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BAND-THEORETICAL APPROACH TO BONDING AT METAL-ALUMINA INTERFACES
M. Kohyama, Y. Ebata, S. Kose, M. Kinoshita, R. Yamamoto
To cite this version:
M. Kohyama, Y. Ebata, S. Kose, M. Kinoshita, R. Yamamoto. BAND-THEORETICAL APPROACH
TO BONDING AT METAL-ALUMINA INTERFACES. Journal de Physique Colloques, 1990, 51 (C1),
pp.C1-861-C1-866. �10.1051/jphyscol:19901135�. �jpa-00230046�
COLLOQUE DE PHYSIQUE
Colloque Cl, suppl6ment au n o l , Tome 51, janvier 1990
BAND-THEORETICAL APPROACH TO BONDING AT METAL-ALUMINA INTERFACES
M. KOHYAMA, Y. EBATA, S. KOSE, M. KINOSHITA and R. YAMAMOTO*
Glass and Ceramic Material Department, Government Industrial Research Znstitute, Osaka, 1-8-31, Midorigaoka, Ikeda, Osaka 563, Japan
Department of Metallurgy and Materials Science, Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo 113, Japan
Abstract - The electronic structure of the interface between a-A1203(0001) and Nb layers has been calculated using the empirical tight-binding method and the slab model.It has been shown that a direct chemical bond of both covalent and ionic characters can be established at the interface between the surface 0 atoms of a-A1203 and the Nb atoms, which is consistent with the recent experiment. General trends of the electronic structure and chemical bond at the interfaces between a-A1203(0001) and a series of 4d transition metals have been examined. It has been observed that the occupancy in the portion of the antibonding peaks of the local density of states at the interface increases as the atomic number of the transition metal increases.
I. INTRODUCTION
The joining of ceramics and metals is an essential technique in order to realize the practical use of ceramics. It is of much importance to understand the microscopic mechanism of bonding between ceramics and metals. Recently, ~ g h l e and co-workers /l/ have obtained HREM images of the interfaces between a-A1203 and Nb where direct bonding is formed without any reaction layers, and several attempts have been made in order to develop new methods to bond metals to ceramics directly by surface activation /2/. It is of much importance to elucidate the microscopic nature of bonding at the abrupt interfaces in these systems. For this purpose, it is essential to study the electronic structure of the interfaces. Several theoretical
approaches to the interfaces between A1203 and metals have been made /3,4,5/. Johnson and Pepper /3/ have applied the self-consistent Xg method to ~ 1 0 cluster with a metal atom ~ ~ - placed on the surface and they found that a chemical bond is established between the metal d- orbitals and the non-bonding p-orbitals of the surface 0. However, in the cluster
calculations, only a small number of atoms are included, and a semi-infinite extension of an interface or solids is excluded. These effects can be taken into account in a band-
theoretical approach.
In this paper, we have carried out a band-theoretical approach to the interfaces between a- A1203(OOOl) surface and transition metals. Because of the relatively low symmetry of the crystal structure of 0-A1203 and the lattice mismatch between Q-A1203(0001) plane and
transition metals, it is difficult to deal with the interface between the two solids directly.
Thus, we have constructed model structures of a-A1203(0001) slab with transition metal layers deposited on both surfaces and calculated the electronic structures of these models.
We have used the empirical tight-binding method coupled with the universal parameters proposed by Harrison and co-workers /6,7/. We have investigated the interface between a-A1203 and Nb, and the interfaces between a-A1203 and a series of 4d transition metals have been examined.
11. METHOD OF CALCULATIONS
One s and three p orbitals of each A1 and 0 atoms and one s and five d orbitals of each transition metal atom are included in the orthogonalised basis set. The interatomic Hamiltonian matrix elements are expressed in terms of two-center integrals between atomic orbitals. The magnitude and the distance dependence of the two-center integrals are derived from Harrison's universal tight-binding theory /6/ as shown in Table I. We have used the atomic term values given by Herman and Skillman / 8 / . The energy of the d-state is very sensitive to the occupancy of the d-orbitals. Thus, the d-levels of respective metal atoms have been determined self-consistently in each system by assuming thefollo~ingde~endence on the effective occupation of the d-states as /7/
The parameters E; and U are shown in Table I1 as well as the atomic term values. n is the total number of s and d electrons. Zd is the effective d-state occupancy and calculated from the partial density of states of respective transition metal atoms. These values and
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19901135
Cl-862 COLLOQUE DE PHYSIQUE
formulations have been successfully used in calculations of transition metal compounds /7,9/.
Table I. The two-center integrals. m and PI are the electron mass and Planck's constant. r is the interatomic distance. rd is the d-state radius of respective transition matal atoms.
S-S, S-p and p-p
2 2 nssu nspu 'IPP~ 'IPP~
'Igg ,m -5 /mr
-1.40 1.84 3.24 -0.81
S-d and p-d
2 1.5,mr3.5 rlsd~ "pdo npdr '~dm'~ d'
-3.16 -2.95 1.36 d-d
Table 11. Atomic term values. All energies are given in electron volts.
111. RESULTS AND DISCUSSION
111-1. Electronic Structure of a-A1203
ENERGY (eV)
Fig. 1. Calculated electronic structure of a-AL2O3. (a) Energy band structure along the lines in the Brillouin zone. (b) Total and partial densities of states.
Figure 1 shows the calculated electronic structure of a-A1203. The lower valence band consists of 0 2s orbitals and the upper valence band consists of 0 2p orbitals. In the conduction band, the A1 3s and 3p contribution dominates. The A1 3s and 3p contribution also exists in the valence bands, which reflects the nature of partly covalent bonding. It should be noted that the top of the upper valence band is flat in Fig. l(a) and there exist a peak at -14.1 eV in the partial density of states, which reflects the non-bonding 0 2p orbital
character. It can be said that general features of the electronic structure are well
reproduced by the present theoretical scheme. Especially, the value of the band gap and the constitution of the respective bands are in good agreement with experiments and other
calculations /10,11/, although the widths of the lower valence band and the upper valence band are somewhatlarge as compared with the results by first-principles cluster calculation /IT/.
111-2. Electronic Structure of the Ideal (0001) Surface of a-A1203
We have calculated the electronic structure of the deal (0001) surface of a-A1203 using the slab model /10/. The slab contains six 0 layers and 12 A1 layers as shown in Fig. 2(a). The unit cell repeats two-dimensionally. A1 atoms form the topmost surface layers. The
calculated electronic structure is shown in Figs. 2(b) and 2(c). The most significant effect of the ideal (0001) surface is the appearance of the surface band within the gap. This band consists of s and pz dangling bonds of the surface A1 atoms. Other effects are observed in the local density of states of the surface 0 atoms. The peak at -14.leV corresponding to the non-bonding p level is much higher than that of the bulk 0 atoms. This effect is caused by the deficiency of neighboring A1 atoms around the surface 0 atoms. A new peak occurs at -21.5eV. This peak reflects the strengthened back bonds between the surface 0 atoms and the A1 atoms in the next layers. The present results qualitatively agree with the results calculated using the extended ~ i c k e l method /10/.
(a) (b) ENERGY (eV) (C) ENERGY (eV)
Fig. 2. (a) Slab unit cell of the ideal (0001) surface of @-Al2O3. (b) Calculated LDOS of the surface A1 atoms. (c) Calculated LDOS of the surface 0 atoms.
111-3. C1-A1203(0001)-Nb Interface
For the interface between c ~ - A ~ ~ O ~ ( O O O ~ ) surface and Nb, firstly, we have calculated the electronic structure of the model shown in Fig. 3(a). We call this structure model A. Each Nb atom is deposited at the center of the triangles of surface 0 atoms and each distance between a Nb atom and an 0 atom is assumed to be equal to the sum of Slater's atomic radii /12/. About the atomic arrangement of the C1-A1203(0001) surface shown in Fig. 2(a), it can be said that the surface A1 atoms are deposited at the center of the triangles of surface 0 atoms.
Metal atoms can be considered to be deposited on remaining similar sites initially. It is possible that this type of interface structure exists in spite of the lattice mismatch because metals are relatively easy to be deformed as observed by HREM /l/.
The calculated electronic structure of the present model is shown in Fig. 3(b). In the local density of states of the surface 0 atoms, the peak at -14.leV corresponding to the non-bonding p leveldisappears and a newpeak appearsat -16.2eV. Also in the local densities of states of Nb atoms, small peaks appear in the same region in the upper valence band. These results indicate that covalent bonding states are formed mainly between the Nb d-orbitals and the non- bonding p-orbitals of the surface 0 atoms. The peaks at -6.0ev, -4.9eV and -3.3eV in the
CI-864 COLLOQUE DE PHYSIQUE
local densities of states at the interface can be considered to correspond to the antibonding levels between the surface 0 atoms and the Nb atoms, and the peaks at -6.5eV and -8.0eV are considered to be caused by the interactions among the Nb atoms. It should be noted that the Fermi-level is located below the antibonding peaks. In addition to the formation of the bonding and antibonding levels, the charge transfer from the Nb atoms to the surface 0 atoms also occurs. Therefore, it is clear that a direct chemical bond of both covalent and ionic characters is established between the surface 0 atoms and the deposited Nb atoms.
Fig. 3. (a) Slab unit cell with Nb atoms deposition sites exist in one unit cell.
Nb I + Nb 11
--
vSURFACE
/Jk
0 .fENERGY (eV)
deposited on both surfaces (model A). Two types of (b) Calculated LDOS at the interface of model A.
ENERGY (eV)
-
-
Fig. 4. (a) Slab unit cell with Nb atoms deposited on both surfaces (model B). Three types of deposition sites exist in one unit cell. (b) Calculated LDOS at the interface of model B.
N b I
Nb II
- - &-
We have calculated the electronic structure of another model shown in Fig. 4(a). We call this structure model B. Additional Nb atoms are located instead of the surface A1 atoms in model
A. As shown in Fig. 4(b), similar results have been obtained. In the local densities of states at the interface, there exist the peaks corresponding to the bonding levels mainly between the d-orbitals of the Nb atoms and the p-orbitals of the surface 0 atoms in the range of the upper valence band. The peak at -6.0eV is considered to be the non-bonding d-levels.
The Fermi-level is located at this peak. Of course, the charge transfer from the Nb atoms to the surface 0 atoms also occurs.
Recently, Ohuchi has carried out XPS and UPS measurements of successive Nb deposition onto a a-A1203(0001) substrate
.
He has found by XPS that the Nb atoms are donating electrons to the surface 0 atoms of a-A1203, and found by UPS that the peak at the top of the valence band in the density of states of 0-Al2O3 consisting of the 0 2p-orbitals is shifted lower by the deposition of Nb at low coverages. These results agree well with our theoretical results.ENERGY (eV) ENERGY (ev)
-
zr I
--.
----Fr-,--A --
y,-7-Zr IT
---.-.-m-"62..
A -
Zr III
ENERGY (eV) ENERGY ( e V )
W-
A
-
M O I T AFig. 5. Calculated LDOS at the interfaces between a-A1203 and 4d transition metals, (a)Zr, (b)Mo, (c)Ru and (d)Pd.
Z r I + Z r l I + z r m
: ,
, -
M O I + M O I I + M O ~
SURFACE 0
Cl-866 COLLOQUE DE PHYSlQUE
111-4. CL-A1203(0001)-4d Transition Metals Interfaces
In order to examine the general trends of the chemical bond and electronic structure of the interfaces between CL-A1203 and transition metals, we have performed sitnilar calculations of the interfaces between CL-A1203 and a series of 4d transition metals. In each system, the structure of model B is dealt with for simplicity. Figure 5 shows the electronic structures at the interfaces between Q-Al2O3(00O1) plane and Zr, MO, Ru and Pd. Nb is located between Zr and MO in the periodic table. In every system, similar characteristics to those observed in the case of Nb can be seen. The primary interaction at the metal-A1203 interface occurs mainly between the metal d-orbitals and the non-bonding p-orbitals of the surface 0 atoms.
The peak corresponding to the non-bonding p level of the surface 0 atoms disappears and the new peaks corresponding to the bonding levels and the antibonding levels appear. In addition to these covalent bonding effects, there also exists the charge transfer from metal atoms to the surface 0 atoms.
The folLowing variation from Zr to Pd are found. As the atomic number of the transition metal increases, firstly, the position of d-bands becomes lower and nearer to the 0 2p level. And the width of d-bands becomes narrower. Secondly, the degree of hybridisation between the metal d-orbitals and the p-orbitals of the surface 0 atoms becomes larger. Thirdly, the larger portion of the local density of states is occupied. For example, in the systems of Zr and Nb shown in Figs. 5(a) and 4(b), the Fermi-level is located at the non-bonding d-levels.
However, in the case of Pd shown in Fig. 5(d), the Fermi-level is located above the peaks corresponding to the antibonding levels. This increase of the occupancy of the antibonding levels should reduce the net energy gain in the bond formation as pointed out by Johnson and Pepper in the cluster calculation / 3 / .
IV. CONCLUSION
We have performed a band-theoretical approach to the interfaces between a-A1203 and Nb and other 4d transition metals using the empirical tight-binding method. It has been shown that the electronic structures of a-A1203 and of the ideal (0001) surface of a-A1203 can be reproduced qualitatively by the present theoretical scheme. By using the models of the CL- A1203(OOOl) slab with Nb layers deposited on both sides, it has been shown that a direct chemical bond of both covalent and ionic characters can be established between the surface 0 atoms and deposited Nb atoms. This result is consistent with the recent photoelectron spectroscopy study. In calculations of the interfaces between CL-A1203 and a series 4d
transition metals, similar characteristics to those in the case of Nb have been found. As the atomic number of the transition metal increases, the occupancy in the portion of the
antibonding peaks in the local densities of states at the interface increases. This effect seems to decrease the energy galn in the bond formation as well as the effect of the charge transfer.
REFERENCES
/l/ FLORJANCIC, M., MADER, W., R ~ ~ H L E , M. and TURWITT, M., J. Physique
3
(1985) C4-129;MADER, W. and R ~ ~ H L E , M - , Acta metall.
37
(1989) 853./2/ SUGA, T., MIYAZAWA, K. and YAMAGATA, Y., Proc. MRS Int. Symp. Joints of Metals and Ceramics (1988), in press.
/3/ JOHNSON, K.H. and PEPPER, S.V., J. Appl. Phys.
21
(1982) 6634./4/ ANDERSON, A.B., MEHANDRU, S.P. and SMIALEK, J.L., J. Electrochem. Soc.
132
(1985) 1695;ANDERSON, A.B., RAVIMOHAN, CH. and MEHANDRU, S.P., Surf. Sci.
183
(1987) 438; NATH, K.and ANDERSON, A.B., Phys. Rev. B
39
(1989) 1013./5/ OHUCHI, F.S., FRENCH, R.H. and KASOWSKI, R.V., J. Appl. Phys.
62
(1987) 2286; KASOWSKI, R.V., OHUCHI, F.S. and FRENCH, R.H., Physica B150
(1988) 44./6/ HARRISON, W.A., Electronic Structure and the Properties of Solids (Freeman, San Francisco, 1980).
/7/ FROYEN, S., Phys. Rev. B
22
(1983) 3119./8/ HERMAN, F. and SKILLMAN, S., Atomic Structure Calculations (Prentice-Hall, Englewood Cliffs, 1963)
/9/ HARRISON, W.A. and STRAUB, G.K., Phys. Rev. B 3 (1987) 2695.
/10/ CIRACI, S. and BATRA, I.P., Phys. Rev. B
2
(1983) 982./11/ XIA SHANGDA, GUO CHANGXIN, LIN LIBIN and ELLIS, D.E., Phys. Rev. B
2
(1987) 7671./12/ SLATER, J.C., Quantum Theory of Molecules and Solids (Mc~raw-Hill, 1965) Vol. 2.
/13/ OHUCHI, F.S., to be published.
