Performance
of the high-resolution
SX700/11 monochromator
M. Domke, T. Mandel, A. Puschmann, C. Xue, D. A. Shirley,a and G. Kaindl
Institut ftir Experimentalphysik,
Freie Universitiit Berlin, Arnimallee
14, O-1000 Berlin 33,Germany
H. Petersen and P. Kuske
Berliner Elektronenspeicherring-Gesellschaft
D-1000 Berlin 33, Germany
ftir Synchrotronstrahlung
m. b.H., LentzealIee iO0,
(Received 7 August 1991; accepted for publication 25 September 1991)
This article reports on the high-resolution performance of the grazing-incidence plane grating
monochromator SX700/11, installed at BESSY by the Freie Universitat. Berlin, in the
photon energy range from about 40 to 900 eV. The high resolving power up to 10 000 achieved
with this monochromator is based on improving the figure error of the ellipsoidal focusing
mirror, on reducing the vertical dimension of the beam source, and on employing a 5-pm exit
slit. We report on high-resolution gas-phase studies in the double-excitation region of He,
as well as at core-excitation thresholds of Ne, Ar, Kr, and Xe in the photon-energy range from
2145 eV to =900 eV. In addition, high-resolution core-excitation spectra at the K
thresholds of C, N, and 0 are presented for gas-phase CO, Nz, and Oz. In all cases, high-n
Rydberg states and/or vibrational sidebands of the electronic excitations were resolved.
The various contributions to the present instrumental linewidths are discussed as well as the
prospects for further improvements in resolution with this monochromator.
I. lNTRODUCTlON
The soft x-ray photon-energy range between approximately 35 and 800 eV is generally considered to be a difficult region in high-resolution studies using synchrotron
radiation. This is mainly due to the fact that monochromatization in this energy range is practically restricted to the
use of optical gratings operated in the grazing incidence
mode, giving rise to large geometrical aberrations. On the
other hand, this photon energy range is particularly interesting from the scientific point of view, since the K thresholds of some of the chemically most interesting low-Z elements (C, N, 0, . ..I are located there. Until very recently,
only moderately high energy resolutions were achieved in
this energy range, preventing the study of many interesting
closely spaced spectral features in the core-excitation spectra of atoms, molecules, and adsorbates, like, e.g., vibrational sidebands of resonance lines and high-n Rydberg
states.
This obvious drawback was overcome in recent developments, including both the design of new types of
monochromators’-3 and the optimization and tuning of the
plane-grating ellipsoidal-mirror
monochromator SX700,
described already in 1982.4*5Most of these monochromators are optimized for a relatively narrow energy range and
require a movable exit slit to achieve approximate focusing.
In contrast, the SX700 concept is based on a fixed exit slit
without an entrance slit; it is a plane-grating instrument
designed for imaging the monochromatized beam by an
ellipsoidal mirror. Formerly, the performance of the
SX700 monochromator suffered from problems in figuring
aspherical optical surfaces with high precision as well as
from limitations caused by the finite size and stability of
*)Permanent address: Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720.
a5
Rev. Sci. Instrum.
63 (‘I), January
1992
the electron beam in the storage ring. With substantial
recent improvements in figuring aspherical surfaces as well
as in electron-storage-ring optics, however, the SX700 design has been shown to be suitable for providing excellent
resolution over a wide energy range from about 35 up to
1000 eV, in conjunction with relatively high photon fluxes.
These recent improvements in the performance of the
SX700 monochromator are the subject of the present article.
II. THE SX700/ll
MONOChROMATOR
The SX700/11 monochromator, designed by Petersen4
and manufactured by Carl Zeiss, Oberkochen (Germany),
.is based on the concept of a fixed virtual source focused
onto a fixed exit slit by an ellipsoidal mirror. No entrance
slit is employed, and the monochromator is thus best utilized in combination with low-emittance electron-storage
rings providing a small vertical beam size. The monochromator has only three optical elements, a movable plane
mirror (640 mm X 30 mm), a movable plane grating ( 110
mm X 30 mm), and a fixed ellipsoidal mirror (225 mm X 30
mm) that image the monochromatic light beam onto a
curved exit slit positioned at the meridial focus of the ellipsoidal mirror (see Fig. 1).
The plane mirror and the plane grating image the real
source (at a distance of 15 m) onto a monochromatic virtual source 76 m away in one of the two foci of the ellipsoid. The photon energy is scanned by rotating both the
plane mirror and the plane grating, whereby both the grazing angle of incidence, a( l“<cr<8”), and the exit angle, p
(2”s& 18”), are changed. These rotations are performed
with high precision and controlled by a computer in such a
way that the monochromatic image of the source is fixed to
the second focus of the ellipsoidal mirror, where the exit
slit is located, For this purpose, the position of the virtual
0034-6748/92/010080-10$02.00
@ 1992 American
institute
of Physics
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80
monochromatic
source
source
15m
wpplak/mirror
monochromatic source at a fixed distance from the grating,
given by the focusing condition of plane gratings,
sin P/sin a = C = const., 4 is made to coincide with the
first focus of the ellipsoid. In this configuration, the defocusing term of the grating equation, Fzo, is zero at all
energies. To achieve a good efficiency of the grating, the
value of C was chosen to be 2.25.
The SX700/11 monochromator, installed in 1988 by
the Freie Universitlt Berlin at the Berliner Elektronenspeicherring fur Synchrotronstrahlung
(BESSY), is optimized
for high energy resolution by diminishing the figuring errors of the optical elements as well as the vertical beam
size. Two gratings, with 1221 and 366 lines/mm, respectively, are presently installed and may be interchanged
without breaking the vacuum. To achieve optimum energy
resolution in the photon energy range from -38 eV to
2: 1000 eV, only the 1221-l/mm grating is useful, because
resolution scales with the square root of the spacing of the
grating.
III. ENERGY RESOLUTION
The achievable energy resolution, AE, depends on the
aperture of the light beam impinging on and leaving the
grating. From the angle-versus-energy dependence in the
grazing-incidence
range, a AE a E3’2 law has been
derived.5 The resolution depends additionally on the diffraction order, m, as AEa m - 1’2. On the assumption of
ideally adjusted optical elements, the resolution is limited
by essentially three contributions: (i) AE, caused by the
finite quality of the optical elements, in particular of the
ellipsoidal mirror, (ii) AEb due to the finite size and stability of the beam source, and (iii) AEs given by the finite
size of the exit slit. The total resolution, AE, may be expressed by addition of these individual contributions in
quadrature,
AE a E312m - “‘( AEZ + AE: + AEZ ) “=.
(1)
The limiting contribution to resolution from the width
of the exit slit, AE, depends linearly on the width s of the
exit slit, AE,as. Five different exit slits varying in width
from 5 to 2: 200 pm are installed and may be interchanged
in ultrahigh vacuum. With a ‘5-pm-wide exit slit and a
given distance between grating and slit of 2.15 m, a value of
AE, = 21 meV is obtained in first diffraction order at the C
K edge (hv-285 eV); this value of AE, is normally much
smaller than either of the contributions (i) and (ii) (see
further below). On the other hand, recent improvements in
aspherical mirror technology as well as in electron-storagering optics have resulted in considerable reductions of
81
FIG. 1. Schematic view of the SX700
monochromator.
these two latter contributions, allowing high energy resolution over the whole soft x-ray energy range covered by
the SX700/11 monochromator.6’7
The contribution of the beam size to finite resolution is
determined by the vertical dimension of the stored electron
beam and the given source-grating distance of 15 m. At
BESSY, the size of the beam source depends on the location of the beamline at the storage ring. When BESSY is
operated with the so-called METRO optics, the vertical
beam size at an outer dipole magnet is approximately 2.5
times smaller than that at an inner dipole magnet. These
facts were taken into account when the SX700/11 monochromator was installed at an outer dipole magnet. Under
normal operating conditions of BESSY, the vertical beam
size at an outer dipole magnet is typically 0.25 mm, resulting in a beam-size contribution to resolution, AE,, of ~40
meV at hv = 285 eV. We have also operated BESSY in a
special mode, where the sextupole magnets of the storage
ring were switched off, leading to a reduction of the coupling between the horizontal and the vertical electron motion and in turn to a vertical beam size reduced by a factor
of-2. In this small-source mode, beam currents up to 50
mA (as compared to 2500 mA with normal METRO optics) could be stored, with lifetimes of fr: 1 h.
The contribution of the optical elements to resolution
may be visualized from their tangent errors. Both the plane
mirror and the plane grating have tangent errors of less
than =tO. 1 arcsec, and their contributions are negligible.
For an aplanar and aspherical surface, however, such as
the ellipsoidal mirror, high-accuracy manufacturing
is
much more difficult. For that reason, these shapes have
often been avoided in monochromator designs. The resolution of the SX700/1 prototype instrument installed in
1982, e.g., suffered from a tangent error of the original
ellipsoidal mirror of = f 3 arcsec, and also the new
SX700/11 monochromator was originally operated with a
f 1.7-arcsec mirror.8*9 Only very recently, ellipsoidal surfaces with tangent errors of less than f 1 arcsec have been
successfully manufactured and characterized. As a consequence, the ellipsoidal mirror of the SX700/11 monochromator was replaced in December 1989 by a *0.65-arcsec
mirror, leading to the present record energy resolution.
Despite these improvements, the main contribution to
finite resolution is still caused by the ellipsoidal mirror.
Therefore, a substantial further improvement in resolution
has been achieved by shadowing off part of the ellipsoidal
mirror; this procedure allows the selection of a part of the
mirror with still smaller tangent errors. For this purpose,
two pairs of diaphragms are available in the SX700/11: one
pair is moved vertically in front of the ellipsoidal mirror
Rev. Scl. Instrum., Vol. 63, No. 1, January 1992
High-resolution
monochromator
81
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limiting the beam meridially; the other pair is moved horizontally in front of the plane mirror limiting the beam
sagittally. With the original I .7 1-arcsec ellipsoidal mirror,
only l%-2% of the ellipsoid could be used to achieve an
acceptable yet still moderate resolution.8*9 With the 0.65arcsec mirror, however, a substantial improvement in resolution is achieved by shadowing the mirror down to
IO%-20% of its full area.
For longer wavelengths, as in the energy range of the
He double-excitation spectra (A = 200 A), diffraction effects at the diaphragms cannot be ignored when the mirror
is strongly shadowed. The effects and consequences of such
diffraction effects will be discussed in the following. Due to
the large source and image distances, diffraction at the
described diaphragms may be treated in the Fraunhofer
approximation, resulting in a diffraction intensity distribution of
1: = (sin mA/mA
) 2,
(2)
with u = (a - a’)/A.
Here a is the angle of incidence
(here a = 0) , a’ is the diffraction angle, and A stands for
the width of the vertical aperture (the latter is relevant due
to diffraction in the plane of dispersion). In this way we
obtain for the width [full width at half maximum
(FWHM)] of the central intensity maximum as a function
of wavelength and width of the aperture:
a’=O.888/2/A.
(3)
If we consider an angular width equal to that of the 5-,um
exit slit 1500 mm behind the aperture (i.e., 3.33 ,urad or
0.7 arcsec), we obtain
A,,=O.888;1/(3.33X
10v6)+
(4)
For further discussion, we give three examples:
A=200
A (He double excitation)
;1= 30 A (N-K
A.= 14 A (Ne-K
AminE5.3 mm,
A min=Ov8 mm,
region)
A min= 0.37 mm.
region)
The full vertical aperture of the ellipsoidal mirror amounts
to 8 mm. With a dispersion of 0.002 A/prad at 200 A (60
eV), a shadowing of the mirror down to N 10% (corresponding to A N 2 mm) is not possible in the photon-energy
range of the double-excitation spectra of He due to diffraction effects, even though the contribution from figuring
errors of the mirror would decrease. The optimum-resolution spectra of He in the double-excitation region were
accordingly taken with ~20% of the ellipsoidal mirror
(see below).
bypass
I
UHV
gas
window
45
pA -meter
FIG. 2. Schematic view of the ionization cell employed in the gas-phase
studies.
viously, only transitions in gas-phase atoms or molecules
are suitable, since in the solid state, interactions such as
band formation, phonon broadening, etc. contribute to line
broadening. Moreover, for many atomic and molecular
gases, values of the natural linewidths as well as the exact
energy positions of absorption lines are known from electron-energy-loss (EELS) studies.” It turns out, however,
that nearly all excited states available in the soft x-ray
range have l? values from Z 100 to 300 meV, i.e., close to
or even larger than the best presently achieved monochromator resolution. With further improvements in monochromator resolution, it will be increasingly possible to
investigate changes in the natural linewidths; on the other
hand, it will also be more and more difficult to measure the
monochromator resolution itself, since resolution will contribute only in a minor way to the total experimental linewidths. For example, if we take a lY value from high-resolution
EELS studies, the derived monochromator
resolution will depend on the accuracy of the I value from
EELS, which is typically -5%. OnIy in some low-energy
cases, e.g., for the higher members in the Rydberg series of
the double-excitation spectra of He, I’ is much smaller
than the achieved monochromator resolutions. Therefore,
these latter measurements are expected to give the most
reliable value for the monochromator resolution.
A. Gas ionization
cell
To test the resolution of the SX700/11 monochromator, excitations of inner-shell electrons into unoccupied
states in atoms or molecules with relatively long core-hole
lifetimes were studied. In an ideal case, the natural linewidth, I, of such a core-excited state should be much
smaller than the value of the monochromator resolution.
With the present high resolutions, however, only very few
atomic or moIecular states fulfill such a requirement. Ob-
The photoionization measurements were performed
with a two-plate ionization chamber (active length: 10 cm)
pumped to < 10 - 6 mbar and filled with 0.005-0.5 mbar of
the gas under study (He, Ne, Ar, Kr, Xe, N2, CO, 02,
etc.). A schematic view of this ionization cell is presented
in Fig. 2. One electrode, used as a repeller electrode, is held
at + 100 V. At the other electrode, the photoionization
current in the 10 - 15-10 - l2 A range is recorded by a commercial picoampere meter as a function of photon energy.
The ionization chamber is separated from the ultrahigh
82
High-resolution
IV. GAS-PHASE MEASUREMENTS
Rev. Sci. Instrum.,
Vol. 63, No. i, January
1992
monochromator
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82
vacuum (UHV) of the SX700/11 monochromator (in the
10 - lo mbar range) by a 1500-A Al ( 1% Si) or a 1000-A
Lexan window.” In order to avoid disturbing effects due to
absorption edges of the window (e.g., Al 2p or C Is), the
window material is selected according to the photon-energy range studied. Special care was taken during pumpdown of the ionization chamber, since the windows cannot
withstand pressure differences exceeding u 10 mbar. The
ionization cell may be used both directly, attached to the
exit port of the SX700/11 monochromator, and parasitically, on an additional UHV chamber employed for solidstate or surface studies.
B. Data-fitting
244
246
Photon
250
248
Energy
(eV)
procedure
The measured spectra were deconvoluted by leastsquares fitting a superposition of Lorentzian/Fano profiles,
AL, convoluted by a Gaussian profile, AG, to the data. The
Gaussian linewidth, AG (FWHM), was typically set equal
to the monochromator resolution. In a more exact analysis,
however, this may not necessarily be the case. Absolute
values of the natural linewidth, I, are known from published EELS results, where the instrumental linewidth is
well known from analysis of the primary electron beam.
In most cases, the fitted AL values turned out to be
somewhat larger than r obtained from EELS. This could
be due to the following reasons: (i) a nonGaussian resolution function of the monochromator, (ii) saturation effects
in the gas-ionization spectra, if the gas pressure in the ionization cell was too high, (iii) existence of additional absorption features close to the measured lines, shifted in
energy by less than the natural linewidth, (iv) inapplicability of the EELS linewidth values due to additional decay
channels in photoexcitation, shortening the lifetime of a
core-excited state as compared to electron excitation. If
(iii) or (iv) apply, only part of the measurements should
show a broadened Lorentzian linewidth. Saturation effects
can be detected by measuring the intensity of an intense
absorption line relative to a weak one at different gas pressures, giving rise to an apparent decrease in the relative
intensity of the stronger line in case of saturation. If the
linewidth of an intense absorption line is investigated, the
gas pressure has to be lowered to a value where saturation
effects vanish. This is, e.g., the case for the Ar (2p - ‘4s)
states close to the Ar L2,3 thresholds for pressures ~0.1
mbar. On the other hand, saturation effects are visible in
case of the (46- ‘6~) state of Xe and the C( Is- ‘rr*> state
of CO even at pressures of only 0.03 mbar.
On the other hand, if deconvolution of unsaturated
spectra results in Lorentzian linewidths consistently larger
in all cases than those reported from EELS measurements,
one has to conclude that the monochromator function is
nonGaussian, containing some Lorentzian-like contribution. The assumption that the nonGaussian contribution to
the monochromator resolution function is Lorentzian is a
crude, but useful, approximation. There are reasons to assume that the monochromator function is nonGaussian,
since both the exit slit (which should lead to a rectangular
contribution) and the ellipsoidal mirror (which will have a
nonuniform distribution in tangent errors) are expected to
83
/
I
I
FIG. 3. Photoionization spectrum of gas-phase Ar close to the Ar L,.,
threshold with 20% of the ellipsoidal mirror used. The 2p,i( ns,nd)
states, converging towards the L3 threshold, are underlined.
give nonGaussian contributions to the resolution function.
Special problems arise in case of the very narrow Fanoprofile lines measured in the He double-excitation region,
which will be discussed explicitly in Sec. IV D.
C. Soft x-ray excitation
spectra of noble gases
A photoionization
spectrum close to the Ar L,,,
thresholds is shown in Fig. 3. In particular, the 2p3,,-+4s
(hv = 244.39 eV”)
has previously
been
transition
used to characterize the resolution of soft x-ray
monochromators”t2 on the basis of its relatively small linewidth of 121 f 6 meV.t3 In our case, this value is indeed
small enough to see an improvement in resolution with
moderate mirror shadowing, but it is still too large to verify the further improvement in resolution by an extreme
shadowing as wtll as by switching from normal to the
small source mode of BESSY. The spectrum in Fig. 3 was
recorded in the normal beam mode, using -20% of the
ellipsoidal mirror. Two sets of lines are visible converging
toward the L3 and the L, thresholds, respectively. The
2p-+Rydberg series is resolved up to n = 7, which was not
achieved before, demonstrating
the high-flux/highresolution features of the SX”IOO/II monochromator. Employing the full ellipsoidal mirror, only slight changes in
the overall spectral features are noted, with the measured
linewidth (FWHM) of the (2p$4s) state increasing from
135 meV in the 20%-mirror mode to 180 meV for the full
mirror. Assuming a Lorentzian natural linewidth of 121
meV, we obtain a Gaussian resolution of 2: 70 meV ( 135
meV) in the 20% (full ellipsoid) mode, respectively. The
least-squares fit, shown as a solid line in Fig. 3, is quite
good. In this case, the fit could not be improved much by
using a nonGaussian monochromator function. It should
be noted here that a resolution of 70 meV was previously
also reported for EELS measurements of Ar L2,3 excitation spectra,13 however, with much worse statistical accuracy despite data acquisition times of -48 h as compared
to -5 min in the present case. In addition, the higher
Rydberg states visible in Fig. 3 (e.g., 2p + 7d) could not be
resolved in the relatively noisy EELS spectrum.
83
High-resolution
monochromator
Rev. Sci. Instrum., Vol. 63, No. 1, January 1992
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Kr
Ne K
M4,,
I.,......,l..l..,...I,..,,....L
91
92
Photon
L
93
Energy
At lower photon energy ((100 eV), an extrapolation
of the resolution measured at the Ar L2,3 thresholds, using
the AE 0: E3’2 relation, predicts a monochromator resolution of (20 meV, when ~20% of the ellipsoidal mirror is
used. In this energy range, innershell excitations of rare
gases are also available: the Kr 3d5,2,3,2+ np transitions (in
the energy range from = 91 to 95 eV>, converging toward
the Kr M4,s thresholds, as well as the Xe 4ds/2,3/2*np
transitions (energy range: 65-70 eV), converging toward
the Xe N4,5 thresholds. The natural widths of these resonances, however, are much wider than the expected monochromator resolution. The natural widths of the Kr
3d5Ti5p and Xe 4d,726p excitations, e.g., reported from
EELS measurements, are 83 14 and 111 A4 meV,
respectively. I3 Nevertheless, these transitions are well
suited for a comparison of the measured natural widths
with the previous EELS results. The Kr M4,s core-excitation spectrum, taken with 10% of the ellipsoid, is shown in
Fig. 4, while that at the Xe N*, thresholds is displayed in
Fig. 5. Note the excellent statistical accuracy of the two
spectra, which again resolve a higher number of Rydberg
states than in the EELS work. The natural Lorentzian
widths determined from the spectra are 105 and 120 meV
I--
4&,,+6p
,““-,“r*-“““,““’
“‘I”‘-Xe N4.5
%,-6p
66
Photon
67
Energy
68
69
Rev. Sci. Instrum.,
Vol. 63, No. 1, January
.
.
1992
.
.
t
,
868
Energy
t
I.
L
c
I
870
(eV)
FIG. 6. Photoionization spectrum of gas-phase Ne close to the Ne K
threshold with 5% of the ellipsoidal mirror used.
for Kr 3d,,, -t 5p and Xe 4d5,* -t 6p, respectively; they are
both larger than the EELS I’ values, which may be a hint
to a nonGaussian monochromator function. Other linebroadening mechanisms, mainly diffraction at the apertures, may contribute as well.
At higher photon energies, core excitations in gasphase Ne close to the Ne-K threshold have been studied, in
particular the ls-3p transition at hv = 867.1 eV,‘e with a
natural width of -230 meV derived from photoemission;i4
a previous EELS study had resulted in a I’ value ~310
meV.” At this photon energy, the ABa E3’2 relation predicts a monochromator resolution of -470 meV. Since the
natural width of the Ne Is-+ 3p line is much smaller, we are
in a position to resolve in this case the effects of all the
various resolution-limiting contributions discussed in Sec.
III. With 20% of the ellipsoidal mirror and a lo-pm exit
slit, e.g., a total experimental linewidth of -650 meV
(FWHM)
is obtained in the normal beam mode. This
value was considerably improved in the small-source mode
of operation with a 5-pm exit slit; in fact, a total linewidth
of 510 meV (400 meV) was obtained in first (second)
order of diffraction, respectively. Figure 6 displays the
Is-np core-excitation resonances of gas-phase Ne recorded in this way in second diffraction order. Unfortunately, an unambiguous fit of the Is- ‘3p resonance at
867.1 eV in terms of a Lorentzian line convoluted by a
Gaussian profile is difficult in this case. This may be caused
by an overlap of the Is-‘3p line with the Is- ‘4~ and
higher resonances, as well as some line asymmetry, which
is presumably inherent in the monochromator function and
is particularly evident at high photon energies. The intrinsic Lorentzian linewidth derived from the fit is 340 meV,
i.e., only slightly larger than the value derived from EELS.
If we assume the natural linewidth of the Ne Is - *3p resonance to be 3 10 meV, we obtain a pseudoGaussian monochromator resolution of 405 meV (265 meV) in first order
(second order) of diffraction.
D. He double-excitation
(eV)
FIG. 5. Photoionization spectrum of gas-phase Xe close to the Xe N4.s
threshold. The 4dsyinp states, converging toward the Ns threshold, are
underlined.
84
.
Photon
(eV>
FIG. 4. Photoionization spectrum of gas-phase Kr close to the Kr M4,s
threshold, with 10% of the ellipsoidal mirror used. The 3dsT;np states,
converging toward the Ms thresholds, are underlined.
.
866
95 i
94
spectra
Extremely narrow core-excitation resonances in the
energy range between 60 and 80 eV are provided in form of
the autoionizing states of double-excited He.16 These states
High-resolution
monoohromator
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84
I
n:2t
.
I
’
He (sp,Zn*)lP’
II
I
*
(al
St
115
-u /.
2
tdII
.IYQ
:
-3
d
.3Q I
3
sI
a
I-*
(5 .o
_A__
1.1,
so
61
1,.
I.,
(2
,
#,
I,
1.
IS
64
I9
.
t
65
I1.
c
I
04
7t
at
I
9t
I
I
I. 65. I
I
.
Photon
15.2
Energy
I
65.S
>
,
I
65.4
(eV)
FIG. 7. Photoionization spectra of the N = 2 series of the autoionization
double-excitation states of He, I?--+ (2~np*22pns): (a) overview; (b) expanded high-n region; (c) ” - ” states. The spectra were taken with 20%
of the ellipsoidal mirror.
couple to the He + continuum, leading to resonance lines
with pronounced Fano profiles.‘7 Particularly in the case of
the higher
Rydberg
states of the N = 2 series
l.? + (2.wp f 2pns), where only one autoionizing channel is
available, the states are quite long lived and hence very
narrow.‘8*‘9 The two excited electrons are strongly correlated, resulting in an intense mixing of the 2mp ‘PO and the
2pns ‘PO states. Two series are observed, which can be described by addition (“ + ” states) or subtraction (“ - ”
states) of the respective wave functions.
These two Rydberg series converging toward the N
= 2 ionization limit of He + are displayed in Fig. 7: The
spectrum is dominated on the intense “ + ” series with
lines at hv = 60.15 eV, 63.67 eV, 64.47 eV, etc., superposed
on the much weaker “ - ” series with lines at hv = 62.77
eV, 64.14 eV, etc.; the intensity of the latter series is = l/30
of that of the “ + ” series. Further details of this work have
been presented elsewhere.7
Rydberg states up to n = 16 and n = 7 have been resolved for the “ + ” and “ - ” series, respectively. The
‘I - ” states are known to be extremely narrow with theo85
retically predicted natural widths of -0.1 meV and less.‘*
The lifetime r of these states increases strongly with n
according to r a n*3, with n* = n - ,u being the effective
principal quantum number (1~ represents the quantum
defect) .I7 Therefore, the natural width of the “ + ” state
decreases rapidly with n: for n = 7 (n* = 6.85) it is only
CT1 meV.7*‘8 The “ + ” states may be observed up to high
n values, with the monochromator resolution causing ultimately an overlap of the highest Rydberg states. Accordingly, the number of resolved “ + ” states provides a direct
picture of the monochromator
resolution. Simulations
show that Rydberg states up to n = 13, 16, or 20 may be
resolved with a monochromator
resolution of 10, 6, or 3
meV (FWHM), respectively. In the spectrum presented in
Fig. 7, the “ + ” states up to n = 16 are resolved, resulting
in a monochromator resolution of z 6 meV. This value has
been confirmed by a careful Fano/Gauss-profile fitting procedure of both the “ + ” and “ - ” states.
The resonance lines of the “ + ” series in Fig. 7 could
be least-squares fitted in a consistent way with Fano line
shapes convoluted by a Gaussian to simulate the spectrometer function, resulting in a Gaussian resolution of AE
= 6.0*0.1 meV (FWHM)
at hv = 60 eV. Both the individual lines and the n = 6-l 1 series with I a (n*) - 3 were
analyzed. Fitting the whole series (up to n = 16) with
I? a (n*) - 3 is quite time consuming due to the rapidly
decreasing F values. Although the measurements were performed with only 1000 points per eV, a huge point density
up to 10 000 points per eV is needed in the fitting procedure to cover each of the very narrow Fano lines with a
sufficient number of points before convolution with the
Gaussian spectrometer function. In this case, a good fit was
obtained with equal Fano-line intensities as required by
theory.” A lower point density is only acceptable, if fitting
is performed with free relative intensities. The x2 values
obtained in these simultaneous fits of the n = 6-l 1 series
are plotted in Fig. 8 as a function of the assumed Gaussian
resolution, AE, defining a clear minimum at AE = 6.0
f 0.1 meV. This corresponds to the best resolving power to
date of E/AE= 10 000 in this energy region.6t7 A deterioration in resolution to a value of 7.8 meV is observed when
we change from the small-source to the normal METRO
mode of BESSY. Note that the spectra in Fig. 7 were taken
with Z 20% of the ellipsoidal mirror; a stronger shadowing
of the mirror is not favorable at these energies, since diffraction effects caused by the aperture lead to a deterioration of the resolution.
E. Ne 2s excitation
spectra
For even lower photon energies, suitable core-excitation resonances with narrow linewidths are provided by
transitions to the Ne 2s- ‘np Rydberg states. The spectra
recorded for this series converging to 48.476 eV are shown
in Fig. 9; Rydberg states up to n = 17 are resolved. Although some overlap with the lowest-lying double-excitation series of Ne is expected [the 2p4( 3P)3~4p ‘fi state
should be in the energy range of the 2s- ‘np series], no
effects of such an interseries interference are observed, in
Rev. Sci. Instrum., Vol. 63, No. 1, January 1992
High-resolution
monochromator
85
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/
”
’ ’ ,
x2
’ 5 q 5 ,‘I
4
1.58-
Ne
*
Zs-‘np
P,
z
2
3
.5
1.54-
46
I t t * 8 I’,
b
41
46
, 5 t r 6 , b 4 * ’ I
Ne 2s-‘np
n=7
1.50-
I I
5.6 *
I
I
6.0
I
2-l
.t:
2
“2
c
I
6.4
AE (meV)
FIG. 8. x2 as a function of the Gaussian resolution, AE, from leastsquares fits of the N = 2 series of the double-excitation spectrum of He.
Only the upper part of the spectrum from n = 6 to 11 was fitted with
constant equal intensities and intrinsic line widths Q l/n*3.
(b)
’
I,
48.1
1 I,,
I I
48.2
Photon
agreement with former observations,20 and the Ne Is- ‘np
series remains undisturbed. For the lowest state (2~~ ‘3p),
a natural linewidth of N 13 meV has been reported;20 analogous to the He double-excitation series, the lifetimes of
the higher Rydberg states are expected to scale with &.
Again, the number of resolved states provides a direct measure of the monochromator resolution. A quantitative fit of
the n = 7 to n = 17 series results in a monochromator resolution of 5.5 meV (FWHM) at hv = 48 eV. Note that the
spectrum in Fig. 9 has been taken with normal METRO
optics; the derived resolution value fits therefore well into
the AEa E3" relation, for first order of diffraction.
a,,
48.3
Energy
, , , I,,
46.4
, , I
48.5
(eV)
FIG. 9. Photoionization spectra of gas-phase Ne in the region of the
;?F-np Rydberg series taken with 20% of the ellipsoidal mirror; (a)
overview, (b) expanded high-n region.
K-shell excitations of low-2 elements, in particular of
C, N, and 0, raise particular interest. The simplest gaseous
molecules containing these elements are CO and N,. in
these cases, the strongest photoabsorption transitions are
observed for the ls-7.r* resonances at 287.40, 400.80, and
534.21 eV, respectively, for C-excited CO, N-excited N2,
and O-excited CO.” It is well known that the C Is- ‘r*
final state of CO, as well as the N Is- ‘r* state of N,, is
split into various vibrational sublevels.21-26 For N2 and Cexcited CO, the quoted energies represent excitations into
the lowest vibrational sublevel (v’ = 0); for O-excited CO,
only a broad unresolved peak had previously been
reported.22
The vibrationally split Is-r*
spectrum of gas-phase
N, (vibrational splitting: hv,. = 235 meV) has recently
been employed in characterizing the resolutions of soft xray monochromators.2*3 The splitting of the r* resonance
originates from excitations into the various vibrational sub-
levels of the core-excited state, with the transition probabilities for excitation into higher v’ sublevels being governed by the difference in equilibrium distances between
the ground state and the excited Is- ‘IT* state. Typical
spectra of gas-phase Nz, taken with the SX7OO/II monochromator in first and second order of diffraction, as well
as in the small-source mode of BESSY are presented in Fig.
10. The spectra were recorded for a N, pressure of 0.015
mbar using = 5% of the ellipsoidal mirror and a 5-pm exit
slit. Despite these strong restrictions, the data acquisition
times for these two spectra ranged only from 5 to 20 min.
In second order of diffraction, a clear improvement in resolution is achieved. A deconvolution of the spectra in
terms of Lorentzian lines, AL, convoluted by a Gaussian
profile, AE, would result in ALc= 150 meV and AE=40
meV (110 meV) in case of the second order (first order)
spectrum. This suggests again that AL contains part of the
monochromator function, since AL is again larger than the
natural width obtained previously by EELS (128*6
meV”’ ). Also, the improvement in monochromator resolution when going from first to second order of diffraction by
a factor of 2.7 is unreasonably high (it should be 4). On
the other hand, if we fix AL to the EELS value (r = 128
meV*’ 1, the fit gets naturally worse, leading to a
pseudoGaussian linewidth of 74 meV ( 129 meV) in second
(first) order of diffraction. These latter values agree quite
well with the AEa E3j2m - “’ relation, where m stands for
the order of diffraction.
86
High-resolution
F. Vibrationally
CO, and Oz
resolved
Rev. Sci. instrum.,
K-excitation
spectra
VoL 63, No. 1, January
of N,,
1992
monochromator
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86
I
1
Nz (gas)
I
IS -) 5T’
I
,
7
r
Photon
FIG. 11. Photoionization
the ellipsoidal mirror.
400
I
401
Photon
I
I
402
Energy (eV)
403
1
FIG. 10. Photoionization at the N IS-T? resonance in gas-phase N,,
measured (a) in first order, (b) in second order of diffraction; 5% of the
ellipsoidal mirror was used.
It should be pointed out here that the gas-phase N2
spectrum in Fig. 10(b) is very similar to the best N Is-r*
spectra reported in the literature;2’24 it seems even slightly
better resolved than those reported previously from work
with the spherical-grating monochromators at SSRL Stanford ( LBL)2 and at NSLS Brookhaven (Dragon) ,24 where
Gaussian resolutions of 80 meV2 and 40 meV,24 respectively, had been reported. While the resolution quoted in
Ref. 2 (80 meV) agrees well with the present findings, the
origin of the 40-meV value given in Ref. 24 remains quite
dubious on the basis of the published spectrum. Its reliability has to be questioned in view of the close similarity of
the N, spectra obtained with these three monochromators.
Likewise, the C 1s - ‘rr* state of CO sp lits into vibrational substates in a highly resolved core-excitation spectrum (vibrational splitting: hv, = 256 meV). These substates were first resolved by EELS.22*23 Compared to N2,
the relative intensities of the higher vibrational states are
much lower, due to a closer matching of the equilibrium
interatomic distances in the ground and core-excited state
of CO; this causes an enhanced probability of the u=O-+ u’
= 0 transition. In the present work, the vibrational splitting of the C 1s - ‘q* resonance is even resolved in spectra
recorded with the whole ellipsoidal mirror. In case of a
shadowed mirror, we have resolved four excited vibrational
substates under conditions where the main O+O transition
is saturated.25 An unsaturated spectrum taken with a CO
pressure of 0.007 mbar in first order of diffraction and the
87
’
”
Energy
at the C ls-+v*
m I
”
288.0
287.5
287.0
I
I
(eV)
resonance in CO, with 5% of
small-source mode (5% mirror, 5+m exit slit) is presented in Fig. 11. It is fitted by assuming Franck-Condon
transitions from the ground state to the excited state. The
quality of the spectrum allows for the first time a definitive
decision that CO is excited to the repulsive, rather than to
the attractive side of the C*O potential, i.e., the equilibrium distance in the excited state is larger than that of the
ground state.25 This question could not be answered with
EELS, and some confusion on equilibrium values can be
found in the EELS literature.23’26 Deconvolution of this
spectrum in terms of a Lorentzian and a Gaussian profile
results in a Lorentzian linewidth of 110 meV, which is
again slightly larger than the natural width derived from
EELS (85 f 3 meV23); also, a Gaussian width of 55 meV is
obtained. This again suggests a nonGaussian contribution
to the monochromator function. On the other hand, if we
fix F to 85 meV, a resolution of 86 meV is obtained. At
hv)292 eV, vibrationally split C-derived Rydberg states
and two-electron states are excited in CO with fine structures that are much better resolved” than previously
possible.23
In contrast to the C Is- ‘n-* state of CO, the fine structure of the 0 Is- ‘r* state had not been resolved before.22
Using the SX700/11 monochromator in optimum conditions (small source, 5% mirror, 5-,um exit slit) and in
second order of diffraction, the vibrational fine structure
was resolved for the first time.25 As shown in Fig. 12, the
0 1s - ‘r* state in CO consists of = 15 peaks separated by
2: 140 meV. At present, this fine structure of the 0 Is- ‘r*
state is only resolved in the small-source mode. At higher
photon energies, but still below the 0 Is- ’ threshold, excitations of the 0 1s electron into molecular Rydberg states
of CO are observed (see Fig. 12). As for the C-excited
Rydberg states, the O-excited states reveal a vibrational
fine structure as well (marked by bars in Fig. 12); again,
this vibrational fine structure was observed for the first
time. This was possible due to the high-energy resolution of
the SX700/11 monochromator, combined with a relatively
high photon flux, enabling us to resolve vibrational struc-
Rev. Sci. Instrum., Vol. 63, No. 1, January 1992
High-resolution
monochromator
87
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+A--’
r
(4
fl
5 r
P
3I
r,6.~
,+
Li~,,~.
Fix
[
k
1 )I
i 1:
!I;
i, ‘4
‘: \tt
‘\ r:\
,’
.?I’*\ t
-4 #U
534
I***-‘*+**Is***11
530
540
595
Photon KnergJ (e-f)
542
I
540
535
t
I
536
I
I
I
1
I
I
I
t
545
I
1
FIG. 12. Photoionization spectrum of gas-phase CO close to the 0 K
threshold. The intense peak at -534.5 eV represents the 0 Is-a* resonance; the spectral features above 538 eV stem from Is-Rydberg-state
transitions with vibrational fine structure. The spectrum was recorded in
second order of diffraction with 5% of the ellipsoidal mirror.
tures of even rather weak Rydberg states25 (see Fig. 12),
Similar to the case of N2 and CO, the K-shell excitation
spectrum of gas-phase 0, shows an intense Is- ‘n* state at
hv- 53 1 eV and transitions into molecular Rydberg states
in the energy region from = 538 to 543 eV ( Is- ‘Ryd), In
contrast to the 0 1s - ‘v* state of CO, no clear vibrational
fine structure is resolved for the 0 Is- ‘7r* state of 02. The
large width of the resonance, however, demonstrates its
composition of a variety of unresolved vibrational substates. On the other hand, the Rydberg states reveal a rich
fine structure [see Fig. 13(b)]; it can be divided into two
main regions from hv = 539 to 540.5 eV and hv = 540.8 to
543 eV, respectively,, This agrees with the results of previous EELS studies, where these lines were assigned to transitions to the 3~0~ state and higher Rydberg states,
respectively.22’27 With the present high resolution, these
features show a multiplicity of states that has not been
properly assigned up to now. Additional complications occur since two Rydberg series converging toward different
ionization limits (28,4Z) at 543.1 and 544.2 eV27 will overlap in this region. Nevertheless, the multiplicity of resolved
Rydberg states again demonstrates the high resolving
power of the SX7OO/II monochromator.
V. RESOLUTION/PHOTON
PHOTON FLUX
ENERGY RELATION,
An overview of the instrumental linewidths as a function of photon energy obtained with the SX700/11 monochromator in different modes of operation is shown in Fig.
14 in a double-logarithmic
plot. The experimental points
are connected by straight lines representing the AEa E3’2
relation. Curve (a) represents measurements performed
with the full ellipsoidal mirror in normal-source mode,
whereas curves (b), (c), and (d) were performed with the
ellipsoid shadowed to u 10%: curve (b) shows measurements in normal-source mode in first order, while curves
(c) and (d) represent data taken in the small-source mode
in first and second order, respectively. The improvements
88
Rev. Sci. Instrum.,
Vol. 63, No. 1, January
1992
I
,
539
540
541
542
Photon Energy (eV)
t
I
543
FIG. 13. Photoionization of gas-phase 0, close to the 0 K threshold: (a)
overview; (b) expanded Rydberg-series region, measured in third order of
diffraction with 5% of the ellipsoidal mirror.
in resolution when using the small-source as well as second
order diffraction are clearly seen. Figure 14 shows also that
the relations AE a .@* and AE a: m - “2 are followed quite
well.
The photon flux beyond the exit slit of the SX7oO/II
monochromator
was derived from Au photo yield
measurements.28 Using the full mirror and the S-pm exit
sht, a photon flux of about 1.5 X lo9 photons/s per lOO-mA
beam current is obtained in the photon energy range from
ti400 to 800 eV. The intensity in second order of diffraction, which is useful for highest resolution studies, amounts
to u 10% of the first-order intensity above photon energies
of a: 300 eV. For photon energies lower than N 250 eV, the
intensity of the second-order light is too low to allow measurements with good statistics, and even close to the C K
threshold only intense features, like the Is- ‘7~* resonances
in CO, can be measured in the second-order mode.
VI. DISCUSSION
Use of the SX7OO/II monochromator at BESSY under
improved conditions, particularly regarding the figure accuracy of the aspherical optical element, .enables measurements over a wide photon-energy range with formerly unachieved resolving power in the soft x-ray region. Due to
the absence of an entrance slit, a small vertical beam size
and good stability of the stored electron beam are essential
requirements for optimum performance. The need to
shadow off part of the ellipsoidal mirror in order to obtain
High-resolution
monochromator
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88
,ooo SX 700/a at BESSY
t
Freie Universittit Berlin
1221 l/mm Orating
!&urn exit slit
Photon
EnerQy E (eV)
FIG. 14. Monochromator resolution AE (FWHM) as a function of photon energy for the SXLIOO/II monochromator: (a) first order, METRO
optics, full ellipsoidal mirror; (b) first order, METRO optics, 10% of the
ellipsoidal mirror; (c) first order, small-source mode, 10% of the ellipsoidal mirror; (d) second order, small-source mode, 10% of the ellipsoidal mirror. The straight lines represent the AEa: E3” relationship.
superior energy resolution, however, shows that even more
accurate figuring in aspherical technology is still required
in order to exploit the full photon flux of the monochromator. We estimate that an accuracy of *O. 1 arcsec
should be available to reach this goal, a value that is still
far beyond the present technological possibilities. On the
other hand, a skillful shadowing of the ellipsoidal mirror
will result in the use of mirror sections with a tangent error
close to this value. To achieve ultrahigh resolution, a further decrease in the vertical beam size is highly desirable,
since a remarkable improvement in resolution has already
been obtained in a special small-source mode of operation
of BESSY, when the vertical dimension of the beam source
was reduced from -0.25 in METRO optics to -0.12 mm.
ACKNOWLEDGMENTS
Experimental assistance by Eric Hudson during part of
the measurements is gratefully acknowledged. D.A.S. was
89
supported by an Alexander-von-Humboldt
Senior Scientist
Award during 1989-1990. This work was supported by the
Bundesminister fur Forschung und Technologie, project
No. 05-413AXL7/TP2
+ 4.
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69
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