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Momentum resolved bremsstrahlung isochromat spectra from Ni(0 0 1)
Solid State Communications, Vol. 49, No. 5, pp. 479-481, 1984. Printed in Great Britain.
0038-1098/84 $3.00 + .00 Pergamon Press Ltd.
MOMENTUM RESOLVED BREMSSTRAHLUNG ISOCHROMAT SPECTRA FROM Ni(001) K. Desinger, V. Dose, M. G6bl and H. Scheidt Physikalisches Institut der Universitiit, Am Hubland, D-8700 Wiirzburg, Germany
(Received 19 August 1983 by P. Wachter) Momentum resolved inverse photoemission spectra from Ni(001) are presented. The experimental dispersion of direct transitions are in good agreement with predictions from a recent band structure calculation and with results from spectra calculated on the basis of a one step theory. Comparison of the present data with earlier normal incidence spectra collected with a different experimental setup reveals a very strong polarization effect. THE DISCOVERY of directional effects in ultraviolet Bremsstrahlung isochromat spectra [1-3] has greatly enhanced interest in further technical developments and physical exploitations of this technique [4, 5]. In particular the measurement of energy versus momentum dispersion for radiative transitions in the bulk of solid samples opens up all the possibilities of band mapping for initially empty electronic states which angular resolved photoemission provides for initially occupied states. As a special merit the Bremsstrahlung technique applies also to the otherwise inaccessible electronic states between the Fermi and the vacuum energy. In this paper we report momentum resolved isochromat spectra for a quantum energy of h~0 = 9.7 eV from a Ni(001) single crystal. The data have been collected with a new experimental setup offering good momentum resolution and luminosity. A schematic of the apparatus is displayed in Fig. 1. A specially designed electron gun delivering currents up to 15 pA at vacuum energies around 4 eV with angular spread of less than five degrees is mounted on the symmetry axis of a concave mirror. The mirror is made from a glass blank by evaporation of aluminum and subsequent coating with MgF2. Radiation emitted by the sample is focused into an ultraviolet band pass Geiger Mtiller counter [6] opposite to the mirror. The spectrometer is mounted in a standard ultra high vacuum system equipped with the usual sample preparation and analyzing facilities. These include a quadrupole residual gas analyzer, flash filament, low energy electron diffraction (LEED), and retarding field Auger analysis. The nickel sample was prepared by well known standard procedures until a sharp LEED pattern with low background intensity was obtained. Auger analysis of this state revealed a residual surface contamination of (5 + 3)% of a monolayer of carbon. Figure 2 displays isochromat spectra from Ni(00 I) for angles of incidence between 0 ° and 25 °. The polar
angle was varied in the I'XULK mirror plane. The normal incidence spectrum exhibits two emission features. An inflection point appears slightly above E•. This feature remains stationary with polar angle variation and develops into a well resolved emission maximum at higher polar angles. This emission is due to transitions into empty final d-bands [3]. The second feature in the normal incidence spectrum is a resonance like emission enhancement at 1.8 eV. This structure shows considerable dispersion and weakens in intensity as the angle of electron incidence is increased. A third slightly dispersive structure shows up in the 25 ° and 22.2 ° spectra and fades out for smaller angles. The observed peak positions of the dispersing structures are plotted as open circles in Fig. 3 as a function Ofkll, the component of momentum of the incident electron parallel to the crystal surface. Interpretation of the observed emission features in terms of a bulk direct transition model requires the evaluation of all values ofkll irrespective of k± for which two bands 9.7 eV apart exist. The f'mal band energy from such pairs is plotted as a function Ofkll as solid lines in Fig. 3. The band structure used to prepare this plot has been kindly supplied by Bross and Schiekel [7] and was obtained from an MAPW calculation. Dashed lines are from Woodruffet al. who used a nickel band structure calculated in a combined interpolation scheme [8]. Experimental results from Woodruffet aL [8] are shown as full diamonds. A theoretically more satisfactory though physically less transparent approach to photoemission and Bremsstraldung spectra is provided by the so-called one step theory [9]. The advantage of this approach as compared to the three step bulk direct transition model is that it treats coherently penetration, transport, and radiation emission. Surface effects are automatically accounted for. Bremsstrahlung data for Cu(00 l) calculated by Th6rner and Borstel have recently been published [10]. The same authors have obtained similar data
479
480
BREMSSTRAHLUNG ISOCHROMAT SPECTRA FROM Ni(001)
Vol. 49, No. 5
!
0.2
Fig. 1. Schematic of the apparatus for k-resolved ultraviolet isochromat spectroscopy.
0./. 0.6 0.6 k.l (~r/o) -- [!10]
Fig. 3. Open dots denote emission peak positions as a function of kll. Diamonds indicate the remits of Woodruff et aL Theoretical predictions on the basis of the bulk direct transition model are shown as solid [7] and dashed [8] curves. Solid dots represent theoretical remits from a one step calculation [11 ].
6
C
r-
E LU
0 I 2 3 /, Energy (E - E F )/eV 0
I
2
3
/,
5
ENERGY (E-EF)/eV
Fig. 2. Ultraviolet isochromats from nickel (00 l) as a function of electron angle of incidence. The polar angle variation is in the I'XULK mirror plane. on Ni(001) which will be published soon [11]. Peak positions from emission features in their work on Ni are displayed in Fig. 3 as full dots. The agreement of the present data with the predictions of the one step theory is considered to be
5
Fig. 4. The apparent intensity of the direct transition at 1.8 eV for normal electron incidence varies strongly with observation angle thus demonstrating strong polarization. excellent, in particular the branching of emission features near k;l = 0.51r/a shows up in experiment and theory. No emission is observed on the left hand part of branch "b" and only weak emission on the right hand part of branch "a" in accord with the predictions of the one step theory. Emission from these parts requires bulk umklapp processes corresponding to "secondary cone
Vol. 49, No. 5
BREMSSTRAHLUNG ISOCHROMAT SPECTRA FROM Ni(0 01)
emission" in photoelectron spectroscopy and is therefore expected to be weak. In fact the bulk transition matrix element [8] vanishes on branch "b" for kll < 0.3n[a while it becomes very small on branch "a" for kll > 0.4~r[a. Predictions of the direct bulk transition model appear to be slightly better when using the BrossSchieckel band structure, especially near normal incidence. The data ofWoodruffet aL coincide with ours for kll ~ 0.5n/a. Larger deviations occur at smaller values ofkll. A more extensive discussion of our normal incidence spectrum compared to their's has been given elsewhere [12]. The largest discrepancy was in the much smaller intensity of the direct transition emission in their work which could be demonstrated to result from carbon contamination. From Fig. 3 we argue that not only intensities but also peak positions were affected. Normal incidence spectra have previously been obtained also in our laboratory with a different experimental setup [3]. These earlier data, reproduced as the lower solid curve in Fig. 4 seem also to disagree with our present data shown as the upper solid trace in Fig. 4. Normalization of the present to our earlier data has been made at the emission minimum at 3.5 eV. As a consequence the direct transition emission at 1.8 eV above EF shows strongly different intensities in both spectra. If we refer the direct transition intensity to the emission minimum at 3.5 eV, it is stronger in the upper spectrum by a factor of 4.5. Normal electron incidence on Ni(00 I) locates a direct transition on the F - A - X high symmetry line. The bands involved (6 and 7) are both of AI symmetry. As a consequence of dipole selection rules the electric field components parallel to the surface vanish for this transition. The intensity of the radiative emission will therefore strongly depend on the observation angle. In particular, no emission should be observed normal to the surface. For our earlier setup we calculate an average observation angle o f ~ = 22 °. This is quite small if one keeps in mind the sin25 intensity distribution of the emitted radiation. The average light collection angle for the apparatus of Fig. 1 has been calculated to be ~"= 46 °. If we account for the sin25 intensity distribution and include the optical properties of the sample from optical constants of nickel at h~oo = 9.7 eV [13] a computer simulation results in a calculated intensity ratio for both setups of 4.0 in close agreement with observation. The emission just above the Fermi level shows equal intensities in both spectra. The absence of polarization effects in this feature is consistent with our earlier interpretation [3]
481
which attributed this emission to transitions from initial evanescent states to final d-bands. Another ~aall difference at E > 3.5 eV between the two spectra indicated by the shaded area in Fig. 4 is worth commenting on. Johnson and Smith [14] have called attention to this step like emission enhancement and have offered explanations in terms of energy losses or radiative transitions into image potential bound states. As a stringent requirement for the latter the associated emission must be polarized with electric field vector normal to the surface as observed in this work. In conclusion we have presented energy vs momentum dispersions for direct transitions between empty bands in nickel. The one step theory prediction shows splendid agreement with the experimental data. The comparison of data collected with two different experimental setups reveals a strong polarization effect.
Acknowledgements - This work has been financially supported by the Deutsche Forschungsgemeinschaft. We thank Professor H. Bross and Dipl. Phys. B. Schiekel for providing the nickel band structure. We are also indebted to Professor G. Borstel and Dipl. Phys. G. Th6mer for communicating their results prior to publication. REFERENCES 1. 2. 3.
4. 5.
6. 7. 8. 9. 10. 11. 12. 13. 14.
G. Denninger, V. Dose & H.P. Bonzel,Phys. Rev. Lett. 48, 279 (1982). D.P. Woodruff& N.V. Smith, Phys. Rev. Lett. 48, 283 (1982). G. Denninger, V. Dose, M. Gl6bl & H. Scheidt, Solid State Commutt 42, 583 (1982); J. Unguris, A. Sefler, R.J. Celotta, D.T. Pierce, P.O. Johnson & N.V. Smith, Phys. Rev. Lett. 49, 1047 (1982). V. Dose, Prog. Surf. Scl 13,225 (1983). D.P. Woodruff, P.O. Johnson & N.V. Smith, J. Vac. ScL TechnoL AI(2), 1104 (1983). V. Dose, AppL Phy& 14, 117 (1977). H. Bross & B. Schiekel, (private communication). D.P. Woodruff, N.V. Smith, P.O. Johnson & W.A. Royer, Phys. Rev. B26, 2943 (1982). J.B. Pendry, J. Phys. C Solid State Phy~ 14, 1381 (1981). G. Th6rner & G. Borstel, Solid State Commun. 47, 329 (1983). G. Th6rner & G. Borstel, (private communcation). V. Dose, M. Gl6bl & H. Scheidt, Phys. Rev. B, (in course of publication). J.H. Weaver, C. Krafka, D.W. Lynch & E.E. Koch, Internal Report DESY F41, HASYLAB 81/01 (1981). P.O. Johnson & N.V. Smith,Phys. Rev. B27, 2527 (1983).
0038-1098/84 $3.00 + .00 Pergamon Press Ltd.
MOMENTUM RESOLVED BREMSSTRAHLUNG ISOCHROMAT SPECTRA FROM Ni(001) K. Desinger, V. Dose, M. G6bl and H. Scheidt Physikalisches Institut der Universitiit, Am Hubland, D-8700 Wiirzburg, Germany
(Received 19 August 1983 by P. Wachter) Momentum resolved inverse photoemission spectra from Ni(001) are presented. The experimental dispersion of direct transitions are in good agreement with predictions from a recent band structure calculation and with results from spectra calculated on the basis of a one step theory. Comparison of the present data with earlier normal incidence spectra collected with a different experimental setup reveals a very strong polarization effect. THE DISCOVERY of directional effects in ultraviolet Bremsstrahlung isochromat spectra [1-3] has greatly enhanced interest in further technical developments and physical exploitations of this technique [4, 5]. In particular the measurement of energy versus momentum dispersion for radiative transitions in the bulk of solid samples opens up all the possibilities of band mapping for initially empty electronic states which angular resolved photoemission provides for initially occupied states. As a special merit the Bremsstrahlung technique applies also to the otherwise inaccessible electronic states between the Fermi and the vacuum energy. In this paper we report momentum resolved isochromat spectra for a quantum energy of h~0 = 9.7 eV from a Ni(001) single crystal. The data have been collected with a new experimental setup offering good momentum resolution and luminosity. A schematic of the apparatus is displayed in Fig. 1. A specially designed electron gun delivering currents up to 15 pA at vacuum energies around 4 eV with angular spread of less than five degrees is mounted on the symmetry axis of a concave mirror. The mirror is made from a glass blank by evaporation of aluminum and subsequent coating with MgF2. Radiation emitted by the sample is focused into an ultraviolet band pass Geiger Mtiller counter [6] opposite to the mirror. The spectrometer is mounted in a standard ultra high vacuum system equipped with the usual sample preparation and analyzing facilities. These include a quadrupole residual gas analyzer, flash filament, low energy electron diffraction (LEED), and retarding field Auger analysis. The nickel sample was prepared by well known standard procedures until a sharp LEED pattern with low background intensity was obtained. Auger analysis of this state revealed a residual surface contamination of (5 + 3)% of a monolayer of carbon. Figure 2 displays isochromat spectra from Ni(00 I) for angles of incidence between 0 ° and 25 °. The polar
angle was varied in the I'XULK mirror plane. The normal incidence spectrum exhibits two emission features. An inflection point appears slightly above E•. This feature remains stationary with polar angle variation and develops into a well resolved emission maximum at higher polar angles. This emission is due to transitions into empty final d-bands [3]. The second feature in the normal incidence spectrum is a resonance like emission enhancement at 1.8 eV. This structure shows considerable dispersion and weakens in intensity as the angle of electron incidence is increased. A third slightly dispersive structure shows up in the 25 ° and 22.2 ° spectra and fades out for smaller angles. The observed peak positions of the dispersing structures are plotted as open circles in Fig. 3 as a function Ofkll, the component of momentum of the incident electron parallel to the crystal surface. Interpretation of the observed emission features in terms of a bulk direct transition model requires the evaluation of all values ofkll irrespective of k± for which two bands 9.7 eV apart exist. The f'mal band energy from such pairs is plotted as a function Ofkll as solid lines in Fig. 3. The band structure used to prepare this plot has been kindly supplied by Bross and Schiekel [7] and was obtained from an MAPW calculation. Dashed lines are from Woodruffet al. who used a nickel band structure calculated in a combined interpolation scheme [8]. Experimental results from Woodruffet aL [8] are shown as full diamonds. A theoretically more satisfactory though physically less transparent approach to photoemission and Bremsstraldung spectra is provided by the so-called one step theory [9]. The advantage of this approach as compared to the three step bulk direct transition model is that it treats coherently penetration, transport, and radiation emission. Surface effects are automatically accounted for. Bremsstrahlung data for Cu(00 l) calculated by Th6rner and Borstel have recently been published [10]. The same authors have obtained similar data
479
480
BREMSSTRAHLUNG ISOCHROMAT SPECTRA FROM Ni(001)
Vol. 49, No. 5
!
0.2
Fig. 1. Schematic of the apparatus for k-resolved ultraviolet isochromat spectroscopy.
0./. 0.6 0.6 k.l (~r/o) -- [!10]
Fig. 3. Open dots denote emission peak positions as a function of kll. Diamonds indicate the remits of Woodruff et aL Theoretical predictions on the basis of the bulk direct transition model are shown as solid [7] and dashed [8] curves. Solid dots represent theoretical remits from a one step calculation [11 ].
6
C
r-
E LU
0 I 2 3 /, Energy (E - E F )/eV 0
I
2
3
/,
5
ENERGY (E-EF)/eV
Fig. 2. Ultraviolet isochromats from nickel (00 l) as a function of electron angle of incidence. The polar angle variation is in the I'XULK mirror plane. on Ni(001) which will be published soon [11]. Peak positions from emission features in their work on Ni are displayed in Fig. 3 as full dots. The agreement of the present data with the predictions of the one step theory is considered to be
5
Fig. 4. The apparent intensity of the direct transition at 1.8 eV for normal electron incidence varies strongly with observation angle thus demonstrating strong polarization. excellent, in particular the branching of emission features near k;l = 0.51r/a shows up in experiment and theory. No emission is observed on the left hand part of branch "b" and only weak emission on the right hand part of branch "a" in accord with the predictions of the one step theory. Emission from these parts requires bulk umklapp processes corresponding to "secondary cone
Vol. 49, No. 5
BREMSSTRAHLUNG ISOCHROMAT SPECTRA FROM Ni(0 01)
emission" in photoelectron spectroscopy and is therefore expected to be weak. In fact the bulk transition matrix element [8] vanishes on branch "b" for kll < 0.3n[a while it becomes very small on branch "a" for kll > 0.4~r[a. Predictions of the direct bulk transition model appear to be slightly better when using the BrossSchieckel band structure, especially near normal incidence. The data ofWoodruffet aL coincide with ours for kll ~ 0.5n/a. Larger deviations occur at smaller values ofkll. A more extensive discussion of our normal incidence spectrum compared to their's has been given elsewhere [12]. The largest discrepancy was in the much smaller intensity of the direct transition emission in their work which could be demonstrated to result from carbon contamination. From Fig. 3 we argue that not only intensities but also peak positions were affected. Normal incidence spectra have previously been obtained also in our laboratory with a different experimental setup [3]. These earlier data, reproduced as the lower solid curve in Fig. 4 seem also to disagree with our present data shown as the upper solid trace in Fig. 4. Normalization of the present to our earlier data has been made at the emission minimum at 3.5 eV. As a consequence the direct transition emission at 1.8 eV above EF shows strongly different intensities in both spectra. If we refer the direct transition intensity to the emission minimum at 3.5 eV, it is stronger in the upper spectrum by a factor of 4.5. Normal electron incidence on Ni(00 I) locates a direct transition on the F - A - X high symmetry line. The bands involved (6 and 7) are both of AI symmetry. As a consequence of dipole selection rules the electric field components parallel to the surface vanish for this transition. The intensity of the radiative emission will therefore strongly depend on the observation angle. In particular, no emission should be observed normal to the surface. For our earlier setup we calculate an average observation angle o f ~ = 22 °. This is quite small if one keeps in mind the sin25 intensity distribution of the emitted radiation. The average light collection angle for the apparatus of Fig. 1 has been calculated to be ~"= 46 °. If we account for the sin25 intensity distribution and include the optical properties of the sample from optical constants of nickel at h~oo = 9.7 eV [13] a computer simulation results in a calculated intensity ratio for both setups of 4.0 in close agreement with observation. The emission just above the Fermi level shows equal intensities in both spectra. The absence of polarization effects in this feature is consistent with our earlier interpretation [3]
481
which attributed this emission to transitions from initial evanescent states to final d-bands. Another ~aall difference at E > 3.5 eV between the two spectra indicated by the shaded area in Fig. 4 is worth commenting on. Johnson and Smith [14] have called attention to this step like emission enhancement and have offered explanations in terms of energy losses or radiative transitions into image potential bound states. As a stringent requirement for the latter the associated emission must be polarized with electric field vector normal to the surface as observed in this work. In conclusion we have presented energy vs momentum dispersions for direct transitions between empty bands in nickel. The one step theory prediction shows splendid agreement with the experimental data. The comparison of data collected with two different experimental setups reveals a strong polarization effect.
Acknowledgements - This work has been financially supported by the Deutsche Forschungsgemeinschaft. We thank Professor H. Bross and Dipl. Phys. B. Schiekel for providing the nickel band structure. We are also indebted to Professor G. Borstel and Dipl. Phys. G. Th6mer for communicating their results prior to publication. REFERENCES 1. 2. 3.
4. 5.
6. 7. 8. 9. 10. 11. 12. 13. 14.
G. Denninger, V. Dose & H.P. Bonzel,Phys. Rev. Lett. 48, 279 (1982). D.P. Woodruff& N.V. Smith, Phys. Rev. Lett. 48, 283 (1982). G. Denninger, V. Dose, M. Gl6bl & H. Scheidt, Solid State Commutt 42, 583 (1982); J. Unguris, A. Sefler, R.J. Celotta, D.T. Pierce, P.O. Johnson & N.V. Smith, Phys. Rev. Lett. 49, 1047 (1982). V. Dose, Prog. Surf. Scl 13,225 (1983). D.P. Woodruff, P.O. Johnson & N.V. Smith, J. Vac. ScL TechnoL AI(2), 1104 (1983). V. Dose, AppL Phy& 14, 117 (1977). H. Bross & B. Schiekel, (private communication). D.P. Woodruff, N.V. Smith, P.O. Johnson & W.A. Royer, Phys. Rev. B26, 2943 (1982). J.B. Pendry, J. Phys. C Solid State Phy~ 14, 1381 (1981). G. Th6rner & G. Borstel, Solid State Commun. 47, 329 (1983). G. Th6rner & G. Borstel, (private communcation). V. Dose, M. Gl6bl & H. Scheidt, Phys. Rev. B, (in course of publication). J.H. Weaver, C. Krafka, D.W. Lynch & E.E. Koch, Internal Report DESY F41, HASYLAB 81/01 (1981). P.O. Johnson & N.V. Smith,Phys. Rev. B27, 2527 (1983).