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The probing depth in photoemission and auger-electron spectroscopy
Journal of Electron
Spectroscopy and Related Phenomena, 3 (1974) 409-413 @ Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
THE PROBING SPECTROSCOPY
I. LINDAU Sranford
DEPTH
IN PHOTOEMISSION
AND
AUGER-ELECTRON
and W. E. SPICER
Electronics
Laborufories,
(First received 1 November
Stanford
University,
Staqford,
Calif-
94305 (U.S.A.)
1973; in final form 2 January 1974)
ABSTRACT
Electron scattering lengths, or escape depths, have been compiled from the literature for twenty different materials in the energy range O-3000 eV. The energy dependence of the escape depth and its implications for interpretation of photoemission and Auger-electron data are discussed.
In this short paper, we report on a compilation from literature of the electron escape depth in solids in the energy range O-3000 eV. The electron escape depth and its implication for data interpretation obtained early attention within ultraviolet photoemission spectroscopy (see, for example, refs. l-3) and have received renewed interest when it became apparent that techniques like x-ray photoemission and Auger-electron spectroscopy are very surface sensitive due to a short probing depth. It is thus necessary to know at least the magnitude of the escape depth to judge if the energy distribution of the outcoming electrons is characteristic of the bulk electronic structure, or of the surface structure, or of a contamination (e.g., oxide) layer covering the surface. The wave function of the electrons belonging to the first few atomic layers on a surface may be distorted by the presence of the surface4. For a short escape length, the photoelectrons may thus not provide information characteristic of the bulk material (i.e., bulk band structure information) but be related to electron structure modified by the surface. However, a distinction should be made between this type of effect due to a very short escape depth and a true surface photoeffect in which the total optical excitation is a surface effect 5. In Figure 1, we have compiled data from the Iiterature about the escape depth for different materials; metals, semiconductors and compounds. The escape depth (linear scale, in A) has been plotted as a function of electron energy above the Fermi level in metals and above the valence band maximum in non metals (logarithmic scale, in eV). The solid line, no. 1 (left part), gives the result for Cu, Ag and Au6- 8,
I
._
I 100
10
ELECTRON
ENERGY AWE
1000
10000
THE FERMI LEVEL W)
Figure 1. The escape depth, in A, is shown as a function of the electron energy above the Fermi level, in eV, for ti large number of materials. Curve 1 is from refs. 6-8; 2 from ref. 11; 3 and 8 from ref. 9; 4 from ref. 14; 5 from ref. 15; 6 from ref. 16; 7 from ref. 17; 9 from ref. 18; 10 and 12 from ref. 19; 11 and 13 from ref. 20; 14 from ref. 21; 15 from ref. 12; 16 and 19 from ref. 22; 17, 18 and 20 from ref. 23; 21,22 and 23 from ref. 24; 24 from ref. 25; 25 from ref. 26; 26 from ref. 27; 27 from ref. 28 and 28 from ref. 3.
The escape depth shows a strong decrease with increasing electron energy which is characteristic for scattering lengths determined by electron-electron interaction. In fact, the escape depth decreases from 10 000 A for electron energies a few tenths of an eV above the Fermi energy (not shown in the figure) to 20-30 8, for electron energies 5-10 eV above the Fermi level. Curve 3 (solid line) represents the results obtained for Au from x-ray photoemission data in the electron energy range l-3 keVg. As seen in the figure, the escape depth increases with increasing electron energy above 1000 eV. Between 10 and 1000 eV (dashed line), experimental data points are not very plentiful, but those that do exist show rather Iittle variation in magnitude. The general behavior of the escape depth as a function of electron energy is thus first a sharp decrease with increasing electron energy, then a fairly flat minimum in the range 50-500 eV, and finally an increase with increasing electron energy. The escape depths in the UVregion have been obtained from data69 ’ interpreted within the so-called three-step model’* 2. Within this model the optical excitation process, the electron transport through the solid and the escape across the surface are treated separately. Electrons moving towards the surface lose energy mainly due to two inelastic scattering events, electron-electron and electron-phonon scattering. The electron-phonon scattering is characterized by relatively weak electron-energy dependence and small energy losses,
411 typically lo-50 meV. The electron-electron scattering is, on the other hand, strongly energy dependent and the losses are a considerable fraction of the excitation energy. Energy losses due to electron-phonon scattering are important only for low energies, say less than 5-6 eV in metals. In all other cases, electron-scattering is the dominant loss mechanism. One further characteristic, besides the strong energy-dependence, of the electron-electron scattering is the very short scattering length of the electrons at higher energies’. The data points and curves in Figure I refer to a number of different materials. The UV-photoemission region, below 10 eV, has the most extensive experimental results. Considerable information is also available in the region 1000-1500 eV. The general behavior of the energy dependence of the escape depths is the same for Cu, Ag , and Au6- * but the absolute magnitude differs considerably from one group of materials to another. Therefore, it appears difficult to establish a “universal curve” applicable to all materials. The listed escape depths shown in Figure 1 have been determined according to several methods. As an example, we again choose the Cu, Ag, and Au curve, which was obtained from energy distribution curves and quantum yield measurements7. For electron energies in the range 5.5-l 1 eV, there are also available electron beam attenuation measurements by Kanter’ and for lower energies independent studies by Crowell et al. (cited in ref. 6) and Sze et al. lo, All three studies are in good agreement with Krolikowski and Spicer’s data6’ ‘. One common method to determine the escape depth is to deposit one material on top of another and study the amplitude increase and decrease, respectively, of the contribution from the two materials as a function of the (hickness of the deposited layer l1 . This requires that no agglomeration occurs and that an accurate calibration method for determining the film thickness is used. As for other methods, the uncertainty in the absolute value of the escape depth may be large, but the consistency between independent methods is encouraging and the overall energy-dependence of the escape depth seems to be well established. In addition to the large energy dependence of the escape depth and the variation from material to material, there are several other striking things regarding the escape depth. For certain metals, like Cs, Ba, Sr and Yb, it is extremely short. Smith and FisherI’ do not give any scattering lengths for Na and K but quote that they are of the same magnitude as for Cs. The trivalent metals Gd and Ce have much larger scattering lengths than the divalent metals Ba, Sr, and Yb. Measurements of the escape depth for secondary electrons’ ’ give for Ba a value about twice as large as the UV-photoemission data (= 8-12 A at - 5 eV above the Fermi energy). For materials like Cs, Ba and Sr, the analysis within the three-step model is fairly easy since the small Fermi energy of these materials22 provides an unambiguous separation between the scattered and unscattered part of the distribution. A scattering length of l-2 A for Cs12 as determined from the three-step model means that the number of scattered electrons is much greater than the number of unscattered electrons and the three-step model seems to be applicable. However, the physical meaning of
412 an escape length less than a unit cell dimension is not clear and the obtained figures should be considered as a lower limit. As discussed at the beginning of this paper, one should be very cautious in interpreting the unscattered distribution in terms of bulk electronic structure in such a case. Except for these extreme cases, most of the studied materials emit photoelectrons originating from within several monolayers of the surface regions (for electron energies < 10 eV and > 1 keV) or at least from within a few monolayers (electron energies 10-1000 eV). It is also obvious from Figure 1 that the contributing surface region goes through a minimum somewhere between 20-500 eV. The escape depths for electrons in alloys can be supposed to be similar to those for the pure metals. The energy dependence and the shortness of the escape depth have obvious consequences for studies of alloys with the photoemission technique. Extreme care has to be taken in interpreting data, since the surface composition of the alloy might differ from that of the bulk. But on the other hand, photoemission should be a useful tool for composition studies of the surface profile, especially when excitation sources (like synchrotron radiation) become available so that the entire electron energy range can be covered. ACKNOWLEDGEMENTS
This work has been supported in part by National Science Foundation and in part by Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR 72-2249. Useful comments by Dr. C. J. Powell are acknowledged and we are thankful to Dr. C. R. Brundle for sending us some results prior to publication. NOTE ADDED
IN PROOF
Since our manuscript was submitted for publication, the following publications containing information about escape depths have appeared or been brought to our attention”. These new results are consistent with the results presented in this paper and do not change our conclusions. An escape length of 13 A at 1260 eV is reported for Cs 30; 6.7 A at 170 eV for Cs31; 9 A at 1403 for Hg3’; 7.5 A at 262 eV for CS~~* 4.7,8.6 and 10.0 A at 60, 110 and 335 eV, respectively for Be34; 6.1, 5.3 and 12.7 8( a; 60, 355 and 935 eV, respectively for CUDS; 5.4 and 6.7 A at 355 and 850 eV, respectively for Ag 3 5; 5.5 A at 200-900 eV for W and Ni36. REFERENCES 1 2 3 4
W. C. W. R.
E. Spicer, Whys. Rev., 112 (1958) 114. N. Berglund and W. E. Spicer, P&s. Rev.. 136 (1964) A1030 and A1044. E. Spicer, J. Phys. Chem. Solids, 22 (1961) 365. Haydock, V. Heine, M. J. Kelly and J. B. Pendry, Phys. Rev. Left., 29 (1972) 86X.
413
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 2& 29 30 31 32 33 34 35 36
J. G. Endriz, Phys. Rev. 8, 7 (1973) 3464. W. F. Krolikowski and W. E. Spicer, Phys. Rev., 185 (1969) 882. W. F. Krolikowski and W. E. Spicer, Phys. Rev. B, 1 (1970) 478. H. Kanter, Phys. Rev. B, 1 (1970) 522. M. Klasson, J. Hedman, A. Berndtsson, R. Nilsson, C. Nordling and P. Melnik, Phys. Scriptu, 5 (1972) 93. S. M. Sze, J. L. Moll and T. Sugano, Solid-State Electron, 7 (1964) 509. P. W. Palmberg and T. N. Rhodin, J. Appl. Phys., 39 (1968) 2425. N. V. Smith and G. B. Fisher, Phys. Rev. B, 3 (1971) 3662. H. Seiler, Z. Angew. Phys., 22 (1967) 249. Y. Baer, P. F. Heden, J. Hedman, M. Klasson and C. Nordling, Solid State Commun., 8 (1970) 1479. T. Huen and F. Wooten, Solid State Commun., 9 (1971) 871. T. F. Gesell and E. T. Arakawa, Phys. Rev. Left., 26 (1971) 377. H. Kanter, Phys. Rev. B, 1 (1970) 2357. R. G. Steinhardt, J. Hudis and M. L. Perlman, Phys. Rev. B, 5 (1972) 1016. T. A. Carlson and G. E. McGuire, J. Electron Spectrosc., 1 (1972/73) 161. M. L. Tarng and G. K. Wehner, J. Appl. Phys., 44 (1973) 1534. H. Thomas, Z, Phys., 147 (1957) 395. C. R. Helms and W. E. Spicer, to be submitted to Phys. Rev. B. G. Brodkn, Phys. Kundens. Mutevie, 15 (1972) 171. D. E. Eastman, Solid State Commun., 8 (1970) 41. J. W. T. Ridgway and D. Hanemann, Srtrjuce Sci., 24 (1971) 451. L. F. Wagner and W. E. Spicer, P&s. Rev. B, 9 (1974) XXX. G. W. Gobeli and F. G. Allen, Phys. Rev., 127 (1962) 141. J. L. Shay and W. E. Spicer, Phys. Rev., 169 (1968) 650. A recent review paper by C. R. Brundle, J. Vuc. Sci. TechnoZ., 11, No. 1 (1974) contains a listing of escape depths for numerous materials. W. A. Frazer, J. V. Floris, W. N. Delgass and W. D. Robertson, Surface Sci., 36 (1973) 661. S. Thomas and T. W. Haas, J. Vuc. Sci. Technol., 10 (1973) 218. C. R. Brundle and M. W. Roberts, Chem. Phys. Lezt., 18 (1973) 380. K. Jacobi and J. Holzl, Surface Sci., 26 (1971) 54. M. P. Seah, Surface Sci., 32 (1972) 703. D. C. Jackson, T. E. Gallon and A. Chambers, Surface Sci., 36 (1973) 381. R. M. Stern and L. Sinharoy, Surface Sci., 33 (1972) 131.
Spectroscopy and Related Phenomena, 3 (1974) 409-413 @ Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
THE PROBING SPECTROSCOPY
I. LINDAU Sranford
DEPTH
IN PHOTOEMISSION
AND
AUGER-ELECTRON
and W. E. SPICER
Electronics
Laborufories,
(First received 1 November
Stanford
University,
Staqford,
Calif-
94305 (U.S.A.)
1973; in final form 2 January 1974)
ABSTRACT
Electron scattering lengths, or escape depths, have been compiled from the literature for twenty different materials in the energy range O-3000 eV. The energy dependence of the escape depth and its implications for interpretation of photoemission and Auger-electron data are discussed.
In this short paper, we report on a compilation from literature of the electron escape depth in solids in the energy range O-3000 eV. The electron escape depth and its implication for data interpretation obtained early attention within ultraviolet photoemission spectroscopy (see, for example, refs. l-3) and have received renewed interest when it became apparent that techniques like x-ray photoemission and Auger-electron spectroscopy are very surface sensitive due to a short probing depth. It is thus necessary to know at least the magnitude of the escape depth to judge if the energy distribution of the outcoming electrons is characteristic of the bulk electronic structure, or of the surface structure, or of a contamination (e.g., oxide) layer covering the surface. The wave function of the electrons belonging to the first few atomic layers on a surface may be distorted by the presence of the surface4. For a short escape length, the photoelectrons may thus not provide information characteristic of the bulk material (i.e., bulk band structure information) but be related to electron structure modified by the surface. However, a distinction should be made between this type of effect due to a very short escape depth and a true surface photoeffect in which the total optical excitation is a surface effect 5. In Figure 1, we have compiled data from the Iiterature about the escape depth for different materials; metals, semiconductors and compounds. The escape depth (linear scale, in A) has been plotted as a function of electron energy above the Fermi level in metals and above the valence band maximum in non metals (logarithmic scale, in eV). The solid line, no. 1 (left part), gives the result for Cu, Ag and Au6- 8,
I
._
I 100
10
ELECTRON
ENERGY AWE
1000
10000
THE FERMI LEVEL W)
Figure 1. The escape depth, in A, is shown as a function of the electron energy above the Fermi level, in eV, for ti large number of materials. Curve 1 is from refs. 6-8; 2 from ref. 11; 3 and 8 from ref. 9; 4 from ref. 14; 5 from ref. 15; 6 from ref. 16; 7 from ref. 17; 9 from ref. 18; 10 and 12 from ref. 19; 11 and 13 from ref. 20; 14 from ref. 21; 15 from ref. 12; 16 and 19 from ref. 22; 17, 18 and 20 from ref. 23; 21,22 and 23 from ref. 24; 24 from ref. 25; 25 from ref. 26; 26 from ref. 27; 27 from ref. 28 and 28 from ref. 3.
The escape depth shows a strong decrease with increasing electron energy which is characteristic for scattering lengths determined by electron-electron interaction. In fact, the escape depth decreases from 10 000 A for electron energies a few tenths of an eV above the Fermi energy (not shown in the figure) to 20-30 8, for electron energies 5-10 eV above the Fermi level. Curve 3 (solid line) represents the results obtained for Au from x-ray photoemission data in the electron energy range l-3 keVg. As seen in the figure, the escape depth increases with increasing electron energy above 1000 eV. Between 10 and 1000 eV (dashed line), experimental data points are not very plentiful, but those that do exist show rather Iittle variation in magnitude. The general behavior of the escape depth as a function of electron energy is thus first a sharp decrease with increasing electron energy, then a fairly flat minimum in the range 50-500 eV, and finally an increase with increasing electron energy. The escape depths in the UVregion have been obtained from data69 ’ interpreted within the so-called three-step model’* 2. Within this model the optical excitation process, the electron transport through the solid and the escape across the surface are treated separately. Electrons moving towards the surface lose energy mainly due to two inelastic scattering events, electron-electron and electron-phonon scattering. The electron-phonon scattering is characterized by relatively weak electron-energy dependence and small energy losses,
411 typically lo-50 meV. The electron-electron scattering is, on the other hand, strongly energy dependent and the losses are a considerable fraction of the excitation energy. Energy losses due to electron-phonon scattering are important only for low energies, say less than 5-6 eV in metals. In all other cases, electron-scattering is the dominant loss mechanism. One further characteristic, besides the strong energy-dependence, of the electron-electron scattering is the very short scattering length of the electrons at higher energies’. The data points and curves in Figure I refer to a number of different materials. The UV-photoemission region, below 10 eV, has the most extensive experimental results. Considerable information is also available in the region 1000-1500 eV. The general behavior of the energy dependence of the escape depths is the same for Cu, Ag , and Au6- * but the absolute magnitude differs considerably from one group of materials to another. Therefore, it appears difficult to establish a “universal curve” applicable to all materials. The listed escape depths shown in Figure 1 have been determined according to several methods. As an example, we again choose the Cu, Ag, and Au curve, which was obtained from energy distribution curves and quantum yield measurements7. For electron energies in the range 5.5-l 1 eV, there are also available electron beam attenuation measurements by Kanter’ and for lower energies independent studies by Crowell et al. (cited in ref. 6) and Sze et al. lo, All three studies are in good agreement with Krolikowski and Spicer’s data6’ ‘. One common method to determine the escape depth is to deposit one material on top of another and study the amplitude increase and decrease, respectively, of the contribution from the two materials as a function of the (hickness of the deposited layer l1 . This requires that no agglomeration occurs and that an accurate calibration method for determining the film thickness is used. As for other methods, the uncertainty in the absolute value of the escape depth may be large, but the consistency between independent methods is encouraging and the overall energy-dependence of the escape depth seems to be well established. In addition to the large energy dependence of the escape depth and the variation from material to material, there are several other striking things regarding the escape depth. For certain metals, like Cs, Ba, Sr and Yb, it is extremely short. Smith and FisherI’ do not give any scattering lengths for Na and K but quote that they are of the same magnitude as for Cs. The trivalent metals Gd and Ce have much larger scattering lengths than the divalent metals Ba, Sr, and Yb. Measurements of the escape depth for secondary electrons’ ’ give for Ba a value about twice as large as the UV-photoemission data (= 8-12 A at - 5 eV above the Fermi energy). For materials like Cs, Ba and Sr, the analysis within the three-step model is fairly easy since the small Fermi energy of these materials22 provides an unambiguous separation between the scattered and unscattered part of the distribution. A scattering length of l-2 A for Cs12 as determined from the three-step model means that the number of scattered electrons is much greater than the number of unscattered electrons and the three-step model seems to be applicable. However, the physical meaning of
412 an escape length less than a unit cell dimension is not clear and the obtained figures should be considered as a lower limit. As discussed at the beginning of this paper, one should be very cautious in interpreting the unscattered distribution in terms of bulk electronic structure in such a case. Except for these extreme cases, most of the studied materials emit photoelectrons originating from within several monolayers of the surface regions (for electron energies < 10 eV and > 1 keV) or at least from within a few monolayers (electron energies 10-1000 eV). It is also obvious from Figure 1 that the contributing surface region goes through a minimum somewhere between 20-500 eV. The escape depths for electrons in alloys can be supposed to be similar to those for the pure metals. The energy dependence and the shortness of the escape depth have obvious consequences for studies of alloys with the photoemission technique. Extreme care has to be taken in interpreting data, since the surface composition of the alloy might differ from that of the bulk. But on the other hand, photoemission should be a useful tool for composition studies of the surface profile, especially when excitation sources (like synchrotron radiation) become available so that the entire electron energy range can be covered. ACKNOWLEDGEMENTS
This work has been supported in part by National Science Foundation and in part by Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR 72-2249. Useful comments by Dr. C. J. Powell are acknowledged and we are thankful to Dr. C. R. Brundle for sending us some results prior to publication. NOTE ADDED
IN PROOF
Since our manuscript was submitted for publication, the following publications containing information about escape depths have appeared or been brought to our attention”. These new results are consistent with the results presented in this paper and do not change our conclusions. An escape length of 13 A at 1260 eV is reported for Cs 30; 6.7 A at 170 eV for Cs31; 9 A at 1403 for Hg3’; 7.5 A at 262 eV for CS~~* 4.7,8.6 and 10.0 A at 60, 110 and 335 eV, respectively for Be34; 6.1, 5.3 and 12.7 8( a; 60, 355 and 935 eV, respectively for CUDS; 5.4 and 6.7 A at 355 and 850 eV, respectively for Ag 3 5; 5.5 A at 200-900 eV for W and Ni36. REFERENCES 1 2 3 4
W. C. W. R.
E. Spicer, Whys. Rev., 112 (1958) 114. N. Berglund and W. E. Spicer, P&s. Rev.. 136 (1964) A1030 and A1044. E. Spicer, J. Phys. Chem. Solids, 22 (1961) 365. Haydock, V. Heine, M. J. Kelly and J. B. Pendry, Phys. Rev. Left., 29 (1972) 86X.
413
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 2& 29 30 31 32 33 34 35 36
J. G. Endriz, Phys. Rev. 8, 7 (1973) 3464. W. F. Krolikowski and W. E. Spicer, Phys. Rev., 185 (1969) 882. W. F. Krolikowski and W. E. Spicer, Phys. Rev. B, 1 (1970) 478. H. Kanter, Phys. Rev. B, 1 (1970) 522. M. Klasson, J. Hedman, A. Berndtsson, R. Nilsson, C. Nordling and P. Melnik, Phys. Scriptu, 5 (1972) 93. S. M. Sze, J. L. Moll and T. Sugano, Solid-State Electron, 7 (1964) 509. P. W. Palmberg and T. N. Rhodin, J. Appl. Phys., 39 (1968) 2425. N. V. Smith and G. B. Fisher, Phys. Rev. B, 3 (1971) 3662. H. Seiler, Z. Angew. Phys., 22 (1967) 249. Y. Baer, P. F. Heden, J. Hedman, M. Klasson and C. Nordling, Solid State Commun., 8 (1970) 1479. T. Huen and F. Wooten, Solid State Commun., 9 (1971) 871. T. F. Gesell and E. T. Arakawa, Phys. Rev. Left., 26 (1971) 377. H. Kanter, Phys. Rev. B, 1 (1970) 2357. R. G. Steinhardt, J. Hudis and M. L. Perlman, Phys. Rev. B, 5 (1972) 1016. T. A. Carlson and G. E. McGuire, J. Electron Spectrosc., 1 (1972/73) 161. M. L. Tarng and G. K. Wehner, J. Appl. Phys., 44 (1973) 1534. H. Thomas, Z, Phys., 147 (1957) 395. C. R. Helms and W. E. Spicer, to be submitted to Phys. Rev. B. G. Brodkn, Phys. Kundens. Mutevie, 15 (1972) 171. D. E. Eastman, Solid State Commun., 8 (1970) 41. J. W. T. Ridgway and D. Hanemann, Srtrjuce Sci., 24 (1971) 451. L. F. Wagner and W. E. Spicer, P&s. Rev. B, 9 (1974) XXX. G. W. Gobeli and F. G. Allen, Phys. Rev., 127 (1962) 141. J. L. Shay and W. E. Spicer, Phys. Rev., 169 (1968) 650. A recent review paper by C. R. Brundle, J. Vuc. Sci. TechnoZ., 11, No. 1 (1974) contains a listing of escape depths for numerous materials. W. A. Frazer, J. V. Floris, W. N. Delgass and W. D. Robertson, Surface Sci., 36 (1973) 661. S. Thomas and T. W. Haas, J. Vuc. Sci. Technol., 10 (1973) 218. C. R. Brundle and M. W. Roberts, Chem. Phys. Lezt., 18 (1973) 380. K. Jacobi and J. Holzl, Surface Sci., 26 (1971) 54. M. P. Seah, Surface Sci., 32 (1972) 703. D. C. Jackson, T. E. Gallon and A. Chambers, Surface Sci., 36 (1973) 381. R. M. Stern and L. Sinharoy, Surface Sci., 33 (1972) 131.