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Topics in ultraviolet inverse photoemission
338
Applications
of Surface
Science
22123 (1985) 338-348
North-Holland,
TOPICS IN ULTRAVIOLET
Amsterdam
INVERSE PHOTOEMISSION
V. DOSE Physikalisches Received
Institut der Universitiit,
27 August
1984; accepted
Am Hubland,
for publication
D-8700 31 October
Wiirzburg, Fed. Rep.
of Germany
1984
Ultraviolet inverse photoemission is an exciting new technique for band mapping of empty electronic states in solids and at surfaces. It includes the energy region between the Fermi and the vacuum level inaccessible by ordinary photoemission. Applications discussed in this paper include band mapping in nickel, spin-resolved studies of iron, and chemisorption of NO and CO on palladium.
1. Introduction Electronic states in the bulk of single crystals and at their surfaces can be characterized by their energy, momentum, spin, and symmetry. Experimental techniques to access these quantities are angular-resolved electron spectroscopies, in particular angular-resolved photoemission. Continuous efforts during the past ten years have developed it to its present mature state [l]. Photoemission requires that an optically excited electron can escape from the solid into the vacuum. This is not possible if the electron’s final state lies in the region between the Fermi level and the vacuum level. Inverse photoemission consists of dropping an electron from an initial state above the vacuum energy into a final empty state above the Fermi level via an optical transition [2]. If the emitted radiation is in the ultraviolet region, the photon momentum can be neglected in the total momentum balance. Consequently, from a knowledge of energy, momentum and spin of the electron in the initial state, the corresponding quantum numbers of the final electronic state in the sample can be deduced. Inverse photoemission is nothing but the production of Bremsstrahlung by electrons impinging on a solid sample. Experimental research on this topic dates back to 1915 [3]. The important step to Bremsstrahlung detection in the ultraviolet region was taken roughly sixty years later in 1977, when a simple energy selective Geiger-Miiller counter with mean detection energy of 9.7 eV was employed in a Bremsstrahlung experiment [4]. The counter has an entrance window of CaF, and a filling of iodine and helium. Its energy selective properties result from a matching of the iodine photo0378-5963/85/$03.30 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
V. Dose
/ Topics in uliraviolet
inverse photoemission
339
electric threshold with the ultraviolet transmission properties of CaF,. The combination provides a band pass centered at 9.7 eV about 0.7 eV (FWHM) wide. The special merits of this band-pass detector are its high quantum efficiency of about 8% [5] with a large solid angle for photon collection. Initial experience showed an overall gain in sensitivity of four orders of magnitude in a Bremsstrahlung experiment compared to conventional setups [6]. This large gain in sensitivity combined with the considerably lower quantum (and consequently electron) energy cuts the power dissipation on the sample from about 10 W/cm2 to 100 p W/cm*, with a concomitant reduction of radiation damage of samples and opens up the possibility of studying unoccupied electronic states at clean and adsorbate covered surfaces. Examples will be given in sections 2 and 4. Inverse photoemission employing light detection at a fixed quantum energy is also called isochromat spectroscopy and is the exact counterpart to angular resolved photoemission research using resonance lamps. Both experiments provide information on restricted regions in momentum space only. In order to reach arbitrary points in the three-dimensional momentum space, the photon energy has to be varied. This requirement has led to the construction of synchrotron radiation facilities for angular resolved photoemission [7]. For inverse photoemission experiments, a grating monochromator combined with multidetection techniques has been employed [8]. The expense for the additional degree of freedom of choosing the quantum detection energy is a loss in overall sensitivity by nearly two orders of magnitude compared to the Geiger counter approach. The measurement of electron spin is an essential requirement in the study of magnetic materials [9]. In photoemission experiments, the spin analysis is performed after determination of energy and momentum using Mott scattering. Even very efficient Mott detectors reduce the overall sensitivity of the photoemission experiment by three orders of magnitude [lo]. Inverse photoemission does not sufier from this drawback. If one chooses a negative electron affinity GaAsP photoemitter as the source of primary electrons, their spin polarization is an available option [ll]. Just by choosing the appropriate polarization of the exciting light, the emitted electrons can be spin polarized without any sacrifice in emission current. For this simple reason I dare forcast that inverse photoemission will play a major role in empty band mapping of magnetic materials. Part of the results obtained so far will be discussed in section 3.
2. Bulk energy bands The measurement occupied bulk bands
of the energy versus momentum shall be discussed with reference
dispersion of unto data for Ni(lOO).
340
V. Dose / Topics in ultravioletinversephotoemission
The left panel of fig. 1 displays isochromat spectra for angles of incidence between 0” and 25” with respect to the surface normal [12]. The polar angle was varied in the rXULK mirror plane. The normal incidence spectrum exhibits two emission features. An inflection point appears slightly above EF. 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. The second feature in the normal incidence spectrum is a resonance-like emission enhancement at 1.8eV. 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” spectra and fades out for smaller angles. The observed peak positions of the dispersing structures are plotted as open circles in fig. 2 as a function of k,,, the component of momentum of the incident electron parallel to the crystal surface. The interpretation of the observed emission features in terms of a bulk direct transition model requires the evaluation of all values of k,, irrespective of k,, for which two bands 9.7 eV apart exist. The final band energy from such pairs is plotted as a function of k,, as solid lines in fig. 2. c
Ni (001)
Ni (001) f1101
Energy
Fig. 1. Isochromat spectra of inverse photoemission.
above
LllOl
EF( eV 1
from Ni(001) compared
to calculations
based on the one-step
theory
V. Dose
k,,/(TTla)
/ Topics in ultraviolet
inverse photoemission
341
-[llOl
Fig. 2. Open circles denote emission peak positions as a function of kll. Diamonds indicate the results of Woodruff et al. Theoretical predictions on the basis of the bulk direct transition model are shown as solid [13] and dashed [14] curves. Solid circles represent theoretical results from a one-step calculation [ 161.
The band structure used to prepare this plot has been kindly supplied by from an MAPW calculation. Bross and Schiekel [13] and was obtained Dashed lines are from Woodruff et al. who used a nickel band structure calculated in a combined interpolation scheme [14]. Experimental results from Woodruff et al. [14] are shown as full diamonds. A theoretically more satisfactory though physically less transparent approach to photoemission and Bremsstrahlung spectra is provided by the one-step theory 1151. The advantage of this method as compared to the three-step bulk direct transition model is that it treats penetration of the electron into the sample, transport in the sample and optical decay to a lower lying band coherently. Calculations for Ni(lOO) are available from the work of Thiirner and Borstel [16]. These calculations are based on the potential generated by Moruzzi et al. [17]. An absorptive part of - 0.4 eV was added to the potential for the final states. For the initial state bands, an absorption part of - 0.75 eV was used. A rectangular surface barrier representing a work function of 5.1 eV was placed at 0.8 interlayer distances outside the outermost atomic layer. The right panel of fig. 1 shows the resulting calculated spectra after convolution with a Gaussian in order to account for the finite experimental resolution. Peak positions from this one-step calculation are shown in fig. 2 as full dots. The agreement of the predictions of the one-step theory with the experimental data is considered to be excellent, in particular the branching of the emission features near k,, = 0.5da shows up in experiment and theory. No emission is observed on the left-hand part of branch “b” and
342
V. Dose / Topics in uliravioletinversephotoemission
only very 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 emission” in photoelectron spectroscopy and is therefore expected to be weak. In fact, the bulk transition matrix element [14] vanishes on branch “b” for k,,< 0.3?r/a while it becomes very small on branch “a” for k,, > 0.4vda. Though the overall agreement in energy positions and intensities between theory and experiment in fig. 1 is excellent, discrepancies in details do exist. While the experimental spectra at small polar angles rise again above 4 eV, the corresponding theoretical spectra remain flat. It is shown in another contribution to this volume [18] that the observed feature is due to transitions into surface states associated with the image potential [19]. The one-step theory accounts automatically for surface effects; however, the simple rectangular barrier used for the actual computations [20] is obviously a highly oversimplified representation of the surface potential.
3. Spin-resolved measurements While the electronic structure of most crystalline materials is completely specified if energies are known as a function of momentum, for ferromagnetic materials still another variable, the electron spin requires attention. Given a particular electron momentum, a particular band in the itinerant ferromagnets iron, cobalt, and nickel, is split into two depending on the direction of electron spin with respect to the magnetization. This ferromagnetic exchange splitting is of the order of 0.3 eV for nickel, but may be as large as 2 eV for iron, depending on electron momentum and energy. This is safely larger than the optical resolution of the iodine band-pass counter and encourages spin-resolved studies of empty energy bands in iron. Fig. 3 shows a selection of isochromat spectra from Fe(ll0) for four angles of incidence [21]. The experiment employed a longitudinally spin polarized beam [22]. For normally incident electrons, the polarization vector and the sample magnetization are orthogonal and the effective polarization vanishes. No spin-resolved data are therefore available for 8 = 0”. The upper curve in each panel labelled &+ + n_) represents spin-averaged data. The lower full dots labelled n, indicate emission from transitions into empty majority states. n_ denotes corresponding data for minority states. The spin-averaged data show two separated emission features for 8 s 20” but exhibit only one broad maximum for 6 2 25” (see also the left panel of fig. 5). The rather similar shape of the spin-averaged data for 8 3 25” emphasizes the necessity for spin resolution in order to derive more detailed information. n, spectra show a single well-resolved emission maximum which disperses with increasing polar angle to higher energies. The energetic
V. Dose / Topics in ultraviolet
inverse photoemission
343
Fe(llO1
0
2
4
ENERGY (E-EF)/eV Fig. 3. Spin-averaged and spin-resolved isochromat spectra at various angles of incidence. Emission from transitions into empty minority states is marked by open circles. Upper full dots represent spin-averaged data, while lower full dots indicate emission from transitions into majority final states.
position
of this maximum is indicated by solid arrows. Emission peaks in the spectra are indicated by dashed arrows. The peak positions are a function of k,,, the component of electron momentum parallel to the surface, are summarized as full circles in fig. 4. Data points from spectra for polar angles other than in fig. 3 have also been included. One majority final band with rapid dispersion and two minority bands are observed, one of which shows practically no dispersion. An indication of a third minority band 4 eV above EF is also present. Full rectangles indicate the theoretical prediction terms of bulk direct transitions derived from a band structure plot along high symmetry lines [23]. Considering both, the experimental uncertainty and the reading error on the theoretical data, the agreement is quite good. Itinerant electron ferromagnetism belongs to the class of solid state phenomena which are still only poorly understood. Various models of itinerant electron ferromagnetism are presently discussed. While there is no debate about the existence of an exchange splitting, its behaviour as a function of temperature, especially near the Curie point is a question of major concern. Fig. 5 shows spin-resolved isochromats for two different temperatures from Fe(ll0) and Fe(lOO) [24]. The n_ emission originates from the flat minority band identified in fig. 4. This band extends with small dispersion all over the Brillouin zone and can therefore also be observed at other points in momentum space using different crystal surfaces. The right panel of fig. 5 provides an example. Increasing the sample temperature to n_
344
V. Dose
minority ’
/ Topics in ultraviolet
band
majority t
k=97eV
5 k z
-
z2
21q;++
0c
?=I
band
dispersion
dispersion
%
inverse photoemission
hw=9.7eV
t ‘A,
t ---A, + i
z
+ c+ It
*,
E+tt
m 0
0.1
0.3
F, I
I
.
ittt
13 t ,Yk+
as
I
0
0.1
I
0.3
I
,
,
0.5
k,,@)
Fig. 4. Full dots show the dispersion of emission features marked indicate theoretical E(/q) values for bulk direct transitions.
by arrows
in fig. 3. Rectangles
86% of the Curie temperature leads to a decrease of the polarization effect. The energetic position of the final minority band remains, however, stationary contrary to expectation from the classical Stoner model. The present data seem to be so clear that one is easily led to premature conclusions. Similar temperature-dependent measurements have been made for rapidly dispersing bands near the H-point of the bee Brillouin zone. The behaviour of these bands was radically different in that they showed by and large classical Stoner behaviour. The complicated dependence of polarization and exchange splitting on momentum, energy and temperature clearly
&--_I Fe(ll0)
0
2
8 = 60°
L
ENERGY
Fig. 5. Spin-resolved temperature.
isochromat
(E-E,)
spectra
/eV
as a function
of temperature
in units
of the Curie
V. Dose
I Topics in ultraviolet
inverse photoemission
345
emphasizes the importance of experimental data from angular-resolved photoemission and inverse photoemission for a solution of one of the outstanding problems in solid state physics.
4. Chemisorption Molecular or dissociative chemisorption of gases on metal surfaces is an important step in heterogeneous catalysis [25]. The chemisorption problem has therefore largely stimulated the development of surface science. Among the vast amount of molecule-substrate combinations, absorption of CO and NO at transition metal surfaces has attracted particular interest because of the quite different tendency of the two molecules to dissociate upon adsorption [26]. While decomposition of CO is observed only at non-noble transition metals, even with noble metals as Pd and Ir at least partial decomposition of NO is detected [27]. The different behaviour of the two molecules is related to the different occupation of the antibonding 27r molecular orbital which is empty in CO and singly occupied in NO. In view of the donation/back donation model of molecular chemisorption [28], increased back donation of substrate electrons into not fully occupied orbitals of the chemisorbed molecule will lead to a weakening of the molecular bonding strength and thus favour decomposition. In case of NO, strong back donation will cause a substantial decrease of the molecule’s stability since the 2~ level is singly occupied even prior to adsorption. Isochromat spectra from a Pd(lOO) sample at 110 K with and without adsorbed NO are shown in fig. 6 [29]. The spectrum from clean Pd is characterized by two peaks, right above Er and 3 eV above Er. The latter structure corresponds to a bulk direct transition between bands 7 and 6 and is exactly analogous to the transition discussed in nickel in section 2. The lower curve in fig. 6 shows its dispersion when the angle of incidence of the electrons is increased to 30”. The feature at Er relates to the empty d-bands of Pd. Upon NO adsorption, a new structure develops at 1.8 eV between the two Pd emission features. It is clearly separated. Corresponding isochromat spectra for CO adsorption on Pd(lOO) are shown in fig. 7. The CO-induced extra emission is again well separated from the substrate emission and is centred around 4.8 eV above Fr. With both adsorbates an attenuation of the Pd substrate emission is observed. The adsorption-induced extra emission in figs. 5 and 6 has to be attributed to the 27r-derived empty energy levels of NO/Pd and CO/Pd, respectively. The extra peaks observed after adsorption are relatively broad. Since the NO-induced peak occurs at only 1.8 eV above Er, it will extend to below the Fermi level. This is equivalent to substantial T back donation. For CO, on the other hand, only a negligible portion of the 2r-derived states will be
346
V. Dose
/ Topics in ultraviolet
Pd (100)
inverse photoemission
+ NO
0123L56789 Energy
above
Fig. 6. Isochromat spectra are for normal incidence.
E,(eV)
from clean and NO covered
_( , , , , , ,;, , E vat
0
1
2
Energy
Fig. 7. Normal
3
.!I
above
incidence
5
6
7
8
Pd(lOO) surfaces.
The top three spectra
( E
E,(eVl
isochromat
spectra
from clean and CO covered
Pd(100).
V. Dose
occupied sociate.
in accord
5. Concluding
/ Topics in ultraviolet
with
the observed
347
inverse photoemission
difference
in the
tendency
to dis-
remarks
Only a few applications of inverse photoemission have been discussed here due to space limitations. It is therefore worth mentioning what else has been achieved to date. Absolute methods of band mapping such as energy coincidence and appearance angle have been applied with Bremsstrahlung spectroscopy. Two- and three-dimensional bands in layered materials have been separated [30]. Atomic chemisorption and the dispersion of adsorbateinduced electronic states is presently investigated. Last but not least, unoccupied electronic surface states of the crystal-induced and the image potential-induced kind have been identified [20]. The latter surface states are of particular interest since they have no predecessor in ordinary photoemission.
Acknowledgements This work has been financially supported by the Deutsche Forschungsgemeinschaft. I am indebted to Mrs. H. Hanft for typing the manuscript and to Mrs. M. Lukacs for preparing the figures.
References [l] F.J. Himpsel, Advan. Phys. 32 (1983) 1. [2] V. Dose, Progr. Surface Sci. 13 (1983) 225; H. Scheidt, Fortschr. Physik 31 (1983) 357; D.P. Woodruff, P.D. Johnson and N.V. Smith, J. Vacuum Sci. Technol. Al (1983) 1104; N.V. Smith, Vacuum 33 (1983) 803; F.J. Himpsel and Th. Fauster, J. Vacuum Sci. Technol. A2 (1984) 815; V. Dose, J. Phys. Chem. 88 (1984) 1681. [3] W. Duane and F.L. Hunt, Phys. Rev. 6 (1915) 166. [4] V. Dose, Appl. Phys. 14 (1977) 117. [5] V. Dose, Rev. Sci. Instr. 39 (1%8) 1055. [6] G. Denninger, V. Dose and H. Scheidt, Appl. Phys. 18 (1979) 375. [7] N.V. Smith and F.J. Himpsel, in: Handbook on Synchrotron Radiation, Vol. 1, Ed. E.E Koch (North-Holland, Amsterdam, 1983) p. 905. [S] Th. Fauster, F.J. Himpscl, J.J. Donelon and A. Marx, Rev. Sci. Instr. 54 (1983) 68. [9] E. Kisker, J. Phys. Chem. 87 (1983) 3597. [lo] D.T. Pierce and R.J. Celotta, Advan. Electron. Electron Phys. 56 (1981) 219. [ll] R.J. Celotta and D.T. Pierce, Advan. At. Mol. Phys. 16 (1980) 101. [12] K. Desinger, V. Dose, M. Glob1 and H. Scheidt, Solid State Commun. 49 (1984) 479. [13] H. Bross and B. Schiekel, private communication.
348
V. Dose
/ Topics in ultraviolet
inverse photoemission
[14] [15] [16] [17]
D.P. Woodruff, N.V. Smith, P.D. Johnson and W.A. Royer, Phys. Rev. B26 (1982) 2943. J.B. Pendry, J. Phys. C (Solid State Phys.) 14 (1981) 1381. G. Thiirner and G. Borstel, Solid State Commun. 47 (1983) 329. V.L. Moruzzi, J.F. Januk and A.R. Williams, Calculated Properties of Metals (Pergamon, New York, 1978). (181 N.V. Smith, Appl. Surface Sci. 22/23 (1985) 349.
[19] V. Dose, W. Altmann, A. Goldmann, U. Kolac and J. Rogozik, Phys. Rev. Letters 52 (1984) 1919. [20] V. Dose, U. Kolac, G. Borstel and G. Thorner, Phys. Rev. B29 (1984) 7030. [21] H. Scheidt, M. Glob], V. Dose and J. Kirschner, Phys. Rev. Letters 51 (1983) 1688. [22] J. Kirschner, H.P. Oepen and H. Ibach, Appl. Phys. A40 (1983) 177. [23] J. Callaway and C.S. Wang, Phys. Rev. B16 (1977) 2095. [24] J. Krischner, M. Globl, V. Dose and H. Scheidt, Phys. Rev. Letters 53 (1984) 612. [25] G. Ertl, J. Vacuum Sci. Technol. Al (1983) 1247. [26] T.N. Rhodin and J.W. Gadzuk, in: The Nature of the Surface Chemical Bond, Eds. T.N. Rhodin and G. Ertl (North-Holland, Amsterdam, 1979). [27] W.F. Egelhoff, in: The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, Eds. D.A. King and D.P. Woodruff (Elsevier, Amsterdam, 1982). [28] G. Blyholder, J. Phys. Chem. 68 (1964) 2772. [29] J. Rogozik, J. Kiippers and V. Dose, Surface Sci. 148 (1984) L653. [30] Th. Fauster, F.J. Himpsel, J.E. Fischer and E.W. Plummer, Phys. Rev. Letters 51 (1983) 430.
Applications
of Surface
Science
22123 (1985) 338-348
North-Holland,
TOPICS IN ULTRAVIOLET
Amsterdam
INVERSE PHOTOEMISSION
V. DOSE Physikalisches Received
Institut der Universitiit,
27 August
1984; accepted
Am Hubland,
for publication
D-8700 31 October
Wiirzburg, Fed. Rep.
of Germany
1984
Ultraviolet inverse photoemission is an exciting new technique for band mapping of empty electronic states in solids and at surfaces. It includes the energy region between the Fermi and the vacuum level inaccessible by ordinary photoemission. Applications discussed in this paper include band mapping in nickel, spin-resolved studies of iron, and chemisorption of NO and CO on palladium.
1. Introduction Electronic states in the bulk of single crystals and at their surfaces can be characterized by their energy, momentum, spin, and symmetry. Experimental techniques to access these quantities are angular-resolved electron spectroscopies, in particular angular-resolved photoemission. Continuous efforts during the past ten years have developed it to its present mature state [l]. Photoemission requires that an optically excited electron can escape from the solid into the vacuum. This is not possible if the electron’s final state lies in the region between the Fermi level and the vacuum level. Inverse photoemission consists of dropping an electron from an initial state above the vacuum energy into a final empty state above the Fermi level via an optical transition [2]. If the emitted radiation is in the ultraviolet region, the photon momentum can be neglected in the total momentum balance. Consequently, from a knowledge of energy, momentum and spin of the electron in the initial state, the corresponding quantum numbers of the final electronic state in the sample can be deduced. Inverse photoemission is nothing but the production of Bremsstrahlung by electrons impinging on a solid sample. Experimental research on this topic dates back to 1915 [3]. The important step to Bremsstrahlung detection in the ultraviolet region was taken roughly sixty years later in 1977, when a simple energy selective Geiger-Miiller counter with mean detection energy of 9.7 eV was employed in a Bremsstrahlung experiment [4]. The counter has an entrance window of CaF, and a filling of iodine and helium. Its energy selective properties result from a matching of the iodine photo0378-5963/85/$03.30 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
V. Dose
/ Topics in uliraviolet
inverse photoemission
339
electric threshold with the ultraviolet transmission properties of CaF,. The combination provides a band pass centered at 9.7 eV about 0.7 eV (FWHM) wide. The special merits of this band-pass detector are its high quantum efficiency of about 8% [5] with a large solid angle for photon collection. Initial experience showed an overall gain in sensitivity of four orders of magnitude in a Bremsstrahlung experiment compared to conventional setups [6]. This large gain in sensitivity combined with the considerably lower quantum (and consequently electron) energy cuts the power dissipation on the sample from about 10 W/cm2 to 100 p W/cm*, with a concomitant reduction of radiation damage of samples and opens up the possibility of studying unoccupied electronic states at clean and adsorbate covered surfaces. Examples will be given in sections 2 and 4. Inverse photoemission employing light detection at a fixed quantum energy is also called isochromat spectroscopy and is the exact counterpart to angular resolved photoemission research using resonance lamps. Both experiments provide information on restricted regions in momentum space only. In order to reach arbitrary points in the three-dimensional momentum space, the photon energy has to be varied. This requirement has led to the construction of synchrotron radiation facilities for angular resolved photoemission [7]. For inverse photoemission experiments, a grating monochromator combined with multidetection techniques has been employed [8]. The expense for the additional degree of freedom of choosing the quantum detection energy is a loss in overall sensitivity by nearly two orders of magnitude compared to the Geiger counter approach. The measurement of electron spin is an essential requirement in the study of magnetic materials [9]. In photoemission experiments, the spin analysis is performed after determination of energy and momentum using Mott scattering. Even very efficient Mott detectors reduce the overall sensitivity of the photoemission experiment by three orders of magnitude [lo]. Inverse photoemission does not sufier from this drawback. If one chooses a negative electron affinity GaAsP photoemitter as the source of primary electrons, their spin polarization is an available option [ll]. Just by choosing the appropriate polarization of the exciting light, the emitted electrons can be spin polarized without any sacrifice in emission current. For this simple reason I dare forcast that inverse photoemission will play a major role in empty band mapping of magnetic materials. Part of the results obtained so far will be discussed in section 3.
2. Bulk energy bands The measurement occupied bulk bands
of the energy versus momentum shall be discussed with reference
dispersion of unto data for Ni(lOO).
340
V. Dose / Topics in ultravioletinversephotoemission
The left panel of fig. 1 displays isochromat spectra for angles of incidence between 0” and 25” with respect to the surface normal [12]. The polar angle was varied in the rXULK mirror plane. The normal incidence spectrum exhibits two emission features. An inflection point appears slightly above EF. 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. The second feature in the normal incidence spectrum is a resonance-like emission enhancement at 1.8eV. 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” spectra and fades out for smaller angles. The observed peak positions of the dispersing structures are plotted as open circles in fig. 2 as a function of k,,, the component of momentum of the incident electron parallel to the crystal surface. The interpretation of the observed emission features in terms of a bulk direct transition model requires the evaluation of all values of k,, irrespective of k,, for which two bands 9.7 eV apart exist. The final band energy from such pairs is plotted as a function of k,, as solid lines in fig. 2. c
Ni (001)
Ni (001) f1101
Energy
Fig. 1. Isochromat spectra of inverse photoemission.
above
LllOl
EF( eV 1
from Ni(001) compared
to calculations
based on the one-step
theory
V. Dose
k,,/(TTla)
/ Topics in ultraviolet
inverse photoemission
341
-[llOl
Fig. 2. Open circles denote emission peak positions as a function of kll. Diamonds indicate the results of Woodruff et al. Theoretical predictions on the basis of the bulk direct transition model are shown as solid [13] and dashed [14] curves. Solid circles represent theoretical results from a one-step calculation [ 161.
The band structure used to prepare this plot has been kindly supplied by from an MAPW calculation. Bross and Schiekel [13] and was obtained Dashed lines are from Woodruff et al. who used a nickel band structure calculated in a combined interpolation scheme [14]. Experimental results from Woodruff et al. [14] are shown as full diamonds. A theoretically more satisfactory though physically less transparent approach to photoemission and Bremsstrahlung spectra is provided by the one-step theory 1151. The advantage of this method as compared to the three-step bulk direct transition model is that it treats penetration of the electron into the sample, transport in the sample and optical decay to a lower lying band coherently. Calculations for Ni(lOO) are available from the work of Thiirner and Borstel [16]. These calculations are based on the potential generated by Moruzzi et al. [17]. An absorptive part of - 0.4 eV was added to the potential for the final states. For the initial state bands, an absorption part of - 0.75 eV was used. A rectangular surface barrier representing a work function of 5.1 eV was placed at 0.8 interlayer distances outside the outermost atomic layer. The right panel of fig. 1 shows the resulting calculated spectra after convolution with a Gaussian in order to account for the finite experimental resolution. Peak positions from this one-step calculation are shown in fig. 2 as full dots. The agreement of the predictions of the one-step theory with the experimental data is considered to be excellent, in particular the branching of the emission features near k,, = 0.5da shows up in experiment and theory. No emission is observed on the left-hand part of branch “b” and
342
V. Dose / Topics in uliravioletinversephotoemission
only very 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 emission” in photoelectron spectroscopy and is therefore expected to be weak. In fact, the bulk transition matrix element [14] vanishes on branch “b” for k,,< 0.3?r/a while it becomes very small on branch “a” for k,, > 0.4vda. Though the overall agreement in energy positions and intensities between theory and experiment in fig. 1 is excellent, discrepancies in details do exist. While the experimental spectra at small polar angles rise again above 4 eV, the corresponding theoretical spectra remain flat. It is shown in another contribution to this volume [18] that the observed feature is due to transitions into surface states associated with the image potential [19]. The one-step theory accounts automatically for surface effects; however, the simple rectangular barrier used for the actual computations [20] is obviously a highly oversimplified representation of the surface potential.
3. Spin-resolved measurements While the electronic structure of most crystalline materials is completely specified if energies are known as a function of momentum, for ferromagnetic materials still another variable, the electron spin requires attention. Given a particular electron momentum, a particular band in the itinerant ferromagnets iron, cobalt, and nickel, is split into two depending on the direction of electron spin with respect to the magnetization. This ferromagnetic exchange splitting is of the order of 0.3 eV for nickel, but may be as large as 2 eV for iron, depending on electron momentum and energy. This is safely larger than the optical resolution of the iodine band-pass counter and encourages spin-resolved studies of empty energy bands in iron. Fig. 3 shows a selection of isochromat spectra from Fe(ll0) for four angles of incidence [21]. The experiment employed a longitudinally spin polarized beam [22]. For normally incident electrons, the polarization vector and the sample magnetization are orthogonal and the effective polarization vanishes. No spin-resolved data are therefore available for 8 = 0”. The upper curve in each panel labelled &+ + n_) represents spin-averaged data. The lower full dots labelled n, indicate emission from transitions into empty majority states. n_ denotes corresponding data for minority states. The spin-averaged data show two separated emission features for 8 s 20” but exhibit only one broad maximum for 6 2 25” (see also the left panel of fig. 5). The rather similar shape of the spin-averaged data for 8 3 25” emphasizes the necessity for spin resolution in order to derive more detailed information. n, spectra show a single well-resolved emission maximum which disperses with increasing polar angle to higher energies. The energetic
V. Dose / Topics in ultraviolet
inverse photoemission
343
Fe(llO1
0
2
4
ENERGY (E-EF)/eV Fig. 3. Spin-averaged and spin-resolved isochromat spectra at various angles of incidence. Emission from transitions into empty minority states is marked by open circles. Upper full dots represent spin-averaged data, while lower full dots indicate emission from transitions into majority final states.
position
of this maximum is indicated by solid arrows. Emission peaks in the spectra are indicated by dashed arrows. The peak positions are a function of k,,, the component of electron momentum parallel to the surface, are summarized as full circles in fig. 4. Data points from spectra for polar angles other than in fig. 3 have also been included. One majority final band with rapid dispersion and two minority bands are observed, one of which shows practically no dispersion. An indication of a third minority band 4 eV above EF is also present. Full rectangles indicate the theoretical prediction terms of bulk direct transitions derived from a band structure plot along high symmetry lines [23]. Considering both, the experimental uncertainty and the reading error on the theoretical data, the agreement is quite good. Itinerant electron ferromagnetism belongs to the class of solid state phenomena which are still only poorly understood. Various models of itinerant electron ferromagnetism are presently discussed. While there is no debate about the existence of an exchange splitting, its behaviour as a function of temperature, especially near the Curie point is a question of major concern. Fig. 5 shows spin-resolved isochromats for two different temperatures from Fe(ll0) and Fe(lOO) [24]. The n_ emission originates from the flat minority band identified in fig. 4. This band extends with small dispersion all over the Brillouin zone and can therefore also be observed at other points in momentum space using different crystal surfaces. The right panel of fig. 5 provides an example. Increasing the sample temperature to n_
344
V. Dose
minority ’
/ Topics in ultraviolet
band
majority t
k=97eV
5 k z
-
z2
21q;++
0c
?=I
band
dispersion
dispersion
%
inverse photoemission
hw=9.7eV
t ‘A,
t ---A, + i
z
+ c+ It
*,
E+tt
m 0
0.1
0.3
F, I
I
.
ittt
13 t ,Yk+
as
I
0
0.1
I
0.3
I
,
,
0.5
k,,@)
Fig. 4. Full dots show the dispersion of emission features marked indicate theoretical E(/q) values for bulk direct transitions.
by arrows
in fig. 3. Rectangles
86% of the Curie temperature leads to a decrease of the polarization effect. The energetic position of the final minority band remains, however, stationary contrary to expectation from the classical Stoner model. The present data seem to be so clear that one is easily led to premature conclusions. Similar temperature-dependent measurements have been made for rapidly dispersing bands near the H-point of the bee Brillouin zone. The behaviour of these bands was radically different in that they showed by and large classical Stoner behaviour. The complicated dependence of polarization and exchange splitting on momentum, energy and temperature clearly
&--_I Fe(ll0)
0
2
8 = 60°
L
ENERGY
Fig. 5. Spin-resolved temperature.
isochromat
(E-E,)
spectra
/eV
as a function
of temperature
in units
of the Curie
V. Dose
I Topics in ultraviolet
inverse photoemission
345
emphasizes the importance of experimental data from angular-resolved photoemission and inverse photoemission for a solution of one of the outstanding problems in solid state physics.
4. Chemisorption Molecular or dissociative chemisorption of gases on metal surfaces is an important step in heterogeneous catalysis [25]. The chemisorption problem has therefore largely stimulated the development of surface science. Among the vast amount of molecule-substrate combinations, absorption of CO and NO at transition metal surfaces has attracted particular interest because of the quite different tendency of the two molecules to dissociate upon adsorption [26]. While decomposition of CO is observed only at non-noble transition metals, even with noble metals as Pd and Ir at least partial decomposition of NO is detected [27]. The different behaviour of the two molecules is related to the different occupation of the antibonding 27r molecular orbital which is empty in CO and singly occupied in NO. In view of the donation/back donation model of molecular chemisorption [28], increased back donation of substrate electrons into not fully occupied orbitals of the chemisorbed molecule will lead to a weakening of the molecular bonding strength and thus favour decomposition. In case of NO, strong back donation will cause a substantial decrease of the molecule’s stability since the 2~ level is singly occupied even prior to adsorption. Isochromat spectra from a Pd(lOO) sample at 110 K with and without adsorbed NO are shown in fig. 6 [29]. The spectrum from clean Pd is characterized by two peaks, right above Er and 3 eV above Er. The latter structure corresponds to a bulk direct transition between bands 7 and 6 and is exactly analogous to the transition discussed in nickel in section 2. The lower curve in fig. 6 shows its dispersion when the angle of incidence of the electrons is increased to 30”. The feature at Er relates to the empty d-bands of Pd. Upon NO adsorption, a new structure develops at 1.8 eV between the two Pd emission features. It is clearly separated. Corresponding isochromat spectra for CO adsorption on Pd(lOO) are shown in fig. 7. The CO-induced extra emission is again well separated from the substrate emission and is centred around 4.8 eV above Fr. With both adsorbates an attenuation of the Pd substrate emission is observed. The adsorption-induced extra emission in figs. 5 and 6 has to be attributed to the 27r-derived empty energy levels of NO/Pd and CO/Pd, respectively. The extra peaks observed after adsorption are relatively broad. Since the NO-induced peak occurs at only 1.8 eV above Er, it will extend to below the Fermi level. This is equivalent to substantial T back donation. For CO, on the other hand, only a negligible portion of the 2r-derived states will be
346
V. Dose
/ Topics in ultraviolet
Pd (100)
inverse photoemission
+ NO
0123L56789 Energy
above
Fig. 6. Isochromat spectra are for normal incidence.
E,(eV)
from clean and NO covered
_( , , , , , ,;, , E vat
0
1
2
Energy
Fig. 7. Normal
3
.!I
above
incidence
5
6
7
8
Pd(lOO) surfaces.
The top three spectra
( E
E,(eVl
isochromat
spectra
from clean and CO covered
Pd(100).
V. Dose
occupied sociate.
in accord
5. Concluding
/ Topics in ultraviolet
with
the observed
347
inverse photoemission
difference
in the
tendency
to dis-
remarks
Only a few applications of inverse photoemission have been discussed here due to space limitations. It is therefore worth mentioning what else has been achieved to date. Absolute methods of band mapping such as energy coincidence and appearance angle have been applied with Bremsstrahlung spectroscopy. Two- and three-dimensional bands in layered materials have been separated [30]. Atomic chemisorption and the dispersion of adsorbateinduced electronic states is presently investigated. Last but not least, unoccupied electronic surface states of the crystal-induced and the image potential-induced kind have been identified [20]. The latter surface states are of particular interest since they have no predecessor in ordinary photoemission.
Acknowledgements This work has been financially supported by the Deutsche Forschungsgemeinschaft. I am indebted to Mrs. H. Hanft for typing the manuscript and to Mrs. M. Lukacs for preparing the figures.
References [l] F.J. Himpsel, Advan. Phys. 32 (1983) 1. [2] V. Dose, Progr. Surface Sci. 13 (1983) 225; H. Scheidt, Fortschr. Physik 31 (1983) 357; D.P. Woodruff, P.D. Johnson and N.V. Smith, J. Vacuum Sci. Technol. Al (1983) 1104; N.V. Smith, Vacuum 33 (1983) 803; F.J. Himpsel and Th. Fauster, J. Vacuum Sci. Technol. A2 (1984) 815; V. Dose, J. Phys. Chem. 88 (1984) 1681. [3] W. Duane and F.L. Hunt, Phys. Rev. 6 (1915) 166. [4] V. Dose, Appl. Phys. 14 (1977) 117. [5] V. Dose, Rev. Sci. Instr. 39 (1%8) 1055. [6] G. Denninger, V. Dose and H. Scheidt, Appl. Phys. 18 (1979) 375. [7] N.V. Smith and F.J. Himpsel, in: Handbook on Synchrotron Radiation, Vol. 1, Ed. E.E Koch (North-Holland, Amsterdam, 1983) p. 905. [S] Th. Fauster, F.J. Himpscl, J.J. Donelon and A. Marx, Rev. Sci. Instr. 54 (1983) 68. [9] E. Kisker, J. Phys. Chem. 87 (1983) 3597. [lo] D.T. Pierce and R.J. Celotta, Advan. Electron. Electron Phys. 56 (1981) 219. [ll] R.J. Celotta and D.T. Pierce, Advan. At. Mol. Phys. 16 (1980) 101. [12] K. Desinger, V. Dose, M. Glob1 and H. Scheidt, Solid State Commun. 49 (1984) 479. [13] H. Bross and B. Schiekel, private communication.
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[14] [15] [16] [17]
D.P. Woodruff, N.V. Smith, P.D. Johnson and W.A. Royer, Phys. Rev. B26 (1982) 2943. J.B. Pendry, J. Phys. C (Solid State Phys.) 14 (1981) 1381. G. Thiirner and G. Borstel, Solid State Commun. 47 (1983) 329. V.L. Moruzzi, J.F. Januk and A.R. Williams, Calculated Properties of Metals (Pergamon, New York, 1978). (181 N.V. Smith, Appl. Surface Sci. 22/23 (1985) 349.
[19] V. Dose, W. Altmann, A. Goldmann, U. Kolac and J. Rogozik, Phys. Rev. Letters 52 (1984) 1919. [20] V. Dose, U. Kolac, G. Borstel and G. Thorner, Phys. Rev. B29 (1984) 7030. [21] H. Scheidt, M. Glob], V. Dose and J. Kirschner, Phys. Rev. Letters 51 (1983) 1688. [22] J. Kirschner, H.P. Oepen and H. Ibach, Appl. Phys. A40 (1983) 177. [23] J. Callaway and C.S. Wang, Phys. Rev. B16 (1977) 2095. [24] J. Krischner, M. Globl, V. Dose and H. Scheidt, Phys. Rev. Letters 53 (1984) 612. [25] G. Ertl, J. Vacuum Sci. Technol. Al (1983) 1247. [26] T.N. Rhodin and J.W. Gadzuk, in: The Nature of the Surface Chemical Bond, Eds. T.N. Rhodin and G. Ertl (North-Holland, Amsterdam, 1979). [27] W.F. Egelhoff, in: The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, Eds. D.A. King and D.P. Woodruff (Elsevier, Amsterdam, 1982). [28] G. Blyholder, J. Phys. Chem. 68 (1964) 2772. [29] J. Rogozik, J. Kiippers and V. Dose, Surface Sci. 148 (1984) L653. [30] Th. Fauster, F.J. Himpsel, J.E. Fischer and E.W. Plummer, Phys. Rev. Letters 51 (1983) 430.