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DENSITY FUNCTIONAL CALCULATIONS OF BONDING AND ADHESION AT METAL

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Dr. L. G. Hector and Dr. Y. Qi at GM. Georg Kresse and authors of VASP ... Siegel, Hector, Adams. PRB 67 (2003) 092105. Kittel. ... – PowerPoint PPT presentation

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Title: DENSITY FUNCTIONAL CALCULATIONS OF BONDING AND ADHESION AT METAL


1
DENSITY FUNCTIONAL CALCULATIONS OF BONDING AND
ADHESION AT METAL CERAMIC INTERFACES
Newton Ooi newton.ooi_at_asu.edu Ph.D student in
Materials Science Engineering Computational
Materials Science group of Dr. J. B.
Adams http//ceaspub.eas.asu.edu/cms/
ASU workshop on Quantum and Many-body effects in
nano-scale devices October 24 25, 2003
2
OUTLINE
  • Uses and properties of aluminum
  • Adhesion to aluminum
  • Computational approaches
  • Density functional theory
  • VASP
  • Methodology
  • Results
  • Future work
  • Acknowledgements and references

3
ALUMINUM
  • Uses
  • Interconnects in IC chips
  • Circuit board material
  • Electrolytic capacitors
  • Properties
  • High thermal and electrical conductivity
  • Forms stable oxide
  • Low cost and low weight
  • Reasonable electro-migration resistance
  • Aluminum forms interfaces with other materials
    when used in microelectronics
  • Need to understand bonding and structure at these
    interfaces

http//www.ssmc.co.jp
http//www.dselectronicsinc.com
4
ADHESION TO ALUMINUM
  • Measure using wetting experiments
  • Oxidation and surface contamination
  • No insight into atomic bonding
  • Difficult to quantify results
  • Examine using computer simulation
  • No concern about oxidation and contamination
  • Find ideal work of separation
    ? work of separation
  • Assumes no plastic deformation
  • Interfacial bonding and geometry is very complex
    ? need reliable quantum mechanical approaches

5
WORK OF SEPARATION


6
DENSITY FUNCTIONAL THEORY
  • Total energy is functional of electron density
  • Proposed first by Thomas and Fermi in 1920s
  • Current model proposed by Hohenberg, Kohn and
    Sham in 1960s and applicable to ground state
  • Replace many-electron Schrödinger equation with
    single particle Kohn-Sham (KS) equation

Potential energy of non-interacting electrons
  • Kinetic energy of
  • non-interacting electrons

Electrostatic energy
Exchange correlation energy
7
VASP
  • Vienna Ab initio Software Package
  • Fortran 90 code for Unix / Linux
  • Plane wave basis set to span Hilbert space
  • Born Oppenheimer approximation
  • Pseudopotentials to represent ion electron
    interactions
  • Projector augmented wave (PAW) Blochl. PRB 50,
    24 (1994) 17953
  • Ultra-soft (US) Vanderbilt. PRB 41 (1990) 7892
  • Super cell method ? 3D periodic boundary
    conditions
  • Variational method with free energy as
    variational quantity
  • Exchange correlation energy
  • LDA Kohn Sham. Physical Review 140 (1965)
    A1133
  • GGA Perdew Wang. PRB 33, 12 (1986) 8800
  • VASP website http//cms.mpi.univie.ac.at/vasp/

8
METHODOLOGY
  • Bulk calculations
  • Surface calculations
  • Generate interface models
  • Interface calculations
  • Calculate work of separation
  • Analyze atomic and electronic structure of
    interface

Aluminum single electron trap http//www.nsf.gov/o
d/lpa/priority/nano/
9
BULK CALCULATIONS
  • Determine irreducible Brillouin zone
  • Plane wave convergence to minimize basis set
  • Finite temperature smearing to quicken
    calculations
  • Calculate energy as a function of volume
  • Fit using equation of state (EOS)
  • Determine cohesive energy, bulk modulus and
    lattice constants
  • Used to select best pseudopotential for surface
    calculations

Aluminum bulk data a (Å) Ec (eV) V (Å3) Bo (GPa)
Calculated with LDA 3.971 -4.22 15.66 82.55
Calculated with GGA 4.039 -3.72 16.47 72.75
Experimental 4.045 -3.39 16.60 72.2
10
Energy versus volume for Al using GGA-PAW
11
SURFACE CALCULATIONS
  • Choose surface with lowest value of ?
  • Construct slabs with symmetric surfaces
  • Determine irreducible Brillouin zone
  • Vacuum convergence to minimize interaction
    between consecutive slabs

12
SURFACE ENERGY CALCULATIONS
  • Calculate surface energy via surface thickness
    convergence
  • Fit results to appropriate surface energy
    equation
  • We used equation of Boettger PRB 49, 23 (1994)
    16798

13
SURFACE ENERGIES
Surface Termination Calculated (J/m2) Experiment (J/m2)
Al (100) Al 0.89 NA
Al (110) Al 1.05 NA
Al (111) Al 0.81 NA
Al2O3 (0001) Al 1.59 NA
Al2O3 (0001) O 7.64 4.45 10.83
WC (0001) W 3.66 3.43 3.88
WC (0001) C 5.92 5.69 6.14
VN (100) VN 0.95 NA
CrN (100) CrN 0.74 NA
14
INTERFACE CALCULATIONS
  • Generate periodic interfaces
  • With or without vacuum?
  • Sandwich or bi-layer?
  • Lattice mismatch?
  • Interface registry?
  • Universal Binding Energy Relationship (UBER)
    curve
  • Determine equilibrium interfacial separation
  • Rough estimate of Ws
  • Works for modeling adsorption
  • Relax interface and isolated slabs to minimal
    energy geometries
  • Calculate Ws
  • Electronic structure analysis
  • Charge density plots
  • Electron localization function

15
TYPES OF INTERFACE MODELS
  • Vacuum or not?
  • Vacuum allows more room for atoms to relax ?
    increases accuracy
  • Vacuum must be populated by plane waves ?
    increases calculation cost
  • Sandwich or periodic?
  • Dipoles must cancel
  • Free surfaces must be paired

16
INTERFACE CREATION
  • Build interface models
  • Minimize lattice mismatch
  • Require symmetric interfaces
  • Al(111) - graphite (0001)
  • Plot out a (32) Al(111) surface, red Al atoms
    and blue cell lines
  • Plot out a (22) C(0001) surface green cell lines
  • Rotate the graphite surface so its corners match
    up with Al atoms

17
LATTICE MISMATCH
  • Real materials can have different
  • Crystal structures
  • Lattice constants
  • Lattice angles
  • Use of periodic boundary conditions
  • Minimize lattice mismatch
  • Eliminate dangling bonds and unmatched surfaces
  • Solutions
  • Rotate surfaces with respect to each other
  • Match up different multiples of each surface
  • Stretch / compress one or both slabs (strain)
  • Examples of lattice strain
  • Al (111) Al2O3 (0001) 4.9
  • Al (110) WC (0001) 0.4
  • Al (100) TiN (100) 5.3

Expand Compress
18
INTERFACE GEOMETRY
  • Also denoted as interface registry or coherency
  • Interface can range from fully coherent to fully
    incoherent
  • Example Al (111) Graphite (0001)
  • Black atoms are carbon, gray atoms are aluminum
  • C1 C2 C3 C4

19
UBER CURVES
20
NITRIDES AND CARBIDES
  • VN a0 4.126 Å
  • VC a0 4.171 Å
  • CrN a0 4.140 Å

Al surface Ceramic surface Ceramic structure Ws (J/m2)
(100) VC (100) Rock salt 2.14
(100) VN (100) Rock salt 1.73
(100) CrN (100) Rock salt 1.45
(100) TiN (100 Hexagonal 1.52
21
SURFACE TERMINATION AFFECT
  • WC
  • Gray C
  • Brown W
  • Al2O3
  • Black O
  • Red Al

Al surface Ceramic surface Calculated Ws (J/m2) Experimental Ws (J/m2)
(111) Al terminated Al2O3 (0001) 1.06 1.13
(111) O terminated Al2O3 (0001) 9.73
(111) W terminated WC (0001) 4.08
(111) C terminated WC (0001) 6.01
22
GRAPHITE AND DIAMOND
  • Al (111) Diamond (111)
  • Clean interface Ws 3.98 4.10 J/m2 depends on
    interface model and registry
  • Hydrogen termination of diamond Ws 0.02 J/m2
    for all registries
  • Calculated results agree with experiments
    hydrogen passivation of diamond surfaces lower
    its coefficient of friction and adhesion to other
    materials
  • Al (111) Graphite (0001)
  • Ws 0.2 0.35 J/m2 depending on interface model
  • Different interface registries does not affect Ws
    ? graphite is great lubricant for Al processing
    because graphite basal planes slide easily over
    Al surface
  • Calculations agree with measured adhesion
    energies of 0.1 0.4 J/m2

23
Al Graphite charge density
Abrupt change at interface negligible Al
graphite bonding
24
Al Graphite ELF
  • ELF (Electron Localization Function) measures
    probability of electrons with same spin being
    near each other
  • Different bonding types are differentiated by
    color
  • Red areas ? bonding pairs ? localized bonding ?
    covalent
  • Blue to green ? unpaired electrons or vacuum
  • Yellow to orange ? metallic bonding

25
Al Al203 ELF
Abrupt change in bonding at interface
Aluminum --------------------- Al2O3
26
SUMMARY
  • Modeling of interfaces involves many issues
  • Lattice mismatch
  • Symmetry and periodicity
  • Coherency
  • Surface termination and composition
  • Adhesion to aluminum increases with the polarity
    of opposing material ? polarity increases bond
    formation
  • Adhesion at interface proportional to the surface
    energies of contacting surfaces ? surface
    reactivity
  • DFT adhesion calculations give results in good
    agreement with available experimental data

System Experiment Ws (J/m2) Calculated Ws (J/m2)
Al Al2O3 1.13 1.06
Al graphite 0.1 0.4 0.2 0.35
27
FUTURE WORK
  • Aluminum Diamond-like carbon (DLC)
  • Influence of surface stresses in carbon
  • Effect of sp3/sp2 bonding ratio in carbon
  • Aluminum BN
  • Hexagonal versus cubic BN
  • Influence of surface stoichiometry B or N or BxNy

ELF of 64-atom DLC cubic supercell with gray
iso-surface of 0.53
28
CREDITS
  • Acknowledgements
  • NCSA at UIUC for computational resources
  • NSF for funding under grant DMR 9619353
  • Dr. D. J. Siegel
  • Dr. L. G. Hector and Dr. Y. Qi at GM
  • Georg Kresse and authors of VASP
  • Newton Ooi and other group members
  • References
  • Siegel, Hector, Adams. PRB 67 (2003) 092105
  • Kittel. Introduction to Solid State Physics 7th
    Edition 2000 John Wiley Sons
  • Adams et al. Journal of Nuclear Materials 216
    (1994) 265
  • Landry et al. Mat. Science and Engineering A254
    (1998) 99
  • www.accelrys.com
  • www.webelements.com
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