Crystal field splitting of core levels in β-Sn

Solid State Communications, Vol. 69, No. 6, pp. 689-692, 1989. Printed in Great Britain.

0038-1098/89 $3.00 + .00 Pergamon Press plc

C R Y S T A L F I E L D S P L I T T I N G OF CORE LEVELS IN/~-Sn G.K. Wertheim and D.N.E. Buchanan AT&T Bell Laboratories, Murray Hill, NJ 07974, USA (Received 11 October 1988 by J. Tauc)

Photoemission spectra of the 4d level of metallic tin, taken with 90 meV resolution exhibit crystal field splittings of t h e j = 3/2 and 5/2 spin-orbit components amounting to 115 and 146meV, respectively. The room temperature phonon broadening is approximately 50meV, in good agreement with a recent theoretical estimate. 1. I N T R O D U C T I O N AS T H E atomic number increases from 46 at Pd to 50 at Sn the 4d electron states move from the Fermi level to a binding energy of 24 eV, losing their band character and becoming core electrons. The 4d spectrum of (white)/~-Sn meets the criteria that characterize a core level. The band dispersion is vanishingly small, and the spectrum has become a spin-orbit doublet with suitable branching ratio and a line shape appropriate for a metal. We will here demonstrate that hidden within that apparent simplicity is unresolved structure, which arises from interaction with the crystal field. Crystal-field effects in compounds of a number of metals, including tin, have been previously studied by photoemission [1-3], but the smaller splitting in the metallic state has not been determined. Crystal-field splitting has also been invoked to account for inconsistencies between thej = 5/2 and 7/2 spin-orbit components of tungsten that emerged in a study of the surface atom core level shift [4], but no attempt was made to assess its magnitude. 2. E X P E R I M E N T A L DETAILS These experiments were carried out on the Bell Laboratories U4 toroidal grating beam line at the National Synchrotron Light Source at Brookhaven National Laboratory. A Vacuum Science Workshop 100mm hemispherical analyzer was used to measure the energy of the photoelectrons. Data acquisition was under the control of an AT&T PC6300 computer. The Sn samples were of two kinds. Vacuum evaporated Sn layers deposited on an oxidized Si surface, and a bulk polycrystalline slab. The data shown here were taken with the solid sample, after argon ion sputtering, but the other samples gave identical results. An anneal at 425 K did not change the observed spectra, indicating that sputter damage anneals rapidly

at room temperature. This is not unexpected since room temperature corresponds to 60% of the melting point at 505K. N o vestige of implanted argon was detected. The surface cleanliness was monitored with Auger spectroscopy, which showed only carbon at levels of a few percent of a monolayer. 3. RESULTS A N D DISCUSSION Typical 4d spectra, taken at three photon energies, are shown in Fig. 1. Except for the change in background, the Sn 4d spectra are identical, and have the same line width. The lines drawn through the data points are the result of a quadratic smoothing. Next we attempt to obtain quantitative information about the line-shape parameters, i.e., the life-time and photon widths and the singularity index by making a least-squares fit to the data at 55 eV photon energy. We use a model function consisting of a spinorbit doublet made up of two Doniach-Sunjic (D-S) lines [5] convolved with a Gaussian, residing on a background represented by a polynomial. Five parameters are required to define a single D-S line: the lifetime width, the singularity index, the line position, the amplitude, and the phonon width. The other spinorbit component requires three additional parameters, on the assumption that the singularity index and phonon broadening will be the same as those of the first line. A single Gaussian was used to represent the combined effects of both phonon broadening and instrumental resolution. In the least-squares analyses of the 55 eV data we used a sloping linear background, specified by two additional parameters, making a total of 10. The curved background in data taken with smaller photon energies was represented by a quadratic or cubic. A 10-parameter fit to the 55 eV data is superficially satisfactory, see Fig. 2. However, the residuals of this fit, shown magnified by a factor of 14, exhibit pronounced structure in the region of the j --- 5/2 line,

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Fig. 1. Photoemission spectra of the Sn 4d electrons in a bulk tin sample at room temperature at three photon energies. The instrumental resolution is ~ 100meV. The lines through the data points are a guide to the eyes.

Fig. 2. Fit to the 55.eV photon energy data of Fig. 1 with a model-function described in the text. The residuals of the fit are shown at the bottom.

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which points to an inadequacy of the model function. The lifetime width of this line is 0.22eV, in good agreement with an early XPS determination [6]. This value depends largely on the fit to the right of the main line, where a Lorentzian behavior is followed over 6 line widths. However, the lifetime width of thej = 3/2 line is 3 percent smaller. This is unphysical, since the 3/2 line has an additional Coster-Kronig decay channel, and should, if anything, be broader. This is the second indication that our simple model is inadequate. The singularity index is 0.1 !, somewhat smaller than the value from earlier XPS work [6]. The spinorbit splitting is 1.056 eV and the spin-orbit ratio 0.66, i.e., close to the statistical value of 2/3. The Gaussian broadening, which includes the phonon broadening and the resolutions of the monochromator and the electron energy analyzer, is 0.195 eV. We next consider the sources of this line width. 3.1. Instrumental resolution We begin with an assessment of the properties of the measurement system. In Fig. 3 we exhibit the

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C R Y S T A L F I E L D S P L I T T I N G O F CORE LEVELS IN/%Sn

Fermi cut-off measured with the bulk tin sample cooled to about 100 K and a photon energy of 40 eV. The settings of the T G M and the electron energy analyzer were the same as those used to obtain the 40eV data in Fig. 1. The 105meV width of the Fermi edge is in accord with a 90 meV contribution from the T G M [7], 40 meV from the electron energy analyzer at 2 V pass-energy, and ~ 30meV from the thermal width of the Fermi function. At the 55eV photon energy and slit widths used to obtain the data in Fig. 2, the T G M resolution is 80 meV [7] and the contribution of the hemispherical analyzer is again 40 meV, leading to a net resolution close to 90 meV. Subtracting this from the 194 meV Gaussian width of the data leaves 173 meV to be accounted for by other processes. 3.2. Phonon broadening Phonon broadening at low photon energy is due almost entirely to the excitation of the lattice by the size-change of the hole-state atom in the final state; recoil effects are negligible. Phonon broadening in metals has been investigated theoretically by Flynn [8], who calculated a value of 46 meV for Sn at room temperature, much smaller than the excess width in our data. To assess the importance of this phenomenon in the Sn 4d photoemission spectrum, data were taken with the sample at ,--100K and 425K. No significant change in line width was found, indicating that the excess width is not due to phonon broadening. The nature of the residuals of the fit to the data shown at the bottom of Fig. 2 also support this conclusion. The distinctive structure of the residual in the vicinity of t h e j = 5/2 line is reproducible from data set to data set, indicating that it is due to an inherent property of the physical system, one which cannot be matched by a simple model function with Gaussian broadening [9]. Gaussian phonon broadening consequently cannot account for the details of the line shape. 3.3. Surface-atom core-level shift The extra width might also be due to an unresolved surface-atom core level shift. This shift should be small for an s-p metal like Sn, and has not been previously reported. Since the escape depth is of the order of 6 A at the kinetic energies where the data were taken, the surface layer makes a significant contribution to the observed spectrum. We used two methods in attempts to identify the surface-atom contribution. First, we increased the take-offangle to 60 ° to enhance the surface signal. No change in line shape was observed. Second, we used photon energies even closer to threshold than those in Fig. 1 to utilize the rapid increase in escape depth at kinetic energies below 10eV. Data taken at 35 and 33eV photon energy,

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Fig. 4. Fit to the 55 eV data from Fig. 1 with a mode: incorporating crystal field splitting. The crystal field states are indicated at the bottom of the figure. where the bulk signal should dominate, had the samc shape and Gaussian width as those taken with largeI photon energies. One is forced to conclude that the tin spectrum is representative of the bulk, and that the surface-atom core-level shift is much smaller in magnitude than 0.1 eV.

3.4. Crystal fieM splitting This motivates us to consider the possibility thal the degeneracy of each of the j = 3/2 and 5/2 spinorbit lines is lifted by crystal field coupling. In tetragonal//-tin all atoms are in equivalent sites with fourfold inversion symmetry, so that the degeneracy will be lifted completely. T h e j = 3/2 level splits into twc components and the j = 5/2 level into three components. We use the eigenvalues from [3], which contain the dominant C o term, to fit the 4d data of Fig. 2. This adds just one parameter to the model, the crystalfield interaction. Since the crystal-field splitting is small compared to the spin-orbit interaction, we assign equal weights to the components of each line. A fit to the 55 eV data with a model function incorporating this interaction is shown in Fig. 4. This function results in a greatly improved fit, as is seen most clearly b~y reference to the residuals which are plotted on the same scale as those in Fig. 2. According to the fit the value of C o is 13.6 meV, which is very much smaller

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CRYSTAL F I E L D S P L I T T I N G OF CORE LEVELS IN/%Sn

than the values found in chemical compounds of tin

[3]. Strong support for the validity of this analysis comes from the observation that the Gaussian width now has a value of 102meV, which is in excellent accord with the 101 meV combined effects of a 90 meV instrumental resolution and a 46 meV phonon broadening. We therefore conclude that the theoretical value for the phonon broadening is of the correct magnitude. The lifetime width of the j = 5/2 is now slightly greater, 0.235 _ 0.005 eV, and the singularity index correspondingly smaller, 0.095 _+ 0.008. The spin-orbit splitting is 1.052 _+ 0.004, i.e., slightly smaller than that obtained in the absence of crystalfield splitting, as anticipated by Ley et al. [10]. These values should be more reliable than those obtained earlier. Another result that supports the crystal-field splitting is that it makes the lifetime width of the j = 3/2 line slightly larger than that of the j = 5/2 line, as required by the Coster-Kronig decay channel. The introduction of crystal-field splitting thus removes all the objections to the one-line fit, and yields physically reasonable values for all parameters. It is unfortunate that the crystal field splitting had to be extracted from data where it manifests itself primarily as an increased line width. This is not due to limitations of the experiment, but rather to the lifetime of the d 9 hole state, which dominates the spectral width. 4. CONCLUSIONS We have shown that high-resolution photoemission measurements can reveal the crystal field splitting in metals. Careful analysis of the Sn 4d data shows that the degeneracy of the spin-orbit doublet is lifted by interaction with the crystal field, resulting in split-

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tings of 115 and 146 meV. Although the magnitude of the interaction is small compared to the spin-orbit splitting, it is (in this case) large compared to the phonon broadening. It is clear that the crystal field splitting must be considered in studies of surface-atom core-level shifts and phonon broadening which make full use of the instrumental resolution now available. Studies of metals with resolved surface-atom corelevel shifts should make it possible to measure the crystal-field splitting of both bulk and surface atoms. Acknowledgements - We are indebted to P.H. Citrin and S.B. DiCenzo for comments on this manuscript. This work was carried out in part at the National Synchrotron Light Source, Brookhaven National Laboratory, which is supported by the U.S. Department of Energy, Division of Materials Sciences and Division of Chemical Sciences (DOE contract number DE-AC02-76CH00016). REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

G.M. Bancroft, I. Adams, H. Lampe & T.K. Sham, Chem. Phys. Lett. 32, 173 (1975). G.M. Bancroft, I. Adams, D.K. Creber, D.E. Eastman & W. Gudat, Chem. Phys. Lett. 38, 83 (1976). G.M. Bancroft, T.K. Sham, D.E. Eastman & W. Gudat, J. Am. Chem. Soc. 99, 1752 (1977). G.K. Wertheim, P.H. Citrin & J.F. van der Veen, Phys. Rev. B3O, 4343 (1984). S. Doniach & M. Sunjic, J. Phys. C3, 285 (1970). G.K. Wertheim & S. Hiifner, Phys. Rev. Lett. 35, 53 (1975). G.K. Wertheim, J.E. Rowe & D.N.E. Buchanan (unpublished). C.P. Flynn, Phys. Rev. Lett. 37, 1445 (1976). G.K. Wertheim & S.B. DiCenzo, J. Electron Spectrosc. Relat. Phenom. 37, 57 (1985). L. Ley, S.P. Kowalczyk, F.R. McFeely & D.A. Shirley, Phys. Rev. B1O, 4881 (1974).