PREDICTION OF THERMODYNAMIC STABILITY OF METAL/OXIDE INTERFACE

14 Sept 2010

Hong Mei Jin Ping Wu

wuping@ihpc.a-star.edu.sg

Institute of High

Performance

Computing

Singapore

Computational Materials Science Department

Michael SullivanDeputy Program Manager

Gan Chee KwanMTS Team Leader

Marco KlähnMM Team Leader

Daniel CheongCC Team Leader

Yu ZhigenEN Team Leader

Oct2008

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Zinc Alloys &

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Ti/Zr Alloys &

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ETPLCominco

IME, DSI, NTUNUS

Ontario-Singapore

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High K ZrO2

NYPU of Montreal

2005 2008

• Introduction

• Density Functional Theory(DFT) calculation of Ni/ZrO2, Cu/ZrO2

• Empirical model for thermodynamic stability of Ni/ZrO2, Cu/ZrO2• Empirical model for thermodynamic stability of Ni/ZrO2, Cu/ZrO2

• Model prediction for Au/TiO2

• DFT verification of empirical prediction for Au/TiO2

• Summary

� Important in engineering applications:� microelectronics packaging, optoelectronics

� structure composites and coatings of nuclear reactors� heterogeneous catalysis, fuel cells

� A challenge to develop a fundamental understanding of theSchottky Barrier formation mechanism

� Well reported in TOFA2010: O1, O47, O53, O72, P31, P38

Crystal structure of Ni (Cu, Au) and c-ZrO2

Ni (Cu, Au) ZrO2

Fm-3mCubic

Fm-3mCubic

Calculation model (Calculation model (supercell approach))

dark blue color: Ni(Cu), light blue color is

Zr, red color is O atom, respectively

Calculation detailsCalculation details

DFT, planewave, pseudopotential method (vasp)Ultrasoft pseudopotential & GGACut off energy: 500 eVK points: 8x8x1Since metal is less rigid, the lattice mismatch induced Since metal is less rigid, the lattice mismatch induced small in-plane strain was assigned to the metalElectronic energy was minimized using a mixture of the blocked Davidson and RMM-DIIS algorithm. Conjugate gradient method for ionic relaxation.

Work of adhesion energyWork of adhesion energy

22

22

,

, 2/)(

ZrOmZrOm

ZrOmtottot

ZrOtotmad AEEEE

γσσ −+=

−+=

where σ is the surface energy, A is interface area, γ is interfacial energy, it can be obtained from Gibbs free energy of the system:

ATSPVNNNE OOZrZrmmtot

ZrOmZrOm 2/)(22 ,, −+−−−= µµµγ

where µ is the chemical potential, N is the number of the atoms in the interface where µ is the chemical potential, N is the number of the atoms in the interface system, V is volume and S is entropy. For typical working temperature and pressure, term PV and TS can be neglected. Further, µZrO2= µZr+2µo.

So the above equation becomes:

ANNENENE oZrobulkZrOZr

bulkmmZrOm

totZrOm 2/)2(( 2,, 22

µγ −−−−=

for stoichiometric interface, the coefficient of µo will be zero, however, for non-stoichiometric interface, it will be a function of oxygen potential.

Calculated interfacial energy, surface energy and work of adhesion for morerelatively stable stoichiometric interface of Ni(110)/ZrO2(110) andCu(110)/ZrO2(110)surface energy (eV) interfacial energy (eV) Work of adhesion (J/m2)

Ni(110) 0.159 Ni/ZrO2 0.185 1.057

Cu(110) 0.085 Cu/ZrO2 0.139 0.6087

ZrO2(110) 0.092

Ref: D. Sotiropoulou et al., Ref: J. Mater. Sci,28(1993)356, Ceramics International, 15(1989)201.

Experiment results [ref]

Summary:

1. In the intermediate range of oxygen partial pressures, (110)Ni/Cu-(110)ZrO2 is more stable

2. At extreme high or low oxygen partial pressure, non-stoichiometricinterface could be more stable

3. The calculated adhesion energies are in agreement with experimentresults

Challenges:to replace the computing intensive DFT calculations bysimple empirical equations!

Based on MacDonald and Eberhart [1], D.Chatain et al [2] and Miedema’s model[3], we define the interfacial energy and work of adhesion as following:

)1()( 211

,><><

>< ∆+

∆−=

M

MinM

o

MinoMOm A

H

A

Hx

γ

where∆Ho in <M1> and∆H M1 in M2 are the partial enthalpy of mixing. For∆Ho in <M1>,the following equation [4] was used:

[1] Trans.Metall.Soc. AIME, 233:512-517, 1965.[2] Revue Phys. Appl. 23, 1055-1064, 1988.[3] Cohesion in metals.[4] Phys. Rev. B, V62(2000):4707[5] J. Alloys. Comp., 236(1996):236-242[6] J. Alloys. Comp., 420(2006):175[7] Appl. Phys. Lett., 69(1996):1701

For ∆H M1 in M2 , we used the literature data from [3,5-7]. A is molar interface area which is defined at the next page.

)(1012.1 15 OJmolHH fMOMino x

−><

∞>< ×+∆≅∆

For molar interface area, it can be calculated as:

234

1:}111{ NaAface =

for fcc lattice: for tetragonal lattice TiO2:

ateterTiOaNcaAface

ateterOTiaNcaAface

−+×+=

−×+=

)min2(211

:}111{

)min/(22

1:}111{

22

22

2

2

2

1:}100{

22

1:}110{

4

NaAface

NaAface

=

=

cNaAface

ateterOcNaAface

ateterTiOcNaAface

ateterTiOaNcaAface

×=

−×=

−+×=

−+×+=

:}100{

)min(22

1:}110{

)min(24

1:}110{

)min2(22

1

3

1:}111{ 22

where N is Avogradro’s number, a ,c are lattice parameters

Apply equation (1) on Ni/ZrO2(110), Cu/ZrO2(110)

Ni/ZrO2(110)

E (J/m2) γNi,ZrO2 (J/m2) Work of adhesion Ead(J/m2)Ni-O Ni-Zr total

Ni(111) 1.205 1.451 2.65 0.54

Ni(110) 1.205 0.888 2.09 1.92

Ni(100) 1.207 1.310 2.46 1.17

Cu/ZrO2(110)

E (J/m2) γCu,Zro2(J/m2) Work of adhesionEad(J/m2)Cu-O Cu-Zr total

Cu(111) 1.107 0.6758 1.78 0.81

Cu(110) 1.107 0.4132 1.52 1.31

Cu(100) 1.107 1.691 1.69 1.04

γσσ −+=2ZrOmadE

* here work of adhesion was calculated by (where σ is surface energy of metal and oxide, respectively):

Predicted interfacial energy and work of adhesion of Au/TiO2 between different crystal orientation

Au/TiO2(110)O-terminate

E (J/m2) γAu,TiO2 (J/m2) Work of adhesion (J/m2)

Au-O Au-Ti total

Au(111) 0.333 0.5419 0.875 1.81

Au(110) 0.333 0.3318 0.664 2.34

Au(100) 0.333 0.4691 0.802 2.08

Au/TiO2(110)O+Ti-terminate

E (J/m2) γ Au/TiO2(J/m2) Work of adhesion (J/m2)

Au-O Au-Ti total

Au(111) 0.669 0.5419 1.209 1.48

Au(110) 0.669 0.3318 0.999 2.01

Au(100) 0.669 0.4691 1.136 1.75

Au/TiO2(111)O-terminate

E (J/m2) γAu/TiO2 (J/m2) Work of adhesion (J/m2)

Au-O Au-Ti total

Au(111) 0.112 0.5419 0.654 1.00

Au(110) 0.112 0.3318 0.443 1.52

Au(100) 0.112 0.4691 0.581 1.03

Au/TiO2(111) E (J/m2) γAu/TiO2 (J/m2) Work of Au/TiO2(111)O+Ti-terminate

E (J/m2) γAu/TiO2 (J/m2) Work of adhesion (J/m2)

Au-O Au-Ti total

Au(111) 0.336 0.5419 0.878 0.78

Au(110) 0.336 0.3318 0.668 1.29

Au(100) 0.336 0.4691 0.805 1.04

Au/TiO2(001)O-terminate

E (J/m2) γ Au/TiO2(J/m2) Work of adhesion (J/m2)

Au-O Au-Ti total

Au(111) 0.455 0.5419 0.9972 0.58

Au(110) 0.455 0.3318 0.7871 1.10

Au(100) 0.455 0.4691 0.8592 0.92

The order of work of adhesion:

110-Au-110-TiO2 (O-ter)

100-Au-110-TiO2(O-ter)

110-Au-110-TiO2 (O+Ti-ter)

111-Au-110-TiO2(O-ter)

100-Au-(O+Ti)-110-TiO2

Different termination of Rutile-TiO2(110) surface

(a) Stoichiometric slab

(b) non-Stoichiometric slab

O deficient Ti deficient

Interface structure

110-Au/110-TiO2 110-Au/110-TiO2 100-Au/110-TiO2

Calculated surface, interfacial energy and work of adhesion(J/m2)

Au on (O- terminate 110-TiO2 surface

σσσσm σσσσTiO2 γγγγAu/TiO2 Ead

Au(100) 0.572 2.319 1.64 1.24

Au(110) 0.690 2.319 1.62 1.27

Au(111) 0.383 2.319 1.67 1.03

Au on (O+Ti)- terminate 110-TiO2 surface

σσσσm σσσσTiO2 γγγγAu/TiO2 Ead

Au(100) 0.5719 2.319 2.717 0.17

Au(110) 0.690 2.319 2.67 0.33

ATSPVNNNE OOTiTiAuAutot

TiOAuTiOAu 2/)( 2,, 2−+−−−= µµµγ

22 ,

2,2 2/)(

TiOAuTiOAu

TiOAutottot

TiOtotmad AEEEE

γσσ −+=−+=

1. DFT calculations were carried out to investigate the interface stability andwork of adhesion between Ni(Cu)/ZrO2. The calculated work of adhesionare comparable with experiment.

2. An empirical equation was proposed to estimate the interfacial energybetween metal and oxide. It was applied on Ni(Cu)/ZrO2 and reasonableagreement with experiment were obtained by comparing to the work ofadhesion.adhesion.

3. The empirical equation was extended to Au/TiO2. The interfacial energyand the work of adhesion were estimated for different surface orientationbetween Au and TiO2.

4. DFT calculation were further performed on Au/TiO2 to verify theempirical estimation results. Good agreement were obtained in terms ofrelative interface stability. The predicted and calculated resultsare also inagreement with experimental observations.

Thank you

谢谢！