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Electron energy loss spectroscopy with resolution below 1 meV
819
Journal of Electron Spectroscopy and R&ted Phenomena, 64&i (1993) 8194323 0368-2046/93/$06.00 @ 1993 - Eleevier SciencePublishers B.V.Au rights reserved
Electron Energy Loss Spectroscopy with Resolution below 1 meV H. Ibach Institut f& Grenzfltichenforschung und Vakuumphysik, Forschungszentrum Jttlich, D-52425 Jtllich, Germany
Presently available electron spectrometers have a theoretical resolution limit of about 1 meV. It is shown that this limitation arises from the combined effect of the angular spread of the space charge limited beam, feeding the energy dispersive elements of the spectrometer and the angular aberrations of the dispersive elements. A new electrostatic dispersive device with controlled angular aberrations is described. An energy loss spectrometer built with such dispersive elements had a theoretical resolution limit of 0.3 meV, and an experimentally achieved resolution of 0.5 meV.
1. INTRODUCTION Electron energy loss spectroscopy (EELS) is the most versatile and sensitive tool in surface vibration spectroscopy, as it combines a wide spectral range with the option of employing different scattering mechanisms of variable cross section and the possibility to exchange momentum with surface phonons, and hence to measure phonon dispersion. The essential problem with this technique has always been the resolution, which was and is significantly less than for the competing techniques, such as infrared spectroscopy and inelastic scattering of helium atoms. In the latter techniques the resolution is typically about 0.25 meV, whereas in EELS a resolution of 5 meV was considered a good result until recently. Fortunately, there were many problems in surface vibration spectroscopy where a resolution of a few meV was sufficient. With the increasing complexity of problems, it became desirable to have a sensitive method with a resolution at least matched to the natural line width of surface vibrational modes. Significant progress in that direction was achieved by an electron optical analysis of all aspects of energy loss spectrometers [l] and the introduction of space charge corrected energy dispersive elements. In the final section of [l] a theoretical model for the resolution eters was described which
limit of spectromwas found to be
consistent with experimental observations. In this paper I want to follow up on those ideas and describe a new energy dispersive element which carries EELS into the submillivolt resolution regime. The paper is organized as follows. In the next section the already mentioned model for the resolution limit is described. Section 3 introduces a new electrostatic deflector with adjustable angular aberrations and in the final section the performance of a new spectrometer equipped with such deflectors is described and results are compared to those of the previous design.
2. THE RESOLUTION
LIMIT
Electron spectrometers require energy dispersive elements. Energy dispersion is provided by deflecting devices. Traditionally cylindrical, spherical or toroidal deflecting fields have been used. The base width of the transmitted electron beam AE, can be described by
Here E, is the pass energy, D the energy dispersion, s the width of entrance and exit slits, which are assumed to be of equal size, and 01, and ~3, are the semiangular apertures of the beam in plane and perpendicular to the disper-
820
sion plane, respectively. Table 1 lists the parameters D, c~, cp and 11 for the ideal cylindrical and spherical field.
Table 1 Dispersion and angular aberration coefficients for the cylindrical and spherical field; r0 is the deflection radius of the central trajectory
Field
Focussing angle
cylindrical
127.3”
spherical
180’
D
c,
cB
n
r0
-r,
0
2
The base width of the monochromatic beam thus depends on the angular aperture of the feed beam of the monochromator. This angular aperture necessarily depends on the energy of the beam at the entrance slit of the monochromator and thus on the pass energy. For any particular layout of the emission system the aperture angle 01, is Ulll
=CQIJEa
(2)
with oE a COtWant characterizing the emission system. This functional dependence arises from the conservation of phase space. For a beam having C,, symmetry with the optical axis being the twofold rotation axis a,JE is approximately constant because the width of the beam at the entrance slit changes only little with energy. Inserting Eq. (2) into Eq. (1) shows that the resolution limit AE,,i, is
A similar consideration applies in principle also to the angle p,. The angular aperture p, can however be kept smaller because of the large aspect ratio of the entrance and exit slits. Hence, the theoretical resolution limit is determined by the ratio of the aberration coef-
ficient c, to the energy dispersion and the constant Ann characterizing the space charge limited beam provided by the emission system. Improving the resolution limit can therefore be achieved by reducing either c,/D or an. It was already reported that a reduction of the constant an can be achieved by using cathodes with an extra-fine tip [2]. The improvement was however not very substantial and the life time of such cathodes is small. Smaller angular apertures of the feed beam could also be achieved by a different layout of the emission system, however only at the price of a lower current in the feed beam, which would then not be large enough to fill the monochromator at larger pass energies. This paper therefore describes the result of an endeavor to follow the second route of reducing c,/D. The theoretical resolution limit has also a substantial effect on the available monochromatic current I, which is Im cc(AE-AEm&K
(4)
with K between 1.5 and 2.5 [3]. Hence a reduction of AE,, also improves the intensity when one works near the resolution limit.
3. AN ELECTROSTATIC DEFLECTOR WITH MODIFIED ANGULAR ABERRATION The angular aberration ccr arises from the fact that beams entering the deflector at angles (11= +a, and 01 = -Q, are both deflected by a larger amount than the central beam at a = 0. Electrons having entered the device with 01 = fol, pass the deflector on trajectories which deviate from the central radius by a distance which depends roughly linearly on a. Hence, if one could construct a device with a deflecting field which continuously decreases towards both sides of the central path, one should be able to eliminate the aberration coefficient c,. This idea was apparently first expressed in a patent by Liebl [4] for the special case of a toroidal deflector. The reduction of the radial deflecting field towards both sides of the central path is achieved by using deflec-
821
tion plates of opposite curvature perpendicular to the dispersion plane. As the calculations were performed analytically for the ideal toroidial field, it was, however, not clear whether the principle would work also for other deflection devices and devices having fringe fields because of metallic entrance and exit slits. We have therefore performed numeric simulations on a device which is of basically cylindrical shape, however equipped with top and bottom cover plates as well as metallic entrance and exit apertures [5]. These devices have been used previously [l]. They were particularly successful in their ability to handle beams of high intensity, because they permit a compensation of the space charge induced aberrations. The present deflection device differs, however, in two aspects. The gap between the inner and outer deflecting plate is much larger so that the field penetration from the top and bottom cover plates is high enough to allow for stigmatic focussing with a negative bias. Hence the device works as a ‘pseudo’ spherical deflector 161. It should be noted in passing that with our device stigmatic focussing is obtainable even in the presence of space charge and despite the large gap and the thereby extended fringe field
02
-
s
z
L - -50 t!
i L
--loo-;, d -150
5
20
40
60
-150
near the entrance and exit apertures. The genuine spherical deflector enjoys stigmatic focussing only because of the spherical symmetry. It looses this property when either the beam current is high or a larger gap gives rise to fringe fields. In high resolution speetroscopy large gaps are required in order to minimize the effect of spurious work functions on the deflection plates. The new device also has a convex curvature of the deflection plates vertical to the dispersion plane [7]. The key result of the numerical analysis of the device is shown in Fig. 1. The results for the angular aberration coefficients c, and cp are plotted versus the radius r, of the curvature of the deflection plates perendicular to the dispersion plane. The radii within the dispersion plane were m20 and ~~60 mm, respectively. The energy dispersion was found to be ry75 mm. We note that c, and cl, vary approximately linearly with log rl in the range of interest. In the entire range the sum c, + cl-, stays constant. Hence, the curvature of the deflection plates perpendicular to the dispersion plane does not change the overall angular aberrations. In particular for a circular symmetric beam the effect of the angular aberrations on the resolution would be independent of rl. In a combination with all other issues involved in spectrometers, such as the space charge and the transport of the beam through the entire spectrometer, curving of the deflection plate perpendicular to the plane of dispersion adds an element of flexibility which can be exploited in order to achieve optimum performance. Unfortunately the effect of the additional curving on the overall performance and the resolution is not amenable to electron optical simulation with present computer power. One therefore has to resort to experimental tests. The results for one particular spectrometer are described in the next section.
120
Vertical curvatureof deflectionplates (II)
4. Figure 1. Angular aberration c, and cP of a deflecting device as a function of the curvature of the deflection plates perpendicular to the dispersion plane.
PERFORMANCE TROMETER
OF THE
SPEC-
The performance of a spectrometer employing in total three energy dispersive devices with modified angular aberration coefficients
822
are described in the following. The spectrometer features two monochromators operating at different pass energies. The first monochromator is a retarding monochromator [l] with different potentials at the entrance and exit slit. For the first time we have also implemented a routine which automatically adjusts all potentials applied to the spectrometer in order to optimize the monochromatic current at the detector for a given set of deflection voltages applied to the dispersive devices, i.e. for a fixed resolution and a fixed energy at the target. Depending on the resolution and hence on the current at the detector, the optimization takes between a few minutes and half an hour. Starting from a moderate resolution the routine also allows for a completely automatic adjustment to a predetermined high final resolution, Owing to this routine, operation of the instrument has turned into a real pleasure. The overall resolution, measured as the full width at half maximum, is plotted in Fig. 2 versus the deflection potential difference AU between the inner and outer deflection plates; AU was equal for the second monochromator and the analyzer. The data points trace a straight line which intersects the ordinate at the resolution limit AE = 0.28 meV. The best resolution which was actually obtained at this point in
Currentq 3_57~10-'~A FWHM ~0.518meV lO%-Width =l.lSmeV
-0.5
0
0.5
Energy (meV1
Figure 3. Current at the detector versus difference in the mean potential of the monochromator and analyzer with the spectrometer in the “straight through” position.
2 ,
0.1
0.2
0.3
lleflection voltqat AU (VI
Figure 2. Resolution versus the deflection voltage applied to the second monochromator and analyzer.
Figure 4. Current measured at the detector versus the resolution (FWHM) of the spectrometer for the new spectrometer (squares) and the penultimate design (circles) as described in [ 11.
823
time is AE = 0.5 meV (Fig. 3). We have also measured the current at the detector versus the resolution AE and the results are compared to the results for the previous design in Fig 4. The current at the detector follows the functional form 5 Id=
14(AE-0.30mcV)~pAmeV~~ 3 3 4OAEz pA meVeT i
5
AE<25meV AE > 3.5 meV (5)
In the entire range for AE < 10 meV the current for the new design is higher than for the penultimate design, with the difference increasing the better the resolution is. For AE = I meV the current at the detector in the straight-through position is 6 pA which is more than sufficient to investigate dipole active vibrations. To provide an example, for a full monolayer of CO on Ni(ll0) [S] one would have a count rate of ~16.10~ Hz for the CO stretching vibration. Impact scattering in particular from surface phonons, requires higher currents, equivalent to about 50 pA at the detector in the straight through position. From Fig. 4 one can expect that a resolution of al.5 meV should be achievable, even for this more demanding application. In summary, I conclude that electron energy loss spectroscopy with a resolution below 1 meV is possible and will be made available to practical applications in our laboratory, and hopefully to other laboratories as well, in the near future,
ACKNOWLEDGEMENTS The construction and making of this and earlier versions of the spectrometer were in the hands of D. Bruchmann. His never waning readiness to put my sometimes well, sometimes not so well, thought-out ideas into reality is gratefully acknowledged. Likewise the spectrometers could not have been realized without the diligent and precise work of our mechanical workshop directed by D. Strobl.
REFERENCES
AND NOTES
I, H. Ibach, Electron Energy loss Spectrometers, Springer Series in Optical Sciences 63, Springer, Berlin - Heidelberg, 1991, ISBN 3-540-52818-o /O-387-52818-0. 2, G. Kisters, J.G. Chen, S. Lehwald, and H. Ibach, Surf. Sci. 245 (1991) 65. 3. K = 5/2 applies when the monochromator is fed with a beam whose energy spread AEi, is independent of the pass energy E, of the monochromator. More typically one has AEh ocE, and K = 3/2 (see ref. 1 for details). 4. H. Liebl, DE 26 20 877 C2. 5. See e.g. ref. 1, pp. 21 ff. 6. K. Jost, J. Phys. Sci. Instrum. 12 (1979) 1006. 7. International patents pending. 8. H. Ebach, M. Balden, D. Bruchmann, and S. Lehwald, Surf. Sci. 269/270 (1992) 94.
Journal of Electron Spectroscopy and R&ted Phenomena, 64&i (1993) 8194323 0368-2046/93/$06.00 @ 1993 - Eleevier SciencePublishers B.V.Au rights reserved
Electron Energy Loss Spectroscopy with Resolution below 1 meV H. Ibach Institut f& Grenzfltichenforschung und Vakuumphysik, Forschungszentrum Jttlich, D-52425 Jtllich, Germany
Presently available electron spectrometers have a theoretical resolution limit of about 1 meV. It is shown that this limitation arises from the combined effect of the angular spread of the space charge limited beam, feeding the energy dispersive elements of the spectrometer and the angular aberrations of the dispersive elements. A new electrostatic dispersive device with controlled angular aberrations is described. An energy loss spectrometer built with such dispersive elements had a theoretical resolution limit of 0.3 meV, and an experimentally achieved resolution of 0.5 meV.
1. INTRODUCTION Electron energy loss spectroscopy (EELS) is the most versatile and sensitive tool in surface vibration spectroscopy, as it combines a wide spectral range with the option of employing different scattering mechanisms of variable cross section and the possibility to exchange momentum with surface phonons, and hence to measure phonon dispersion. The essential problem with this technique has always been the resolution, which was and is significantly less than for the competing techniques, such as infrared spectroscopy and inelastic scattering of helium atoms. In the latter techniques the resolution is typically about 0.25 meV, whereas in EELS a resolution of 5 meV was considered a good result until recently. Fortunately, there were many problems in surface vibration spectroscopy where a resolution of a few meV was sufficient. With the increasing complexity of problems, it became desirable to have a sensitive method with a resolution at least matched to the natural line width of surface vibrational modes. Significant progress in that direction was achieved by an electron optical analysis of all aspects of energy loss spectrometers [l] and the introduction of space charge corrected energy dispersive elements. In the final section of [l] a theoretical model for the resolution eters was described which
limit of spectromwas found to be
consistent with experimental observations. In this paper I want to follow up on those ideas and describe a new energy dispersive element which carries EELS into the submillivolt resolution regime. The paper is organized as follows. In the next section the already mentioned model for the resolution limit is described. Section 3 introduces a new electrostatic deflector with adjustable angular aberrations and in the final section the performance of a new spectrometer equipped with such deflectors is described and results are compared to those of the previous design.
2. THE RESOLUTION
LIMIT
Electron spectrometers require energy dispersive elements. Energy dispersion is provided by deflecting devices. Traditionally cylindrical, spherical or toroidal deflecting fields have been used. The base width of the transmitted electron beam AE, can be described by
Here E, is the pass energy, D the energy dispersion, s the width of entrance and exit slits, which are assumed to be of equal size, and 01, and ~3, are the semiangular apertures of the beam in plane and perpendicular to the disper-
820
sion plane, respectively. Table 1 lists the parameters D, c~, cp and 11 for the ideal cylindrical and spherical field.
Table 1 Dispersion and angular aberration coefficients for the cylindrical and spherical field; r0 is the deflection radius of the central trajectory
Field
Focussing angle
cylindrical
127.3”
spherical
180’
D
c,
cB
n
r0
-r,
0
2
The base width of the monochromatic beam thus depends on the angular aperture of the feed beam of the monochromator. This angular aperture necessarily depends on the energy of the beam at the entrance slit of the monochromator and thus on the pass energy. For any particular layout of the emission system the aperture angle 01, is Ulll
=CQIJEa
(2)
with oE a COtWant characterizing the emission system. This functional dependence arises from the conservation of phase space. For a beam having C,, symmetry with the optical axis being the twofold rotation axis a,JE is approximately constant because the width of the beam at the entrance slit changes only little with energy. Inserting Eq. (2) into Eq. (1) shows that the resolution limit AE,,i, is
A similar consideration applies in principle also to the angle p,. The angular aperture p, can however be kept smaller because of the large aspect ratio of the entrance and exit slits. Hence, the theoretical resolution limit is determined by the ratio of the aberration coef-
ficient c, to the energy dispersion and the constant Ann characterizing the space charge limited beam provided by the emission system. Improving the resolution limit can therefore be achieved by reducing either c,/D or an. It was already reported that a reduction of the constant an can be achieved by using cathodes with an extra-fine tip [2]. The improvement was however not very substantial and the life time of such cathodes is small. Smaller angular apertures of the feed beam could also be achieved by a different layout of the emission system, however only at the price of a lower current in the feed beam, which would then not be large enough to fill the monochromator at larger pass energies. This paper therefore describes the result of an endeavor to follow the second route of reducing c,/D. The theoretical resolution limit has also a substantial effect on the available monochromatic current I, which is Im cc(AE-AEm&K
(4)
with K between 1.5 and 2.5 [3]. Hence a reduction of AE,, also improves the intensity when one works near the resolution limit.
3. AN ELECTROSTATIC DEFLECTOR WITH MODIFIED ANGULAR ABERRATION The angular aberration ccr arises from the fact that beams entering the deflector at angles (11= +a, and 01 = -Q, are both deflected by a larger amount than the central beam at a = 0. Electrons having entered the device with 01 = fol, pass the deflector on trajectories which deviate from the central radius by a distance which depends roughly linearly on a. Hence, if one could construct a device with a deflecting field which continuously decreases towards both sides of the central path, one should be able to eliminate the aberration coefficient c,. This idea was apparently first expressed in a patent by Liebl [4] for the special case of a toroidal deflector. The reduction of the radial deflecting field towards both sides of the central path is achieved by using deflec-
821
tion plates of opposite curvature perpendicular to the dispersion plane. As the calculations were performed analytically for the ideal toroidial field, it was, however, not clear whether the principle would work also for other deflection devices and devices having fringe fields because of metallic entrance and exit slits. We have therefore performed numeric simulations on a device which is of basically cylindrical shape, however equipped with top and bottom cover plates as well as metallic entrance and exit apertures [5]. These devices have been used previously [l]. They were particularly successful in their ability to handle beams of high intensity, because they permit a compensation of the space charge induced aberrations. The present deflection device differs, however, in two aspects. The gap between the inner and outer deflecting plate is much larger so that the field penetration from the top and bottom cover plates is high enough to allow for stigmatic focussing with a negative bias. Hence the device works as a ‘pseudo’ spherical deflector 161. It should be noted in passing that with our device stigmatic focussing is obtainable even in the presence of space charge and despite the large gap and the thereby extended fringe field
02
-
s
z
L - -50 t!
i L
--loo-;, d -150
5
20
40
60
-150
near the entrance and exit apertures. The genuine spherical deflector enjoys stigmatic focussing only because of the spherical symmetry. It looses this property when either the beam current is high or a larger gap gives rise to fringe fields. In high resolution speetroscopy large gaps are required in order to minimize the effect of spurious work functions on the deflection plates. The new device also has a convex curvature of the deflection plates vertical to the dispersion plane [7]. The key result of the numerical analysis of the device is shown in Fig. 1. The results for the angular aberration coefficients c, and cp are plotted versus the radius r, of the curvature of the deflection plates perendicular to the dispersion plane. The radii within the dispersion plane were m20 and ~~60 mm, respectively. The energy dispersion was found to be ry75 mm. We note that c, and cl, vary approximately linearly with log rl in the range of interest. In the entire range the sum c, + cl-, stays constant. Hence, the curvature of the deflection plates perpendicular to the dispersion plane does not change the overall angular aberrations. In particular for a circular symmetric beam the effect of the angular aberrations on the resolution would be independent of rl. In a combination with all other issues involved in spectrometers, such as the space charge and the transport of the beam through the entire spectrometer, curving of the deflection plate perpendicular to the plane of dispersion adds an element of flexibility which can be exploited in order to achieve optimum performance. Unfortunately the effect of the additional curving on the overall performance and the resolution is not amenable to electron optical simulation with present computer power. One therefore has to resort to experimental tests. The results for one particular spectrometer are described in the next section.
120
Vertical curvatureof deflectionplates (II)
4. Figure 1. Angular aberration c, and cP of a deflecting device as a function of the curvature of the deflection plates perpendicular to the dispersion plane.
PERFORMANCE TROMETER
OF THE
SPEC-
The performance of a spectrometer employing in total three energy dispersive devices with modified angular aberration coefficients
822
are described in the following. The spectrometer features two monochromators operating at different pass energies. The first monochromator is a retarding monochromator [l] with different potentials at the entrance and exit slit. For the first time we have also implemented a routine which automatically adjusts all potentials applied to the spectrometer in order to optimize the monochromatic current at the detector for a given set of deflection voltages applied to the dispersive devices, i.e. for a fixed resolution and a fixed energy at the target. Depending on the resolution and hence on the current at the detector, the optimization takes between a few minutes and half an hour. Starting from a moderate resolution the routine also allows for a completely automatic adjustment to a predetermined high final resolution, Owing to this routine, operation of the instrument has turned into a real pleasure. The overall resolution, measured as the full width at half maximum, is plotted in Fig. 2 versus the deflection potential difference AU between the inner and outer deflection plates; AU was equal for the second monochromator and the analyzer. The data points trace a straight line which intersects the ordinate at the resolution limit AE = 0.28 meV. The best resolution which was actually obtained at this point in
Currentq 3_57~10-'~A FWHM ~0.518meV lO%-Width =l.lSmeV
-0.5
0
0.5
Energy (meV1
Figure 3. Current at the detector versus difference in the mean potential of the monochromator and analyzer with the spectrometer in the “straight through” position.
2 ,
0.1
0.2
0.3
lleflection voltqat AU (VI
Figure 2. Resolution versus the deflection voltage applied to the second monochromator and analyzer.
Figure 4. Current measured at the detector versus the resolution (FWHM) of the spectrometer for the new spectrometer (squares) and the penultimate design (circles) as described in [ 11.
823
time is AE = 0.5 meV (Fig. 3). We have also measured the current at the detector versus the resolution AE and the results are compared to the results for the previous design in Fig 4. The current at the detector follows the functional form 5 Id=
14(AE-0.30mcV)~pAmeV~~ 3 3 4OAEz pA meVeT i
5
AE<25meV AE > 3.5 meV (5)
In the entire range for AE < 10 meV the current for the new design is higher than for the penultimate design, with the difference increasing the better the resolution is. For AE = I meV the current at the detector in the straight-through position is 6 pA which is more than sufficient to investigate dipole active vibrations. To provide an example, for a full monolayer of CO on Ni(ll0) [S] one would have a count rate of ~16.10~ Hz for the CO stretching vibration. Impact scattering in particular from surface phonons, requires higher currents, equivalent to about 50 pA at the detector in the straight through position. From Fig. 4 one can expect that a resolution of al.5 meV should be achievable, even for this more demanding application. In summary, I conclude that electron energy loss spectroscopy with a resolution below 1 meV is possible and will be made available to practical applications in our laboratory, and hopefully to other laboratories as well, in the near future,
ACKNOWLEDGEMENTS The construction and making of this and earlier versions of the spectrometer were in the hands of D. Bruchmann. His never waning readiness to put my sometimes well, sometimes not so well, thought-out ideas into reality is gratefully acknowledged. Likewise the spectrometers could not have been realized without the diligent and precise work of our mechanical workshop directed by D. Strobl.
REFERENCES
AND NOTES
I, H. Ibach, Electron Energy loss Spectrometers, Springer Series in Optical Sciences 63, Springer, Berlin - Heidelberg, 1991, ISBN 3-540-52818-o /O-387-52818-0. 2, G. Kisters, J.G. Chen, S. Lehwald, and H. Ibach, Surf. Sci. 245 (1991) 65. 3. K = 5/2 applies when the monochromator is fed with a beam whose energy spread AEi, is independent of the pass energy E, of the monochromator. More typically one has AEh ocE, and K = 3/2 (see ref. 1 for details). 4. H. Liebl, DE 26 20 877 C2. 5. See e.g. ref. 1, pp. 21 ff. 6. K. Jost, J. Phys. Sci. Instrum. 12 (1979) 1006. 7. International patents pending. 8. H. Ebach, M. Balden, D. Bruchmann, and S. Lehwald, Surf. Sci. 269/270 (1992) 94.