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Momentum-dependent low energy losses in angle-resolved core level photoemission spectra
Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 407–411
Momentum-dependent low energy losses in angle-resolved core level photoemission spectra Hartmut Höchst∗ , Christian R. Ast Synchrotron Radiation Center, University of Wisconsin-Madison, 3731 Schneider Drive, Stoughton, WI 53589, USA Available online 25 March 2004
Abstract Angle-resolved photoemission spectra of the Sb 4d and Bi 5d core levels show spectral features split-off in energy by E ∼ 170–320 meV from the main peaks. The appearance of a second component in the Bi 5d spectrum was previously assigned to a surface related binding energy shift. However, use of synchrotron radiation ranging from 30 to 150 eV and angular scans along different symmetry directions of the (1 1 1) surface Brillouin zone show that the split-off peaks disperse as a function of the electron momentum k. Additionally, the peak width and intensity of the split-off peak oscillates between final state symmetry points. Since the d5/2 and d3/2 components show the same features symmetry arguments rule out crystal-field effects as the source of the observed peak splitting. The data can be explained by a k-dependent loss function consisting of several characteristic direct and indirect low energy interband transitions excited in various parts of the bulk Brillouin zone. © 2004 Elsevier B.V. All rights reserved. Keywords: Photoemission spectroscopy; Core level; Electron energy loss; Sb; Bi
1. Introduction The availability of high-quality samples having low impurity levels and good structural quality combined with instrumental improvements in synchrotron radiation beam lines and electron energy analyzers of high energy resolution led recently to photoemission core-level spectra exhibiting additional features which were previously not seen. Photoemission line-shape changes or multiple core-level components can occur through surface modifications, crystal-field splitting, vibrational contributions and excitations of electrons or phonons. [1,2] The theory of core-level photoemission and aspects of intrinsic and extrinsic excitations associated with the photo-hole, or photoelectron, were recently restated in a series of papers by Hedin and Lee [3]. The relative strength of low energy excitations accompanying the “main line” photoemission spectrum is directly related to the dc resistivity and can be quite significant in materials of poor conductivity such as small-gap superconductors and semimetals [4].
We report angle-resolved core-level photoemission spectra of the semimetals Sb and Bi where we observe a multiple peak structure separated by ∼170–320 meV towards higher energy from the main 4d and 5d components, respectively. Utilizing photons ranging from 30–150 eV, angular scans along the k-direction normal to the (1 1 1) surface and k|| scans along high symmetry directions of the surface Brillouin zone (SBZ), we find dispersion in the split-off components commensurate with the bulk and surface Brillouin zone periodicity. From the wealth of accumulated information, we dismiss an earlier claim by Patthey et al. [5] assigning the additional feature in the Bi 5d spectra to a surface-shifted component. From a variety of possible different mechanisms such as crystal field-splitting, dispersive core states, surface shift and electron energy losses, we conclude that losses by means of interband transitions excited in various parts of the BBZ are the most likely source of the split-off components accompanying the Sb 4d and Bi 5d core-level spectra.
2. Experimental ∗
Corresponding author. E-mail address: [email protected] (H. Höchst).
0368-2048/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2004.02.119
Photoemission experiments were carried out at the Synchrotron Radiation Center of the University of Wisconsin-
408
H. Höchst, C.R. Ast / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 407–411
Madison using the undulator Plane Grating Monochromator (PGM) beam line. The electron analyzer parameters were selected so that the combined energy resolution, as determined from the fitted width of Au-Fermi level measurements, was E ∼ 25 meV from which the beam-line contributed about 5 meV. The momentum resolution of the core level spectra is on average k|| ∼ 0.04 Å−1 [6]. Photoemission data were obtained from Sb samples which were epitaxially grown on Bi (1 1 1) substrates and then transferred under ultra high vacuum into the photoemission chamber. Details of the sample preparation will be discussed elsewhere. The Bi samples were prepared by cleaving single crystals at low temperatures inside the preparation chamber. Both sample types were of good crystalline quality as documented by data mapping the dispersion of the valence bands and by Fermi-surface maps. To minimize phononassisted spectral broadening, the samples were measured at 50 K.
3. Results and discussion Fig. 1 shows a selection of normal-emission spectra of the 4d core level of Sb (1 1 1). The spectra do not resemble the simple two-peak profile typical of the 5/2 and 3/2 spinorbit-split components of the 4d core level. Rather they show additional spectral components that rapidly vary with photon energy. The solid lines through the data were obtained by simulating each spin–orbit component with three independent Lorentzian line shapes and a general background function simulating the contributions due to inelastic electron scattering. The individual Lorentzians are indicated by solid, dotted and dashed lines, respectively. By varying the photon energy, each peak contributes differently in intensity. In addition, the peak positions of the dotted and dashed components varies while the positions of the main 5/2 and 3/2 components, indicated by the solid lines, remain fixed at initial state energies of Ei (4d5/2 ) = 32.05 eV and Ei (4d3/2 ) = 33.31 eV. The ratio of the sum of the intensity as a function of the final state energy ratios of the two dispersing peaks to the non-dispersive intensity, (I1 + I2 )/I0 are shown in Fig. 2. As one can see, the components associated with the d5/2 states (filled dots) and d3/2 states (open dots) share the same final-state dependence. From normal-emission valence-band spectra which will be discussed elsewhere, it appears that the intensity maxima in Fig. 2 occur in the region of the final-state band gaps near T, while the minima are related to emission regions closer to the -point. Similarly strong finalstate intensity dependencies were found by Balasubramanian et al. [7] for a weak split-off component in the C 1s core level spectra of highly ordered graphite. While these authors consider the additional weak emission feature to be related to the surface and the relative intensity increase is explained by the lack of bulk emission at photon energies for which the final-state energy falls within a bulk
Fig. 1. Normal-emission spectra of the Sb 4d core level for the indicated photon energies. The d5/2 and d3/2 components were each fitted with three Lorentzians as shown in the figure.
band gap, we can not draw the same conclusions regarding the origin of the split-off components in Sb. We identify the additional components in Sb to be at higher binding energies than the main peak and, more importantly, find that these components experience dispersion periodic with k⊥ in normal emission and with k|| for off-normal spectra. Fig. 3 shows the final-state energy dependencies of the energy differences E1 and E2 relative to the main peak E0 . The oscillatory behavior of E2 is somewhat less pronounced than that of E1 ; however, similar to the relative intensities, the individual components related to the 4d5/2 and 4d3/2 states follow the same dispersive path. Our general findings are not unique to Sb. We observed similar effects in the 5d core spectra of Bi. Here the energy
H. Höchst, C.R. Ast / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 407–411
409
Fig. 4. Energy difference E1 and relative peak intensity I1 /I0 of the Bi 5d5/2 component measured at k|| = 0 as a function of final-state energy.
Fig. 2. Intensity ratios of the components shown by the dotted and dashed lines in Fig. 1 to the components shown by solid lines, (I1 + I2 )/I0 , of the Sb 4d5/2 (filled dots) and 4d3/2 (open dots) components as function of final state energy.
of the split-off component appears at slightly smaller energy varying between 160 and 270 meV, and requires only one split-off component in the line-shape analysis. Fig. 4 summarizes the photon-energy dependent results of fits to
Fig. 3. Energy differences E1 and E2 of the Sb 4d5/2 (filled symbols) and 4d3/2 (open symbols) components as a function of final state energy. The solid and dashed lines are polynomial fits through the data for the purpose guide the eye.
the normal emission spectra of the 5d5/2 part of the Bi (1 1 1) core spectrum consisting of two independent Lorentzians and a background function. The relative intensity of the dispersive peak at higher binding energy versus the intensity of the non-dispersive I1 /I0 has a broad minimum at a final state of Ef ∼ 40 eV. Superimposed are intensity modulations showing local maxima and minima coinciding again with the T- and -points, which were determined independently in separate experiments investigating the bulk band structure of Bi. It is noteworthy that the maxima of the relative intensity ratios between the loss and the main peak are about three times stronger in Bi than in Sb. The reason why the relative loss intensity is more pronounced in Bi can be related to the dc conductivity, which is significantly lower than in Sb. Measurements were also performed off-normal with the electron momentum along the M and K directions. The combined results for measurements with hv = 60 eV are shown in Fig. 5. Excitation of the Bi 5d core levels with this photon energy results in a final state energy of Ef ∼ 36 eV. Normal emission valence-band spectra indicate that at this energy k⊥ is about half way between T of the bulk Brillouin zone (BBZ). However, for this energy region, the bands are
Fig. 5. Energy difference E1 (filled dots) and relative peak intensity I1 /I0 (open dots) of the Bi 5d5/2 component measured at hν = 60 eV as a function of parallel momentum along M and K.
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H. Höchst, C.R. Ast / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 407–411
far from being free-electron-like and thus prevent a simple determination of the exact k⊥ values. Instead, for guidance we chose to display the projections of the BBZ boundaries in Fig. 5. The relative intensity ratios indicated by open dots are not quite as pronounced as in the normal-emission spectra. The relative emission intensity (open dots) and energy difference E (filled dots) both show modulations with k|| . The fact that E is not reaching the same values at consecutive (dashed) -line or K-lines shows that the momentum dependence is a bulk effect. Combining our findings from Sb and Bi lets us conclude that the split-off components following the main peaks are the result of k-dependent energy losses with maxima near and minima around the boundaries of the BBZ. Our conclusion regarding the energy losses can be further substantiated by low energy electron loss (LEELS) data. For Bi (1 1 1) LEELS consist of four loss features ranging in energy from ∼50 to 250 meV. Using the transition energies ω1 to ω4 reported by De Renzi et al. [8] we can construct a model loss function [9]: Im
4. Conclusions Photoemission data of Sb (1 1 1) and Bi (1 1 1) show additional components with pronounced momentum and final-state dependencies in the 4d and 5d spectra. The observation of the same energy differences and relative
4 ωi ωi2 −1 = ci ε(ω) (ω2 − ωi2 )2 + ω2 2i i=1
The coefficients ci are the relative transition probabilities. This function can be used to simulate the shape and position of the Bi photoemission loss peaks [10]. Fig. 6 compares the fitted loss function (dashed line) with the photoemission loss peaks (solid line) of E = 170 meV (top) measured near T and E = 260 meV (bottom) measured near . The fitted loss function is the convolution of the effective loss function Pk (ω) with the main peak of loss zero. The fitted functions Pk (ω) are shown as inserts in Fig. 6. The simulated curves agree well in width and energy position with the experimentally determined loss peaks. Assuming a smoothly varying k-dependent matrix element ci (kf ), one can then explain the apparent energy dispersion E(k) of the loss peaks in the angle-resolved core level spectra. Using the projected bulk band structure of Bi near the Fermi level region can be helpful in identifying transitions possibly related to the loss features L1 to L4 . Fig. 7 shows the projection of the bulk band structure along the K and M directions. The calculation is based on the pseudopotential parameters listed in ref. [11]. Bands are calculated in steps of 0.02 Å−1 for k⊥ values along the line T. From this calculation it is obvious that the LEELS transitions L1 and L2 are directly associated with transitions marked D1 and D2 located close to the L-point of the bulk Brillouin zone. Losses L3 and L4 can be associated with several indirect transitions I from regions near the T-point. Due to the lack of similarly useful LEELS data for Sb we could not pursue the same quantitative analysis. However, band structure calculation of Sb also identifies regions that could potentially be the source for electron losses associated with interband transitions.
Fig. 6. Comparison of photoemission loss peak in Bi (solid line) with the fitted loss function (dashed line) obtained by convoluting the simulated loss functions Pk (ω), as shown in the inserts, with the zero-loss peak L0 .
Fig. 7. Fermi level region of the projected bulk band structure of Bi (1 1 1). Arrows indicate indirect (I) and direct (D) interband transitions related to the loss features L1 to L4 .
H. Höchst, C.R. Ast / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 407–411
intensity ratios for the d5/2 and d3/2 components indicates that crystal-field effects are not the source for the observed split-off components. The additional spectral components do not seem to be sensitive to surface alterations thus ruling out the chemical shift of surface atoms as the origin of the split-off components. Unlike Zn, Cd and Hg where d-states overlap in energy with the lowest lying VB states and experience some hybridization [12,13], the d-states of Sb and Bi are more than 12 eV separated from the valence band minima and remainders of band-structure effects should not be present in these deeper core states. Our data can, however, be interpreted by low energy electron losses by interband excitations in various parts of the BBZ close to the Fermi level. For Bi we find good agreement of the experimental loss spectrum with a k-dependent loss function based on energy transitions measured by LEELS [8]. Acknowledgements The Synchrotron Radiation Center (SRC) is funded by the National Science Foundation (NSF) under Contract No. DMR-0084402.
411
References [1] S. Hüfner, Photoelectron Spectroscopy, Springer, Berlin, Heidelberg, New York, 1996. [2] J.N. Andersen, T. Balasubramanian, C.-O. Almbladh, et al., Phys. Rev. Lett. 86 (2001) 4398. [3] L. Hedin, J.D. Lee, Phys. Rev. B 64 (2001) 115109. [4] D.L. Mills, Phys. Rev. B 62 (2000) 11197. [5] F. Patthey, W.D. Schneider, H. Micklitz, Phys. Rev. B 49 (1994) 11293. [6] C.R. Ast, H. Höchst, Phys. Rev. B 66 (2002) 125103. [7] T. Balasubramanian, J.N. Andersen, L. Walldén, Phys. Rev. B 64 (2001) 205420. [8] V. De Renzi, M.G. Betti, C. Mariani, Phys. Rev. B 48 (1993) 4767. [9] M.R. Norman, M. Randeria, H. Ding, Phys. Rev. B 59 (1999) 11191. [10] L. Hedin, J. Michiels, J. Inglesfield, Phys. Rev. B 58 (1998) 15565. [11] Y. Liu, R.E. Allen, Phys. Rev. B 52 (1995) 1566. [12] F.J. Himpsel, D.E. Eastman, E.E. Koch, Phys. Rev. B 22 (1980) 4604. [13] H. Höchst, D.W. Niles, I. Hernández-Calderón, Phys. Rev. B 40 (1989) 8370.
Momentum-dependent low energy losses in angle-resolved core level photoemission spectra Hartmut Höchst∗ , Christian R. Ast Synchrotron Radiation Center, University of Wisconsin-Madison, 3731 Schneider Drive, Stoughton, WI 53589, USA Available online 25 March 2004
Abstract Angle-resolved photoemission spectra of the Sb 4d and Bi 5d core levels show spectral features split-off in energy by E ∼ 170–320 meV from the main peaks. The appearance of a second component in the Bi 5d spectrum was previously assigned to a surface related binding energy shift. However, use of synchrotron radiation ranging from 30 to 150 eV and angular scans along different symmetry directions of the (1 1 1) surface Brillouin zone show that the split-off peaks disperse as a function of the electron momentum k. Additionally, the peak width and intensity of the split-off peak oscillates between final state symmetry points. Since the d5/2 and d3/2 components show the same features symmetry arguments rule out crystal-field effects as the source of the observed peak splitting. The data can be explained by a k-dependent loss function consisting of several characteristic direct and indirect low energy interband transitions excited in various parts of the bulk Brillouin zone. © 2004 Elsevier B.V. All rights reserved. Keywords: Photoemission spectroscopy; Core level; Electron energy loss; Sb; Bi
1. Introduction The availability of high-quality samples having low impurity levels and good structural quality combined with instrumental improvements in synchrotron radiation beam lines and electron energy analyzers of high energy resolution led recently to photoemission core-level spectra exhibiting additional features which were previously not seen. Photoemission line-shape changes or multiple core-level components can occur through surface modifications, crystal-field splitting, vibrational contributions and excitations of electrons or phonons. [1,2] The theory of core-level photoemission and aspects of intrinsic and extrinsic excitations associated with the photo-hole, or photoelectron, were recently restated in a series of papers by Hedin and Lee [3]. The relative strength of low energy excitations accompanying the “main line” photoemission spectrum is directly related to the dc resistivity and can be quite significant in materials of poor conductivity such as small-gap superconductors and semimetals [4].
We report angle-resolved core-level photoemission spectra of the semimetals Sb and Bi where we observe a multiple peak structure separated by ∼170–320 meV towards higher energy from the main 4d and 5d components, respectively. Utilizing photons ranging from 30–150 eV, angular scans along the k-direction normal to the (1 1 1) surface and k|| scans along high symmetry directions of the surface Brillouin zone (SBZ), we find dispersion in the split-off components commensurate with the bulk and surface Brillouin zone periodicity. From the wealth of accumulated information, we dismiss an earlier claim by Patthey et al. [5] assigning the additional feature in the Bi 5d spectra to a surface-shifted component. From a variety of possible different mechanisms such as crystal field-splitting, dispersive core states, surface shift and electron energy losses, we conclude that losses by means of interband transitions excited in various parts of the BBZ are the most likely source of the split-off components accompanying the Sb 4d and Bi 5d core-level spectra.
2. Experimental ∗
Corresponding author. E-mail address: [email protected] (H. Höchst).
0368-2048/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2004.02.119
Photoemission experiments were carried out at the Synchrotron Radiation Center of the University of Wisconsin-
408
H. Höchst, C.R. Ast / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 407–411
Madison using the undulator Plane Grating Monochromator (PGM) beam line. The electron analyzer parameters were selected so that the combined energy resolution, as determined from the fitted width of Au-Fermi level measurements, was E ∼ 25 meV from which the beam-line contributed about 5 meV. The momentum resolution of the core level spectra is on average k|| ∼ 0.04 Å−1 [6]. Photoemission data were obtained from Sb samples which were epitaxially grown on Bi (1 1 1) substrates and then transferred under ultra high vacuum into the photoemission chamber. Details of the sample preparation will be discussed elsewhere. The Bi samples were prepared by cleaving single crystals at low temperatures inside the preparation chamber. Both sample types were of good crystalline quality as documented by data mapping the dispersion of the valence bands and by Fermi-surface maps. To minimize phononassisted spectral broadening, the samples were measured at 50 K.
3. Results and discussion Fig. 1 shows a selection of normal-emission spectra of the 4d core level of Sb (1 1 1). The spectra do not resemble the simple two-peak profile typical of the 5/2 and 3/2 spinorbit-split components of the 4d core level. Rather they show additional spectral components that rapidly vary with photon energy. The solid lines through the data were obtained by simulating each spin–orbit component with three independent Lorentzian line shapes and a general background function simulating the contributions due to inelastic electron scattering. The individual Lorentzians are indicated by solid, dotted and dashed lines, respectively. By varying the photon energy, each peak contributes differently in intensity. In addition, the peak positions of the dotted and dashed components varies while the positions of the main 5/2 and 3/2 components, indicated by the solid lines, remain fixed at initial state energies of Ei (4d5/2 ) = 32.05 eV and Ei (4d3/2 ) = 33.31 eV. The ratio of the sum of the intensity as a function of the final state energy ratios of the two dispersing peaks to the non-dispersive intensity, (I1 + I2 )/I0 are shown in Fig. 2. As one can see, the components associated with the d5/2 states (filled dots) and d3/2 states (open dots) share the same final-state dependence. From normal-emission valence-band spectra which will be discussed elsewhere, it appears that the intensity maxima in Fig. 2 occur in the region of the final-state band gaps near T, while the minima are related to emission regions closer to the -point. Similarly strong finalstate intensity dependencies were found by Balasubramanian et al. [7] for a weak split-off component in the C 1s core level spectra of highly ordered graphite. While these authors consider the additional weak emission feature to be related to the surface and the relative intensity increase is explained by the lack of bulk emission at photon energies for which the final-state energy falls within a bulk
Fig. 1. Normal-emission spectra of the Sb 4d core level for the indicated photon energies. The d5/2 and d3/2 components were each fitted with three Lorentzians as shown in the figure.
band gap, we can not draw the same conclusions regarding the origin of the split-off components in Sb. We identify the additional components in Sb to be at higher binding energies than the main peak and, more importantly, find that these components experience dispersion periodic with k⊥ in normal emission and with k|| for off-normal spectra. Fig. 3 shows the final-state energy dependencies of the energy differences E1 and E2 relative to the main peak E0 . The oscillatory behavior of E2 is somewhat less pronounced than that of E1 ; however, similar to the relative intensities, the individual components related to the 4d5/2 and 4d3/2 states follow the same dispersive path. Our general findings are not unique to Sb. We observed similar effects in the 5d core spectra of Bi. Here the energy
H. Höchst, C.R. Ast / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 407–411
409
Fig. 4. Energy difference E1 and relative peak intensity I1 /I0 of the Bi 5d5/2 component measured at k|| = 0 as a function of final-state energy.
Fig. 2. Intensity ratios of the components shown by the dotted and dashed lines in Fig. 1 to the components shown by solid lines, (I1 + I2 )/I0 , of the Sb 4d5/2 (filled dots) and 4d3/2 (open dots) components as function of final state energy.
of the split-off component appears at slightly smaller energy varying between 160 and 270 meV, and requires only one split-off component in the line-shape analysis. Fig. 4 summarizes the photon-energy dependent results of fits to
Fig. 3. Energy differences E1 and E2 of the Sb 4d5/2 (filled symbols) and 4d3/2 (open symbols) components as a function of final state energy. The solid and dashed lines are polynomial fits through the data for the purpose guide the eye.
the normal emission spectra of the 5d5/2 part of the Bi (1 1 1) core spectrum consisting of two independent Lorentzians and a background function. The relative intensity of the dispersive peak at higher binding energy versus the intensity of the non-dispersive I1 /I0 has a broad minimum at a final state of Ef ∼ 40 eV. Superimposed are intensity modulations showing local maxima and minima coinciding again with the T- and -points, which were determined independently in separate experiments investigating the bulk band structure of Bi. It is noteworthy that the maxima of the relative intensity ratios between the loss and the main peak are about three times stronger in Bi than in Sb. The reason why the relative loss intensity is more pronounced in Bi can be related to the dc conductivity, which is significantly lower than in Sb. Measurements were also performed off-normal with the electron momentum along the M and K directions. The combined results for measurements with hv = 60 eV are shown in Fig. 5. Excitation of the Bi 5d core levels with this photon energy results in a final state energy of Ef ∼ 36 eV. Normal emission valence-band spectra indicate that at this energy k⊥ is about half way between T of the bulk Brillouin zone (BBZ). However, for this energy region, the bands are
Fig. 5. Energy difference E1 (filled dots) and relative peak intensity I1 /I0 (open dots) of the Bi 5d5/2 component measured at hν = 60 eV as a function of parallel momentum along M and K.
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H. Höchst, C.R. Ast / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 407–411
far from being free-electron-like and thus prevent a simple determination of the exact k⊥ values. Instead, for guidance we chose to display the projections of the BBZ boundaries in Fig. 5. The relative intensity ratios indicated by open dots are not quite as pronounced as in the normal-emission spectra. The relative emission intensity (open dots) and energy difference E (filled dots) both show modulations with k|| . The fact that E is not reaching the same values at consecutive (dashed) -line or K-lines shows that the momentum dependence is a bulk effect. Combining our findings from Sb and Bi lets us conclude that the split-off components following the main peaks are the result of k-dependent energy losses with maxima near and minima around the boundaries of the BBZ. Our conclusion regarding the energy losses can be further substantiated by low energy electron loss (LEELS) data. For Bi (1 1 1) LEELS consist of four loss features ranging in energy from ∼50 to 250 meV. Using the transition energies ω1 to ω4 reported by De Renzi et al. [8] we can construct a model loss function [9]: Im
4. Conclusions Photoemission data of Sb (1 1 1) and Bi (1 1 1) show additional components with pronounced momentum and final-state dependencies in the 4d and 5d spectra. The observation of the same energy differences and relative
4 ωi ωi2 −1 = ci ε(ω) (ω2 − ωi2 )2 + ω2 2i i=1
The coefficients ci are the relative transition probabilities. This function can be used to simulate the shape and position of the Bi photoemission loss peaks [10]. Fig. 6 compares the fitted loss function (dashed line) with the photoemission loss peaks (solid line) of E = 170 meV (top) measured near T and E = 260 meV (bottom) measured near . The fitted loss function is the convolution of the effective loss function Pk (ω) with the main peak of loss zero. The fitted functions Pk (ω) are shown as inserts in Fig. 6. The simulated curves agree well in width and energy position with the experimentally determined loss peaks. Assuming a smoothly varying k-dependent matrix element ci (kf ), one can then explain the apparent energy dispersion E(k) of the loss peaks in the angle-resolved core level spectra. Using the projected bulk band structure of Bi near the Fermi level region can be helpful in identifying transitions possibly related to the loss features L1 to L4 . Fig. 7 shows the projection of the bulk band structure along the K and M directions. The calculation is based on the pseudopotential parameters listed in ref. [11]. Bands are calculated in steps of 0.02 Å−1 for k⊥ values along the line T. From this calculation it is obvious that the LEELS transitions L1 and L2 are directly associated with transitions marked D1 and D2 located close to the L-point of the bulk Brillouin zone. Losses L3 and L4 can be associated with several indirect transitions I from regions near the T-point. Due to the lack of similarly useful LEELS data for Sb we could not pursue the same quantitative analysis. However, band structure calculation of Sb also identifies regions that could potentially be the source for electron losses associated with interband transitions.
Fig. 6. Comparison of photoemission loss peak in Bi (solid line) with the fitted loss function (dashed line) obtained by convoluting the simulated loss functions Pk (ω), as shown in the inserts, with the zero-loss peak L0 .
Fig. 7. Fermi level region of the projected bulk band structure of Bi (1 1 1). Arrows indicate indirect (I) and direct (D) interband transitions related to the loss features L1 to L4 .
H. Höchst, C.R. Ast / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 407–411
intensity ratios for the d5/2 and d3/2 components indicates that crystal-field effects are not the source for the observed split-off components. The additional spectral components do not seem to be sensitive to surface alterations thus ruling out the chemical shift of surface atoms as the origin of the split-off components. Unlike Zn, Cd and Hg where d-states overlap in energy with the lowest lying VB states and experience some hybridization [12,13], the d-states of Sb and Bi are more than 12 eV separated from the valence band minima and remainders of band-structure effects should not be present in these deeper core states. Our data can, however, be interpreted by low energy electron losses by interband excitations in various parts of the BBZ close to the Fermi level. For Bi we find good agreement of the experimental loss spectrum with a k-dependent loss function based on energy transitions measured by LEELS [8]. Acknowledgements The Synchrotron Radiation Center (SRC) is funded by the National Science Foundation (NSF) under Contract No. DMR-0084402.
411
References [1] S. Hüfner, Photoelectron Spectroscopy, Springer, Berlin, Heidelberg, New York, 1996. [2] J.N. Andersen, T. Balasubramanian, C.-O. Almbladh, et al., Phys. Rev. Lett. 86 (2001) 4398. [3] L. Hedin, J.D. Lee, Phys. Rev. B 64 (2001) 115109. [4] D.L. Mills, Phys. Rev. B 62 (2000) 11197. [5] F. Patthey, W.D. Schneider, H. Micklitz, Phys. Rev. B 49 (1994) 11293. [6] C.R. Ast, H. Höchst, Phys. Rev. B 66 (2002) 125103. [7] T. Balasubramanian, J.N. Andersen, L. Walldén, Phys. Rev. B 64 (2001) 205420. [8] V. De Renzi, M.G. Betti, C. Mariani, Phys. Rev. B 48 (1993) 4767. [9] M.R. Norman, M. Randeria, H. Ding, Phys. Rev. B 59 (1999) 11191. [10] L. Hedin, J. Michiels, J. Inglesfield, Phys. Rev. B 58 (1998) 15565. [11] Y. Liu, R.E. Allen, Phys. Rev. B 52 (1995) 1566. [12] F.J. Himpsel, D.E. Eastman, E.E. Koch, Phys. Rev. B 22 (1980) 4604. [13] H. Höchst, D.W. Niles, I. Hernández-Calderón, Phys. Rev. B 40 (1989) 8370.