Angular dependences in u.v.-photoemission from single crystals of Au

Pergamon Press.

Solid State Communications, Vol. 17, pp. 667—671, 1975.

Printed in Great Britain

ANGULAR DEPENDENCES IN u.v.-PHOTOEMISSION FROM SINGLE CRYSTALS OF Au P.O. Nilsson and L. flyer Department of Physics, Chalmers University of Technology, Fack, S-402 20 Gothenburg 5, Sweden (Received 7 May 1975 by L. Hedin)

Photoemitted electron energy distributions from single crystals of Au at a photon energy of 16.8 eV are reported. Measurements have been taken for different surface orientations and electron emission angles. An anisotropic version of the three step model can describe the main features of the observed data.

THE UV PHOTOEMISSION technique has been successfully applied during the last decade to investigations of the electronic structure of solids. Comparison of measured energy distributions of photoemitted electrons (EDCs) with calculations using a three step model1 has often yielded detailed information about the band structure,2 and further information should be obtained by studying the anisotropy of photoemission.3 A few reports on this topic have already appeared.4 A system which allows the independent variation of the angles of incident photons and emitted electrons without breaking the vacuum has been used in the present measurements.5 The specimens are oriented single crystals which are cleaned in situ by cycles of argon ion bornbardement and subsequent heating. The electrons are analyzed with a deflecting type of cylindrical analyzer. The whole apparatus is connected on-line to a computer which monitors the experiment.

The results reported here are for single crystals of gold, which has two particular advantages. Firstly, pure gold single crystals are easy to prepare and these give rise to experimental EDCs exhibiting well defined peaks; secondly, earlier photoemission studies6 on polycrystalline samples at photon energies below 11.6 eV were successfully analyzed7 using the isotropic three step model. Thus the used band structure could be a good starting point for analysis of other photoemission data from Au. In the present work we have employed higher photon energies (16.8 and 21.2 eV) and therefore extend the earlier isotropic

calculations.7 For a polycrystalline sample, the experimental peaks in the EDCs for 16.8 eV usually appear at 2.6, 3.7, 5.1, 5.8 and 6.3 eV below the Fermi level.8 Our calculations (including a 0.4 eV Lorentzian broadening) yield 2.5, 3.7, 5.1, 5.8 and 6.3 eV, i.e., we obtain just as good agreement as for the case of by ~ 11.6 eV. The agreement is quite satisfactory considenng the current approximations in band calculations and anisotropy effects, which we discuss below. In Figs. 1—3 we show examples of spectra from the three low index faces (100), (111) and (110). The angle of incidence of the unpolarized light, ~L’,is specifled in each figure as is the angular position of the electron detector, 0, for each EDC. For the data presented here, both angles are in the plane perpendicular to the [Oil] axis. The sample orientations were checked by measuring EDCs symmetrically around the normal of the specimen surface. The orientation was found to be correct within the accuracy of the angle measurements (±2°).When the angle of incidence of the light i,li is changed, small variations in the relative amplitudes of the EDC peaks are observed. As the amplitude should be proportional to the dipole matrix element projected onto the electric vector, such variations are expected. The i~dependence of the EDCs does not give direct information about the energy band locations, and we therefore focus our discussion on the 0-dependence. Figures 1—3 show that variation of the detection angle 0 shifts the observed EDC peaks. This qualitative

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668

u.v.-PHOTOEMISSION FROM SINGLE CRYSTALS OF Au

Vol. 17, No.6 (111) A~ hv-16.8.V

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FIG. 1. EDCs from (100) Au for different electron emission angles 0. The bars show calculated peak positions for 0 = 00.

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The experimental peak at 7.3 eV must be associated with transitions from bands I and 2—7, which theoretically give peaks at —6.8 and —7.1 eV(the electron bands are enumerated from low to high energies). The next peak, due to transitions between band 3 and 7, should appear at —4.3 eV. Experimentally, a shoulder is detected at 4.3 eV. A third peak is observed at 3.4 eV, but close to this energy six different band pairs could, according to the band structure, give contributions. An inspection of how the experimental peak is displaced in the non-normally emitted distributions may provide further information about the origin of the main part of this peak. We have obtained atween best fit with the band for transitions beband 5 and 7 and structure between band 4 and 7. The next experimental peak appears at —2.9 eV. Theband structure predicts three possible interband transitions between —2.7 and —2.8 eV, namely 5—9, 6—7, and 5—8, but only the second transition has the observed displacement of the structure towards lower energies for non-normally emitted distributions. The fifth —

observation can be explained with an anistropic version of the three step model where one allows for direct interband transitions in the bulk (including several g-vectors) and for specular refraction through the surface. For high resolution the energy spectrum is then expected to consist of a series of delta functions, each one associated with a transition at a certain k-point between a certain pair of bands. It is evident that by changing 0 other parts of the Brillouin zone are sampled, causing displacements, appearances and disappearances of the delta functions. first examine spectrum from may the (100) 9We shown in Fig. 1.the A simple analysis be perface formed for 0 = o°.If we assume that the prominent excitations are those with the R-vector perpendicular to the surface an inspection of the band diagram7 immediately results in 14 possible transitions. The energies of these are plotted as bars in Fig. 1. In the measured spectrum, 5 clearly resolved structures are detected.

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FIG. 2. EDCs from (lii) Au for different electron emission angles 0. The bars show calculated peak positions for 0 = 00.

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u.v-PHOTOEMISSION FROM SINGLE CRYSTALS OF Au

Vol. 17, No.6

Table I

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FIG. 3. EDCs from (110) Au for different electron emission angles 0. The bars show calculated peak positions for 0 = 0°. observedstructureisapeakat—2.OeV.Inthisregion we have two possible interband transitions, 6—9 and 6—8,at—2.2and—2.3eVrespectively.Thetransition from band 6 to 9 should approach the Fermi level as o increases towards 300, while the transition from band to 8 remains essentially constant around —2 eV. Our experimental peak behaves as is predicted by transitions

669

Theory Energy (eV) k-point (100)-surface —7.1 —6~ —4.3 —3.7 —3.5 —3.5 —3.4 3.2

Experiment Band pair Energy (eV)

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9.

These results are summarized in

When the detection angle 0 is varied from the [100]gradually normal towards direction between the spectrum changes.the For[111] a comparision these experimental results and the model described above, a computer program has been constructed. For a given photon energy we scan the Brillouin zone to locate the k-points and final energies of interband transitions. A number of different reciprocal lattice vectors are then added to the generated k-vectors. The resulting beams are finally transmitted through the surface under specular refraction. This procedure means that we obtam all possible combinations of energies and emission angles. Sometimes detailed comparision with

experimental results becomes difficult because the analysis does not give the correct relative amplitudes. However, we have found no contradiction between the model and the experimental results. In many cases, it is possible to identify the movement of0in specific Fig. 1.transitions,e.g. the peakthe at —2 for 0 towards = 0 When 0 is increased peakeV moves the Fermi level. The calculations show that the peak is associated with an excitation between band 6 and 9 with a [200] reciprocallattice vector. For 0 = 30°,a peak again appears just below the Fermi level and moves down into the d-band emission region. The model identifies this peak as an excitation between the same band pair as above but now assisted by a [111] vector, i.e. a seeondary cone in Mahan’s terminology.3 Alternatively this peak can be described as a [01] surface Umldapp scattering of a state originally excited by [200]. Most

670

u.v.-PHOTOEMISSION FROM SINGLE CRYSTALS OF Au

of the other features of the (100) spectra can also be identified with this model, though for a quantitative fit small adjustments of the bands are sometimes necessary. For example, the analysis of the discussed transition above between band 6 and 9 indicates that band 9 is too low in energy. For the (111) face a similar analysis has been performed. In Fig. 2 the transitions caused by the [Ill] vector are indicated. The result of the identifications, together with that’ for the (100) face is summarized in Table 1. For the (110) face the situation is more cornplicated (15 band pairs) and it is not convenient to make the simple type of analysis applied for the other two surfaces. ‘

The results for the (Ill) and (110) faces are complementary in that for the (111) face the analyzer was rotated towards the [110] direction and vice versa. For the (111) face, peaks above —5 eV are found to move towards the Fermi level while peaks below —5 eV move towards lower energies. For the (110) face the corresponding peaks move in the opposite directions, as required by the model. A striking feature of the spectra is that at 0 75° for the (100) face a spectrum similar to that observed from the (111) face at 0 = 0°is found. The angle between [111] and [100] ~ 550 so the phenomenon could be described as a refraction from the surface normal. A similar observation is made for the (110) face, which at 0 = 50°produces a typical (111) spectrum. The angle between [111] and [1101 is 35°.Here the energy dependence of the refraction is evident. The peaks at —2 and —4 eV have the typical (111)-shape at 0 = 45°while the peaks at —6 eV do not narrow in the characteristic way until 0 = 60°.A corresponding behaviour is also observed in recent work on Cu.’°The results can be explained by assuming that states on I’ L are mainly excited by a [111] reciprocal lattice vector. Then the final state k-vector will have a large surface component. Our calculations show that the —

Vol. 17, No. 6

(100) face has contributions from these states at angles close to 90°and the (110) face at about 60°,in reasonable agreement with our results. An interesting observation is the variation of the total photocurrent as a function of 0. The (ill) surface gives the highest intensity for 0 = 00. The other two faces, and in particular the (110) face, have a low intensity of normally emitted electrons. In contrast they give a more intense emission with increasing 0 as the EDC approaches the typical (Ill) normal emission spectrum. This finding verifies that the intensity depends on the degree of symmetry in the initial state, which influences the excitation probability and propagation of excited electrons. In summary, EDCs from single crystals of gold have been measured as a function of electron emission angle. The observed peaks can be attributed to bulk transitions followed by an escape under ordinary refraction conditions, i.e. conservation of momentum parallel to the surface. This conclusion follows from the qualitative fit to our calculations using a band structure by Christensen and Seraphin.7 If the photoemission model is valid to a high degree some smaller adjustments of the bands are necessary. In particular, the two lowest d-bands should be displaced 0.2 eV towards lower energies, as we stated earlier,’1 and high lying conduction bands to higher energies. It is interesting to note in this connection that such a conclusion cannot be reached from the analysis using a polycrystaffine sample (see above). This is due to the absence of angular resolution which effectively means an integration and thus less sensitivity. Introduction of surface induced excitations, as in the case of tungsten,’2 does not seem to be necessary in the present case for identifying the main features. A more complete report is in preparation.’° Acknowledgements We are indebted to S. Andersson and R. Jones for valuable discussions. The work has been supported by grants from the Swedish National —

Science Research Council.

REFERENCES 1. 2. 3.

BERGLUND C.N. & SPICER WE.,Fhys. Rev. 136, A1030 (1964). See eg. NILSSON P.O., in Elementary Excitations in Solids, Molecules and Atoms (Edited by DEVREESE J.T., KUNZ A.B. & COLLINS T.C.) Part B, p. 351. Plenim Press, London and NY (1974). MAHAN G.D.,Phys. Rev. BI, 4334 (1970); SCHAICH W.L. & ASHCROFT N.W.,Phys. Rev. B3, 2452 (1971).

Vol. 17, No.6 4. 5.

u.v.-PHOTOEMISSION FROM SINGLE CRYSTALS OF Au

671

See e.g. SMITh N.y. &TRAUM M.M.,Phys. Rev. Lett. 31, 1247 (1973) and references therein. The original set-up is described in GUSTAFSSON T., Ph.D. Thesis, Chalmers University of Technology, Gothenburg, Sweden (1973).

6.

7. 8.

NILSSON P.O., NORRIS C. & WALLDEN L., Phys. Kor.d. Mat. 11,220(1970).

CHRISTENSEN N.E. & SERAPHIN B.O., Phys. Rev. B4, 3321(1971). EASTMAN D.E. & CASHION J.K.,Phys. Rev. Lett. 24,310(1970). 9. We do not discuss here a possible reconstruction of the (100) surface as discussed by GRANT J.T., Surf ScL 18, 228 (1969) and references therein. 10. NILS~ONP.O. & ILVER L. Proc. mt. Symp. Electron Spectroscopy, Kiev, 1975, (to be published). 11. NILSSON P.O. & ILVER L., in Vacuum Ultraviolet Radiation Physics (Edited by KOCH E., HAENSEL R. & KUNZ C.) Pergamon/Vieweg (1975). 12. FEUERBACHER B. & CHRISTENSEN N.E., Phys. Rev. BlO, 2373 (1974).