Angular dependence of photoemission from intrinsic surface states on W(100)

Solid State Communications, Vol. 18, pp. 13 15—1319, 1976.

Pergamon Press.

Printed in Great Britain

ANGULAR DEPENDENCE OF PHOTOEMISSION FROM INTRINSIC SURFACE STATES ON W(100) R.F. Willis, B. Feuerbacher and B. Fitton Surface Physics Group, Astronomy Division, European Space Research and Technology Centre, Noordwijk, Holland (Received 20 December 1975 by A.R. Miedema) Angle-resolved photoemission measurements of the intensity of the intrinsic surface state feature on W(100) are presented, and its dispersion relative to the (10) and (11> symmetry directions in the surface Brillouin zone determined. The results are discussed in terms of existing theories of spin— orbit coupling between d-bands and local density of states effects at transition metal surfaces. A PRONOUNCED FEATURE found in fleld-emission energy-distribution spectra from the W(100) crystallographic plane has attracted a great deal of attention. This peak, located at 0.35 eV below the Fermi level, was first observed by Swanson and Crouser.1 Energy distribution spectra of field emitted electrons may be related to the local density of states at the surface.2 On the basis of calculations of possible surface states on d-band metals,3 Plummer and Gadzuk4 proposed that the origin of the feature in the W(100) spectrum was due to field emission from a surface state associated with a gap between the spin—orbit split d-bands along the [‘H symmetry direction of the b.c.c. Brillouin zone. An analogous feature located about 0.4 eV below EF and highly sensitive to low-coverage gas adsorption was subsequently observed in the energy distribution of electrons photoemitted from W(l00) surfaces.5’6 The band structure of Mo is very similar and a related peak, though reduced in intensity, has also been reported in field emission7 and photoemission8 from Mo(lOO). The peak in question is strongest for photoemission into a narrow angle about the direction normal to the W(100) surface.6 Electron emission in this case is resolved such that momentum parallel to the surface is zero, k 11 0. Since the parallel k-vector relates component conserved, this implies that the spectrum to theisone-dimensional density of states along the [‘Hsymmetry line if Umklapp effects are neglected.9 Similarly, it has been argued2 that field emission also measured electrons with momentum normal to the surface only, the tunnelling probability being highest in this case. However, although the resemblance of the field emission, photoemission and calculated one-dimensional density of states at the surface is good there are significant points of discrepancy between them,10 and between existing theories, which raise doubts as to the detailed interpretation of the origin of this feature. Starting from a three-band model, tight-binding fit —

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to an energy band calculation of the bulk crystal’1 along the [‘Hsymmetry line in the Brillouin zone, Feder and Sturm12 have noted that for energies within a range of a few eV below EF, spin—orbit coupling produces two gaps; a “relative gap” and an “absolute gap” between the three d-bands’3 of symmetry /.~7.The numerical application of a Green’s function formalism to the determination of the local densities of states in the surface region predicts a very pronounced surface “resonance” in the relative gap, 0.4 eV below EF, and a ~-shaped surface “state” in the absolute gap, 1.5 eV below EF. Only one peak, 0.3 5—0.4 eV below EF, has clearly been resolved in both photoemission and field emission spectra, its high intensity and sensitivity to surface contamination indicating that it is associated with a surface feature. An augmented-plane-wave calculation, including relativistic corrections, by Christensen’4 places the upper i~,d-band above EF, in agreement with Fermi surface studies,’5 such that the surface state associated with the “absolute” gap now shows the closest agreement with the experimental results. On the other hand, Kasowski’6 has shown, on the basis of an ab-initio linear-combinationof-muffin-tin-orbitals technique, that the energy associated with the formation of an s—dy surface states, 3 isasmuch originally by effects, Forstmann larger thanproposed spin—orbit and and that Pendry, surface reconstruction could cause such states to shift up into the energy region where the observed peak occurs. The fact that the origin of the peak may not be due to spin—orbit coupling is also implied by calculations of the local densities of states on successive atomic layers of cleaved Mo and W surfaces [Desjonqueres and Cyrot-Lackmann (l975)].’~Using the moments method in the continued fraction technique, based on a tight-binding approximation, these workers found that a sharp structure in the surface local density of states, just below EF, appears irrespective of whether spin—orbit coupling is included in the calculations or not. They suggested that, contrary

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INTRINSIC SURFACE STATES ON W(100)

Fig. 1. Schematic of angle-resolved photoemission arrangement. The 127°electrostatic analyzer moves in a plane at right angles to that containing the light beams and the surface normal direction, as defined by the slit in the spherical metal screen. The analyzer entrance slit is normal to this plane, so a 2°x 2°angular range is sampled. to the conclusions by Sturm and Feder,’2 the observed surface-state effect is not necessarily due to k = 0 states within the snin—orbit ~an Discrepancies exist also on the width of the structure under discussion. The calculated spin—orbit induced surface resonance12 is smaller than the observed peak widths by a factor of lOin the case of field emission, and by 20—40 times that observed in photoemission, depending on experimental conditions. It has been argued’2 that the photoemission peak is broader because a larger region of k-space, k~ 1~ 0, is 6sampled due to the finite size Measurements with smaller of the electron slit.do not produce a peak which collection angles,analyzer however, is noticeably narrower,10 even allowing for the finite experimental energy resolution. Also, the mechanism of field emission itself is not sufficiently well understood that contributions to the tunnelling probability from states with k~ 1~ 0 cannot be discounted. Calculations 18 have recently indicated that by Nicolaou states withand k Modinos 1 may contribute signifias large as current 0.4A responsible for the obcantly to the11 tunnelling served W(100) peak. The tight-binding results by Desjonquères and Cyrot-Lackmann’7 are also integrated over all parallel k-vector components. Their theoretical resolution is only about 1 eV, so ajudgement of the width of the features from this calculation is not possible. It is apparent that, in spite of the widespread interest in this specific feature, its origin is debatable. In order to provide therefore studiedmore the k experimental information, we 11 dependence of the peak assigned to a surface resonance on W(l00) by measuring photoemission spectra in various directions about the surface normal. In the present paper, we present the results of

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Fig. 2. Energy distribution spectra of photoelectrons emitted into a narrow angle (2°x 2°)about directions corresponding to normal the polar angle U (0 increasing in 5°steps from the surface direction = 0°)for the (11) azimuth of a W(l00) surface at a photon energy, hw = 10.2 eV. Energy resolution = 0.2 eV. angle-resolved measurements on the intensity of the “surface resonance peak” observed in photoemission from W(lOO), and its dispersion relative to the (10) and (11) symmetry directions of the surface Brillouin zone. experimental arrangement is shown callyThe in Fig. 1. A spherical metal screen of 25 schematimm radius ensures a field-free region around the target crystal T. A slot in the screen of width 1 mm, together with the entrance-slit dimensions of a 127°electrostatic analyzer, limits the acceptance angle to about 2°x 2°.The analyzer itself was operated at an energy resolution of 0.2 eV, and rotated in 2.5°steps in athe plane normal to that containing the light beams and surface normal direction. Light of energy hw = 10.2eV was excited in an intense hydrogen-discharge source, operated under such conditions that essentially only the 10.2 eV resonance line was produced.’9 The light source was sealed off with a MgF 2 window to the vacuum chamber, which was maintained at a pressure of about 2 x lOb0 torr during the measurements. The preparation and maintenance of a clean crystal surface was by successive heating cycles in oxygen atmosphere followed by subsequent flashing to temperatures in excess 6 of 2500°C,as described in a previous publication. Typical energy distribution spectra of photoelectrons emitted into a narrow angle (2°x 2°)about directions corresponding to U increasing in 5°steps from the surface normal direction (0 = 0°)to 0 = 25° in the (11)

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INTRINSIC SURFACE STATES ON W(lOO) 20

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Fig. 3. Surface-state peak intensity as a function of polar angle 0 (or 1k11 I) for the two principal azimuthal directions, (10) and (11) of the W(100) surface; hw = 10.2 eV. The error bars represent the standard deviation of 10 separate measurements. azimuth of a W(100) surface are shown in Fig. 2. The intense peak R centered at 0.4 eV represents the feature which is assigned to a surface resonance. The smaller peak B centered about 5 eV is not particularly sensitive to surface conditions, and has been interpreted as arising from bulk k-conserving transitions betweenatthe 20 Feature A, centered upper and islower ~ bands. 2.9 eV, spurious in that it arises as a consequence of a secondary line in the H 2 discharge spectrum, hw = 7.7 eV, producing a lower intensity “shadow” of the Peak~eangle-resolved spectral behaviour of peakR,

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Fig. 2, exhibits four specific features: (1) the peak is sharply defined and most intense for emission normal to the surface (0 = 0°);(2) both the intensity and the position of the peak have been shown to be insensitive to the exciting photon thereproducible range 7.7 ~ shift hw ~in 2°(3) there is aenergy slight,inbut 16.8 eV; peak energy towardsE —EF = 0 with increasing 0 (arrowed, Fig. 2); and (4) the peak intensity decays

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rapidly and its width at half-height broadens from about 0.5 eV for normal emission to about 1.0 eV for 0 10 The peak intensity as a function of k11 for the two principal azimuthal directions, (10) and (11>, of the W(100) surface is plotted in Fig. 3. The angle-dependent data show that the emission associated with peak R (Fig. 2) is confined to a narrow and approximately circular lobe about the surface normal direction. This explains the reduced intensity of peak R observed in photoemission spectra from polycrystalline8 tungsten films or integrated On the assumption that over off-normal peak R is due todirections. emission from a surface :state localized

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Fig. 4. Plot of the dispersion characteristics of the surface state peak as a function of the parallel momentum, 1k111, about k11 = 0, relative to the surface Brillouin zone dimensions in the (10> and (11> azimuths. in the surface plane, but delocalized parallel to it, its dispersion may be determined from a plot of the observed peak-energy shift as a function of polar angle 0. Assuming conservation of k11 at the surface, the magnitude of with respect toof thethe surface Brillouin zone dimensions is1k111obtained. A plot two-dimensional “surfacestate energy-band structure”, of peak R in the W(100)

1318

INTRINSIC SURFACE STATES ON W(l0O)

photoemission spectra, is shown in Fig. 4. The peak intensity reduces to the background level for 0 ~ 20°,so that a shallow parabola extending over an energy range of less than 0.2eV is found, defined only over about 20% of the surface Brillouin zone dimensions. The data shown in Figs. 3 and 4 were averaged over 10 separate spectral measurements, and the error bars represent the standard deviation of the individual data points. Early field emission results21 on the surface resonance structure have also shown a decrease in amplitude combined with a movement of the peak position towards the Fermi level for off-normal directions. This confirms that the results presented here may be interpreted in terms of a (local) density of states rather than a joint density of states that would depend on the final electron state in the photoemission process. A surface feature on a periodic crystal is defined completely by the parallel components of the k-vector. The dispersion relation in Fig. 4 therefore characterizes the structure. No theoretical calculations are available as yet of the dispersion of a possible surface resonance or state. However, as pointed out by Feder and Sturm,’2 the spin—orbit gap will be of different position and width in directions that deviate from [‘H(i.e. 0 0°).Relativistic band structure 4 indeed support this view,calcuand it lations by Christensen’ is apparent that the spin—orbit gap moves closer to the Fermi level and widens away from the [‘Hline, fairly symmetrically with respect to this symmetry line. Such a behaviour is in qualitative agreement with the present observations. There remains however a large discrepancy 12 and experimental5’6 peak betweenforthe theoretical widths emission normal to the W(lOO) surface. Broadening of the resonance due to hybridization with the ~ d-band cannot satisfactorily’2 account for the observed peak width of 0.5 eV for normal emission. The narrow-angle selectivity and the 0.2 eV energy resolution

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of the present measurements would suggest that the observed width is intrinsic. The field emission calculations of Nicolaou and Modinos’8 predict relatively large parallel k-vectors to contribute to the surface state feature; much larger than those found experimentally. It is not obvious what dispersion the latter calculations would predict. The results of Desjonquères and Cyrot-Lackmann17 show a pronounced structure in the local density of states on W(100), whose position and (possibly) width is in close agreement with the experimental data. However, such surface states in the surface local state density have been determined integrated over all k 1~It would be interesting to see whether calculations for particular k11 show dispersion and decay of the peak in agreement with the results presented here. To conclude, the experimental evidence to date, and that presented above, provides support for the existence of a strong, well-defined feature in the density of electron states at the W(100) surface. What remains unclear, however, is the relationship between similar features in the calculated LDS and the energy band structure. Particular relativistic band-structure features may induce a surface resonance which may owing to various state broadening indistinguishable from surface effectseffects associatedbewith “absolute” rather than “relative” band gaps.12”6 On the other hand, spin— orbit coupling effects are not necessarily a prerequisite for sharp features in the surface LDS.’7 In such circumstances, it is important to establish the k 11-dependence of these features, as we ahave above. With this inforniation available, fullyreported self-consistent calculation over all k-points and surface states in the surface Brilbum zone should resolve the remaining ambiguities and discrepancies in interpretation. Acknowledgement The authors thank M. Adriaens for his skilled assistance. —

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MUROTANI T., FUJIWARA K. & NISHIJIMA M., Proc. 2nd mt. Conf on Solid Surfaces, Jap. J. Appi. Phys. Suppl. 2, Pt. 2 (1974); AL KHOURY NEMEH E., CINTI R.C. & HUDSON J.B.,J. Phys. 35, Ll79 (1974). FEUERBACHER B. & WILLIS R.F.,J. Phys. C: Solid State Phys. 8, 169 (1975).

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INTRINSIC SURFACE STATES ON W(lOO)

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STURM K. & FEDER R.,Solid State Commun. 14, 1317 (1974); FEDER R. & STURM K.,Phys. Rev. B12, 537 (1975). The “absolute” gap is only absolute in the sense that decay into the energy-degenerate ~ band is symmetry forbidden. CHRISTENSEN N.E. & FEUERBACHER B., Phys. Rev. BlO, 2349 (1974).

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NICOLAOU N. & MODINOS A, Phys. Rev. BI 1,3687 (1975); MODINOS A. & NICOLAOU N., Phys. Rev. (to be published). STEINMANN W (private communication).

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