Surface state effects on the electroreflectance spectroscopy of Au single crystal surfaces

J Electroanal Chem, 176 (1984) 325-338

325

Elsevwr Sequoia S A , Lausanne - Printed in The Netherlands

S U R F A C E STATE EFFECTS O N T H E E L E C T R O R E F L E C T A N C E S P E C T R O S C O P Y OF Au SINGLE CRYSTAL S U R F A C E S

S H. LIU

Sohd State Dwtston, Oak Rtdge Nattonal Laboratory *, Oak Rtdge, TN 37831 ( U S A ) C H I N N E N , C N G U Y E N V A N H U O N G and N R DE TACCONI **

Laboratotre d'Electrochtmte lnterfactale du C N R S, 1, PI A Brtand, 92190 Meudon -Bellevue (France) K M . HO

Ames Laboratory--USDOE*** and Department of Physws, lowa State Unwerstty, Ames, 1,4 50011 (USA) (Received 27th February 1984; m revised form 28th March 1984)

ABSTRACT The electroreflectance spectra of Au (100), (110) and (111) surfaces are interpreted with success in terms of optical transitions revolving surface states. It is revealed that there are subtle differences m structure between the metal surface m contact with an aqueous solutmn and the same surface in vacuum

INTRODUCTION

Electroreflectance (ER) spectroscopy has been a valuable tool in probing the microscopic nature of the metal electrolyte interface. In a series of recent articles the ER spectra of single crystal surfaces of Ag are successfully interpreted in terms of optical transitions between electron levels on the metal surfaces [1-3]. The signal at 4 eV photon energy seen on all surfaces arises from lnterband transitions in the bulk band structure. The additional absorption features are due to transitions involving surface states as either the initial state or the final state or both. These features are very sensitive to the bias potential, and this effect has been shown to originate from the Stark shift of the surface states. The width of the absorption line reflects the random nature of the dipole field generated by the water molecules near the metal surface.

* Operated by Umon Carbide Corporation for the U S Department of Energy under Contract W-7405eng-26. ** On leave from the "Instltuto de Investlgaclones FlSlCOquirntcas Teoricas y Aphcadas" (I N I F T A ), 1900 La Plata, Argentina * * * Operated for the U S. Department of Energy by Iowa State University under Contract W-7405-eng82. Tlus research was supported by the Director for Energy Research, Office of Basic Energy Sciences 0022-0728/84/$03.00

© 1984 Elsevier Sequoia S A.

326

In this paper we carry out the same study on single crystal surfaces of Au. The two metals have very similar electronic structures in the s, p band region, but the 5d band of Au is broader and closer to the Fermi level than the 4d band of Ag. This latter fact is responsible for the difference in the optical properties of these metals. In the following we will outline our theoretical and experimental investigations of Au single crystal surfaces and explain the observed ER signals in terms of the theoretical results. THEORETICAL INVESTIGATION

We have used the first principles self-consistent pseudo-potential method to investigate the electronic structure of the bulk and the surfaces of Au [4,5]. We include s, p and d electrons in the trial wavefunction. The surface is simulated by periodic slabs each seven atomic layers thick and separated from the neighboring slabs by empty spaces of two atomic layers wide. We have neglected the spin-orbit coupling of the 5d electrons. As a result the bulk band structure is not very accurate in detail, but is adequate for the calculation of integrated properties. Since the surface states have s or p symmetry, they are affected insignificantly by the spin-orbit interaction. The bulk band structure is plotted in Fig. 1. From this result we generate the projected band structures for the (100), (110) and (111) surfaces as shown in Figs. 2 - 4 as the shaded regions. The surface states, also shown in these three graphs, are found by performing the surface band calculations. They appear as extra energy levels in the gaps of the projected bulk bands. As a double check the wavefunctions of the surface states have been calculated and found to be highly locahzed within the first two or three layers of the surface. As a typical example the probability density of the surface state on Au (111) is plotted in Fig. 5.

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The bias field is simulated by an applied potential with a long wavelength [1]. After reaching self-consistency the potential reside the metal slab is screened out completely, and the potential in the gap outside the slab imposes an electric field on the surface. The surface states are very sensitive to the field because they are situated where the field is not screened. We determine by self-consistent calculations the energy of the surface states for a range of b~as field. The optical absorption spectrum is determined by calculating the dipole matrix elements and joint density of states between the filled and the empty states. For noble metals it is sufficient to sample a small region in the Brillouin zone around the

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L point in Fig. 1. This point is projected onto X for (100), X and M for (110) and for (111) surfaces. By doing these calculations we locate the energetic position of the expected absorption features for neutral as well as charged surfaces. Finally, we use the induced charge on the metal surface to relate the theoretical bias field to the experimental bias potential. The charge is calculated from the field by electrostatics. Experimentally the charge is determined as a functton of the bias potential by integrating the differential double layer capacitance. The comparison between theory and experiment will be carried out in the last section of this paper.

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329 EXPERIMENTAL The electrodes were single crystal discs of (111), (100) and (110) orientations, prepared by mechanical and electrochemical polishing as described earlier [6]. The electrolytes are 0.01 M N a F (pH = 5) and 0.01 M HC104 (pH 2) solutions, made of suprapur chemicals and highly purified water (provided by a super Q Millipore system). The use of 0.01 M HC104 allows us to reach high positive potentials and then large positive charges without introducing any oxide layer on the electrode. The fluoride and perchlorate anions do not adsorb at the surface of the electrode, so the layer adjacent to the electrode is almost entirely composed of water molecules. The potentials are measured and quoted with respect to a mercurous sulphate electrode (MSE) whose potential difference with a saturated calomel electrode (SCE) is - 0 . 4 V (UMs E = Use E - 0.4). The experimental techniques and apparatus used for obtaining the electrical admittance Ot/OU and the differential reflectivity (1/R)(OR/OU) have been described previously [7]. Briefly, a dc bias is applied to the electrode and superimposed on it is an ac bias of small amplitude ( 0 U = 50 mV rms) and low frequency ( f = 15 Hz). An optical set up allows us to measure the relative change of the reflectivlty R due to this alternating perturbation DU. The electrical and optical responses are analyzed simultaneously by two lock-in amplifiers. The data are acquired and treated immediately with the aid of a microcomputer. We exhibit the electroreflectance (ER) by plotting the differential reflectance (1/R)(OR/ao) vs. the induced charge density on the electrode. Optical measurements were performed at nearly normal incidence, with a polarized light, in the 2 - 4 eV energy range. The charge

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330

density of the electrode was calculated by integrating capacity-potential curve (C(U)), the potential of zero charge being located at the minimum of the C(U) curve. Before the experiments, a procedure of " i n situ" cleaning of the electrode surface is performed. It consists of a series of voltage sweeps during which the electrode surface is oxidized then subsequently reduced. The cleanliness of the surface is checked by characteristic voltammograms and capacity curves [6]. After the cleaning procedure the potentials are limited to a range where no electrochemical process takes place. In the case of the Au (100) plane, even within this potential range where the electrode behaves as a pure capacitor, the superficial characteristics of the electrode in terms of C(U) and ER depend on the negative potential of the polarization domain as is shown in Fig. 6. There are two extreme types of capacmve and optical behavior corresponding to structures called here a and b for which the most negative potential reached is respectively - 1.1 V and - 0.55 V [8]. C O M P A R I S O N BETWEEN T H E O R Y A N D E X P E R I M E N T

Au (100) A set of ER signals for Au (100) is shown in Fig. 7. In this graph the differential reflectance is plotted versus the photon energy, with surface charge as a parameter. The signal nses at around 2 eV of photon energy due to the onset of interband transition from the filled d band near L to the p band at the Fermi level (see Fig. 1). Between 2.5 and 3.5 eV the signal makes a large swing such that the actual absorption curve has a bell shape with m a x i m u m at the point where the signal

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crosses the horizontal axis. Clearly the energy of maximum absorption depends strongly on the surface charge, which measures the bias potential. Above 3.5 eV the signal again drops significantly to suggest a second absorption feature. However, the ER signal fails to cross the horizontal axis presumably because the lnterband transition contributes to a sloping background. Nonetheless, the minimum is seen to shift with the bias potential. In our electromc structure calculation for Au (100) we find two unoccupied bands of surface states, labelled A and B, around X (Fig. 2), which is the projection of the L point of the bulk Brillouin zone. Optical transitions are possible by exciting an electron from the bulk d band into these two surface bands. The energetic positions of the two resulting absorpuon features are compared with the experimental results m Figs. 8-10. In making the comparison we face the difficulty of locating the center of the absorption features from the data, especially the one near 4 eV. Since it is relatively easy to locate the minima of the ER signals, we make a somewhat arbitrary choice by comparing the positions of the minima with the calculated absorption energies. This choice certainly underestimates the absorption energy, but the error is of the order 0.2 eV, which is roughly the uncertainty in the surface band calculation. In Fig. 8 we summarize previous data from other laboratories, published and unpublished, plotted versus the bias potential [9-11]. The sohd curves are the calculated results. There is good agreement between theory and experiment in the 2-3 eV feature. The much larger discrepancy in the 4 eV feature must be due in part to our inability to identify the absorption energy from the data. What is noteworthy is that the observed bias dependence is faithfully reproduced by the calculation. Our data for Au (100) in N a F and HC104 are in Figs. 9 and 10, m which the absorption

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energies are plotted as functions of the surface charge. The hnearity of the absorption energy vs. charge plots demonstrates clearly that the surface states undergo linear Stark shifts relative to the bulk states. It can be noted that the agreement between experimental data and theoretical predictions for large charge values is better in the case of HC104 solution than in the case of NaF. The discrepancy in the latter case may be explained by the incipient oxidation of the surface [12]. It is also interesting to note that the two assumed surface structures a and b y~eld the same curves. Apparently the two structures are not different enough to cause a visible change in electromc structure. The lower surface band B has been seen by angle resolved photoemisslon [13,14]. Since only occupied states can be seen by photoemisslon, this experiment contradicts our finding that the surface band B is empty. On the other hand, a band model with occupied surface band B can not explain the ER experiments because these states are not available as final states of optical transition. We must conclude from these conflicting facts that: (a) the surface in ER experiment is not the same as that in photoemisslon experiment, and (b) the theoretical surface model represents more closely a metal-electrolyte interface than a metal-vacuum interface. Au (100) in vacuum undergoes a 5 × 20 reconstruction [15], and this is not incorporated into the theoretical model. We are led to speculate that the surface state is sensitive to surface reconstruction, and the presence of an electrolyte helps to relieve the strain on the metal surface so that the (5 x 20) reconstruction is inhibited. In this way, neither a nor b "structures" would correspond to such a reconstructed surface.

Au (11o) The L point in the bulk Brillouin zone projects onto the points X and M of the (110) surface (Fig. 3). The M point is unmterestmg from the optical point of view because there is no band gap. Two bands of surface states A and C are found around X. We expect a strong absorption feature due to excitations from the occupied state C to the unoccupied state A. The excitation energy is 1.3 eV for the neutral surface and shifts slightly with bias potential. In addition we find two weaker absorptions due to transitions from two different initial states in the bulk d band complex to A. The intensities of all three absorption features are sensitive to the photon polarxzation such that they are present when the polarization vector ~ It [001] and absent when ~ II [110]. As predicted by out calculations, there is no appearance of absorption features with changes on the measured E R spectra for ~ II [110] (Fig. 11) for ~ II [001], there appear one or two minima as shown in Fig. 12. We associate the minima with surface state absorptions, and the measured energetic positions agree quite well with predicted ones, as shown in Fig. 13. The two theoretical hnes are not parallel. The lower line reflects the Stark effect of the surface state, because the initial state is at the top of the bulk d band. The upper line comes from excitations of deeper d levels, and we observe that the wavefunction of the surface state changes with bias in a subtle way so that the initial state which gives the maximum dipole moment tends to

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335

move down when the surface bias is more positive. We are not certain whether the data support this observation. All three sets of data m the 3 eV region show a distinct dip in transition energy vs. surface charge. There is no evidence of this behavior in our calculated results. There may be a totally different explanation of the ER data. Au (110) surface in vacuum reconstructs in a massive manner [16,17]. It is conceivable that the surface does not remain simple in an electrolyte. A 2 × 1 reconstruction can shift the energies of the surface states and split them into pairs. If this is the case the two ER features may both be attributable to the predicted strong C and A absorption. Our oversimplified surface state calculation has revealed some subtle problems that merit closer investigation. Kolb et al. [18] reported a low energy absorption feature for ~ II (001) for a nearly uncharged surface. This result is not yet firmly established and it is unclear whether this feature is related to the C to A transition anticipated by our calculation. The occupied surface state C has been seen by photoemission [13,14]. There is reasonable agreement between theory and experiment.

Au (111) A band of partly occupied surface states is found around F (Fig. 4), which is the projection of the L point of the bulk crystal. The surface band is sensitive to the bias

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336

such that it moves above the Fermi level when the surface charge reaches 18.5 /LC/cm 2. We expect a surface state absorption feature to appear just above the bulk interband threshold when the surface is biased sufficiently in the posmve dlrectton. The experimental results, shown in Fig. 14, contain such a feature for surface charges of 10 f f C / c m 2 and higher. The discrepancy between theory and experiment can be caused by a small error in the theoretical deterlmnatlon of the surface state energy, about 0.1 eV too low. The Stark shift of the surface state is very well reproduced by the calculation, as shown in Fig. 15. The experimental curves in Fig. 14 exhibit a m l m m u m around 3 eV. This feature shifts with the bias, so it must be related to the surface band. We find that the unfilled part of the surface band gives rise to an absorption band starting at the bulk interband threshold and ending at the point where the surface band merges into the bulk band. We propose that the minimum near 3 eV is caused by this absorption band. On Fig. 15 we compare the center of the absorption band with the position of the minimum for a range of charge to show that there is good agreement between theory and experiment. The occupied part of the surface band has been mapped out by photoemission [13,19]. The calculated energy is higher than the experimental result by about 0.2 eV. Recall that the calculated surface state energy is too low compared with ER experiments. Thus, we again see evidence that the presence of an electrolyte causes the surface state to shift upward in energy, presumably by either inhibiting surface relaxation and reconstruction or by promoting a different kind of surface arrangement from the m e t a l - v a c u u m interface.

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ACKNOWLEDGEMENTS

We would like to acknowledge the fact that this collaboration (between C. Hlnnen, C. Nguyen, N. de Tacconi, and S.H. Liu and K.-M. Ho) began during a CECAM workshop at Bellevue, April 1983, organized by Roger Parsons who also stimulated this work in Bellevue. REFERENCES 1 2 3 4 5 6 7 8 9

K - M . Ho, B N H a r m o n and S H Lm, Phys Rev L e t t , 44 (1980) 1531. D.M. Kolb, W Boeck, K -M Ho and S H Llu, Phys Rev Lett, 47 (1981) 1921 K - M Ho, C -L. Fu, S.H Llu, D.M. Kolb and G. Piazza, J Electroanal C h e m , 150 (1983) 235 M L Cohen, M Schluter, J.R Chehkowsky and S.G Loule, Phys Rev B, 12 (1975) 5575 D.R. H a m a n n , M Schluter and C. Ctuang, Phys Rev Lett, 43 (1979) 1494 C. Nguyen van Huong, C. Hlnnen, J Lecoeur and R Parsons, J Electroanal Chem., 92 (1978) 239 J P. Dalbera, C H m n e n and A Rousseau, J Phys. C, 38 (1977) 185 C Hmnen, C Nguyen van Huong and J-P. Dalbera, J Ctum P h y s , 79 (1982) 37. R Kofman, R Garngos, L Dutell and P. Cheyssac, J Electroanal C h e m , 150 (1983) 253, and their earher papers cited thereto. 10 W. Boeck and D.M Kolb, Surf ScL, 118 (1982) 613 and unpubhshed 11 D.M. Kolb and G. Piazza, unpubhshed

338 12 13 14 15 16 17 18 19

C. Nguyen van Huong, C Hlnnen and R Parsons, J Electroanal. Chem, 106 (1980) 185. G V Hansson and S.A. Flodstrom, Phys Rev B, 18 (1978) 1572. P. Helmann, J Hermanson, H Mlosga and H Neddermeyer, Phys. Rev Lett., 43 (1979) 1757. J.F. Wendelken and D M Zehner, Surf Scl., 71 (1978) 178 J R. Noonan and H.L. Davis, J. Vac SCL Technol, 16 (1979) 587 L.D Marks, Phys Rev. Lett, 51 (1983) 1000. D M Kolb, unpubhshed. Z Hussaan and N.V Smith, Phys Lett A, 66 (1978) 492.