STRUCTURAL AND ELECTRONIC PROPERTIES OF ARTIFICIAL METALLIC SUPERLATTICES

HAL Id: jpa-00224195

https://hal.archives-ouvertes.fr/jpa-00224195

Submitted on 1 Jan 1984

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

STRUCTURAL AND ELECTRONIC PROPERTIES OF ARTIFICIAL METALLIC SUPERLATTICES

C. Falco

To cite this version:

C. Falco. STRUCTURAL AND ELECTRONIC PROPERTIES OF ARTIFICIAL METAL- LIC SUPERLATTICES. Journal de Physique Colloques, 1984, 45 (C5), pp.C5-499-C5-507.

�10.1051/jphyscol:1984574�. �jpa-00224195�

J O U R N A L DE PHYSIQUE

Colloque C5, supplCment a u n04, Tome 45, a v r i l 1984 page C5-499

STRUCTURAL AND ELECTRONIC P R O P E R T I E S OF A R T I F I C I A L M E T A L L I C SUPERLATTICES~

C.M. F a l c o

Departments of Physics and of Optical. Sciences and i n t h e Arizona Research Laboratories, University o f Arizona, !t'ucson, Arizona 85721, U.S.A.

Rkum'e

-

l ' i n t g r e s s e m e n t a u x s u p e r r g s e a u x m & t a l l i q u e s pr'epar'es a r t i f i c i e l l e m e n t . C e s d e r n i e r s m o n t r e n t d e s p r o p r i 6 t ' e s p h y s i q u e s d i f f k e n t e s d e c e l l e s d e s m a t s r i a u x p r o d u i t s n a t u r e l l e m e n t . C e t a r t i c l e d ' e c r i t l a t e c h n i q u e d e p u l v ' e r i s a t i o n c a t h o d i q u e u t i l i s g e p o u r l a p r g p a r a t i o n d e c e s s u p e r r ' e s e a u x m k a l l i q u e s , a u s s i b i e n q u e l e s

c o n s i d e r a t i o n s a f f e c t a n t l e u r s p u r e t ' e s , l e s q u a l i t ' e s d e s i n t e r f a c e s e t l e s o r i e n t a t i o n s c r i s t a l l o g r a p h i q u e s . La c o n t r i b u t i o n d e s i n t e r f a c e s a u x p r o p r i ' e t e s d u t r a n s p o r t ' e l e c t r o n i q u e e s t d g c r i t e e n t e r m e s d e t h k o r i e s d e s e f f e t s d e t a i l l e f i n i e .

A b s t r a c t

-

e x h i b i t i n g d i f f e r e n t p h y s i c a l p r o p e r t i e s t h a n t h o s e i n n a t u r a l l y o c c u r i n g m a t e r i a l s . T h i s p a p e r d e s c r i b e s t h e s p u t t e r i n g t e c h n i q u e u s e d t o p r e p a r e t h e s e m e t a l l i c s u p e r l a t t i c e s , a s w e l l a s c o n s i d e r a t i o n s a f f e c t i n g t h e i r p u r i t y , i n t e r f a c i a l q u a l i t y a n d c r y s t a l l o g r a p h i c o r i e n t a t i o n . T h e c o n t r i b u t i o n o f t h e i n t e r f a c e s t o t h e e l e c t r o n i c t r a n s p o r t p r o p e r t i e s i s d e s c r i b e d i n t e r m s o f f i n i t e s i z e e f f e c t t h e o r i e s .

I - PREPARATION OF METALLIC SUPERLATTICES

O u r p r e s e n t d e p o s i t i o n s y s t e m w a s s p e c i f i c a l l y d e s i g n e d f o r p r e p a r i n g m e t a l l i c s u p e r l a t t i c e s ; w i t h t h r e e m a g n e t i c a l l y -

c o n f i n e d - p l a s m a s p u t t e r g u n s o f v a r i a b l e t a r g e t s i z e c o n t a i n e d i n a d i f f u s i o n pumped v a c u u m s y s t e m w i t h b a s e p r e s s u r e < 7 x lo-'

t o r 1 . A s c h e m a t i c d i a g r a m o f t h e s y s t e m i s s h o w n i n F i g . 1.

As w e l l a s u s i n g t a r g e t s o f p u r e e l e m e n t s o r a l l o y s , t h e d e s i g n a l l o w s f o r g e n e r a t i o n o f a l l o y l a y e r s i n s i t u b y c o - s p u t t e r i n g f r o m t w o o f t h e g u n s w h i c h a r e c l o s e l y s p a c e d .

+work s u p p o r t e d by t h e D i r e c t o r , O f f i c e o f Energy Research, O f f i c e of B a s i c Energy S c i e n c e s , M a t e r i a l s S c i e n c e s D i v i s i o n o f t h e U.S. Department of Energy under C o n t r a c t No. DE-AC02-83ER45025.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984574

JOURNAL DE PHYSIQUE

Moss Flow Controller

F i g . 1 - S c h e m a t i c d i a g r a m o f s p u t t e r i n g s y s t e m u s e d f o r t h e p r e p a r a t i o n o f a r t i f i c i a l m e t a l l i c s u p e r l a t t i c e s .

S a m p l e s a r e d e p o s i t e d o n t e m p e r a t u r e c o n t r o l l e d , h e a t e d o r c o o l e d s u b s t r a t e s i n t h e r a n g e - 9 0 O K - ^{8 0 0} O C ( n o t e : t h e c o n f i g u r a t i o n w i t h t e m p e r a t u r e c o n t r o l l e d p l a t f o r m i s n o t s h o w n i n F i g . 1).

A c t i v e f e e d b a c k c o n t r o l o f t h e s p u t t e r g u n s ' p o w e r s u p p l i e s i s a c h i e v e d u s i n g a m i c r o p r o c e s s o r - b a s e d s y s t e m w h i c h m o n i t o r s b o t h t h e c u r r e n t a n d v o l t a g e a n d r e g u l a t e s t h e p r o d u c t t o f 0.1%.

T h u s s p u t t e r i n g r a t e s , a n d h e n c e s u p e r l a t t i c e l a y e r t h i c k n e s s e s , a r e c o n t r o l l e d t o + ^0.1%

if

p a r a m e t e r s a r e h e l d c o n s t a n t . I t s h o u l d b e n o t e d t h a t s p u t t e r i n g r a t e s a r e p r e s s u r e d e p e n d a n t , a n d t h a t i o n i z a t i o n g u a g e s a n d c a p a c i t a n c e m a n o m e t e r s a r e o n l y s e n s i t i v e t o "21-5% i n t h i s p r e s s u r e r a n g e . To e n s u r e a c o n s t a n t p r e s s u r e w i t h r e p r o d u c i b l e r e s u l t s f r o m r u n t o r u n , a m i c r o m e t e r a d j u s t a b l e , v a r i a b l e o r i f i c e v a l v e i s u s e d i n t h e m a i n p u m p i n g l i n e a n d t h e A r g a s f l o w r a t e s ( a n d h e n c e s p u t t e r i n g p r e s s u r e ) a r e r e g u l a t e d t o 2 0 . 2 % b y m a s s f l o w c o n t r o l l e r s . R e g u l a t i o n o f a l l o f t h e s e f a c t o r s i s e s s e n t i a l f o r t h e p r o d u c t i o n o f h i g h q u a l i t y m e t a l l i c

s u p e r l a t t i c e s .

T h e s e q u e n c e a n d t i m i n g o f t h e d e p o s i t i o n o f e a c h l a y e r i s c o n t r o l l e d b y a m i c r o p r o c e s s o r w h i c h e n a b l e s a c c u r a t e t h i c k n e s s c o n t r o l a s w e l l a s m i n i m i z i n g t h e t i m e e a c h l a y e r i s e x p o s e d t o t h e p a r t i a l p r e s s u r e s o f a n y i m p u r i t y g a s e s i n t h e s y s t e m . T h e i m p o r t a n c e o f t h i s l a t t e r f a c t o r i s d i s c u s s e d b e l o w .

F i g . 2 s h o w s a R u t h e r f o r d B a c k s c a t t e r i n g S p e c t r u m (RBS) o b t a i n e d

i n c o l l a b o r a t i o n w i t h P r o f . J. L e a v i t t o f a Ta/Mo s u p e r l a t t i c e o f i n d i v i d u a l l a y e r t h i c k n e s s " 3 5 0 !&. T h e s e d a t a w e r e o b t a i n e d w i t h 3.78 MeV 4 ~ e i o n s a t 22.5' i n c i d e n c e t o t h e s a m p l e . T h e

i n d i v i d u a l l a y e r s a r e v e r y w e l l r e s o l v e d a t t h i s h i g h e n e r g y . I n a d d i t i o n , t h e y a r e w e l l s e p a r a t e d f r o m a n y p e a k s d u e t o t h e s u b s t r a t e ( s i n g l e c r y s t a l s a p p h i r e i n t h i s c a s e ) .

Channel number

F i g . 2 - R u t h e r f o r d B a c k s c a t t e r i n g (RBS) s p e c t r a f r o m a Ta/Mo s u p e r l a t t i c e o f i n d i v i d u a l l a y e r t h i c k n e s s ' 3 5 0

a.

I t i s n e c e s s a r y t o know w h a t s p u t t e r i n g c o n d i t i o n s a r e o p t i m u m f o r t h e g r o w t h o f t h e s e m e t a l l i c s u p e r l a t t i c e s . S i n c e s p u t t e r i n g t a k e s p l a c e a t r e l a t i v e l y h i g h p r e s s u r e s ("1-20 m t o r r ) , t h e q u e s t i o n o f c o n t a m i n a t i o n o f t h e m a t e r i a l s m a k i n g u p t h e l a y e r s , a s w e l l a s c o n t a m i n a t i o n a t t h e i n t e r f a c e s b e t w e e n l a y e r s i s o f p r i m e i m p o r t a n c e . We h a v e p r o p o s e d s e v e r a l F i g u r e s o f M e r i t f o r S p u t t e r e d S u p e r l a t t i c e s (FMSS) w h i c h a r e b r i e f l y d e s c r i b e d b e l o w ( u n p u b l i s h e d ) . T h e s e FMSS d e m o n s t r a t e s e v e r a l c o n d i t i o n s o n t h e s p u t t e r i n g p a r a m e t e r s w h i c h a r e n o t w i d e l y a p p r e c i a t e d .

W i t h a g i v e n p a r t i a l p r e s s u r e o f i m p u r i t y g a s s e s ( m e a s u r e d i n t o r r ) i n t h e c h a m b e r d u r i n g a d e p o s i t i o n , t h e t i m e f o r f o r m a t i o n o f a m o n o l a y e r o f i m p u r i t y a t o m s o n a f r e s h s u r f a c e a s s u m i n g a u n i t y s t i c k i n g c o e f f i c i e n t i s / 2 /

T h e r e f o r e t h e p e r c e n t a g e o f i m p u r i t i e s i n c o r p o r a t e d i n a f i l m w h i c h i s b e i n g s p u t t e r e d a t a c e r t a i n r a t e i s

4 0

9 . 1 ~ 1 0 P ( m t o r r ) Qleak(sccm)

% I m p u r i t i e s t FMSSl( s p u t t (2)

nsPutt ( x i s e c )

dA,

C5-502 JOURNAL DE PHYSIQUE

Eq. 2, the "calculated quality" of the sputtered film, shows several features which are not generally appreciated. One wants to use the lowest possible Ar sputtering pressure as w e l l as the highest Ar f l o w rate. These parameters should be kept in mind when depositing metallic superlattices. Considerable effect on the calculated quality of the sputtered films is possible using a reasonable range for each of the parameters contained in Eq. 2.

It should be emphasized at this point that there are several implicit assumptions in deriving the above FMSS which make it o n l y a n u p p e r l i m i t o n the i m p u r i t i e s i n c o r p o r a t e d i n a film. It is likely that the actual impurity content in metals which are not highly reactive w i l l be considerably smaller. The

assumptions are: 1) a l l gaseous impurities in the chamber are reactive. 2) sticking coefficient of impurities is unity. 3) Ar sputtering gas contains no contaminants (this latter can be shown to be an excellent approximation for laboratory grade Ar gas).

A second FMSS, which characterizes the quality of the interfaces between layers, can also be stated. During the preparation of a metallic superlattice, the substrate is alternately moved between two (or more) sputtering guns, or is alternately shuttered from several sputtering sources. During the interval between the completion of one layer and the start of the next layer, impurity atoms in the chamber can react with the surface. This is

particularly important for sputtered metallic superlattices, where one is attempting the epitaxial growth of the layers on each other. It is reasonable to assume that an impurity layer w i l l interfere with the epitaxy process. Of equal importance, such an impurity layer w i l l also affect the electronic properties of the interfaces, e.g. w i l l increase the electron scattering probability. The fraction of an impurity monolayer which w i l l form depends on the time the fresh surface is exposed before deposition of the subsequent layer is initiated. This fraction of an impurity monolayer is defined as a second FMSS

Again, it can be seen that the sputtering pressure should be minimized and the Ar f l o w rate maximized.

I1

-

Of key importance for studying short wavelength excitations at metallic interfaces is the ability to grow epitaxial layers with

little or no interdiffusion. There are a number of

considerations which go into the choice of metals for attempting to grow such epitaxial superlattices 131. Some of these have been discussed in previous publications 14-81. It should be noted that most combinations of metals do not grow as coherent superlattices. Here we wish to mention several geometrical considerations which give some insight into which materials are suitable candidates.

It is found that most materials preferentially grow with their lattices oriented such that the density of atoms (atoms/a2) in the plane is maximized 131. This is by far the most common situation; however, it is not the only one. Fig. 3 shows the in- plane density of atoms for most common metals and for various crystallographic orientations 191.

hcp basal ("fcc 111")

0 0.05 0.10 0.15 0.20

I n - plane Density ( a t o r n ~ / ~ ~ )

Fig. 3 - The in-plane density of atoms of various

crystallographic orientations for most metals which can be deposited by sputtering

The u s e f u l n e s s of s u c h a p l o t is that it is p o s s i b l e that epitaxial growth between metals of different symmetry is most likely to occur when the in-plane densities of the two elements are nearly equal. Such a criterion directly leads to a

relationship between the lattice constants which must be

satisfied. For an FCC (111) plane (lattice constant f) growing on a BCC (110) plane (lattice constant b) we

have

Another criterion, obtained by minimizing the misfit of the atoms in the two-dimensional conventional unit c e l l , leads to

Similiar criteria for ratios of lattice constants can be obtained for other crystallographic orientations, e.g. FCC (100) on BCC (110). Extensive work now exists using with two BCC/FCC

combinations which form superlat tices: Nb/Cu and Mo/Ni 14-8,lO-

C5-504 JOURNAL DE PHYSIQUE

1 2 1 . F o r b o t h o f t h e s e , t h e r a t i o o f l a t t i c e c o n s t a n t s i s "0.9;

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

111 - ELECTRONIC PROPERTIES

M e a s u r e m e n t s o f e l e c t r o n i c t r a n s p o r t p r o p e r t i e s c a n p r o v i d e i n s i g h t i n t o t h e s t r u c t u r a l p r o p e r t i e s o f m e t a l l i c s u p e r l a t t i c e s . E l e c t r o n s a r e s c a t t e r e d a t t h e i n t e r f a c e s , a n d c o n s e q u e n t l y c a n s e r v e a s a l o c a l p r o b e o f t h e s h a r p n e s s o f t h e p o t e n t i a l a n d o f t h e e l e c t r o n i c t r a n s m i s s i o n c o e f f i c i e n t a t t h e i n t e r f a c e when we a r e i n t h e r e g i m e w h e r e t h e i n s t r i n s i c m e a n f r e e p a t h , l i , o f o n e o f t h e m a t e r i a l s i s g r e a t e r t h a n t h e l a y e r t h i c k n e s s . I n t h e c a s e o f Cu f o r Nb/Cu s u p e r l a t t i c e s , t h e m e a n f r e e p a t h v a r i e s f r o m a p p r o x i m a t e l y 2 5 0

a

a

M a y a d a s a n d S h a t z k e s (M-S) / 1 3 / c o n s i d e r e d t h e e f f e c t o f g r a i n b o u n d a r y s c a t t e r i n g o n t h e t o t a l r e s i s t i v i t y o f m e t a l f i l m s o f f i n i t e t h i c k n e s s . I n t h e c a s e w h e r e t h e g r a i n s i z e i s

p r o p o r t i o n a l t o l a y e r t h i c k n e s s ( w h i c h i s t y p i c a l l y t h e c a s e f o r t h i n f i l m s ) , t h e M-S t h e o r y a l l o w s o n e t o o b t a i n t h e p e r c e n t a g e o f e l e c t r o n s s c a t t e r e d s p e c u l a r l y f r o m e a c h i n t e r f a c e p , a n d t h e r e f l e c t i o n p a r a m e t e r r f r o m t h e g r a i n b o u n d a r i e s . A p a r t i c u l a r l y c o n v e n i e n t l i n e a r i z e d f o r m o f t h e M-S t h e o r y h a s b e e n o b t a i n e d b y M o l a a n d H e r a s / 1 4 / . F o r g r a i n b o u n d a r i e s w i t h s i z e p r o p o r t i o n a l t o l a y e r t h i c k n e s s , we h a v e

w h e r e t h e s u b s c r i p t s r e f e r t o t h e f i l m a n d i n t r i n s i c p r o p e r t i e s , a n d w h e r e

F i g . 4 i s a p l o t o f p ( T ) d v s . d f o r Nb/Cu s u p e r l a t t i c e s a t t h r e e t e m p e r a t u r e s .

T h e i n t r i n s i c r e s i s t i v i t y a n d m e a n f r e e p a t h c a n b e o b t a i n e d f r o m t h e s l o p e s a n d i n t e r c e p t t o o b t a i n % ( T ) a n d p i M p r T h i s l a t t e r s h o u l d b e a c o n s t a n t d e p e n d a n t o n l y u p o n t h e m a t e r i a l , a n d e x p e r i m e n t a l l y we f i n d t h i s i s t r u e t o a b o u t 1 % , i . e . p i l i M ( p , r )

= 1 1 4 5

+

T h e M a y a d a s - S h a t z k e s t h e o r y c a n a l s o b e u s e d t o a n a l y z e t h e t e m p e r a t u r e c o e f f i c i e n t o f r e s i s t i v i t y B ( 1 1 p ) d P / d T . I f we a g a i n i n t e r p r e t t h e l a y e r t h i c k n e s s d a s b e i n g t h e s i z e l i m i t i n g p a r a m e t e r i n t h e M-S t h e o r y , we h a v e

F i g . 4 - R e s i s t i v i t y t i m e s l a y e r t h i c k n e s s v s . l a y e r t h i c k n e s s f o r a s e r i e s o f Nb/Cu s u p e r l a t t i c e s a t t h r e e t e m p e r a t u r e s .

w h e r e P ( p , r ) r M ( p , r ) . F i g . 5 i s a p l o t o f t i m e s l a y e r t h i c k n e s s v s . l a y e r t h i c k n e s s f o r Nb/Cu s u p e r l a t t i c e s a t t h r e e t e m p e r a t u r e s . U s i n g E q s . 7 a n d 9 we f i n d t h a t d p / d T a t a n y t e m p e r a t u r e s h o u l d b e c o n s t a n t i n d e p e n d a n t o f l a y e r t h i c k n e s s d.

I n d e e d , t h i s i s f o u n d t o b e t h e c a s e , i n d i c a t i n g t h a t t h e a p p l i c a t i o n o f t h e M-S t h e o r y t o t h e s e m e t a l l i c m u l t i l a y e r s i s v a l i d .

I V - ACKNOWLEDGEMENTS

I am p l e a s e d t o a c k n o w l e d g e p r e v i o u s c o l l a b o r a t i o n s o n r e l a t e d w o r k w i t h I v a n K. S c h u l l e r . T h e RBS d a t a w a s o b t a i n e d i n c o l l a b o r a t i o n w i t h J o h n A. L e a v i t t a n d Wayne B e n n e t t . I w o u l d a l s o l i k e t o a c k n o w l e d g e u s e f u l c o n t r i b u t i o n s b y T h o m a s A.

W e r n e r a n d P a u l F o u r n i e r . T h i s w o r k s u p p o r t e d by t h e D i r e c t o r , O f f i c e o f E n e r g y R e s e a r c h , O f f i c e o f B a s i c E n e r g y S c i e n c e s , M a t e r i a l s S c i e n c e s D i v i s i o n o f t h e U. S. D e p a r t m e n t o f E n e r g y u n d e r C o n t r a c t No. DE-AC02-83ER45025.

C5-506 JOURNAL DE PHYSIQUE

F i g . 5 - L a y e r t h i c k n e s s d i v i d e d b y t e m p e r a t u r e c o e f f i c i e n t o f r e s i s t i v i t y v s . l a y e r t h i c k n e s s f o r Nb/Cu s u p e r l a t t i c e s a t t h r e e t e m p e r a t u r e s

V - REFERENCES

1. L. M. S i m a r d , I n c . 7 5 9 B W a r d D r i v e , S a n t a B a r b a r a , C A 9 3 1 1 1 . 2. S e e , f o r e x a m p l e , DUSHMAN, S. T h e S c i e n t i f i c F o u n d a t i o n o f Vacuum

T e c h n i q u e , W i l e y , New Y o r k , 1 9 6 1 .

3. S e e , f o r e x a m p l e , v a r i o u s a r t i c l e s i n MATTHEWS, J . W . E p i t a x i a l G r o w t h , A c a d e m i c P r e s s , New Y o r k , 1 9 7 5 .

4. SCHULLER, I. K. a n d FALCO, C. M., i n I n h o m o g e n e o u s

S u p e r c o n d u c t o r s - 1 9 7 9 , D. _U. G u b s e r , T. L. F r a n c a v i l l a , J.R.

L e i b o w i t z a n d S.A. W o l f , e d i t o r s , ( A m e r i c a n I n s t i t u t e o f P h y s i c s , New Y o r k ) 1 9 8 0 .

5. FALCO, C. M. a n d SCHULLER, I. K., i n N o v e l M a t e r i a l s a n d T e c h n i q u e s i n C o n d e n s e d M a t t e r , G.W. C r a b t r e e a n d P.

V a s h i s h t a , e d s . , ( N o r t h - H o l l a n d , New Y o r k ) 1 9 8 2 .

6 . LOWE, W. P., BARBEE,JR, T.W., GEBALLE, T. H. a n d M C W H A N , D.B., P h y s . R e v . B 2 4 , ( 1 9 8 1 ) 6 1 9 3 .

7 . DURBIN, S. M., CUNNINGHAM, J.E., MOCHEL, M.F. a n d FLYNN,C.P., J.

P h y s . F: M e t a l P h y s . 1 1 , ( 1 9 8 1 ) L 2 2 3 .

8. H E R T E L , G., MCWHAN, D.B. a n d R O W E L L , J.M., i n

S u p e r c o n d u c t i v i t y i n d - a n d f - B a n d M e t a l s , W. B u c k e l a n d W.

W e b e r , e d s . ( K e r n s f o r s c h u n g s z e n t r u m K a r l s r u h e ) 1 9 8 2 . 9 . I a m g r a t e f u l t o D r . J o h n R o w e l 1 f o r p o i n t i n g o u t t h e

u s e f u l n e s s o f s u c h a p l o t f o r t h e u s u a l B C C ( l l O ) / F C C ( l l l ) o r i e n t a t i o n s .

1 0 . S C H U L L E R , I . K . , P h y s . R e v . L e t t e r s 44 ( 1 9 8 0 ) 1 5 9 7 . 1 1 . KHAN, M. R., C H U N , C. S . L., F E L C H E R , G., G R I M S D I T C H , M.,

K U E N Y , A., F A L C O , C. M. a n d S C H U L L E R , I. K., P h y s . R e v . t o b e p u b l i s h e d ) .

1 2 . G R I M S D I T C H , M., K H A N , M. R., K U E N Y , A. a n d S C H U L L E R , I.

K . , P h y s . R e v . L e t t e r s 51 ( 1 9 8 3 ) 4 9 8 .

1 3 . MAYADAS, A. F . a n d S H A T Z K E S , M., P h y s . R e v . B 1 ( 1 9 7 0 ) 1 3 8 2 .

1 4 . M O L A , E. E . a n d H E R A S , J. M., T h i n S o l i d F i l m s 1 8 ( 1 9 7 3 ) 1 3 7 .

1 5 . T E L L I E R , C.R. AND T O S S E R , A.J., S i z e E f f e c t s i n T h i n F i l m s , ( E l s e v i e r , New Y o r k ) 1 9 8 2