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