Optimisation of a spherical grating monochromator for soft X-ray microscopy applications

Nuclear Instruments and Methods in Physics Research A 349 (1994) 263-268 North-Holland

NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH Section A

Optimisation of a spherical grating monochromator for soft X-ray microscopy applications Werner Jark, Patrizia Melpignano

Stncrotrone Trieste, Padriciano 99, 34 012 Trieste, Italy Received 28 April 1994

This report describes the optimisation of a spherical grating monochromator operated with variable included angle as proposed by Padmore for microscopy experiments utilizing soft X-ray synchrotron radiation. The projected working range is for photon energies between 200 eV and above 1000 eV . The resolving powers requested for zone-plate microscopy are of the order of 3000 . This will be achieved in a monochromator exit slit of 30 wm, which is just the ideal source size for the following zone-plate . Further optimisations of the resolution and the tuning range for more general use are discussed .

1. Introduction

2. Experimental boundary conditions

A soft X-ray monochromator of the family of spherical

grating monochromators for the use at synchrotron radia-

tion sources is described in this paper [1]. It has been

optimised for providing the beam to a soft X-ray microscopy project. The beamline will be installed at an

undulator of the third-generation storage ring Elettra . Mi-

croscope objective will be an e-beam written zone-plate . A diffraction limited spot size with diameter 50 nm and a resolution of 0.1 eV at the carbon K-edge (photon energy

284 eV) are the goal for the experiments . The monochromator uses an entrance slit and has only 3 optical components. A toroidal mirror in vertical orientation illuminates the monochromator entrance slit with the sagittal focus in this slit and the tangential focus in the monochromator exit

slit . The only other optical components are a plane mirror

and a spherical grating between the two slits. In this configuration the angle of deflection at the grating can be tuned, an operation mode which Padmore suggested for keeping both monochromator slits fixed [2].

Section 2 will justify within the experimental requirements the decision for the optical concept of the beamline .

Section 3 presents the optimisation of the design for the requested performance. In Section 4 we will discuss in

how far this spherical grating monochromator concept can

be optimised for increased tuning range with improved suppression of higher harmonics.

* Corresponding author. Tel. + 39 (40) 37581, fax + 39 226338 .

The project that will utilise the monochromator here

described carries the name ESCA-microscopy [3]. The aim is to combine high spatial resolution soft X-ray scanning photoelectron microscopy (SPEM) with scanning tunneling microscopy (STM) in a UHV station at an undulator beamline at Elettra . A zone-plate has been chosen for the micro-focusing because of the fact that it will focus quite well over a relatively large photon energy range [4,5]. Goal for the experimental station is to have a photon spot diameter at the sample of 50 nm . Tuning from 200 eV to

about 1000 eV photon energy is requested with a resolving power E/CIE of 3000 at a photon energy around 300 eV .

At higher photon energies the resolving power should remain as high as possible . The matching of monochroma-

tor and zone-plate should be made in such a way that the indicated numbers will be achieved simultaneously with the losses in photon flux being minimised to the "theoretically" unavoidable .

The fact that a soft X-ray microscope objective in a UHV experimental chamber is a difficult to align object implies certain boundary conditions for the monochromator configuration. In order to keep the objective stationary

in a photon energy scan also the monochromator exit slit, which is the source for the objective, needs to be kept fixed. In addition changes of the beam direction in this slit

need to be kept at a minimum, this especially when the angular divergence of the beam in the slit matches almost perfectly the angular acceptance of the objective.

Here we opted for an entrance slitted monochromator in order to have the possibility to adjust better the resolu-

0168-9002/94/$07 .00 © 1994 - Elsevier Science B.V . All rights reserved SSDI0168-9002(94)00588-X

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W. Jark, P . Melpignano/Nucl. Instr. and Meth . in Phys. Res. A 349 (1994) 263-268

tion . In principle the source size at Elettra undulators would permit to achieve the indicated resolving power even without this slit . The matching of source and monochromator can easily be discussed by comparing the photon source emittance (which is the product of photon source size and divergence) with the monochromator acceptance [6]. The first number is conserved in perfectly focusing optical configurations. Consequently one can easily calculate the required magnifications along the beamline once the requirements for beam size or divergence at important positions have been defined. The ratio zone-plate acceptance/ source emittance will determine the percentage of flux that because of geometrical limitations will have the chance to arrive at the sample . Our zone-plate will be electron-beam written and will have the state-of-the-art values of 50 nm for the outermost zone-width and 0.2 mm diameter. For carbon K-alpha radiation with photon energy 284 eV this leads to a focal length of about 2 mm . At this photon energy the angular acceptance of the zone plate is thus 50 nm X 0.2 mm/2 mm = 5 nm rad, which compares to the smallest electron beam emittance values realised at present in storage rings. The amount of flux that will arrive in our case at the sample depends linearly on the brightness of the source . Consequently the central cones of undulators with their extraordinarily large brightness values are the superior sources for this application . The ESCA-microscopy beam-line will take the synchrotron radiation from an undulator of U2 type at Elettra [7]. This device is 4.5 m long with 81 periods of 56 mm period length (A ) and a maximum value for the deflection parameter K of 3.4 at an electron energy of 2 GeV. The wavelengths provided by the undulator (for different harmonics, indicated by n) can be calculated, varying K up to its maximum value, by the equation (1+K 2/2) where y is the ratio electron energy/mec2 (me is the electron mass, c the velocity of light). Our undulator parameters allow us to scan the photon energy from 100 eV to 1800 eV if one takes also the 3 harmonic and assumes a smallest gap of 20 mm . The characteristics of an undulator of length L as radiation source emitting the wavelength A are described by the following equations: UR=1 .3(A/L)~~~, , ) 1/2 , 0,2 X=

X- l

Q,

a.

+QR

R

i/2

UR

= 0 .15(AL)1/2,

~Y = Y

-

rTy

2 y

2) 1/2

+QR

,

R

o,R and o-R are the angular and spatial width of the radiation in both vertical and horizontal plane, due to

diffraction. Q, , ,, and QX.y represent the electron beam size and divergence in horizontal (x) and vertical (y) direction and x .y and -vx ,y finally represent the photon source size and divergence in horizontal and vertical direction. Operating this device slightly detuned for maximising the photon flux in a fixed aperture will lead at a photon energy of around 300 eV to a diffraction-limited vertical source size of (31y) = 0.14 mm and a central cone opening angle of (3 Y) = 0.125 mrad [8]. This corresponds to a vertical photon beam emittance of 17 .5 nm rad. Horizontally the electron beam is larger than vertically (0 .240 mm instead of 0.054 mm) and consequently in this direction one obtains an emittance of 85 nm rad. In any case the source emittance both in vertical and horizontal directions is bigger than the zone-plate acceptance and thus geometrical losses are unavoidable . In order to keep them at a minimum we consequently need to reduce any reflectivity losses and any further beam distortion to a minimum. Zone-plates are usually operated at around 1-2 m from their sources which will here lead to an angular acceptance of the order of 0.1 mrad . Comparing the zone-plate angular acceptance with the source angular divergences which are in a range between 0.11 and 0.15 mrad in horizontal direction and between 0.08 and 0.13 mrad in vertical direction (in the photon energy range from 200 to 800 eV), we see immediately that we do have already a good matching of our objective and the source in terms of the angular divergences involved . Consequently we can try to keep the magnification ratios in the beamline at a rather low level . This will allow us to minimise the losses due to aberrations even using not aberrations-free optics like spherical or toroidal mirrors. It also offers the possibility to tailor the beam in the monochromator exit slit already suitable for the following zone-plate. This way further reflectivity losses in additionally needed refocusing mirrors can be avoided keeping the overall reflectivity losses at a low level . 3. The variable angle SGM Based on the above described considerations we made the decision for the general monochromator concept. The smallest number of optical components will be realised in spherical grating monochromators [6,9-11] . Only at the Rowland circle condition we will find an ideal operation, which means an aberration free monochromatization . In the existing Rowland circle monochromator designs our requirement for fixed focus positions and beam directions is normally not realised . Only recently Serif et al . [121 presented a concept that respects this point at the expense of a translation of a combination plane mirror-spherical grating along a 0.5 m path in beam direction. With our intention to keep the beam divergence small along the beamline also off-Rowland circle concepts can be considered . Padmore presented [2] a solution that respects all our

W. Jark, P. Melptgnano/Nucl. Instr. and Meth. 2n Phys. Res. A 349 (1994) 263-268 requirements . The basic idea behind his concept is to accept a certain amount of aberrations for the ease of use of the device . This was also the idea behind the concepts of the DRAGON [9] and the NOGARD [11], which do not keep all focal spots at constant position . A convenient way to discuss the aberrations in monochromators is by use of the optical path function in the form presented by Noda et al . [13] for spherical gratings . The most important aberration is the defocus which in the notation of West and Padmore [14] reads F20 - ~ COSY a _ cosR a - coYZ ß - Cos ß with r being the source-grating distance, r' the gratingimage distance and R the radius of curvature of the grating. a and ß are the angles of incidence and diffraction, respectively . While essentially all the other aberrations are negligible [6] the coma aberration will still have to be considered : - (cos 2 a cos a sin a _ F3oI\ r R ) r cos2 ß ( r'

Cos ß R

)

sin ß r'

The optimum resolution will be found when the defocus term vanishes . This can be achieved in several different ways: a) By making equal to zero separately the terms containing a or ß. With fixed values of r, r' and R this is exactly the Rowland circle condition at which also the coma vanishes . b) By making F20 zero in varying only r' . This is the DRAGON scheme [9]. 'ft)1' V11M' 'l'muidal

Nlüiui

c) By making FZO to zero in varying only r. This is the NOGARD scheme [11] . d) By keeping all dimensions constant and varying only the included angle a + ß with the constraint of the grating equation NKÀ = sin ce+ sin ß . Here N is the groove density and K the diffraction order being considered . Neither of the solutions b) to d) will simultaneously reduce the coma to zero. Thus in the beamline optimisation one needs to keep this contribution to the resolution negligible compared to the slit-width contributions. In taking some rules of thumb for undulator sources we can already arrive at some reasonable starting values for our further optimisation . A demagnification of about 5 to 8 for spherical focusing mirrors will produce still negligible aberrations [15] . It allows one to achieve good transmission through a slit with a vertical opening of 30 p,m. With the same dimension for the monochromator exit slit it is possible to obtain a resolving power of 3000 at 300 eV in an instrument of about 3 to 4 m length . A 30 [im spot size in the exit slit requires the reasonable objective demagnification of 1000 in order to achieve our microfocus dimension of 50 nm . For this ratio the above specified zone-plate has to be positioned about 2 m from the exit slit . The further optimisation started with these values . The prefocusing will be done by use of a toroidal mirror with a demagnification for the vertical source size of 5 . This focus will be achieved in sagittal focusing configuration . The horizontal focus will lie in the monochromator exit slit obtained by tangential focusing in the same with a demagnification of 2.45. Compared to the traditional Kirkpatrick-Baez configuration this saves one reflecting sur-

Vnliani.c

Slit

Sphevical

17oaIWl;

MI S I

Maim

Mirim N12

r

IsSCA MICROSCOPY - SGM

S

SII)F VIENV

265

NI 2

Fig. 1 . Optical layout of the variable angle spherical grating monochromator for the ESCA-Microscopy beam-line.

266

W. Jarh P. Melpignano/Nuel. Instr. and Meth . in Phys. Res. A 349 (1994) 263-268 178

Table 1 Horizontal and vertical divergences of the exit beam (in lLrad) for the two gratings at different photon energies .

177

Pli Eu uOa12

v

v

Energy (eV)

176

v b G

175

277 400 500 800 1200

W

a

G

174

Q

w z

172

0

200

400

600

PI-IOTON FNFRGY [ eV

800

Grating 6001/mm

Grating 12001/mm

Vert div. ([rad)

Hor. dtv. (lr,rad)

Vert . dtv. ([rad)

Hor. div. ([.rad)

645.75

388.7

759.3 763.2

331.8 301 .9

1548 611 .9 570.9 6103

333.2 331.8 301 .9 263

~1000

Fig. 2 Dotted line : Theoretical operation curve of an SGM operating with variable included angle for negative diffraction order and for a spherical grating of 600 1/mm, with R = 32490 mm and r/ r' = 2.45. Solid line : Dependence of horizon wave length for a grating with 600 I/mm (diffracted ray tangential to surface) on included angle .

N is the number of illuminated grooves, n is the diffrac-

tion order, x is half of the length of the illuminated area at

the grating and d its groove density. S' is the monochromator exit slit dimension, r' is the exit arm length and )3

is the diffraction angle. The different terms are presented

for the chosen parameters in Fig. 3. It is evident that the coma and diffraction contributions are negligible compared face without performance deterioration because of exces-

to the slit width limited resolution .

scans the wavelength by changing the included angle at the

outside diffraction orders compared to inside orders pro-

direction while scanning one needs to introduce an addi-

optimises always the exit slit opening.

curvature of the grating R as well as the ratio r/r' for

lated from the grating dispersion in the exit slit plane,

optimised. They were chosen in such a way that the

8A

d cos ß

30

n

sive aberrations. Our choice of monochromator concept grating. In order to do this without changing the beam

tional plane mirror in front of the grating. The radius of entrance arm length r and exit arm length r' are still to be

variation of the included angle will be minimum in the

photon energy scanning range 200 eV to 1200 eV . Using a

grating with 600 grooves/mm and a radius of curvature of 32 .49 m the variation of the included angle remains below

0.5 ° at a deflection angle around 174°, as shown in Fig. 2.

In the following (see Fig. 4) it will be shown that

vide better resolution in the requested turning range if one The slit width limited resolution can easily be calcu-

which is

The angular acceptance of the exit slit is t1 (~ = S'/r'. The exit slit setting S' can be matched to the entrance slit

For the operation outside diffraction orders have been chosen and the instrument requires an entrance arm length

of 2.57 m and an exit arm length of 1 .05 m, respectively . This final layout of the monochromator is shown in Fig. 1.

An additional grating with 1200 grooves/mm works with the same scanning conditions with the only difference that

at corresponding situations twice the photon energy will be available. The

present

optical configuration

provides

in

the

monochromator exit slit the small beam divergences which are tabulated in Table 1 . The instrumental resolution is the convolution of the different terms, diffraction limit, coma and slit width limited resolution : ADIFF

ô F â PHOTON ENERGY [ eV

ACOMA - T3o x 0AEXIT -

â

2

dS cos' ß nr

Fig. 3. Contributions to the resolving power of the exit slit (AAExrr), the diffraction limit (AADIFF) and the coma aberration (0 A30) calculated for a spherical grating of 6001/mm, R = 32490 mm, diffr. order = - 1, r / r' = 2.45.

267

W. Jark, P. Melpignano/Nucl. Instr and Meth . 1n Phys Res . A 349 (1994) 263-268

considering that a spherical grating ideally operates with a magnification cos a r' M(A) cos ß r ' given entrance slit dimension S one thus obtains For a r' cos a S' =S r cos /3 ' assuming conservation of emittance in the monochromator. Varying the exit slit width according to this scheme one obtains the slit width limited resolving powers in Fig. 4 for the operation of the instrument with the chosen outside (negative) diffraction orders and with the equivalent inside (positive) diffraction orders. In particular the ratio of the slit width limited resolution for two equivalent cases is cos ß r'

'à AEXIT+1

cos a r

0 ÀEXIT-1

Then, as far as the grating efficiency is concerned, the reciprocity theorem predicts the same efficiency if one exchanges incidence and diffraction angles keeping otherwise the included angle constant [16] . For the resolution instead we are then going from inside orders to outside orders which leads to significantly different diffraction angles and thus a different behaviour of the resolution . The theoretical results for the two equivalent configurations are presented in Fig. 4. The crossover point of the two curves is at the Rowland condition (which means cos /3/cos a = r'/r, then O AEX1T+ 1 = " A EXIT- 1)' In taking this point as a reference point the decision for the choice of the diffraction order can be based on the variation of the resolving power. In total it becomes obvious from Fig. 4 that in using outside orders the variation of the resolving power is reduced. The Rowland condition on the other hand does not necessarily have to be included into our tuning range. In this case the decision for the diffraction order can be

.0025

11 IIuo

U 0015

1) 110 10

II UI1U5

0 0000

I -

I

I . ~ - I--I,,,,I, .,

250

500 750 PHOTON ENERGY [ eV J

1000

1- 1 1250

Fig. 4. Resolution limit for the exit slit set at the monochromatic image dimension for negative and positive diffraction order calculated for a spherical grating of 600 1/mm, R = 32490 mm .

( *1d1111g

rffl(

,

11 11(

c

mdi)

1o

Eff

w wCa

Fff , c '2

U

W a

-

25

5

75

10

125

WAVELENGTH [nm]

Fig. 5. Grating efficiency map for a grating with 1200 1/mm, 1.5° blaze angle [18]. The solid lines indicate the curve for maximum efficiency and for half these numbers. Compared are the design explained in the text (solid line, curve c) using a grating of 1200 1/mm, R = 32000 mm and C = 5 with a Grasshopper [19] monochromator with fixed angle of grazing incidence of 3 ° (curve a) and with an SGM with 8° deflection angle (curve b), (dashed lines) .

made based on the behaviour of the resolution in the branch of interest . 4. Conclusions Up to now we have discussed a design that minimises the variation of the included angle. As far as the behaviour for the efficiency and higher order suppression is concerned such a scheme does not present any advantage compared to a constant-included-angle solution . Also the additional premirror will only suppress higher harmonics in a small range on the expense of an overall reduced transmission . The grating efficiency maps being introduced by Petersen [17] and extended by Jark [18] present for fixed grating parameters the behaviour of the grating efficiency as a function of angle of grazing incidence. An example is in Fig. 5. A closer look will show that the most promising curves for efficient grating operation (good efficiency and sufficient second harmonic suppression) are linear relationships between the angle and the wavelength . SGMs and TGMs usually have straight lines which intercept the angle axis at half the deflection angle. The wavelength axis is intercepted at the horizon wavelength . The Grasshopper [19] instead has a constant angle of incidence. The SGM performance will already improve significantly if one succeeds to arrive at almost constant angle of incidence . A relationship : the angle of incidence increases with increasing wavelength is not possible. Our second optimisation had thus in mind to improve the grating working curve into the above mentioned direc-

268

W. Jark P. Melpignano/Nuel. Instr. andMeth. in Phys. Res. A 349 (1994) 263-268

tion, i.e . goal was to make the diffraction angle increase more significantly with increasing wavelength .

Setting the parameters C = r'/r = 5000 mm/ 1000 mm,

R = 32 000 mm and N= 1200 1/mm it is possible to

[2]

obtain a variation of the included angle of 3.5 ° between E = 125 eV and E = 1200 eV . This operation is presented in

Fig. 5c as the solid curve. Because we are using

negative orders the diffraction angle is drawn, which,

according to the reciprocity theorem [16], is equivalent to

[3]

the angle of incidence for operation with positive diffrac-

[4]

prepared .

[5]

tion orders for which the grating efficiency map has been In this case the Rowland condition was found at a

photon energy of 125 eV . Consequently negative diffrac-

tion orders will have smaller variation of the resolving power in the working range.

[6] [7]

The interesting properties of this monochromator are:

extended tuning range with good grating efficiency by use of only one grating (from 125 eV to 1200 eV and more),

rather promising and slightly improved higher harmonics suppression.

To give some example: with an entrance slit dimension

of 20 wm an ideal resolving power of the order of 13 000 can be achieved for E = 200 eV and of 4000 for E = 1000

eV . These values are obtained for a grating with a slope error of 0.2".

[8] [9] [10] [11] [12] [13]

For the discussion of the resolving power only the

[14]

with the program package SHADOW for the parameters of the Elettra undulator U2 indeed confirm these results .

[15]

defocus and coma aberrations introduced by the grating have been considered . More exact ray-tracing calculations

References [1] The reader more interested in the general topic of monochromator design is referred to the Proceedings of Synchrotron Radiation Instrumentation Conferences, which appeared in Nuel . Instr. and Meth. 152 (1978) 177 (1980); 195 (1982) ;

208 (1983) ; 222 (1984); A 246 (1986); A 266 (1988) ; A 291 (1990); A 319 (1992) ; and in Rev. Sci. Instr. 60 (1989) ; 63 (1992) . H.A Padmore, Rev. Sci. Instr 60 (1989) 1608, H.A . Padmore, Proc . Int. Workshop on High Performance Monochromators and Optics for Synchrotron Radiation in the Soft X-ray Region, March 1991, BESSY. P. Nataletti, S. Contarini, C. Gariazzo, N. Minnaja, M. Musicanti, W. Jark, M. Kiskinova, P. Melpignano, D. Morris and R. Rosei, Surf . Interf. Anal. 18 (1992) 655. A G. Michette, Optical Systems for Soft X-rays (Plenum, New York, 1986). G. Schmahl and D. Rudolph, X-ray Microscopy (Springer, Berlin, 1983). H. Hogrefe, M.R . Howells and E. Hoyer, Proc . SPIE 733 (1986) 274. R. Rosei and R.P . Walker, Rev. Sci. Instr. 60 (1989) 1809 ; B. Diviacco, R. Bracco, C. Poloni, R.P . Walker and D. Zangrando, Rev. Sci. Instr. 63 (1992) 1368 . R. Coisson, Opt. Eng. 27 (1988) 250. C.T Chen, Nucl Instr. and Meth. A 256 (1987) 595; C.T . Chen, Rev. Sci. Instr. 60 (1989) 1616 . H.A. Padmore, Proc . SPIE 733 (1986) 253. F Zanini, S. Di Fonzo, P. Melpignano and W. Jark, Rev, Sci. Instr. 63 (1992) 1359 F. Sent, F. Eggenstein and W. Peatman, Rev. Sci. Instr. 63 (1992) 1326 . H. Noda, T. Namioka and M. Seya, J. Opt. Soc. Am . 64 (1974) 1031 . J.B. West and H.A. Padmore, in : Handbook of Synchrotron Radiation ed . E.E. Koch, vol . 2 (North-Holland, Amsterdam, 1987) Chap . 2. P. Melpignano and W. Jark, Soft X-ray monochromators at ELETTRA undulators: beam transmission through the entrance slit dependent on the prefocusing optics properties, SINCROTRONE Trieste, Internal Report ST/S-R-90/15

(1990). [16] D. Maystre and R.C. McPhedran, Opt . Commun . 12 (1974) 164. [17] H. Petersen, Opt. Commun . 40 (1980) 402 [18] W. Jark, Nucl . Instr. and Meth. A 266 (1988) 414. [19] F.C. Brown, R.Z . Bachrach and N. Lien, Nucl . Instr and Meth . 152 (1978) 73.