X-RAY GRAZING INCIDENCE OPTICS FOR THE ELECTRON MICROPROBE

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X-RAY GRAZING INCIDENCE OPTICS FOR THE ELECTRON MICROPROBE

A. Kozlenkov, A. Shulgin

To cite this version:

A. Kozlenkov, A. Shulgin. X-RAY GRAZING INCIDENCE OPTICS FOR THE ELEC- TRON MICROPROBE. Journal de Physique Colloques, 1984, 45 (C2), pp.C2-157-C2-160.

�10.1051/jphyscol:1984235�. �jpa-00223948�

X-RAY GRAZING INCIDENCE OPTICS FOR THE ELECTRON MICROPROBE A . I . Kozlenkov and A . I . Shulgin

Baikov Institute of Metallurgy, Academy of Sciences, U.S.S.R.

Résumé.

On évalue le rendement d'un spectromètre à réseaux avec une source ponctuelle et une configuration de réseaux réflecteurs croisés pour différentes longueurs d'onde et différents types de matériaux de revêtement.

A b s t r a c t .

The e f f i c i e n c y of t h e g r a t i n g s p e c t r o m e t e r w i t h a p o i n t source and t h e c r o s s e d m i r r o r - g r a t i n g c o n f i g u r a t i o n i s e v a l u a t e d f o r d i f f e r e n t wavelengths and c o a t i n g m a t e r i a l s .

I t has been shown i n t h e p r e v i o u s p a p e r s / I - 5 / t h a t t h e g r a t i n g s p e c - t r o m e t e r s can be e f f e c t i v e l y used i n l i g h t element m i c r o a n a l y s i s and u l t r a - s o f t x - r a y v a l e n c e band s t u d i e s / 5 / . G r a t i n g s p e c t r o m e t e r (GS) o f f e r s p o t e n t i a l l y s u p e r i o r r e f l e c t i o n e f f i c i e n c y , peak t o background r a t i o , r e s o l u t i o n and i n t e n s i t y compared w i t h a c o n v e n t i o n a l p s e u d o - c r y s t a l s p e c t r o m e t e r . The e f f i c i e n c y of GS can be enhanced by u s i n g t h e optimum b l a z e d g r a t i n g , t h e concave r e f l e c t o r s d i s c r i m i n a t i n g a g a i n s t s h o r t wavelength r a d i a t i o n and windowless e l e c t r o n m u l t i p l i e r s / 5 , 6 / . The main d i s a d v a n t a g e of GS with a p o i n t s o u r c e i s , however, i t s low x - r a y c o l l e c t i o n e f f i c i e n c y due t o a small s o l i d angle s u b t e n - ded by t h e g r a t i n g a t t h e microprobe source and s e v e r e a s t i g m a t i s m i n h e r e n t i n t h e g r a z i n g i n c i d e n c e mounting. Prom t h i s p o i n t of view t h e s o - c a l l e d " c r o s s e d m i r r o r - g r a t i n g c o n f i g u r a t i o n " / 7 / w i l l be of p r a c t i c a l importance f o r l i g h t element m i c r o a n a l y s i s and u l t r a - s o f t x - r a y g r a t i n g s p e c t r o s c o p y .

I n t h e p r e s e n t p a p e r t h e e f f i c i e n c y of GS w i t h a p o i n t source and c r o s s e d o p t i c s i s e v a l u a t e d i n more d e t a i l . The optimum geometry of t h e o p t i c a l system comprising t h e concave g r a t i n g and t h e concave r e f - l e c t o r ( s t i g m a t o r ) i s found f o r d i f f e r e n t wavelengths and c o a t i n g m a t e r i a l s . The s t i g m a t o r whose r e f l e c t i n g s u r f a c e has a form of a p a -

r a b o l i c c y l i n d e r i s p l a c e d i n t h e p a t h of t h e x - r a y p r i m a r y beam between t h e source and t h e c y l i n d r i c a l concave g r a t i n g ( P i g . I ) so t h a t i t s a x i s i s p a r a l l e l t o t h e Rowland p l a n e and p e r p e n d i c u l a r t o t h e g r a t i n g r u l i n g s whereas a p o i n t source l i e s on t h e f o c a l l i n e of t h e p a r a b o l i c c y l i n d e r . I t can be shown / 7 / t h a t t h e r a y s r e f l e c t e d from t h e s t i g m a t o r s u r f a c e a r e p e r p e n d i c u l a r t o t h e r u l i n g s and may be c o n s i d e r e d a s being emerged from a l i n e a r imaginary source l y i n g on t h e d i r e c t r i x of t h e c e n t r a l p a r a b o l a . The x - r a y r a d i a n t f l u x i n c i d e n t on t h e s t i g m a t o r s u r f a c e i s p r o p o r t i o n a l t o t h e s o l i d a n g l e subtended by t h e s t i g m a t o r ,

( I ) where W is the optimum width of the grating, R is the radius of cur- vature of the grating, u' = x/p, u"= x7p, p is the parameter of the parabolic curve (whose equation is ty

= x?+ 2p.x ) with the x axis directed from the source to the grating centre). The x-ray flux ref- lected from the stigmator surface toward the grating is given by:

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984235

C2-158 JOURNAL DE PHYSIQUE

I 1

u , - < - Y

I = wp J, ~ ; j u ) ( u + ~ ) ( z u + I ) au ,

M U

( 2 )

where KJU) is t h e r e f l e c t a n c e of t h e stigmator c o a t i n g m a t e r i a l M a t t h e wavelength A and u i s r e l a t e d t o t h e grazing incidence angle &

a s follows :

-I/2

t g 6' = (2u+I) , u = x/p.

Fig.1. The crossed mirror-grating configuration.

The microprobe source is i n t h e point 0; &I -

stigmator, G - g r a t i n g , S - ^{e x i t} s l i t .

The i n t e n s i t y of t h e x-ray be= i n c i d e n t on t h e g r a t i n g can be o p t i - mised by s u i t a b l e choice of

XI' , ^{p and M} f o r a p a r t i c u l a r wave- l e n g t h range. For f i x e d x' and s" t h e r e e x i s t s t h e optimum value of \I

a t which I reaches a maximum. On t h e o t h e r hand, f o r a given /I t h e r e f l e c t e d beam i n t e n s i t y i n c r e a s e s with i n c r e a s i n g x" and decreasing x' . I n p r a c t i c e t h e minimum value of x J ( o r u') i s r e s t r i c t e d by t h e s i z e of t h e specimen h o l d e r while x u must not exceed t h e minimum source-grating distance, ^t = R s i n y , where y i s t h e grazing angle of incidence. The g r a t i n g spectrometers with d i f f e r e n t W, R and y a r e commonly used i n t h e u l t r a - s o f t x-ray region t o cover t h e t o t a l wavelength range 1-30 nm, f o r example, t h e G S with R = 6 m and Y) = 2O f o r s h o r t e r wavelengths and t h e GS with R = 2 m and Y = 6 O f o r l o n g wavelengths. The minimum value of ^'2 i s equal t o -- 210 mm i n both cases. Hynce, t h e maximum value of ^x" w i l l be no more t h a n 180-200 mm.

Taking x = 20 mm and x"= ₂₀₀ mm, we o b t a i n t h e dependence I on

represented i n Pig. 2 a, b f o r d i f f e r e n t wavelengths and two coating m a t e r i a l s , aluminium and polystyrene. It is seen t h a t t h e s t i g m a t o r s

cut o f f e f f e c t i v e l y r a d i a t i o n with wavelength s h o r t e r t h a n I nm (Al) o r 5 nm (polystyrene). W e choose, t h e r e f o r e , t h e s t i g m a t o r s with t h e following parameters: I ) aluminium coated m i r r o r with p = 0.25 ^mm, h' = 3.17 mm, h " = 10 mm, a h = 6.83 mm and 2) polystyrene coated m i r r o r with p = I mm, d = 6.4 rnm, h"= 20 mm, a h = 13.6 mm ( ~ l g . 1 1 , using them i n t h e s h o r t wavelength region (1-5 nm) and f o r l o n g e r wavelengths ( 5 - 3 0 nm) r e s p e c t i v e l y . A l l o t h e r coatings ( T i , C r , N i , LiF, Au) a r e i n f e r i o r t o t h e above m a t e r i a l s due t o t h e lower x-ray r e f l e c t a n c e o r i n a b i l i t y t o d i s c r i m i n a t e e f f e c t i v e l y unwanted radia- t ion,

I n order t o i n c r e a s e (by

f a c t o r of 2) x-ray c o l l e c t i o n from t h e

microprobe source two input s t i g m a t o r s faced t o each o t h e r (Fig.3)

vent i o n a l grazing incidence g r a t i n g monochromator. For t h e l a t t e r x-ray i n t e n s i t y i s proportional t o

nhere i s t h e e x i t s l i t length, Z = R s i n and z'= R s i n yJ a r e t h e d i s t a n c e s from t h e c e n t r e of t h e g r a t i n g t o t h e source and t h e e x i t s l i t , r e s p e c t i v e l y , and Y a r e t h e grazing angles of incidence and d i f f r a c t i o n .

Fig.2. I n t e n s i t y of X-rays r e f l e c t e d from t h e input s t i a t o r a s a f u n c t i o n of p (parameter of t h e p a r a b o l i c c g l i n d e r y f o r d i f f e - rent wavelengths and two c o a t i n g m a t e r i a l s - ^{A 1} and polystyrene.

Fig. 3. The o p t i c a l system of t h e micropro be g r a t i n g spectrometer with two input stigmators.

The s l i t of 10-15 mm long should be used i n t h e G S t o avoid a l o s s of

i n t e n s i t y and r e s o l u t i o n due t o t h e a s t i g m a t i c curvature of t h e spec-

t r a l l i n e o r a f i n i t e s i z e of t h e d e t e c t o r window. For t h i s reason we

compare i n Fig.4 t h e e f f i c i e n c y of t h e conventional GS comprising only

t h e c y l i n d r i c a l o r s p h e r i c a l g r a t i n g and t h e s t r a i g h t e x i t slit of

I5 nun l o n g with t h a t of t h e ^{G S} equipped with two input stigmators

C2-160 JOURNAL DE PHYSIQUE

mentioned above. A s i g n i f i c a n t g a i n i n t h e d i f f r a c t e d beam i n t e n s i t y i s expected i n o u r arrangement. It w i l l be accompanied by a marked i n c r e a - s e i n P/B r a t i o and r e s o l u t i o n due t o t h e e l i m i n a t i o n of t h e a s t i g m a t i c c u r v a t u r e and o t h e r image i m p e r f e c t i o n s and p o s s i b i l i t y of u s i n g

narrower slits.

6 -

4 -

R = ^6m R = 2 m

\C'= ^6"

2 - p ⁼ 0.25 p ⁼ r,o

- CuLe OK, NK, c&

A, ^nm BK, BeK- LiK,

I I I

-

^{, -.Al, nm}

652 236 346 44 7 676 If6 2g8-

Fig.4. The i n t e n s i t y r a t i o of t h e X-ray beams a r r i v i n g a t t h e g r a t i n g s u r f a c e i n t h e o p t i c a l system with two i n p u t s t i g m a t o r s and i n t h e conventional u l t r a - s o f t g r a t i n g spectrometer with t h e microprobe source.

I n t h e g r a t i n g spectrometer o f a Romand-Vodar type /9/ two a d d i t i o n a l s t i g m a t o r s can be mounted on t h e p l a t e c a r r y i n g t h e g r a t i n g and t h e e x i t s l i t i n t h e p a t h of t h e d i f f r a c t e d beam. I n t h i s case t h e c e n t r e of t h e e x i t s l i t must be c o i n c i d e n t with t h e focus of t h e p a r a b o l i c c y l i n d e r , and t h e s t i j g n a t i c image of a p o i n t source w i l l be obtained f o r a l l wavelengths, of course a t t h e expense of an a d d i t i o n a l l o s s (20-40 Q ) i n x-ray i n t e n s i t y a t t h e s t i g m a t o r s u r f a c e . This o p t i c a l

system may be of p r a c t i c a l i n t e r e s t f o r designing high r e s o l u t i o n u l t r a - s o f t x-ray monochromators/I0 /.

Ref e r e n c e s

I . N I 0 , ON J.B. and HASLER M.F., Adv.X-Ray Analysis 9 (1966) 420.

2. Dzk'V., IIAKAJUU Y., OHMOR1 Y., SHIRAIWA T. and PUJINO N., Proc.

6 t h I n t e r n . Conf, X-Ray 0 t i c s and Microanalysis, ed. Shinoda (Tokyo : Tokyo Univ. Press?, 1972, p.333.

3. FRANKS A,, STEDUB I. and BRAYBROOK R,F., J.Phys .E :Scient .In&r. 6

(1973) 233.

4. KOZUNKOV A . I . and BELOV YU.I., Mikrochhnica Acta /3-4 (1982) 159.

5. K O Z L ~ O V A.I., Optics and Spectroscopy (USSR) 48 (1980) 390.

6. K o Z E E ~ V A.I., BEMV YU.I., BOGDANOV V.G. and T J ~ I K o V A.M., Zavod- skaya Laboratoria (USSR) 46 (1980) 313.

7. KoZLEMEOV A.I., Optics a n m p e c t r o s c o p y ( ~ 3 ~ ~ 1 4 6 (1979) 579*

8. LUKIRSKII A.P., Thesis, Leningrad S t a t e ~ n i v . TUSSR) 1964.

9. R O W J. and VODAR B., Optica Acta 9 (1962) 371.

IO,KOZLEI9HOV A.I., BELoV YU.1. and BoGDXNOVV.G., L e t t e r s t o J.T .P.

(USSR) 2 (1979) 363.