Atomistic Front-End Process Modeling
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Atomistic Front-End Process Atomistic Front-End Process ModelingModeling
A Powerful Tool for
Deep-Submicron Device Fabrication
Martin Jaraiz University of Valladolid,
SpainSISPAD 2001, Athens
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Thanks to:Thanks to:
P. Castrillo (U. Valladolid)
R. Pinacho (U. Valladolid)
I. Martin-Bragado (U. Valladolid)
J. Barbolla (U. Valladolid)
L. Pelaz (U. Valladolid)
G. H. Gilmer (Bell Labs.)
C. S. Rafferty (Bell Labs.)
M. Hane (NEC)
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PDE Solver
Atomistic KMC
ParameterValues:
Di=0.1,Em=1.2,
…
PhysicalModels:
DiffusionClusteringAmorphiz.
Charge EffectsSurfaces
Precip./Segreg.
Deep-Submicron Device
Front-End Process ModelingFront-End Process Modeling
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KMC Simulator
The Atomistic KMC ApproachThe Atomistic KMC Approach
OutputLattice Atoms are just vibrating
Defect Atoms can move by diffusion hops
KMC simulates Defect Atoms only
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Ion Implantation: The "+1" modelIon Implantation: The "+1" model
Atomistic KMC made quantitative calculations feasible (I):
“One excess Interstitial per Implanted Ion" (M. Giles, 1991)
Dependence on Ion Mass and Energy
(Pelaz, APL 1998)
Free
Sur
face
Annealing of 40 KeV,
2x1013 Si/cm2
"+1.4" (Jaraiz, APL 1996) In agreement with Eaglesham's measurements
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KMC Simulations (Pelaz, APL 1999)
Dependence on:• Dose• Temperature / Dose-Rate
Total diffusivity almost constant for T<500C, in agreement with Jones et al.
Ion Implantation: The "+1" modelIon Implantation: The "+1" modelAtomistic KMC made quantitative calculations feasible (II):
Sub-linear increase for intermediate doses, as observed by Packan et al.
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Impurity Atoms: Boron (I)Impurity Atoms: Boron (I)
KMC Simulations (Pelaz, APL 1999): Kick-out mechanism InBm complexes
Annealed B Profiles
Accurate annealed profiles:• Diffused B (substitutional)
• Immobile B (InBm complexes)
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KMC Simulations (Pelaz, APL 1999): Accurate prediction of electrically active B
InBm PathwayElectrically active B
Impurity Atoms: Boron (II)Impurity Atoms: Boron (II)
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Impurity Atoms: Carbon (I)Impurity Atoms: Carbon (I)KMC Simulations (Pinacho, MRS 2001): Kick-Out Mechanism InCm Complexes
Frank-Turnbull Mech.900 'C, 1h anneal
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Impurity Atoms: Carbon (II)Impurity Atoms: Carbon (II)
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InCm Pathway
In agreement with experimentally observed C2I complexes
Impurity Atoms: Carbon (III)Impurity Atoms: Carbon (III)
Carbon is normally above its solubility
Clustering/Precipitation
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Extended Defects: InterstitialsExtended Defects: Interstitials{311} defects Faulted loops Perfect loopsSmall clusters
TEM images from Claverie et al.
Cowern et al. Cristiano et al.
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Extended Defects: Interstitial {311}Extended Defects: Interstitial {311}Simulated in DADOS with their actual crystallographic parameters
Interst. Supersat. (Hops)
3D View
{311} defects
2D
Projection
High B diffusivity
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311-defects dissolution311-defects dissolution• Full damage simulation: No “+N” assumption• Defect cross-section automatically given by
defect geometry 200 s
600 s
1200 s
1800 s
738ºC
Simulation
1.E+11
1.E+12
1.E+13
1.E+14
1.E+15
1 10 100 1000 10000 100000
Anneal time (s)
inte
rstit
ials
in d
efec
ts (
cm-2
)
815ºC738ºC705ºC670ºC
Experimental:
Lines: simulation
Experimental data from Eaglesham et al.
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Interstitial supersaturationInterstitial supersaturation
Determines dopant diffusivity
Experimental data from Cowern et al.
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05Anneal time (s)
Inte
rstit
ial s
uper
satu
ratio
n
600ºC700ºC800ºC
Experimental:
Lines: simulation
Simulation
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DADOS Simulation
Dislocation LoopsDislocation Loops
However, {311} can in fact reach sizes >> 345
From Claverie et al.
{311}Loop: Activation Energy?
Loop energy < {311} energyif Number of atoms > 345
Therefore, the {311} Loop transformation cannot be based just on minimum configurational energy.
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Extended Defects: VacanciesExtended Defects: Vacancies
But chemical / electrical effects are evident from experiments (Holland et al.):
P Implant
Si Implant
• Big V-clusters are spheroidal (Voids)• Energies from Bongiorno et al. (Tight-Binding)
Ge Implant
As Implant
Isoelectric
Dopants
Nearly same atomic Number & Mass
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Extended Defects: Vacancies (II)Extended Defects: Vacancies (II)Chemical / electrical effects
Si Implant
P Implant
Simulation with negative Eb at sizes 7, 11, 15
No negative Eb at n=7
P ImplantSi Implant
Si Implant
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Bongiorno et al. Non-Lattice KMCLattice KMC
Lattice / Non-Lattice KMCLattice / Non-Lattice KMC
The dominant factor seems to be the energetics.
It is not clear the need for Lattice KMC
Attributed to the mobility of small
clusters in Lattice-KMC
Do we need Lattice KMC?
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Amorphization / RecrystalizationAmorphization / RecrystalizationAmorphization:Massive lattice disorderContinuum spectrum of time-constants and atomic configurations involved
Not amenable to atomic-scale KMC description for device sizes.
Implant: 50 KeV, 3.6x1014 Si/cm2 (Pan et al., APL 1997)
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Amorphization / RecrystalizationAmorphization / Recrystalization
Implementation (3D):• Small (2nm-side) “damage boxes”• Accumulate Interst. & Vacs. (“disordered
pockets”) up to a maximum number per box (MaxStorage)
• This allows for dynamic anneal between cascades
• Maintain the correct I-V balance in each box
• When a box reaches a given damage level becomes an “Amorphous region”
• Amorphous regions in contact with the surface or with a crystalline region recrystalize with a given activation energy.
• Any I-V unbalance is accumulated as the amorphous region shrinks (“dumped” onto adjacent amorphous boxes).
Top View
Cross Sect.
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KMC SimulationImplant: 50 KeV, 3.6x1014 Si/cm2
(Pan et al., APL 1997)
Amorphization / RecrystalizationAmorphization / Recrystalization
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800 C, 60 s
(Pan et al., APL 1997)Simulation
<100> <110>
No net I excess within the amorphised layer
I,V recombination dissolves {311} and Loops
Are V’s being held in small, stable clusters, that prevent recombination?
Amorphization / RecrystalizationAmorphization / Recrystalization
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Charge state update– static (immobile species)– dynamic (mobile species)
Charge EffectsCharge Effects: Implementation: Implementation
[I-[Io___
= ni
___n(x)·I
-
I-
n(x)ni
I-(x) I+(x)
x
con
cen
trati
on
?
• n(x) calculated from charge neutrality approximation
• no interaction between repulsive species
P(+x)P(-x) = exp( )
kTq··
Electric field() drift– modeled as biased diffusion
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Equilibrium conditions Non equilibriumPhosphorous in-diffusion
Charge EffectsCharge Effects: Examples: Examples
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Surface: I,VSurface: I,V Inert
– Emission Rate = D0*exp(-(Ef+Em)/kT)
– Recomb. Probability = Recomb. LengthJump Distance
Atomistic KMC can incorporate any currently available injection rate model (from SUPREM, etc)
Oxidation:– I-supersaturation
Nitridation:– V-supersaturation
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Surface: Impurity AtomsSurface: Impurity Atoms Surface-to-Bulk: (Diffusion from the Surface)
Given the Surface concentration calculate the corresponding mobile species emission rate.
Bulk-to-Surface: (Grown-in, Implant,…)1. Monitor the number (NA) of Impurity atoms that arrive at the surface.
2. Emit the mobile species at a rate proportional to NA up to the solubility
limit.
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Unforeseen effects can show-up when all Unforeseen effects can show-up when all mechanisms are included simultaneouslymechanisms are included simultaneously
Examples:1. Nominally “non-amorphising” implants (e.g. 40 KeV, 8×1013 cm-2 Si)
can still generate small, isolated amorphous regions due to cascade overlapping.
2. Self-diffusion Data (Bracht, Phys. Rev. B 52 (1995) 16542): V parameters (Formation + Migration)
The split (Formation, Migration) was chosen such that (together with the V cluster energies from Bongiorno, PRL) V clustering spontaneously generates Voids.
In Atomistic KMC In Atomistic KMC all mechanisms are mechanisms are operative operative simultaneously
Missing mechanisms can lead to missed side-effects.
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Example: A 20-nm NMOSFET
(Deleonibus et al., IEEE Electron Dev. Lett., April 2000)
Device ProcessingDevice Processing
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Device ProcessingDevice ProcessingDADOS Simulation
As Implanted
1s @ 950 C
15s @ 950 C
Anneal CPU time on a 400 MHz Pentium-II:
32 min
Deep-Implant also simulated
(Extension only: 5 min)
Calculation region: 100x70x50 nm3
S/D Extension: 3 KeV, 1014 As/cm2
S/D Deep-Implant: 10 KeV, 4x1014 As/cm2 (?)
Anneal: 15 s @ 950 C
Deleonibus et al., IEEE Elec. Dev. Lett., April 2000
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ConclusionsConclusions
Atomistic KMC can handle: All these mechanisms Simultaneously Under highly non-equilibrium
conditions In 3D
Atomistic Front-End Process Simulation can
advantageously simulate the processing steps of current deep-submicron device
technology.