The electronic band structure of a material can explain many physical properties such as optical absorption and electrical conductivity. Generally they are described with respect to high symmetry points in the Brillouin zone as discussed in chapter 2.
Experimental techniques [2,3] and theoretical calculations [4] have been the foundation for the current understanding of the electronic structure of the Ag(110) surface. Figure 5.3 shows the surface band structure which was obtained using momentum resolved inverse photoemission spectroscopy at . The states labelled S1 and S2 show the intrinsic surface states at the and points of the surface Brillouin zone respectively.
Figure 5.3: Electronic band structure for the Ag(110) surface [3].
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Goldmann, A., Dose, V. and Borstel, G., Phys. Rev. B. 32
100 5.3.2 Reflection Anisotropy Spectroscopy of the Ag(110) Surface in UHV
The features observed using RAS can provide vital information about the surface structure of Ag(110). The RA profile of the Ag(110) surface in UHV at room temperature is shown in figure 5.4 with three main features labelled a, b and c. The lowest energy feature, a, at 1.70 eV is attributed to a transition between surface states at the point of the surface Brillouin zone [5]. The transition is between an occupied state 0.10 eV below the Fermi level and an unoccupied surface state 1.60 eV above the Fermi level. This feature is sensitive to contamination such as oxygen absorption [6]. These surface states exist in projected s,p-like band gaps of the bulk Brillouin zone. The occupied state has py type character and the unoccupied state has s type character. There is a similar transition between surface states at the point on the Cu(110) surface which will be discussed in detail in chapter 6. However, the peak intensity for the transition on the Cu(110) surface is much higher than the peak intensity on the Ag(110) surface because there are more occupied states present on the Cu(110) surface. This has been confirmed with pseudopotential calculations of the band structure [2]. Another difference is that this transition between surface states at the point on the Ag(110) is the sole contributor to the resulting peak intensity in the RA profile, whereas for the transition on the Cu(110) surface there are other contributions from bulk bands and interband transitions which will be discussed in full later.
101
Figure 5.4: RA profile of Ag(110) at room temperature in UHV. Inset showsn the transition between surface states at 1.7 eV [6].
As seen in figure 5.4 the higher energy features in the RA spectrum are more dominant than the feature attributed to a transition between surface states at 1.7 eV. At ~3.8 eV there is a sharp positive peak followed immediately by a sharp negative feature at ~3.9 eV. These peaks do not appear to be sensitive to surface contamination [5] which suggests this feature is related to the bulk dielectric response. This is further confirmed since interband transitions for silver begin at an energy of ~3.8 eV [8]. In particular, transitions at ~3.9 eV and ~4.1 eV have been attributed to transitions around the L point of the Brillouin zone [17]. At lower energy there is a transition from and at higher energy from as
shown schematically in figure 5.5. There is a further transition shown in figure 5.5 from [9] although this is not discussed in this research.
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Hansen, J. –K., Bremer, J. and Hunderi, O., Surf. Sci. 418 (1998) L58
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Figure 5.5: Schematic diagram about the L point of the Brillouin zone showing three transitions.
The dependence of these peaks on surface morphology has been studied by J. Bremer et al [10] who used RAS alongside STM images to show how the peaks change as the surface changes. When the two peaks are present, STM images show step edges aligned parallel to the crystallographic direction. In contrast, when the lower energy peak is no longer present in the spectrum the steps on the surface have an isotropic structure. This is confirmed theoretically although the theory predicts a much smaller magnitude than is observed by experiment. This discrepancy is explained by the absorption of light by surface plasmons induced by the steps which increase the peak intensity in the RA spectrum. These peaks coincide with the plasmon resonance energy at 3.90 eV [11]. Furthermore the surface plasmons present on the Ag(110) surface show strong dependence on the crystal azimuth [12] which agrees with the results of theoretical calculations [13,14,15]. Consequently, the RA spectrum of the Ag(110) surface in UHV at room temperature may, or may not, include the lower energy peak at 3.80 eV depending on whether the surface possesses terraces parallel to the direction or ordered terraces in no preferred direction.
103 5.3.3 The Temperature Dependence of the Ag(110) Surface
As discussed in chapter 4 understanding how surface properties change with temperature can provide information relevant to many practical applications.
The results of photoemission experiments [16] show that the energy of the occupied surface state reduces linearly as the temperature is increased from 60 K to 450 K at a rate of ~1.7 meVK-1. In addition, RAS experiments have shown that as the temperature of the Ag(110) surface increases the peak energy of the feature that has been attributed to the transition between surface states at 1.70 eV reduces [17]. This is consistent with a decrease in binding energy of the initial occupied surface state, as seen in the photoemission experiments, since when the binding energy of this state is reduced the energy required to induce transitions to the unoccupied state is also reduced. The energy of the unoccupied state is independent of temperature. Consequently, the RA peak attributed to the transition between surface states at the point is shifted to lower energies. Martin
et al [17] also observed the 1.70 eV peak reduce in intensity at temperatures up to ~520 K. Above 520 K the feature is no longer present in the RA profile. The reduced peak intensity as temperature is increased is due to the initial occupied state being shifted up towards, and then over, the Fermi level causing a depopulation of the state. The depopulation of the occupied state reduces the number of possible transitions between the two surface states hence reducing the overall RA peak intensity.
The temperature dependence of the higher energy features at ~3.90 eV also show a decrease in peak energy in the RA spectrum at higher temperatures. The peak energy positions have been observed to vary linearly with temperature and the gradients are shown in table 5.1 alongside gradients calculated using other techniques. In this case the RAS data has been produced using an Ag(110) surface prepared by annealing to 1000 K. By preparing the crystal in this way, the sharp
104 positive feature observed at ~3.8 eV is not present as the terraces on the surface have no particular directional alignment.
Peak Energy (eV) ~3.9 eV ~4.1 eV
Data Set Temperature Dependence (10-4eVK-1)
A ~4.8 ~5.9
B ~8.5 ~8.5
C ~6.6 ~6.0
Table 5.1: Table showing the temperature gradients using various techniques. All values are quoted to an error of 0.1 x 10-4eVK-1.
In table 5.1, A are RAS experiments performed by Martin et al [17], B are experiments using a polarimetric method which measures
[18] and C used
thermoreflectance measurements [19]. Table 5.1 shows reasonable consistency between the three gradients despite the different techniques used.
5.3.4 The Azimuthal Dependent Reflection Anisotropy Spectroscopy of the