DENSITY FUNCTIONAL CALCULATIONS OF BONDING AND ADHESION AT METAL – CERAMIC INTERFACES

1. DENSITY FUNCTIONAL CALCULATIONS OF BONDING AND ADHESION AT METAL – CERAMIC INTERFACES Newton Ooi: newton.ooi@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.  1 E2 ET E1 A 2 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 Kinetic energy of non-interacting electrons Potential 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/od/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

10. Energy versus volume for Al using GGA-PAW

11. Cell Slab Vacuum 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

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. 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 TYPES OF INTERFACE MODELS

16. INTERFACE CREATION • Build interface models • Minimize lattice mismatch • Require symmetric interfaces • Al(111) - graphite (0001) • Plot out a (3*2) Al(111) surface, red Al atoms and blue cell lines • Plot out a (2*2) 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

21. SURFACE TERMINATION AFFECT • WC • Gray = C • Brown = W • Al2O3 • Black = O • Red = Al

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

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