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COMPUTER TECHNIQUES FOR TOPOGRAPHICAL ANALYSIS IN THE SCANNING ELECTRON
MICROSCOPE
P. Atkin, K. Smith
To cite this version:
P. Atkin, K. Smith. COMPUTER TECHNIQUES FOR TOPOGRAPHICAL ANALYSIS IN THE
SCANNING ELECTRON MICROSCOPE. Journal de Physique Colloques, 1984, 45 (C2), pp.C2-219-
C2-222. �10.1051/jphyscol:1984248�. �jpa-00223961�
JOURNAL DE PHYSIQUE
Colloque C2, supplément au n°2, Tome 45, février 1984 page C2-219
COMPUTER TECHNIQUES FOR TOPOGRAPHICAL ANALYSIS IN THE SCANNING ELECTRON MICROSCOPE
P . A t k i n and K.C.A. Smith
University Engineering Department, Trumpington Street, Cambridge CB2 1PZ, U.K.
Résumé
Nous rappelons les techniques utilisant l'ordinateur et permettant les mesu- res en trois dimensions dans le SEM.
Abstract
We s u r v e y t h e computer t e c h n i q u e s which can f a c i l i t a t e t h r e e - d i m e n s i o n a l measurements i n t h e SEM.
1 INTRODUCTION
There are several means by which three-dimensional (3D) surface microscopy may be performed with the SEM, and computer techniques can generally assist in this.
The basis of the stereo technique is to record a pair of images, the specimen, or beam, being tilted between exposures. The images may be recorded photographically, or by an on-line digital system. To obtain the 3D shape from the stereo pair, the correspondence problem must first be solved; that is, the point in each image corresponding to each specimen point must be located. Knowledge of the projection geometry of the two views then permits the calculation of the surface topography. The human visual system can perform this correspondence analysis when the appropriate micrograph is presented to each eye, and allows the SEM user to visualise the specimen topography.
Contrast interpretation techniques have been developed, based upon models of contrast formation mechanisms. Analysis of the signals from one or more detectors (whose response varies with surface slope) permits the computation of topographical data.
Finally, automatic rangefinding techniques have been used, where a region containing a point of interest is scanned repeatedly as the focus current is varied. The focus current giving optimum image contrast may be used to calculate the surface height.
These techniques are now described in more detail.
2 STEREOMETRY
The stereometric technique, because it is based upon precise geometrical relation- ships, is potentially the most accurate of the methods discussed here. It is also convenient, generally needing no modifications to the microscope, and approximate or qualitative results may be obtained very simply. For accurate quantitative results, however, the method can be very time-consuming, and a complex calibration procedure may be required.
Various aspects of the correspondence and geometrical stages of the analysis are discussed in the following sections.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984248
C2-220
JOURNAL
DE PHYSIQUE 2.1 Correspondence a n a l y s i sCorrespondence a n a l y s i s of a s t e r e o p a i r i s e a s i l y achieved by eye, although t h e procedure becomes t e d i o u s and error-prone i f t h e number o f p o i n t s t o be measured i s l a r g e . Matching p o i n t s may be found by s c r u t i n y of t h e two p i c t u r e s , when t h e p o s i t i o n of a f e a t u r e i s measured independently i n each image. An a l t e r n a t i v e i s t o p r e s e n t t h e images s t e r e o s c o p i c a l l y , and t o use a d e v i c e such a s a ' f l o a t i n g s p o t ' marker i n j e c t e d i n t o t h e images. The f u s i o n mechanism of t h e human s t e r e o p s i s system allows t h e o p e r a t o r t o judge when t h e s p o t a p p a r e n t l y l i e s on t h e s u r f a c e of t h e specimen. An e x t e n s i o n of t h i s i d e a is t h e s t e r e o p l o t t e r , which permits simultaneous t r a c i n g o f t h e h e i g h t contours.
A p o s s i b i l i t y f o r t h e f u t u r e i s automatic correspondence a n a l y s i s using image
processing techniques. Many a t t e m p t s have been made t o achieve t h i s , both i n t h e f i e l d of photogrammetry, and with t h e aim of modelling human v i s u a l processes. A popular approach is t h a t of c r o s s - c o r r e l a t i o n of t h e images [ I ,2]. It has been pointed o u t by s e v e r a l a u t h o r s , however, t h a t t h i s scheme i s b a s i c a l l y unsound. The remaining a l g o r i t h m s may be divided i n t o symbolic approaches [7,4,5,6 $71, and whole-field o r non-symbolic
approaches [8,9]. I n t h e former, an a l g o r i t h m s e a r c h e s f o r f e a t u r e s i n both images independently, t h e n an attempt i s made t o l o c a t e t h e correspondence p a r t n e r f o r each f e a t u r e . The whole-field techniques t r y t o l o c a t e a p a r t n e r f o r every p o i n t i n each image.
None of t h e s e methods has y e t been demonstrated t o work r e l i a b l y on n a t u r a l images.
A new algorithm under d e v e l o p e n t a t t h i s l a b o r a t o r y u s e s a 7D p r o b a b i l i t y s p a c e , modified by s u r f a c e smoothness c o n s t r a i n t s , t o e s t i m a t e t h e most l i k e l y topography of a specimen s u r f a c e from a s t e r e o p a i r . It e x p l i c i t l y c a t e r s f o r t h e p r o j e c t i o n geometry used, and t h e n o i s e l e v e l of t h e images.
2.2 Geometrical parameters
I n t h e s i m p l i f i e d case of approximately p a r a l l e l p r o j e c t i o n , and a laown specimen tilt about an a x i s i n t h e image p l a n e , t h e i n t e r p r e t a t i o n o f s t e r e o p a i r correspondence d a t a is s t r a i g h t f o r w a r d (101. Complications a r i s e i n p r a c t i c e , however, which r e q u i r e c o n s i d e r a t i o n
.
( i ) The p a r a l l e l p r o j e c t i o n approximation i s i n a p p r o p r i a t e f o r m a g n i f i c a t i o n s below 500 t o 1000 x (depending on working d i s t a n c e - s e e [ I l l ) .
( i i ) The parameters r e q u i r e d t o model t h e p r o j e c t i o n s ( e q u i v a l e n t f o c a l l e n g t h ; p o s i t i o n of t h e t i l t a x i s ; amount of t i l t ; x, y , and z s h i f t s r e q u i r e d t o m a i n t a i n t h e f i e l d of view w h i l s t t i l t i n g ) may n o t be known s u f f i c i e n t l y p r e c i s e l y . ( i i i ) There a r e s y s t e m a t i c d i s t o r t i o n s i n t h e imaging system.
I n t h e p a s t i t has been considered d e s i r a b l e t o u s e t h e p a r a l l e l p r o j e c t i o n approximation because of t h e complexity of t h e p e r s p e c t i v e p r o j e c t i o n equations. The a v a i l a b i l i t y of inexpensive small computers now makes t h e s e c a l c u l a t i o n s much more p r a c t i c a l .
Attempts have been made t o c a l i b r a t e t h e SEM such t h a t t h e r e l a t i o n s h i p s between the o p e r a t o r c o n t r o l s and t h e parameters o f ( i i ) a r e p r e c i s e l y known [12]. This reduces t h e u n c e r t a i n t y c o n s i d e r a b l y , b u t f o r t h e g r e a t e s t accuracy photogrammetric
self-
c a l i b r a t i o n i s r e q u i r e d [13,14]. I n t h i s procedure, e q u a t i o n s a r e s e t up connecting t h e p r o j e c t i o n parameters with t h e p o s i t i o n s of corresponding p o i n t s , and a r e solved so a s t o minimise some e r r o r c r i t e r i o n . The accuracy obtained i n t h i s way i s one o r two o r d e r s of magnitude b e t t e r than can be achieved with o t h e r methods.
Systematic d i s t o r t i o n s ( i i i ) can occur due t o [15] : a ) non-linear scanning i n t h e e l e c t r o n - o p t i c a l column;
b) non-linear scanning i n t h e r e c o r d i n g CRT;
c) t h e o p t i c a l system (camera and l e n s e s ) ;
d) t h e photographic process i t s e l f { f i l m s h r i n k a g e ) .
These d i s t o r t i o n s have been measured and c a l i b r a t e d by imaging a s t a n d a r d specimen. The d i s t o r t i o n s have been r e p r e s e n t e d both by a s e l f - d i s t o r t i o n g r i d [12], and by t a n g e n t i a l , symmetric and s p i r a l d i s t o r t i o n polynomials [ I 41. Maune [14] found t h a t a d i f f e r e n t s e t o f d i s t o r t i o n parameters was s i g n i f i c a n t f o r each a n g l e of t i l t of t h e specimen s t a g e .
It should be pointed o u t t h a t on-line d i g i t a l s t o r a g e o f t h e images a v o i d s d i s t o r t i o n s o u r c e s b , c , and d [15].
I t i s suggested t h a t f o r high p r o d u c t i v i t y and moderate accuracy, t h e f o l l o w i n g scheme i s a p p r o p r i a t e :
a ) D i g i t a l s t o r a g e of t h e s t e r e o p a i r micrographs.
b) Once-only c a l i b r a t i o n o f t h e column d i s t o r t i o n s .
c ) S o l u t i o n f o r t h e p r o j e c t i o n parameters from a number o f corresponding p o i n t c o o r d i n a t e s , using e i t h e r l e a s t - s q u a r e s adjustment o r d i r e c t s o l u t i o n (161.
7 CONTRAST INTERPRETATION
Lebiedzik and White [ I T ] developed a system whereby t h e l o c a l s l o p e and o r i e n t a t i o n of t h e s u r f a c e may be i n s t a n t a n e o u s l y determined. The s i g n a l s from f i v e d e t e c t o r s ( a secondary e l e c t r o n d e t e c t o r and f o u r e l e c t r o n b a c k s c a t t e r (EBS) d e t e c t o r s ) were analysed by a computer, which compared them with c a l i b r a t i o n responses. A disadvantage o f t h i s method is t h a t t h e specimen must be coated with a l a y e r of m e t a l of known response. Also, it r e q u i r e s t h e i n s t a l l a t i o n of t h e EBS d e t e c t o r s . It i s not v e r y a c c u r a t e , p a r t i c u l a r l y when the s u r f a c e c o n t a i n s d i s c o n t i n u i t i e s i n h e i g h t . The p r i n c i p a l a t t r a c t i o n s of t h e technique a r e t h a t t h e a n a l y s i s can be v e r y r a p i d , and microtopographical c h a r a c t e r i s a t i o n of t h e s u r f a c e ( t h e c a l c u l a t i o n of s t a t i s t i c a l p r o p e r t i e s o f t h e s u r f a c e ) may r e a d i l y be performed.
A more s o p h i s t i c a t e d , i t e r a t i v e a l g o r i t h m was a p p l i e d i n [ 181 t o o b t a i n t h e 7D shape of a specimen from a s i n g l e secondary e l e c t r o n image.
4 AUTOMATIC RANGEFINDING
I t i s r e l a t i v e l y simple t o measure s p o t h e i g h t s i n t h e SEM using t h e automatic r a n g e f i n d i n g method (19,201, and computer c o n t r o l speeds t h e process c o n s i d e r a b l y , although each h e i g h t d e t e r m i n a t i o n t a k e s approximately 30 seconds [20]. The method r e q u i r e s two o p e r a t i o n s f o r each p o i n t :
( i ) The focus c u r r e n t which maximises t h e image i n t e n s i t y g r a d i e n t a t t h e p o i n t of i n t e r e s t i s found.
( i i ) This value of focus c u r r e n t i s converted t o t h e e q u i v a l e n t h e i g h t by means of a c a l i b r a t i o n t a b l e .
The fundamental l i m i t t o the accuracy a t t a i n a b l e by t h i s means i s t h e ( r a t h e r l a r g e ) depth of f i e l d o f the SEM, although t h e p r e c i s i o n t o which t h e o b j e c t i v e c u r r e n t can be s e t may prove t o be t h e p r a c t i c a l l i m i t . R e s u l t s have been obtained with a h e i g h t u n c e r t a i n t y of 10 p, although t h e t h e r o r e t i c a l l i m i t i s 1 p f o r a t y p i c a l SEM.
JOURNAL DE PHYSIQUE
5 CONCLUSIONS
The c h a r a c t e r i s t i c s of t h e methods d i s c u s s e d i n t h i s paper a r e summarised below.
*
Approximately i n v e r s e l y p r o p o r t i o n a l t o m a g n i f i c a t i o n .REFERENCES TECHNIQUE
S t e r e o m e t r y (photogrammetric c a l i b r a t i o n ) S t e r e o m e t r y ( ~ n s t r u m e n t a l c a l i b r a t i o n ) C o n t r a s t I n t e r p r e t a t i o n Automatic Rangef ind i n g
[ I ] LEVINE M.D. O'HANDLEY D.A. Y A G I G.M., Comp. Graph. I m . Proc.
2
(1 973) 171.121 MORI K - I . KIDODE M. ASADA H., Comp. Graph. I m . Proc. 2 (1977) 797.
[7] MARR D. POGGIO T., Proc. Roy. Soc. London
B204
(1 979)-701.[4] BARNARD S.T. THOMPSON W.B., IEEE Trans. P a t t . A n a l y s i s & Machine I n t e l l . PAMI-2 ( 4 ) (1980) 373.
TIME p e r p o i n t 1-30 s +photo 1-70 s +photo s c a n r a t e 70 s COST
M o d i f i c a t i o n s Computation
-
High
-
Low
High Moderate
High Moderate
[ 5 ] BAKER H.H. BINFORD T., Proc. I n t
.
Soc. Photogrammetry & Remote Sensing Commission 11, Symp. Advances i n I n s t r u m e n t a t i o n f o r P r o c e s s i n g and A n a l y s i s o f Photogrammetric d Remotely Sensed Data. Ottowa, Canada, August 1982.[6] SUETENS P. JANSEN P. HAEGEMANS A. OOSTERLINCK A. GYBELS J., Image and V i s i o n Computing 1 No.1 (1983) 47.
[ 7 ]
MAYHEW
J.E.W. FRISBY J.P., P e r c e p t i o ng
(1980) 69.[8] JULES2 B., Proc. IFIPS Congress 1962 Popplewell C.M. ( ~ d . ) Amsterdam North-Holland (1963) 439.
[ 9 ] MARR D. POGGIO T., Science
194
(1976) 283.[ l o ] HOWEZL P.G.T. BOYDE A., Scanning E l e c t r o n Microscopy ( p a r t I ) (1972) 233.
[ l l
]
HOWELL P.G.T.. Scanning1
(1 978) 118.[12] BOYDE A. ROSS H.F., Photogrammetric Record ~ ( 4 6 ) (1 975) 408.
[ I T ] MAUNE D.F., Photogrammetric Engineering & Remote S e n s i n g
42
No.9 (1976) 1161.[14] MAUNE D.F., Ph.D. T h e s i s , The Ohio S t a t e U n i v e r s i t y (1 973).
[ I ? ] HOLBURN D.M. SMITH K.C.A., I n s t . Phys. Conf. Ser. No.
j 6
(1977) 99.[16] LONGUET-HIGGINS H.C., Nature
297
(1 981 ) 177.[17] LEBIEDZIK J. WHITE E.W., Scanning E l e c t r o n Microscopy ( p a r t I) (1975) 1 8 1 . 1181 IKEUCHI K. HORN B.K.P., i n : Computer V i s i o n ( BRADY J.M. Ed .)
,
Amsterdam North-Holland(1981) 141.
[19] HERSENER J. RICKER T., B e i t r a g e z u r elektronenmikroscopischen D i r e k t a b b i l d u n g von Oberflachen
5
(1972) 777.[20] HOLBURN D.M. SMITH K.C.A., Scanning E l e c t r o n Microscopy ( p a r t 11) (1979) 47.
OPERATOR REQUIREMENT
Very g r e a t
Very g r e a t
- -
LIMITING ACCURACY
-330 m ( 5 0 0 0 ~ )
i
-7000 nm ( 5 0 0 0 ~ )
*
specimen
-
dependent
I
P
CALIBRATION PROCEDURE
Complex
Tedious
Moderate Simple
