Pd(001) surfaces

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Surface Science 331-333 (1995) 691-696

Overlayer and interface resonances and bound states at Pd/Ag (001 ) and Ag/Pd(001 ) surfaces M.V. Ganduglia-Pirovano a,.,l, M.H. Cohen a, J. Kudrnovsk~)b a Corporate Research Science Laboratories, Exxon Research and Engineering Company, Annandale, NJ 08801, USA b Institute of Physics, Academy of Sciences of the Czech Republic, CZ-180 40 Prague 8, Czech Republic Institute of Technical Electrochemistry, Technical University, ,4-1060 Vienna, Austria Received 23 July 1994; accepted for publication 3 November 1994

Abstract

We have calculated the kll-, symmetry-, and layer-resolved density of states (DOS) at &ll = 0 for complete pseudomorphic monolayers of Pd on Ag(001) and Ag on Pd(001 ). For the xy and x 2 - y2 subbands, which do not hybridize with any other low-lying orbitals, the resulting DOS agrees quantitatively with that of a 1D-semi-infinite chain perturbed only at the overlayer, i.e. terminal, site and at the interface, i.e. penultimate, site. The Pd overlayer presents a repulsive potential to the silver. This results in a surface (overlayer) state strongly bound above each subband, in pushing an existing surface (x 2 - y2) state on pure Ag(001 ) further above the band and in converting an existing resonance (xy) into an interface bound state. The Ag overlayer on the other hand presents an attractive potential to the Pd, resulting in a bound state below each subband and greatly weakened interface resonances at the subband tops. Keywords: Density functional calculations; Green's function methods; Low index single crystal surfaces; Metallic surfaces; Metal-metal interfaces; Palladium; Silver; Single crystal epitaxy; Surface electronic phenomena

The local electronic structure of a perfect, unreconstructed single-crystal surface differs from that of the bulk crystal primarily for two reasons. The termination of the bulk structure leads to reflection of the Bloch waves, and the reflected waves interfering with the incoming waves lead to layer dependent oscillations in energy of the symmetry-, layer-, and surfacewave-vector-(kll) resolved density of states (DOS). There is also a repulsive perturbation of the crystal potential in the outer layer(s). In a previous publication [ 1 ], we pointed out that these effects would be simply * Corresponding author. I Present address: Max Planck Institut fur Physik komplexer Systeme, Aussenstelle Stuttgart, Heissenbergstrasse 1, D-70569 Stuttgart, Germany.

and dramatically displayed in the symmetry-, layer-, and kll-resolved density of states A(kll, a,p; E) at kll = 0 (F) for fcc (001) transition (or noble) metal surfaces, where a specifies the symmetry type, p is the layer index and E the energy. We carried out accurate computations of A(kll = 0, a,p; E) and found for the x 2 - y2 subband a bound state just above the bulk continuum and clear evidence for interferences persisting deep into the material in both Pd(001 ) and Rh(001 ). On the other hand, the xy subbands of both materials showed strong resonances just below the band edges. The computed energy dependences of A(kl[ = 0, ct, p; E) could be closely fitted in all four cases for the first four layers and the bulk by a remarkably simple model.

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M.V. Ganduglia-Pirovano et al./Surface Science 331-333 (1995) 691-696

The DOS calculations were performed by means of an efficient scalar-relativistic self-consistent, surface Green's function technique based on the tight-binding linear muffin-tin orbital (TB-LMTO) theory. The details of the method have been described elsewhere [2,3]. In the TB-LMTO representation, the shortranged character of the screened structure constants allows one to view the semi-infinite solid as a stack of so-called principal layers with only nearest-neighbor interactions between them [4]. For the fcc (001) surface the x y and x 2 - y2 d-states each does not couple to any states of angular momentum l lower than 3 at kll = 0, and a principal layer consists of one atomic layer. Thus, the bulk x y and x 2 - y2 subbands are well fitted by an apparently one-dimensional, non-degenerate, nearest-neighbor cosine band. Accordingly, consistent with this three-dimensional symmetry, we replaced the one-dimensional stacking of layers by a corresponding semi-infinite chain with a perturbing potential V1 on the top site. The band width 4t and center of gravity E = 0 were fixed by fitting to the bulk subband. The value of V1 was fixed by fitting a zero in the DOS in a single layer. The resulting fits for the full energy and layer dependence were extraordinary. The critical value of V1/2t for a bound state in the model is 0.5. For both x 2 - y2 subbands the critical value was exceeded, resulting in a bound state, whereas for both x y subbands the value was subcritical, resulting in a band-edge resonance. The interferences were readily apparent as zeroes in the DOS. Corresponding results for Ag(001) are qualitatively very similar to those of Ref. [ 1 ]. For the x 2 _ y2 subband the value I,~/2t = 0.79 was found, resulting in a bound state, whereas for the x y subband the subcritical value E / 2 t = 0.49 leads to a strong band-edge resonance. It is natural to attempt to extend these findings to more complex situations, other values of kll, or more complicated surface structures. In the present paper, we follow the latter route and examine the same subbands at kll = 0 for pseudomorphic, complete monolayers of Pd on Ag (001 ) and Ag on Pd (001 ). The possibility of such detailed analysis of surface and interface states occurrence combined with angular-resolved photoemission measurements can be extremely helpful in determining the basic features of the electronic structure of the overlayer and the interface, and the character of the localized states at the surface avail-

able for chemisorption [ 5 ]. The DOS calculations were performed in a manner entirely analogous to that for Pd(001) and Rh(001) [ 1 ]. Here the potentials were calculated selfconsistently in an intermediate region consisting of the overlayer, three substrate layers, and two layers of empty spheres simulating the vacuum-sample interface. This intermediate region was coupled to the semi-infinite vacuum on one side and to the semi-infinite crystal on the other, with frozen potentials. In general, there are three different types of stationary states that can exist in structures of pseudomorphic overlayers on clean substrates. There are bulk states, recognizable distortions of states existing in the infinite crystal, which occur over the energy interval of the full band width of the infinite crystal, true interface states, localized mainly at the first substrate layer, and true surface states, localized mainly in the overlayer. True interface and overlayer states occur at energies outside the energy interval of the full band of the infinite crystal for the particular kll. The location and the nature of the overlayer and interface states depend on the perturbation of the clean substrate surface by the deposited monolayer. The center of gravity of the d-bands of Pd lies substantially higher than that of Ag so that the Pd overlayer presents a strong repulsive perturbation to the Ag surface [2]. We show below that this results in converting weak surface resonances in pure Ag to bound interface states and in surface states above the subbands localized almost entirely in the overlayer. On the other hand, the Ag d-bands lie below the Pd d-bands so that the Ag overlayer presents an attractive perturbation to the Pd surface [6]. This results in converting the bound surface state above the subband (x 2 - y2) and the strong surface resonance at the upper subband edge ( x y ) [1] to weak interface resonances and in surface states below the subbands localized primarily in the overlayer. Figs. 1 and 2 show A ( O , a , p ; E ) , a = x 2 - y2, x y , p = 1, 2, 3, 4 and c~ (i.e, infinite crystal), for a complete pseudomorphic overlayer of Pd/Ag(001) and Figs. 3 and 4 corresponding results for Ag/Pd(001 ). Note that the presence of the Pd (Ag) overlayer produces modifications of the Ag (Pd) clean surface states but the interferences remain, manifesting themselves as oscillations in the DOS. Once again, the results can be fitted quantitatively

M. V Ganduglia-Pirovano et al./Surface Science 331-333 (1995) 691-696

693

Pd/Ag(001) x~-y2 subband

m=2

rn=l

m=3

k._,

,

-0.5

,i

.0~.3

E

,

-0.5

-0.3

E F -0.5

-0.4

m=rnc~

m=4

J2 <

J -0.5

-0.4 Energy (Ry)

_

L -0.4

-0.5

Fig. 1. The dotted lines are the local density of states for the end site m = 1 and penultimate site m = 2 and first two interior neighbors for the two-site perturbed semi-infinite chain for the values Vl/2t = 9.79 and V2/2t = 1.35. m = moo refers to any site of the unperturbed infinite chain. The solid lines are the x 2 - y2 contributions to the layer- and kll-resolved DOS's at the F point for the ovedayer (p = 1), the interface (p = 2) and top two sample layers of a Pd/Ag(001) surface. The position of the bulk substrate Fermi level is at -0.13 Ry. Note that the energy scale for m = 1 differs from that for m = 2 and both differ from that for m = 3, 4 and bulk.

Pd/Ag(001) xy subband

m=l

-0.6

m=2

-0.5

-0.4

-0.3

..,=_

-0.7

m=3

-0.6

-0.5

-0.4

-0.7

-0.6

-0'.5

m=mc~

m=4

v

< -0.7

-

,

-0.6 -0.5 Energy (Ry)

i

-0.7

-0.6

-0.5

I

Fig. 2. The same as in Fig. 1 but for the xy-subband and for the values Vi/2t = 4,35 and V2/2t = 0.73. Here the energy scale for m = 1 differs from that for m = 2 and both differ from that for the other cases.

M.V. Ganduglia-Pirovano et al./Surface Science 331-333 (1995) 691-696

694

Ag/Pd(001) x2-y2 subband

m=l

I

-0.5

I

m=2

m=3

i

-0.3

E'F -0.5

-0.3

m=4

E'F -0.3

-0.2

E'F

lm=m~

v

..,¢= ,< -0.2 E Energy (Ry)

-0.3

-0.3

-0.2

E'F

Fig. 3. The dotted lines are the local density of states for the end site m = 1 and penultimate site m = 2 and first two interior neighbors for the two-site perturbed semi-infinite chain for the values V~/2t = -3.92 and V2/2t = 0.24. m = m ~ refers to any site of the unperturbed infinite chain. The solid lines are the x 2 - y 2 contributions to the layer- and kll-resolved DOS's at the r point for the overlayer (p = 1), the interface (p = 2) and top two sample layers of a Ag/Pd(001) surface. The position of the bulk substrate Fermi level is at -0.16 Ry. Here the energy scale for m = 1 and 2 differs from that for m = 3, 4 and bulk.

Ag/Pd(001) xy subband

m=l

Jr

J -0.7

-0.6

-0.5

m=3

m=2

-0.7

i

-0.6

-0.5

-0.7

l -0.6

-0.5

i

m=4

m=mc<3

v

< -0.7

-0.6

-0.5 Energy (Ry)

,

i

-0.7

-0.6

-0.5

Fig. 4. The same as in Fig. 3 but for the xy-subband and for the values Vj/2t = - 1 . 4 6 and V2/2t = 0.07.

M.V. Ganduglia-Pirovano et al./Surface Science 331-333 (1995) 691-696 by a simple one-dimensional model, but now with a perturbing potential VI on the end site and V2 on the penultimate site. In the two-site perturbed 1D semiinfinite chain, the question of the existence of discrete levels is slightly more complex than for the onesite perturbed case. To illustrate this increased complexity, we point out that Economou has examined the case of two nearest-neighbor impurities in an infinite chain [7]. The qualitative behavior of that model is that the V1-V2 plane is separated by two hyperbolae (V1/2t) - l + ( ½ / 2 t ) -1 = - 2 and (Vi/2t) -I + (V2/2t) - l = 2 into regions such that outside them one or two discrete levels, i.e. true bound states, appear below and/or above the band energy interval. The region where no discrete levels appear collapses to a single point, namely the origin of the Vi -V2 plane. We have derived similar equations for a semi-infinite chain and for the perturbed sites being the terminal and the penultimate ones. The boundaries are the hyperbolae (2 - 2t/V1 ) ( 4 - 2t/Vz) = 4 governing bound states above the continuum and (2 + 2t/Vl ) (4 + 2t/V2) = 4 governing bound states below the continuum. The main qualitative difference from the infinite case is the existence around the origin of the V1-V2 plane of a region where no discrete levels appear at all. We have calculated the local density of states at any site m = 1,2 . . . . . ~ for a 1D semi-infinite chain with a perturbing potential Vl on the end site and !/2 on the penultimate site. By fitting the results of this model to the calculated DOS A ( O , a , p ; E ) , a = x 2 - y2, xy, p = 1, 2, 3, 4, and ~z for the P d / A g ( 0 0 1 ) and A g / P d ( 0 0 1 ) surfaces, four sets of (VI,V2) values were determined. For P d / A g ( 0 0 1 ) , we examine the case where both V1/2t and Vz/2t are positive. In Fig. 1 the local DOS for the terminal site (m = 1 ), the penultimate site (m = 2), and the two interior atomic sites for the two-site perturbed 1D-semi-infinite chain for the case V1/2t = 9.79, V2/2t = 1.35 (2t = 0.03 Ry) are compared with the calculated x 2 - y 2 subband contributions to the spectral DOS at F for P d / A g ( 0 0 1 ) . The corresponding results are shown in Fig. 2 for the xy subband for Vl/2t = 4.35, V2/2t = 0.73 (2t = 0.06 Ry). First, we note that very strongly bound overlayer states are formed both for x 2 - y2 and xy subbands. These are localized almost entirely within the overlayer (p = 1) at - 0 . 1 3 Ry and - 0 . 3 4 Ry, respectively. There is at most a few percent leakage of probability into the Ag interface layer adjacent to the

695

overlayer, Moreover, the energies at which they occur are very close to the tops of the bulk bands in pure Pd and correspond closely to the positions of the surface bound state for x 2 - y2 and surface resonance xy in Pd(001), when measured with respect to the corresponding bulk substrate Fermi level [ 1]. These results would suggest that the selfconsistent potential in the Pd overlayer and in the vacuum layer is close to that of pure Pd(001 ) and that the effect of the Ag substrate is simply to remove the coupling to the bulk, leaving strictly two-dimensional Bloch states in the Pd overlayer. However, we mention that there are significant changes when one considers states with different symmetries along other symmetry directions in which states no longer retain the character they have in the isolated monolayer [8]. Second, we note that the increased repulsive potential of Pd pushes an existing x 2 - y2 surface state on pure Ag further above the band, resulting in an interface bound x 2 - y2 state at - 0 . 3 8 Ry (p = 2), and turns an existing xy resonance into a bound interface state at - 0 . 5 3 Ry (p = 2). The interface bound states are primarily localized in the interface layer with just a bit leaking up into the overlayer and decrease monotonically in probability as one proceeds inwards. Finally, we point out that the resulting fits for the full energy and layer dependence are once again extraordinary and that we can clearly demonstrate the existence of surface and interface bound states, interface resonances, and interferences of a particularly simple nature at kll = 0. The model enables us to understand A g / P d ( 0 0 1 ) equally well. For this system, we examine the case V2/2t > 0 but V~/2t < 0. In Fig. 3 the local DOS for the terminal site (m = 1), the penultimate site (m = 2), and the two interior atomic sites for the two-site perturbed 1D-semi-infinite chain for the case 1/I/2t = - 3 . 9 2 , V2/2t = 0.24 (2t = 0.05 Ry) are compared with the calculated x 2 - y2 subband contributions to the spectral DOS at [" for A g / P d ( 0 0 1 ) . The corresponding results are shown in Fig. 4 for the xy subband for VL/2t = - 1.46, Vz/2t = 0.07 (2t = 0.09 Ry). The additional attractive potential that Ag presents to Pd substantially reduces V2 and pushes the discrete surface levels for pure Pd down all the way inside the continuum [ 1 ]. where they become greatly weakened interface resonances (p = 2) at the subband tops (for x 2 - y2 at - 0 . 1 6 Ry and for xy at - 0 . 4 0 Ry)

696

M.V. Ganduglia-Pirovano et al./Surface Science 331-333 (1995) 691-696

Moreover, that attractive potential produces a highlylocalized overlayer state ( p = 1 ) below each subband (for x 2 - y2 at - 0 . 3 9 Ry and for x y at - 0 . 6 2 Ry) 2 The values o f V1/2t and V2/2t we obtain for the four cases studied are all consistent with the criteria for existence o f discrete level(s) discussed above. The earliest surface-state calculation using a Green's function formalism to investigate the density of states o f both extended and surface states in semi-infinite crystals was performed by Kalkstein and Soven, who analysed the case o f a non-degenerate band in a simple cubic lattice [9]. In the previous [ 1 ] and present work, we have analysed the results of first-principles electronic structure calculations o f realistic bare metallic surfaces and ultrathin overlayers deposited on metal substrates, in an attempt to further our understanding of transition-metal surface and interface state properties. The similarity of these x y and x 2 _ y2 subband contributions to the kll, symmetry-, and layer-resolved densities of states at kLi = 0 to the simple 1D-semi-infinite models enables us to analyse the existence condition for bound surface and interface states o f that particular symmetry at the (001) surface o f Pd, Ag, P d / A g ( 0 0 1 ) and A g / P d ( 0 0 1 ) as examples. We have shown that a simple 1D-model can account quantitatively for essentially all of the basic features o f the electronic structure o f the overlayer and substrate including overlayer and interface bound states and resonances and interference phenomena.

2 The finite width of the overlayer aad interface bound states shown in Figs. 1-4 for the simple model arises from the fact that it is not strictly A(0, a, p; E) which we compute but l/or times the imaginary part of the Green's function at E - is with s = 1 x 10-3 Ry. The greater broadening of the peaks in A(0, or, p; E) and the filling in of the minima apparent in the computations are artifacts which can be eliminated.

Acknowledgements This work is part o f the program o f the Consortium on "The Physical Aspects of Surface Chemistry on Metals, Alloys, and Intermetallics". M.V. GandugliaPirovano would like to thank Professor E Fulde for his hospitality at the Max Planck Institute in Stuttgart, where part o f this work has been carried out. One of us (J.K.) acknowledges the financial support from the Grant Agency o f the Czech Republic (Project No. 2 0 2 / 9 3 / 0 6 8 8 ) and the Austrian Science Foundation (P10231).

References l 1] M.V. Ganduglia-Pirovano, M.H. Cohen and J. Kudmovsk3~, Phys. Rev. B 50 (1994) 11142. [21 J. Kudmovslo), I. Turek, V. Drchal, P. Weinberger, N.E. Christensen and S.K, Bose, Phys. Rev. B 46 (1992) 4222. [31 J. Kudmovsk~,1. Turek, V. Drchal, P. Weinberger,S.K. Bose and A. Pasturel, Phys. Rev. B 47 (1993) 16525. 14] B. Wenzien, J. Kudmovsk2~,V. Drchal and M. Sob, J. Phys.: Condensed Matter I (1989) 9893. [51 M.H. Cohen, M.V. Ganduglia-Pirovano and J. Kudrnovsk~, Phys. Rev. Lett. 72 (1994) 3222. [6] M.V. Ganduglia-Pirovano,J. Kudrnovsk~,I. Turek, V. Drchal and M.H. Cohen, Phys. Rev. B 48 (1993) 1870. [7] E.N. Economou, Green's Functions in Quantum Physics, Vol.7 of Springer Series in Solid-State Sciences, Eds. M. Cardona, P. Fulde and H.J. Queisser (Springer, Heidelberg, 1983) ch. 7. [8] O. Bisi and C. Calandra, Surf. Sci. 67 (1977) 416. 19] D. Kalkstein and P. Soven, Surf. Sci. 26 (1971) 85.