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Lattice Kinetic Monte Carlo: Building a bridge between
ab-initio calculationsand process simulation
Polycrystalline Materials
E. Rubio, M. Jaraiz, L.A. Bailon, J. Barbolla, M.J. LopezUniversity of Valladolid, Spain
G. GilmerBell Labs Lucent Tech., USA
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ChiPPS 2000 M. Jaraiz, Univ. Valladolid, Spain2
100 nm
0.5 µm
• Kang et al, J. Electron. Mater. , 1997• Murarka, “Metallization”, 1993
Why Lattice KMC?Aluminum, Polysilicon, …: Polycrystalline structure
!Surface texture!Grain Boundary diffusion!Electromigration
deposition ratedepends on: temperature
substrate
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ChiPPS 2000 M. Jaraiz, Univ. Valladolid, Spain3
This Work: Polycrystalline 3-D atomistic approach
"""" Continuum equations:SPEEDIE, SAMPLE, EVOLVE, DEPICT
"""" 2-D ballistic simulator:SIMBAD, GROFILMS
"""" 3-D atomistic approach: ADEPT
Simulation approaches
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ChiPPS 2000 M. Jaraiz, Univ. Valladolid, Spain4
# Atoms are attached to the sites of a perfect fcc lattice.
# As a first approximation, the binding energy of each site depends on the number of occupied nearest neighbors
Simulation Box
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ChiPPS 2000 M. Jaraiz, Univ. Valladolid, Spain5
Energies from MD Embedded Atom Method using Gupta Potential
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ChiPPS 2000 M. Jaraiz, Univ. Valladolid, Spain6
# Initial position and velocity according to desired distribution# Atom travels in a straight line until it either:
# Finds some neighbors: gets attached to that grain# Finds no neighbors: starts a new grain (orientation).
Deposition
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ChiPPS 2000 M. Jaraiz, Univ. Valladolid, Spain7
# Atoms not fully coordinated can jump to a neighboring empty site.
#The jump probability depends on the number of nearest neighbors and on the migration energy.
Surface Diffusion
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ChiPPS 2000 M. Jaraiz, Univ. Valladolid, Spain8
If the destination site of a jump (A2) is at a grain boundary:
1. Check the energy of sites belonging to other orientations (B) around destination site.
2. If energy (B1) < energy(A2) then the jump final site is B1.
A1A2B1
Grain Boundaries
B1A1
A2
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ChiPPS 2000 M. Jaraiz, Univ. Valladolid, Spain9
Lattice KMC: Simulation Examples
! Nucleation! Crystalline Substrates: Orientation! Amorphous Substrates: Wetting
! Annealing:! Texture evolution
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ChiPPS 2000 M. Jaraiz, Univ. Valladolid, Spain10
STM images of Cu islands on Pd(100) at 265K and 300 K and coverage of 0.1 ML and 0.07 ML
50 nm10 nm
Simulation:Al on Al (110) @ 200K, 350K, 500K, 600KCoverage=0.1 ML
Nucleation on Al (110)
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ChiPPS 2000 M. Jaraiz, Univ. Valladolid, Spain11
Simulation:Al on Al (111) @ 200K and 400K
20 nmSTM measurements:Pt on Pt(111) @ 200K and 455K
20 nm
Nucleation on Al (111)
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ChiPPS 2000 M. Jaraiz, Univ. Valladolid, Spain12
“Wetting” substrate(Strong bonding)=> smaller grains
“Non-wetting” substrate(Weak bonding)
Bonding to substrate: effect on the grain size
Nucleation on Amorphous Substrates
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“Wetting substrate”(Strong bonding)=> smaller grains
“Non wetting substrate”(Weak bonding)
Nucleation on Amorphous Substrates
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ChiPPS 2000 M. Jaraiz, Univ. Valladolid, Spain14
Number of atoms: 20000Simulation size: 0.012 µm ⇒ Actual size: 0.25µm
Tdep = Tann = 663 KAnnealing time = 2.7 ms
Tdep = Tann = 513 KAnnealing time = 0.18 s
Annealing: Texture Evolution
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ConclusionsConclusions# Atomistic Process Simulators provide a bridge
between ab initio calculations and standard process experimental data.
# Efficient and accurate 3D simulation.# Straighforward implementation of new
mechanisms.# Microelectronics Device Processing: “Continuum
physics models are no longer sufficient below 100nm. Tools are needed for the physical and chemical processes at an atomic level” (1997 USANational Technology Roadmap for Semiconductors)