

50 1Sn 5p 3d10 4s2 4p6 4d10
5s2 5p2 50 2Sn 5p 3d10 4s2
4p6 4d10 5s2 5p1 50 3Sn 5s
3d10 4s2 4p6 4d10 5s2 50 4Sn 5s
3d10 4s2 4p6 4d10 5s1 50 5Sn 4d
3d10 4s2 4p6 4d10 50 6Sn 4d
3d10 4s2 4p6 4d9 50 7Sn 4d
3d10 4s2 4p6 4d8 50 8Sn 4d
3d10 4s2 4p6 4d7 50 9Sn 4d
3d10 4s2 4p6 4d6 50 10Sn 4d
3d10 4s2 4p6 4d5 50 11Sn 4d
3d10 4s2 4p6 4d4 50 12Sn 4d
3d10 4s2 4p6 4d3 50 13Sn 4d
3d10 4s2 4p6 4d2 50 14Sn 4d
3d10 4s2 4p6 4d1 50 15Sn 4p
3d10 4s2 4p6 50 16Sn 4p 3d10
4s2 4p5 50 17Sn 4p 3d10 4s2
4p4 50 18Sn 4p 3d10 4s2 4p3
50 19Sn 4p 3d10 4s2 4p2 50
20Sn 4p 3d10 4s2 4p1 50 21Sn
4s 3d10 4s2 50 22Sn 4s
3d10 4s1 50 23Sn 3d
3d10
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1. Atomic physics Question

• Which sources emit at 13.5 nm?

• Possible sources include
• Sn, Xe, F, L, I (in original SFI proposal)
• Also Sb and perhaps In, Te

• Sn VIII to Sn XIII ions
• Sb VIII to Sb X
• Xe XI

Sn XI Sb VIII
Xe XI
In, Sn, Sb, Te, I, Xe ions (Z 49 to Z 54 all
have similar transitions) n 4 ? n 4, n 5 ?
n 5 (4p ? nd, 4d ? nf, 4d ? np )
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1. Atomic physics Question

• Which sources emit at 13.5 nm?

Sn VIII to Sn XIII
Sb VIII to Sb X
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2. Plasma physics ion density rate equations
What is (a) plasma?

• ionised gas
• linear dimensions much greater than the Debye
  length
• characterized by
• electron density, ne
• electron temperature, Te
• ion distribution, fz (or average charge, ltzgt)
• found in lightning, aurorae, tokomak fusion
  reactors, laboratory laser-produced plasmas (LPPs)

plasma coined by Langmuir (1928) to suggest
collective electrical behaviour in an ionised gas
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2. Plasma physics Some plasma photos

• lightning (N, O, Ar), aurorae (solar wind
  interaction with B), tokomaks (D, T shaped by
  magnets)

northern lights over Finland
lightning
hot hydrogen plasma burning in the START
spherical tokamak at Culham
UCD laser-produced plasma
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2. Plasma physics Plasmas characterised by ne, Te
Density (cm-3) versus Temperature (eV) Caroll
and Kennedy

• CE, CR, LTE
• laboratory laser-produced plasmas are in CR range
• small size
• short lifetime
• high density, temperature, pressure Key and
  Hutcheon

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2. Plasma physics CR steady-state model

• C R (1020 1022 cm-3) Colombant and Tonon
• Plasma temperature
• Electron density
• CR validity

The coronal equilibrium (CE), collisional-radiativ
e (CR), and local thermodynamic equilibrium (LTE)
models apply under different temperature and
density conditions.
C lt R C R
C gt R
CE
CR
LTE
sparse 1020 1022
dense ne cm-3
The average electron temperature, Te, is a
function of laser wavelength (?), laser flux (?),
and target atomic number (Z). Te ? Z1/5 (?2?)3/5
The electron density, ne, is a function of the
incident laser wavelength. ne ? 1021 ?-2
Cut-off density Plasma is optically thick

• Maxwellian distribution
• ion rate (nz1/nz) small
• plasma optically thin

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2. Plasma physics Density, ne, nec

• During the heating phase

ne lt nec plasma transparent ne nec electrons
oscillate as a group (SHM) ne gt nec plasma opaque
(expands, thus decreasing density)
From Maxwell, ??E ?/?0, Lorentz, F e(E v x
B), and SHM,
? in microns nec in cm-3
for a NdYAG at 1.064 microns, ne ? 1021
cm-3 LPP typically of the order of 1020-1022 cm-3
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2. Plasma physics Temperature, Te

• reasonably complicated, semi-empirical derivation
  Colombant and Tonon
• function of
• atomic number Z
• wavelength ? (m)
• laser flux ? in W/cm2
• Te is assumed to be an average temperature within
  the whole plasma

Te in eV
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2. Plasma physics Atomic processes

• ion distribution from rate equations
• rate equations from atomic processes
• collisional ionisation, S(z-1)
• radiative recombination, ?r (z)
• three-body recombination, ?3b(z)

ionisation
C photo collisional auto
S
?r ?3b Dj
R radiative three body dielectronic
recombination
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2. Plasma physics Rate equations

• not intending to muddle with equations, but
• important things to note are
• semi-empirical
• all are a function of ?, ?, and Te
• ?3b rate depends on density
• most importantly, fz from a balance of ionisation
  and recombination
• as well, equations for ? and ltzgt also derived
  semi-empirically

• S 9 x 10-6 ?z (Te / ?z)1/2 e (-?z / Te)
• ?z3/2 (4.88 Te / ?z)
• ?r 5.2 x 10-14 (?z / Te)1/2 Z
• 0.429 .5 log(?z / Te) 0.469 (Te /
  ?z)1/2
• ?3b 2.97 x 10-27 ?z
• Te ?z2 (4.88 Te / ?z)
• S collisional ionisation,
• ?r radiative recombination,
• Dj dielectronic recombination,
• ?3b three-body recombination,
• Te electron temperature,
• ne electron density,
• Z atomic number,
• ?z ionisation potential,

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2. Plasma physics Ion distribution, fz

• sum up rates recursively over all ion states (?fz
  1)
• but typically interested in one Te at a time (a
  Colombant and Tonon slice) from which the ion
  distribution can easily be seen for a given
  temperature and the average charge, ltzgt,
  determined.

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2. Plasma physics Ion distribution, fz

• Electron density 9.84e20 cm-3
• Sn electron temperature 36 eV
• Sn average charge 8.1 (CT approx.) 10.7
  (computationally)

Laser wavelength 1.064 microns, ion density
(ne) 9.84E20 cm-3 Tin Ion outer
shell Ionization fnz nz1/nz nz stage el
ectrons potential (eV) (35.89 eV) (cm-3) Sn
I 2 7.08
0 3340 0 Sn II 1 14.41
0 760 0 Sn III 2 29.36
0 1010 0 Sn IV 1
40.06 0 72.5 0 Sn V 10
76.52 0 132 0 Sn VI 9
96.02 0 70.6 0 Sn
VII 8 116.48
0 36.6 0 Sn VIII 7 137.84
0.0105 18.1 1.03E19 Sn IX 6
160.02 0.0872 8.33 8.58E19
Sn X 5 183.02
0.306 3.51 3.01E20 Sn XI 4
206.8 0.402 1.32 3.96E20 Sn
XII 3 231.33
0.173 0.431 1.71E20 Sn XIII 2
256.59 0.0203 0.117 2E19 Sn
XIV 1 282.58
0 0.0158 0 Sn XV 6 383.78
0 0 0 Sn XVI 5 412.22
0 0 0
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2. Plasma physics Plasmod (a first look)

• ion distribution as a function of temperature and
  atomic parameters (graph and table)
• rate equations
• ion fraction versus charge state (CT slice)
• average charge (CT versus computational)

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2. Plasma physics Notes

• CR model -- balance of ionisation and
  recombination
• distribution of ions versus temperature
• ion density dependent on atomic parameters ? and
  ?
• ? from tables (Moore), experiment, Cowan, Edlen
  fit  
• ? from tables, Cowan
• order of shells?, which if more than one open
  shell?, outer shell?, all open shells? 
• both play a part in determining ion density from
  rate equations
• ionisation potential lowering, ?? (not all atoms
  in ground state) and dielectronic recombination
  (excited states) not included
• average charge, ltzgt, determined computationally

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Q. Plasma physics Question

• Which ion stages are present in the plasma?

Ion densities 32 eV
36 eV 43 eV Sn VII 1 --
-- Sn VIII 23 -- --
Sn IX 41 9 -- Sn X
25 31 7 Sn XI 1
40 30 Sn XII -- 17
43 Sn XIII -- -- 19
Sn XIV -- -- 1

• If we know the temperature, density, and atomic
  parameters, we know the ion stages Colombant and
  Tonon.

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3. Optics mirror reflectivity CXRO

• multilayer mirror (N 40)
• high and low Z (e.g., Mo/Si)
• required in EUV (because of low reflectivity
  below crystal transmission limit)
• Mo/Si is the industry choice for 13.5 nm

Reflectivity is calculated using the Fresnel
equations and the analytic formula given by V. G.
Kohn in Phys. Stat. Sol. (b) 187, 61,
1995.   Paddy will give details of his two
mirrors made at Lawrence Berkeley National Lab.
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3. Optics CXRO web site

• Input data multi-layer period (d 6.9 nm),
  ratio of bottom layer thickness/period (0.4),
  number of periods (N 40), substrate SiO2

R(?) is currently digitised to 100 points in
Plasmod
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3. Optics Question

• What percentage reflectivity is in the required
  bandwidth?

• 75 reflectivity at 13.5 nm
• R (?) from 12.5 nm 14.5 nm

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4. All together FOM

• Figure of merit

• FOM ?z(?gf(z) ? f(z)) x R(?)
• ?gf(z) summed oscillator strengths for ion z
• f(z) fractional weighting of ion z
• R(?) reflectivity of Mo/Si multilayer

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4. All together FOM

• oscillator strength (Sn IX Sn XII)
• fractional weighting (36 eV)
• Reflectivity (12.5 14.5 nm)

A figure of merit at different laser fluxes (or
electron temperatures) can be calculated.
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4. All together FOM

• Sn 28 eV, 36 eV, 43 eV with CI

FOM 238 477 361
FOM quantifies in-band emission
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5. Plasmod a quick demo

• ? from energy, pulse length, focal radius
• ne from ?
• Te from Z, ?, and ?
• atomic parameters from Cowan
• CR rate equations
• fractional ion density distribution, fz
• FOM from Cowan, CT, and CXRO

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5. Plasmod FOM

• Sn, Sb, Xe (4 configurations only)
• Sn (Small and Large)

Figure of merit for Sn, Sb, and Xe
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6. Whats next?

• All OEUVLSB sources (Li, F, I, Xe, Sn)
• also Sb and possibly In, Te
• compare theoretical FOM in Plasmod to
  experimental data on GIS
• Slater-Condon scaling
• Plasmod
• dielectronic recombination
• IP lowering (??)
• mixtures (oxides, by ) how are the rate
  equations effected?
• configuration interaction survey (CI), harmonics
  (512 nm)
• analytical mirror solution (gt 100 points) Paddy
• Paddys actual mirror response
• time-dependent rate equations (space and time)
• Medusa (Li ), Hullac
• spatial deliniation (LTE core, CR middle, CE
  edge)
• absorption

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6. Whats next? NGL

• Abacus (600 BC)
• Napiers bones (1617)
• Jacquard loom (1801)
• ENIAC (1946)
• integrated circuit (1956)
• Moores law (1968)

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6. Whats next? OEUVLSB

• A clean, bright, narrow source?

Thanks to Gerry, Padraig, Emma, Deirdre, Anthony,
Nicola, Kenneth, Andy, Lynn, Paddy, Dariusz,
Michael, Luke, and Paul
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6. Whats next? Plasmod revisited

• Possible name for Plasmod?

Plasma Analyser Diagnostic Recombination And
Ionisation Guestimator
Plasma Analyser Diagnostic Recombination And
Ionisation Guestimator
General Energy Radiative Recombination Ion
Estimator
General Energy Radiative Recombination Ion
Estimator
Everyday Meta-Maser Actualizer
Everyday Meta-Maser Actualizer
PERSEUS who slew MEDUSA
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