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THE EFFECTS OF MANUFACTURING
INACCURACIES ON THE IMAGING PROPERTIES OF ZONE PLATES
M. Simpson, M. Browne, R. Burge, P. Charalambous, P. Duke, A. Michette
To cite this version:
M. Simpson, M. Browne, R. Burge, P. Charalambous, P. Duke, et al.. THE EFFECTS OF MAN-
UFACTURING INACCURACIES ON THE IMAGING PROPERTIES OF ZONE PLATES. Journal
de Physique Colloques, 1984, 45 (C2), pp.C2-93-C2-96. �10.1051/jphyscol:1984223�. �jpa-00223887�
THE EFFECTS OF MANUFACTURING INACCURACIES ON THE IMAGING PROPERTIES OF ZONE PLATES
M.J. Simpson, M.T. Browne, R.E. Burge, P. Charalambous, P.J. Duke* and A.G. Michette
Physics Department, Queen Elizabeth College, University of London, Campden Hill Road, London W8 7AH, U.K.
Daresbury Laboratory, Daresbury, Warrington, WA4 4AD, U.K.
Résumé - Tous les procédés utilisés pour réaliser des lentilles à zone de Fresnel pour rayons X mous présentent des imperfections de fabrication qui affectent les images. On discute les erreurs possibles en microlithographie par microscopie électronique à balayage en transmission et on en conclut que ce procédé peut être utilisé en donnant une précision suffisante.
Abstract - Any process for making soft X-ray zone plates will have associated manu- facturing errors which will affect the imaging properties. The errors possible in a lithographic manufacturing technique using a scanning transmission electron micro- scope are discussed, and it is concluded that sufficiently accurate zone plates may readily be made.
Introduction
Another contribution to these proceedings describes the manufacture of Fresnel zone plates, for use in soft X-ray microscopy, by a high resolution process using a STEM [1]. Manufacturing inaccuracies in this, and other, techniques lead to a reduction in the efficiency (which, in the first diffraction order of a perfect Fresnel zone plate, is 1/7T2) and affect other imaging properties. Studies have been made of i) partial transmission through the absorbing zones and partial absorption in the transmitting zones; ii) displacements of whole or part zones; and iii) displace- ments of whole or part sectors. The calculations were carried out for 100 zones and an absorbing centre zone, although the results will be presented in a form, so far as possible, independent of the zone plate parameters. All the calculations were based on the Fresnel-Kirchoff diffraction integral for the image amplitude at an on- axis point. More detail is given in [2], where the effects of elliptical zones and stabilizing spokes are also discussed.
Since the effects considered do not move the major peaks of the diffraction pattern off-axis, how closely the imaging properties of an aberrated zone plate approach the ideal may be estimated using the Strehl ratio [3], i.e. the ratio of the peak inten- sity of the aberrated spread function.(at a focus) to that of the equivalent perfect function. The tolerance limit is generally accepted to be when this has a value of 0.8 (the Strehl limit). When the zone boundaries are shifted or distorted, the foc- al lengths of the resulting zone plate are altered; in the results presented, re- focussing has been carried out, where necessary, before calculating the Strehl ratio.
Incomplete Absorption or Transmission
If ¥* is the fractional amplitude absorption in the absorbing zones (Y* = 1 for complete absorption) then the diffraction pattern is not distorted but the intensity in a focus is reduced by a factor X ^ . Hence the focussed intensity is reduced while the background (unfocussed) radiation level is increased, leading to reduction in contrast. Alternatively, the focussed intensity could be enhanced if the radiation transmitted by the absorbing zones undergoes a phase change. Due to the lack of good measurements of soft X-ray optical constants, this is difficult to quantify.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984223
C2-94 JOURNAL DE PHYSIQUE
Partial absorption in the transmitting zones is equivalent to inserting an attenu- ator in the beam so that less of the available radiation is focussed. However the image quality is not affected.
The first (uncoated) STEM generated zone plates have- 0 . 1 5 ~ m of carbon in the ab- sorbing zones (giving Y, 2 S 0.75 for a wavelength of r 4 nm) and
-
2 0 nm of carbon in the transmitting zones (leading to an attenuation of .r 15%).Displaced Zones
The displacements of zones may be characterised in terms of zone boundary shifts.
For the case where the complete boundaries are displaced, each boundary may be left unshifted (0)
,
moved inwards (-1, or moved outwards (+).
Expressing the boundaryshifts in pairs, such as (+,-) which means that the odd-numbered boundaries are mov- ed outwards and the even ones inwards, the situations indicated in figure 1 can be identified. These fall into 4 groups, (i) all zones left unchanged, (ii) every other boundary moved outwards or inwards resulting in the absorbing zones being too wide and the transmitting zones too narrow or vice-versa, with the zone centres displaced,
(iii) successive boundaries moved in opposite directions, resulting in zones too wide or too narrow with undisplaced zone centres, and (iv) all zones moved outwards or in- wards. The Strehl ratio for each of these groups is plotted against C , the zone boundary displacement as a fraction of the outermost zone width in,figure 2 . The re- quirement for the on-axis intensity not to fall below the Strehl limit gives
E <
0 . 2 1Fig. 1
-
Dashed lines, correct positions. Fig.2-
Strehl ratios for displaced zones Full lines, actual positions of zoneboundaries.
for the worst case, (iii). Combinations of shifts involving more than two zones,e.g.
(+,+,-), (+,o,-,+), give less stringent limits on 6 . Zone plates made on the STEM will tend to have more random zone displacements - the envelope obtained from 100 separate computations in each of which the zone boundaries were displaced in random directions with random values of 6 is also shown in figure 2. This gives the re- quirement
f 6
0 . 3 . The first zone plates made on the STEM have boundary positions correct to-
5 nm with an outermost zone width of -75 nm, i.e. £-
0.07 giving a Strehl ratio of 0 . 9 9 for first order imaging. For higher order foci, which can in prin- ciple give better resolutions, the Strehl limit is reached for smaller values ofE ,
i.e. the manufacturing tolerances are stricter. This is shown for the third order focus in figure 2.
In the STEM manufacturing method, the zone plate patterns are drawn in 2 4 equal ang- ular sectors, misalignments of which could result in discontinuities (steps) in the zone boundaries. Possible configurations of steps are shown in figure 3 , and the re- sulting Strehl ratios in finure 4
-
these calculations were carried out assuming thatI I
F i g . 3
-
Stepped zone b o u n d a r i e s .Max. radlus error/aurer zone width
F i g . 4
-
S t r e h l r a t i o s f o r s t e p p e d zone b o u n d a r i e s .t h e c o n f i g u r a t i o n s shown a r e r e p e a t e d e v e r y two s e c t o r s . F o r t h e w o r s t c a s e ,
6 < 0.21; groups of more t h a n two s e c t o r s g i v e l e s s s t r i n g e n t l i m i t s . For random s t e p p o s i t i o n s and s i z e s ( s e e f i g u r e 3
-
t h i s c o u l d happen i f , f o r example, t h e STEM s t a g e d r i f t e d between r e g i s t r a t i o n s ) , t h e envelope shown i n f i g u r e 4 i s o b t a i n e d , g i v i n g E4
0.35. For a s t e p s i z e o f - 5 nm and a-75 nm o u t e r m o s t zone w i d t h , t h e S t r e h l r a t i o i s 0.99.S i n c e each s e c t o r of t h e zone p l a t e on t h e STEM i s drawn a s t h r e e f i e l d s [ I ] , a p o s s i b l e ( p e r h a p s t h e most l i k e l y ) combination of d i s p l a c e d zones i s t h a t a whole
( o r p a r t ) f i e l d i s drawn i n t h e i n c o r r e c t p l a c e . T h i s c o u l d happen i f , f o r example, a r e g i s t r a t i o n mark i s p a r t l y obscured by a n i m p e r f e c t i o n i n t h e f i l m . I f one f i e l d (of t h e whole zone p l a t e ) i s d i s p l a c e d , t h e r e s u l t i n g S t r e h l r a t i o , a s a f u n c t i o n of
f , i s shown i n f i g u r e 5. Displacement of an o u t e r f i e l d ( i . e . o f a n o u t e r p a r t of t h e zone p l a t e ) h a s a l a r g e r e f f e c t t h a n d i s p l a c e m e n t s of a m i d d l e o r i n n e r f i e l d , due t o t h e l a r g e r a r e a . F i g u r e 5 a l s o shows t h e e f f e c t of d i s p l a c i n g more t h a n one
rhree \.
outer . f i e l d s \ ,
f l e l d poslrion e r r o r /outer zone width
F j g . 5
-
S t r e h l r a t i o s f o r d i s p l a c e d f i e l d s .o u t e r f i e l d . F o r f i e l d d i s p l a c e m e n t s o f - 5 nm, t h e S t r e h l r a t i o remains w e l l above t h e S t r e h l l i m i t . The f i e l d p o s i t i o n s c a n be monitored v i s u a l l y t h r o u g h o u t t h e manu- f a c t u r i n g p r o c e s s , and s o any g r o s s e r r o r s c a n b e d e t e c t e d and, i f n e c e s s a r y , t h e p r o c e s s r e s t a r t e d .
C2-96 JOURNAL DE PHYSIQUE
Conclusions
Of the effects considered, the major degradation in focussed intensity arises from incomplete absorption and transmission in the absorbing and transmitting zones respectively. The other effects cause very small decreases in the focussed inten-
sity. Although they have been considered separately above, the various effects will all contribute to varying extents, but the accuracy of the manufacturing process is such that the Strehl ratio should always be well above the limit of 0.8 for STEM generated zone plates.
Acknowledgements
We are grateful to the Science and Engineering Research Council (SERC) for financial support. MJS is supported by an SERC grant.
References
[I] BROWNE M.T., CHARALAMBOUS A., BURGE R.E., DUKE P.J., MICHETTE A . G . and SIMPSON M.J., these proceedings p.
[ 2 ] SIMPSON M.J. and MICHETTE A.G., to be published in Optica Acta (1983).
[3] WELFORD W.T., in "Aberrations of the Symmetrical Optical System", p.206, Academic Press (1974).
