EXTENDED DEPTH PROFILING WITH THE IAP

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EXTENDED DEPTH PROFILING WITH THE IAP

S. Walck, T. Buyuklimanli, J. Hren

To cite this version:

S. Walck, T. Buyuklimanli, J. Hren. EXTENDED DEPTH PROFILING WITH THE IAP. Journal

de Physique Colloques, 1986, 47 (C2), pp.C2-451-C2-458. �10.1051/jphyscol:1986269�. �jpa-00225703�

EXTENDED DEPTH PROFILING WITH THE IAP

S.D. WALCK, T. BWUKLIMANLI and J.J. HREN

Department of Materials Science and Engineering. U n i v e r s i t y Of F l o r i d a , G a i n e s v i l l e , F1 32611, U.S.A.

A b s t r a c t - Depth p r o f i l i n g w i t h t h e FIM/IAP can be e x t r e m e l y accurate i f

-.p

done i n c o n j u n c t i o n w i t h r i n g c o l l a p s e counting. However, under UHV c o n d i t i o n s depth s c a l e s are n o t e a s i l y assigned, e s p e c i a l l y i f depths o f 0.1 um o r more are required, such as those needed f o r range determinations i n

i o n i m p l a n t a t i o n studies. We describe a method u s i n g t h e IAP s i g n a l from t h e m a t r i x , and t i p parameters measured by FIM and transmission e l e c t r o n mi c r o s c o p y (TEM).

Ni specimens were dc f i e l d evaporated t o 6 kV. Both FIM and TEM images were recorded b e f o r e and a f t e r t h e I A P d a t a was c o l l e c t e d . The image was

observed d u r i n g a n a l y s i s and t h e p u l s e number recorded when a r i n g c o l l apsed. Each spectrum was s i g n a l -averaged t o minimize storage. The p u l s e number i s c o r r e l a t e d w i t h t h e s p e c t r a l data. The c u m u l a t i v e Ni s i g n a l versus t h e r i n g number was then generated.

INTRODUCTION

A1 though i t i s n o t w i d e l y recognized o u t s i d e t h e FIM community, t h e atom probe and imaging atom probe a r e superb f o r compositional depth p r o f i l i n g . With an imaging gas present, depth r e s o l u t i o n s o f one atomic p l a n e a r e expected. O f course, t h e l a t e r a l r e s o l u t i o n i s a1 so excel l e n t , b u t t h e r e remain t h e r e s t r i c t i o n s o f specimen geometry (j.e., p o i n t e d e m i t t e r s , o r i e n t a t i o n f i x e d , t o t a l v01 ume smal l, etc.).

U n f o r t u n a t e l y , these c a p a b i l i t i e s a r e n o t so e a s i l y a t t a i n e d i f an imaging gas cannot be used, f o r example, when t h e species monitored o r t h e m a t r i x has a low e v a p o r a t i o n f i e 1 d.

F i e l d e v a p o r a t i o n r a t e s v a r y s t r o n g l y w i t h as t h e dc v o l t a g e and/or the p u l s e h e i g h t change, f u r t h e r exacerbating attempts t o m o n i t o r t h e c h a r a c t e r i s t i c a l l y s t r o n g s i g n a l s as r i n g s c o l lapse. When l a r g e depths a r e needed t o a t t a i n u s e f u l p r o f i l e s (100 nm), t h e requirement f o r a l t e r n a t i v e means t o m o n i t o r depths i s even more obvious. The a l t e r n a t i v e method described here r e l i e s upon t h e geometry o f f i e l d e m i t t e r s observed b y TEM, t h e b a s i c p r i n c i p l e s o f FIM, and a s t r a i g h t f o r w a r d c a l i b r a t i o n procedure.

SPECIMEN GEOMETRY

The t i p geometry assumed i s a c o n i c a l shank w i t h a s p h e r i c a l cap which j o i n s t h e shank t a n g e n t i a l l y . I n o u r IAP o n l y a s m a l l p o r t i o n o f t h e specimen i s imaged because t h e t i p t o screen d i s t a n c e i s approx. 15 cm. The subtended v i e w i n g h a l f - a n g l e i

about 20 degrees. With t h i s model, t h e r a d i u s o f c u r v a t u r e R i s

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986269

JOURNAL DE PHYSIQUE

R = ( h + l o ) s i n

/ ( l - s i n u )

where 1, i s t h e d i s t a n c e f r o m t h e i n i t i a l s u r f a c e t o t h e apex o f t h e cone,

i s t h e shank h a l f - a n g l e and h i s t h e d i s t a n c e probed f r o m t h e i n i t i a l s u r f a c e t o t h e f i n a l surface. F i g u r e 1 i s a montage o f an e v a p o r a t i o n sequence o f a N i specimen

p e r f o r m e d w i t h t h e " f i e 1 d - e f f e c t " (FIMITEM) h01 d e r [l 1. T h i s f i g u r e i l l u s t r a t e s t h e v a l i d i t y o f t h e g e o m e t r i c model and t h e c o n s i d e r a b l e d e p t h t o w h i c h t h e FIM/IAP i s c a p a b l e o f p r o b i n g . The computed r a d i i a t t h e v a r i o u s v o l t a g e s a r e a1 1 v e r y c l o s e t o t h e a c t u a l r a d i i e x c e p t f o r one, t h e r a d i u s drawn a t t h e i n d i c a t e d v o l t a g e o f 3 kV. T h i s r a d i u s was measured f r o m t h e m i c r o g r a p h and drawn a t t h e d i s t a n c e g i v e n b y e q u a t i o n ( 1 ) . When i t was drawn b y t h e computer, i t d i d n o t match t h e

l o c a t i o n i n t h e montage. A f t e r examining t h e montage more c a r e f u l ly, i t was found t h a t one micrograph, t a k e n a t 2.9 kV was m i s s i n g and t h a t t h e o f f s e t between t h e s u r f a c e drawn and t h e one i n t h e montage i s a p p r o x i m a t e l y t h e d i s p l a c e m e n t due t o t h i s e r r o r . T h i s suggests a p r e c i s i o n o f b e t t e r t h a n 1 0 nm.

THE PROBED VOLUME

The e f f i c i e n c y and g a i n o f t h e Chevron p l a t e s used as t h e IAP d e t e c t o r a r e c o n s t a n t o v e r t h e e n e r g y r a n g e employed h e r e [2]. I f a1 l th e atoms w i t h i n t h e d e t e c t e d a r e a s t r i k e t h e d e t e c t o r and t h e d e t e c t o r e f f i c i e n c y i s c o n s t a n t , t h e i n t e g r a t e d s i g n a l s h o u l d b e p r o p o r t i o n a l t o t h e number o f atoms c o n t a i n e d w i t h i n t h e probed volume.

I n t u r n , t h e number o f atoms i s s i m p l y r e l a t e d t o t h e volume probed b y t h e specimen d e n s i t y . T h i s i n t e g r a t e d s i g n a l i s easy t o measure, s i n c e i t i s j u s t t h e

c u m u l a t i v e m a t r i x s i g n a l f r o m t h e s p e c t r a c o l l e c t e d . Furthermore, t h e accumulated s p e c t r a approximate an i n t e g r a t i o n v e r y c l o s e l y because o f t h e smal 1 i n c r e m e n t s i n v o l v e d . The one assumption i s t h a t t h e c o n c e n t r a t i o n o f t h e e l e m e n t used f o r t h e a c c u m u l a t i o n process ( t h e m a t r i x ) i s c o n s t a n t and p r o p o r t i o n a l t o t h e probed volume. T h i s may n o t b e v a l i d , f o r example i n t h e case o f i o n i m p l a n t a t i o n o f m a s s i v e i o n s o r i n t h e presence o f p r e c i p i t a t e s . The p r o b l e m i n l a r g e

c o n c e n t r a t i o n s o f d e p t h p r o f i l i n g u s i n g t h e model j u s t d e s c r i b e d i s reduced t o f i n d i n g t h e f u n c t i o n a l dependence o f t h e volume w i t h d e p t h and g e o m e t r i c a l parameters o f t h e specimen and t h e n t o comparing t h e s e w i t h a c a l i b r a t i o n

e x p e r i m e n t i n w h i c h t h e r i n g s a r e c o u n t e d and t h e c u m u l a t i v e s i g n a l i s f o u n d f r o m t h e s p e c t r a .

VOLUME CALCULATION

The v o l u m e o f i n t e r e s t , F i g u r e 2, i s t h e shaded r e g i o n bounded b y t h e two s p h e r i c a l caps r e p r e s e n t i n g t h e i n i t i a l and f i n a l s u r f a c e s , and t h e s i d e s o f t h e cone

r e p r e s e n t i n g t h e l i m i t o f t h e a r e a o f t h e e m i t t e r s u r f a c e p r o j e c t e d o n t o t h e d e t e c t o r . The bases o f t h e s p h e r i c a l caps a r e i n d i c a t e d b y d o t t e d l i n e s . T h i s volume can be seen t o be:

where V i s t h e volume o f t h e f r u s t r u m o f t h e cone bounded t o p and b o t t o m by t h e d o t t e d f i n e s , V 2 i s t h e s p h e r i c a l cap o f r a d i u s R , and V 3 i s t h e s p h e r i c a l cap o f r a d i u s R. The v a l u e h i s e q u a l t o t h e number o f pqanes e v a p o r a t e d normal t o t h e e m i t t e r ' s a x i s , ( N dhkl). These v01 umes can be expressed r e s p e c t i v e l y as:

Vl = 6 3 [K: s i n 2 B + ^K: ( l - c o s 8 ) s i n z 8 ] [ h 3 + 3 h Z l o + 3 h l o Z ] (3a)

the i n i t i a l s u r f a c e t o apex o f t h e cone made by extending t h e s i d e s o f t h e e m i t t e r t o t h e i r p o i n t o f convergence, 1 ,. The system parameters t o be determined a r e t h e d e t e c t o r v i e w i n g h a l f - a n g l e , 6 , and t h e p r o p o r t i p n a l i t y c o n s t a n t between t h e volume and t h e accumulated s i g n a l . This constant, KD, i s comprised o f s e v e r a l

d i s t i n g u i s h a b l e constants: t h e e m i t t e r density, t h e e f f i c i e n c y o f t h e detector, t h e g a i n o f t h e detector, t h e g a i n o f t h e a m p l i f i e r and o t h e r system constants.

F o r t h e depth evaporated i n an IAP experimefit t h e v i e w i n g h a l f - a n g l e , 6, i s assumed constant and i s a reasonable approximatidn, s i n c e t h e image i s n e a r l y a

stereographic p r o j e c t i o n o f t h e surface, o f t h e t i p o n t o the screen. Since the p r o j e c t i o n p o i n t i s n e a r l y t h e same r e g a r d l e s s o f t i p radius, t h e a n g u l a r p o s i t i o n s between p o l e s o f the c r y s t a l p1 anes i s approximate1 y constant. (e.g., t h e

p r o j e c t i o n p o i n t w i t h v a r y w i t h depth by about .l um, whereas t h e p r o j e c t i o n d i s t a n c e t o t h e screen i s o f the o r d e r o f 0.1 m.) F o r o u r system, B i s 20".

DETERMINATION OF KD

K i s the p r o p o r t i o n a l i t y c o n s t a n t between t h e c u m u l a t i v e N i s i g n a l and

tRe volume (see equation 4). With t h e v a l u e o f KD and t h e geometric parameters o f an e m i t t e r , a depth s c a l e can be a s c r i b e d t o the c u m u l a t i v e N i s i g n a l d a t a by graphing a c a l c u l a t e d c u r v e versus t h e depth probed f o r t h a t e m i t t e r . The depth s c a l e i s g i v e n as the number o f r i n g s c o l lapsed; t h e t o t a l depth g i v e n as N d where dhkl i s t h e d-spacing o f the s e t o f planes used f o r t h e determination o ? ~ $ , and N i s t h e t o t a l number o f p l a n e s evaporated. Supplementary d a t a from t h e TEM 1s r e q u i r e d t o determine geometric parameters o f t h e specimen, and t o check t h e depth s c a l e i n t h e r i n g - c o u n t i n g experiment. I t i s r e l a t i v e l y easy t o f i n d KD by c o l l e c t i n g data w i t h an imaging gas present, n o t i n g t h e number o f r i n g s c o l lapsed, adding the s i g n a l s o f a1 l t h e spectra, s u b s t i t u t i n g t h i s v a l u e i n t o t h e

r e l a t i o n s h i p and s o l v i n g f o r KD. However, the r i n g - c o u n t i n g c o n t r o l experiment which w i 1 1 be described a l s o checks t h e v a l i d i t y o f t h e model used f o r t h e volume

probed by t h e use o f a c u r v e matching procedure. The s e l e c t i o n c r i t e r i a f o r specimens used f o r imp1 a n t a t i o n and subsequent a n a l y s i s i s i m p o r t a n t as we1 l and w i l l be discussed be1 ow.

EXPERIMENTAL PROCEDURE

The number o f steps i n v o l v e d i n g e t t i n g t h e d a t a i n f i n a l form i s r a t h e r large, b u t i s straighforward. F i g u r e 3 i s a f l o w c h a r t o f t h e procedure i n f i n d i n g KD, t h e experimental curve, and t h e c a l c u l a t e d curve. The l a t t e r wi 1 1 be used t o e s t a b l i s h a depth p r o f i l e which does n o t use t h e imaging gas. The o n l y d i f f e r e n c e i n t h e f l o w c h a r t f o r an a c t u a l depth p r o f i l e experiment i s t h a t t h i s experimental c u r v e and KD w i l l n o t be an o u t p u t o f t h e program. The reason, o f course, i s t h a t t h e r i n g counting i s n o t performed and t h e "pul senum" i n f o r m a t i o n i n t h e f l o w c h a r t i s n o t c o l l e c t e d .

N i c k e l specimens a r e p o l i s h e d w i t h a t a p e r a n g l e as sharp as p o s s i b l e i n o r d e r f o r them t o f i r s t image we1 l below 5.5 kV. The reason f o r t h i s i s t h a t t h e specimen i s f i e l d evaporated up t o a v o l t a g e o f 6.0 kV, a t which v o l t a g e t h e s e l e c t i o n

c r i t e r i o n f o r a t i p i s t h a t t h e p o r t i o n o f t h e specimen imaged i s l arger than t h e d e t e c t o r area.

A f t e r t h e specimen i s evaporated t o 6 kV i n t h e FIM, i t i s t r a n s f e r r e d t o t h e TEM f o r imaging. The p o s i t i o n o f the s t a i n l e s s s t e e l specimen mount i s noted because the specimen w i l l be re-imaged again under approximately t h e same "2-beam" imaging conditions. The micrograph obtained w i l l be used t o determine a, and 1,. The specimen must have a smooth, s t r a i g h t shank and the s u r f a c e must meet t h e shank t a n g e n t i a1 l y .

A f t e r TEM imaging, t h e specimen i s t r a n s f e r r e d back t o t h e FIM/IAP where t h e

v o l t a g e i s r a i s e d t o t h e imaging v o l t a g e again. FIM micrographs are recorded o v e r

JOURNAL DE PHYSIQUE

t h e complete imagable area o f t h e t i p i n o r d e r t o determine t h e c r y s t a l l ographic o r i e n t a t i o n and radius. The specimen i s then o r i e n t e d toward t h e d e t e c t o r w i t h t h e ( 1 1 1 ) p o l e i n t h e c e n t e r o f t h e creen ( f o r Ni). The imaging gas pressure i s lowered t o approx.mately 5 f

10-% T o r r and t h e Chevron g a i n i s increased t o maximum (approximately 1 0 . The dc v o l t a g e i s lowered i n a n t i c i p a t i o n o f u s i n g a 2 kV pu l se which remains c o n s t a n t throughout t h e experiment.

The d i g i t i z e r i s now prepared f o r c o l l e c t i n g s p e c t r a and t h e p u l s e counter i s r e s e t t o zero. The number o f waveforms averaged p e r spectrum i

s e l e c t e d a t t h i

time.

The l a t t e r s h o u l d n o t be t o o smal l since: 1 ) the number o f s p e c t r a s t o r e d may be t o o l arge f o r t h e a v a i l a b l e memory and 2) t h e time t o s t o r e a spectrum can i n t e r f e r e w i t h t h e a c t o f c o l l e c t i o n o f a subsequent waveform. For o u r system, a v e r a g i n g e i g h t t r a c e s g i v e s a good balance between storage requirements, background averaging, and t h e assumption t h a t t h e r e s u l t o f each p u l s e w i t h i n a spectrum i s a p p r o x i m a t e l y t h e same. The r i n g - c o u n t experiment i s s t a r t e d and automatic l o o p i n g o f t h e d a t a a c q u i s i t i o n and storage s e c t i o n s o f t h e program occurs. When a r i n g c o l l a p s e i s seen a t t h e screen, t h e p u l s e number i s noted.

The v01 tage may be increased manual l y o r by program c o n t r o l . The experiment i

continued u n t i l a predetermined number o f r i n g s have c o l lapsed. I t i s i n f o r m a t i v e t o n o t e t h e amount o f data which would be c o l l e c t e d t o t h i s p o i n t . For a t y p i c a l experiment, 650 (1 1 1 ) r i n g s o f a N i specimen, 3366 s p e c t r a were c o l l e c t e d , r e q u i r i n g 26,920 pulses. The t i m e r e q u i r e d t o perform t h e experiment was l o n g e r t h a n seven hours. A t t h e end o f t h i s experiment, t h e specimen i s re-imaged i n t h e FIM mode and t r a n s f e r r e d t o t h e TEM. TEM imgaging i s done as c l o s e t o t h e i n i t i a l c o n d i t i o n s as p o s s i b l e . I t i

i m p e r a t i v e t h a t when specimens a r e imaged a t d i f f e r e n t times f o r comparison t h a t t h e TEM be s e t up i n as i d e n t i c a l a mode o f o p e r a t i o n as p o s s i b l e . T h i s assures t h a t t h e two images have been taken w i t h t h e same m a g n i f i c a t i o n , hence t h e d i s t a n c e probed can be a c c u r a t e l y determined between t h e two micrographs. (Of course, t h e a b s o l u t e v a l u e o f TEM m a g n i f i c a t i o n must be separately, c a l i b r a t e d . ) FIM and TEM n.icrographs o f t h e i n i t i a l and f i n a l s t a t e s o f an e m i t t e r a r e shown i n F i g u r e 4.

A f t e r t h e s p e c t r a a r e c o l l ected, t h e p u l se numbers corresponding t o r i n g c o l l apses a r e e n t e r e d i n t o t h e computer. The N i s i g n a l

must a1 so be found. A general r o u t i n e f o r " p i c k i n g - o f f " up t o e i g h t mass peaks from t h e s t o r e d s p e c t r a on t h e f i l e manager ( T e k t r o n i x 4909) i

employed. A t i m e window f o r each peak must be d e f i n e d u s i n g t h e marker s e c t i o n o f the program. The program then c a l c u l a t e s t h e t i m e o f f l i g h t f o r t h e mass peak and a l s o s h i f t s t h i s window w i t h r e s p e c t t o t h e p r e v i o u s p o s i t i o n o f t h e peak. These peak v a l u e s a r e then s t o r e d on a f i l e . A f t e r t h e N i peak v a l u e s a r e s t o r e d i n t h e f i l e manager, t h e y a r e summed w i t h r e s p e c t t o t h e p u l s e numbers recorded d u r i n g t h e r i n g c o u n t i n g experiment. These v a l u e s a r e accumulated u s i n g another program which c r e a t e s a f i l e i n t o which t h e accumulated Ni s i g n a l a r r a y w i l l be put. The program works i n t h e f o l l o w i n g manner. I t reads t h e f i r s t p u l s e number from t h e storage f i l e and d i v i d e s t h i s number by t h e v a l u e used i n c o l l e c t i n g t h e spectra. The r e s u l t i n g i n t e g e r i s t h e spectrum number i n which t h a t r i n g c o l l a p s e d . The N i peak v a l u e s a r e t h e n summed t o t h i s p o i n t . The f r a c t i o n a l p a r t o f t h e r e s u l t g i v e s t h e mu1 t i p 1 i e r f o r t h e N i peak t o be added t o t h e accumulated value. The r e s u l t i s then s t o r e d as t h e f i r s t v a l u e i n t h e accumulation f i l e . The n e x t pu7 se number i s r e a d and t h e process repeated, the v a l u e a t each r i n g c o l l a p s e being p u t i n t o the accumulation f i l e . The index o f t h e p o s i t i o n o f each c u m u l a t i v e N i v a l u e corresponds t o t h e r i n g c o l lapse number. T h i s i s t h e experimental d a t a which i s used t o graph t h e c u r v e which i s p r o p o r t i o n a l t o the volume c u r v e g i v e n by equation (4). F i g u r e 5 shows the range o f v a l u e s f o r the Ni s i g n a l s used t o generate the experimental c u r v e i n F i g u r e 6. I t can be seen t h a t i t i s m o n o t o n i c a l l y i n c r e a s i n g and smooth. This c u r v e i s i n s e n s i t i v e t o the f l u c t u a t i o n s i n t h e o r i g i n a l data. (This i s an important p r e r e q u i s i t e f o r f i n d i n g a method f o r assigning a depth scale.) DETERMINATION OF GEOMETRIC PARAMETERS

To f i t t h e experimental c u r v e i n F i g u r e 6, the parameters a and 1, must be

t h e shank. A "least-squares" s t r a i g h t l i n e i s found f o r each s i d e and t h e

i n t e r s e c t i o n o f t h e two l i n e s g i v e s t h e apex o f t h e cone. The shank h a l f - a n g l e i s s i m p l y h a l f o f the angle between these two l i n e s . A p o i n t a l o n g the l i n e o f the e m i t t e r and a t the surface i s a l s o d i g i t i z e d . The d i s t a n c e between t h i s c e n t e r p o i n t and t h e apex o f the cone g i v e s t h e v a l u e 1 T h i s program can a l s o be used t o f i n d the d i s t a n c e evaporated. The same proce&re i s used on t h e micrograph b e f o r e e v a p o r a t i o n and a f t e r . The d i f f e r e n c e i n the o u t p u t of the two l. v a l u e s i s the d i s t a n c e evaporated.

CALCULATED CURVE

The procedure f o r e s t a b l i s h i n g the depth s c a l e f o r an imp1 anted t i p i s s t r a i g h t f o r w a r d . The geometric parameters are measured w i t h t h e TEM and the c u m u l a t i v e c u r v e versus r i n g count i s generated. The steps i n t h i s procedure would be e s s e n t i a l l y t h e same as those a t t a i n e d i n the f l o w . c h a r t o f F i g u r e 3, except t h a t t h e i m p l a n t a t i o n occurs j u s t p r i o r t o a n a l y z i n g i n the IAP. O f course, no r i n g c o u n t i n g i s performed. The i n d i c e s o f the c a l c u l a t e d c u r v e a r r a y g i v e t h e depth a t t h a t p o i n t i n Nhkl u n i t s (h/dhkl). For the p r o f i l e d t i p , an a r r a y o f cumulated v a l u e s are found. The i n d i c e s o f t h i s a r r a y are the s p e c t r a number taken d u r i n g the p r o f i l e . The depth a t each spectra i s obtained by f i n d i n g the

corresponding r i n g count from the c a l c u l a t e d c u r v e f o r each c u m u l a t i v e Ni value.

REFERENCES

[ l J ^{Walck, S. D. and Hren, J. J., Mat.} Res. Soc. Symp., 2, Boston, MA, 325-30 (1984).

[2] Wiza, J. L., Instrum. and Meth., 162, 587-601 (1979).

ACKNOWLEDGEMENT

The authors would l i k e t o thank the Major A n a l y t i c a l I n s t r u m e n t a t i o n Center (MAIC)

a t t h e U n i v e r s i t y o f F l o r i d a f o r t e c h n i c a l assistance. This work was funded by

OOE, c o n t r a c t #DE-FG05-84ER45172. Thanks are a l s o due t o t h e U n i v e r s i t y o f F l o r i d a

Col l ege o f Engineering Center o f Excellence.

C2-4.56

JOURNAL DE PHYSIQUE

APPLIED VOLTAGES C k V )

F i g u r e 1. Montage o f TEM micrographs f i e l d evaporated i n s i t u TEM i n the FIM/TEM

"Fie1 d - E f f e c t " h01 der. A1 so shown f o r c o m p a ~ s ~ s a computer- generated sequence u s i n g the model f o r t h e tCp geometry discussed i n t e x t .

F i g u r e 2. Representation o f t h e volume probed by t h e FIM/IAP i n an e m i t t e r . The

v a l u e h i s t h e d i s t a n c e probed, B i s t h e d e t e c t o r subtended ha1 f-angle,

R. i s the i n i t i a l r a d i u s o f curvature, and R i s the r a d i u s a t h.

F i g u r e 3. Flow c h a r t o f t h e procedures i n v o l v e d w i t h f i n d i n g t h e p r o p o r t i o n a l i t y c o n s t a n t o f t h e c u m u l a t i v e m a t r i x s i g n a l as a f u n c t i o n o f depth. The

l a r g e s o l i d arrow i n d i c a t e s t r a n s f e r o f t h e specimen between instruments. The s m a l l e r arrows i n d i c a t e t h e f l o w o f data i n the i n d i c a t e d form.

F i g u r e 4. TEM and FIM micrographs b e f o r e and a f t e r r i n g count experiment.

2) I m a g e & R e c o r d

3) S e l e c t S p e c i m e n ? C o r r e c t O r ? e n t a t i o n ?

v

I m a g e F o r '0,'

M e e t s S e l e c t i o n c r i t e r i a ? 2) S e l e c t S a m p l e ?

F I M t I A P ( b e f o r e )

1 ) I m a g e R e c o r d FI"/IAP 2 ) S e t u p IAP I n T O F M o d e R e i m a g e F114 ³¹ R u n , C o l l e c t , & S t o r e Data

- S p e c t r a

R i n g N u m b e r

JOURNAL DE PHYSIQUE

SPECTRA NUMBER Cx1@8>

F i g u r e 5. N i peak v a l u e s f o r t h e s p e c t r a which generated t h e c u r v e i n F i g u r e 6.

288 . . .

1SB-

108-

EXPERMEWAL

148- CALCULATED - - - - -

- -

z 128-

2 -

188-

48 -

-

C111> RING CMaJT CxlBQ)

F i g u r e 6. Cumulative N i s i g n a l versus N i ( 1 1 1 ) r i n g count f o r two specimens. Both

c u r v e s were us t o f i n d two v a l u e s o f K These were averaged t o g i v e :

Kg = 5.28 x 10- Y' . Using t h i s value, t h e &o c a l c u l a t e d c u r v e s were

found and compared t o t h e o r i g i n a l data.