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

OUTLINE

• Uses and properties of aluminum• Adhesion to aluminum• Computational approaches• Density functional theory• VASP• Methodology• Results• Future work• Acknowledgements and

references

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.dselectronicsinc.com

http://www.ssmc.co.jp

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

WORK OF SEPARATION

= +

E2

2

E1

1

A

ET

AEEEW Ts /2121

DENSITY FUNCTIONAL THEORY

Kinetic energy of

non-interacting electronsElectrostatic

energyExchange

correlation energy

Potential energy of non-interacting electrons

• 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

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/

j

riGGeA

*

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/

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

Energy versus volume for Al using GGA-PAW

-3.8

-3.7

-3.6

-3.5

-3.4

-3.3

-3.2

-3.1

-3.0

0.65 0.75 0.85 0.95 1.05 1.15 1.25 1.35

Volume / Equilibrium Volume

en

erg

y /

ato

m (

eV

)

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

CellVacuum

Slab

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

2ns 2

n

2

1NN HHHH

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

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

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

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

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

INTERFACE GEOMETRY

C1 C2 C3 C4

• 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

UBER CURVES

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

SURFACE TERMINATION AFFECT

Al surface Ceramic surfaceCalculated

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

• WC– Gray = C– Brown = W

• Al2O3

– Black = O– Red = Al

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

Al – Graphite charge density

Abrupt change at interface = negligible Al – graphite bonding

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

Al – Al203 ELF

Aluminum

---------------------

Al2O3

Abrupt change in bonding at interface

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

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

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