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Radiation Effects Lerters, 1979, Vol. 50,pp. 3-7
0142-2448/79/5001-0003$04.50/0
@ 1979, Gordon and Breach, Science Publishers, Inc.
Printed in the United States of America
ENERGY DEPENDENCE OF THE MOLECULAR EFFECT I N SPUTTERING
A.R.OLIVA-FLORIO:
E.V.ALONS0,
R.A.BARAGIOLA,
J.FERRON
and M.M.JAKAS
C e n t r o At6mico B a r i l o c h e ' f - I n s t i t u t o B a l s e i r o t #
8400
-
S.C.
d e Bariloche, R.N.,
Argentina.
(Received for Publication October 30, 1979)
t
t
ABSTRACT: We r e p o r t measurements of s p u t t e r i n g y i e l d s o f Au f o r Xe and Xe2
impact i n t h e energy r a n g e 1-50 keV. I t was found t h a t n o n - l i n e a r e f f e c t s
e x i s t w e l l o u t s i d e t h e r a n g e p r e d i c t e d i n a r e c e n t t h e r m a l s p i k e model.
Many s p u t t e r i n g e x p e r i m e n t s have been a n a l y z e d u s i n g t h e l i n e a r
COL
l i s i o n c a s c a d e t h e o r y , however, s e v e r a l w o r k e r s have r e p o r t e d e v i d e n c e
t h a t p o i n t s o u t t h a t i n c e r t a i n c o n d i t i o n s t h e v a l i d i t y range o f t h e
l i n e a r c a s c a d e a p p r o x i m a t i o n i s e x c e e d e d , f o r example, when t h e e n e r g y
d e n s i t y i n t h e c a s c a d e r e g i o n i s h i g h enough as n o t t o a l l o w any l o n g e r
t o assume as n e g l i g i b l e t h e p r o b a b i l i t y o f c o l l i s i o n between mxringatams.
T h i s c o n d i t i o n i s e a s i l y r e a c h e d u s i n g heavy m o l e c u l a r i o n beams,
and r e s u l t s u s i n g t h e s e p r o j e c t i l e s have been r e p o r t e d 1-4
.
To
have
some f u r t h e r i n s i g h t i n t h e e n e r g y dependence o f t h e s e mn-linear effects,
w e have measured t h e s p u t t e r i n g y i e l d of b o t h atomic and d i a t o m i c X e
i n c i d e n t on A u a t e n e r g i e s between 1 and 50 keV f o r X e and 2 . 5 and 1 2
keV/atom f o r X e 2 , u s i n g a q u a r t z c r y s t a l o s c i l l a t o r t e c h n i q u e . The g o l d
was e v a p o r a t e d o n t h e f a c e o f t h e q u a r t z c r y s t a l a t a p r e s s u r e of 8 x
lo-' T o r r o r less. The c r y s t a l s u s e d were AT c u t and s i m i l a r t o t h o s e
used by E e r N i s s e 5 , and t h e s p u t t e r i n g y i e l d w a s c a l c u l a t e d as:
s =
k Nav
Af
M1
+-
M2Nl
M2
where k i s t h e c a l i b r a t i o n c o n s t a n t o f t h e c r y s t a l , measured to be 1 . 7 8
-2
-1
x 10-8g cm Hz , A f i s t h e f r e q u e n c y change and Nav i s Avogadro's num_
b e r . M1 and M 2 a r e t h e masses o f i n c i d e n t and t a r g e t atoms, respectively,
and N1
i s t h e number o f i n c i d e n t atoms p e r u n i t area. The t e r m M1/M2
3
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4
A. R. OLIVA-FLORIA, E. V. ALONSO, R. A. BARAGIOLA, J. FERRON and hi. hi. J A M S
measurements by o t h e r work
er s 3' 7-11 f o r X e on Au.The
100 -
1
I
I
I
t
I
I
I
1
-
a
sponding y i e l d and e n e r g y
p e r i n c i d e n t atom. I t i s
found t h a t d i f f e r e n c e s
w
lie
within the variations int r o d u c e d by t h e d i f f e r e n t
measurement f l u e n c e s 3 , 5
with previous
data
.
~
-
L
"J
10 -
1
z
Z
w
l
s
j
P'
-
A
-
-
A
3
% 1-
l
0
0
measured
a r e p l o t t ed di a taotmtihc ey correields
I
A
I l l
1
mate of t h e sputterirg y i e l d
in the linear collision
!
I
I
l
l
I
I
1 -
ENEkGY PER ATOY [keV)
cascade
choose t h e one g i v e n by
Figure 1 S p u t t e r i n g y i e l d s p e r atom f o r Au bombard
Sigmund's theory
i n g 1 2 , which i s :
b e r g and Wehner8;0 fB Andersen and Bay3; V Nenado-
Of
ed with Xe and Xe2. '
I Almen and Bruce7; A Rosem9
v i c e t a1 ;0
Vries";
X Sn(E) a
S(E) =
UO
8
EerNisse"
; 0 Szymonski and de
Xe and O X e 2 , t h i s work; -Sigmund's
theoretical prediction.
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ENERGY DEPENDENCE OF THE MOLECULAR EFFECT IN SPUTTERING
5
where X i s a c a l c u l a b l e m a t e r i a l c o n s t a n t , U, i s t h e s u r f a c e b i n d i n g
e n e r g y , t a k e n as 3.8 e V f o r g o i d l 3 , S,(E)
i s t h e n u c l e a r s t o p p i n g power,
which was c a l c u l a t e d by Lindhard e t a l l 4 , and a i s p l o t t e d i n r e f . 1 2 .
The c a l c u l a t e d s p u t t e r i n g y i e l d s a r e a l s o shown i n F i g . 1 , and when comp a r e d w i t h t h e e x p e r i m e n t a l d a t a , it i s s e e n t h a t t h e agreement i s within
t h e s t a t e d a c c u r a c y of t h e t h e o r y , a l t h o u g h t h e r e i s a d i f f e r e n c e i n
t h e e n e r g y dependence similar t o what was found i n o t h e r cases (see,
f o r example, f i g s . 1 7 and 1 8 of r e f . 1 2 ) .
T h e r e i s no p r e v i o u s l y p u b l i s h e d d a t a f o r X e 2 on Au. However, w e
may compare o u r o b s e r v e d enhancement i n t h e y i e l d s € o r m o l e c u l a r i o n s
w i t h r e p o r t e d d a t a on i o n s of similar mass, T e 3 and Sb4 , i n c i d e n t
a l s o on Au. The r a t i o o f m o l e c u l a r t o atomic y i e l d s are c o m p a r e d i n F i g . 2
a s a f u n c t i o n o f t h e i n c i d e n t e n e r g y p e r atom i n r e d u c e d u n i t s 1 4
In
t h i s p r e s e n t a t i o n , t h e r e seems t o b e a d e f i n i t e e n e r g y d e p e n d e n c e , c h a r a c t e r i z e d by a r a n g e E < 0 . 0 1 , where n o n l i n e a r e f f e c t s a r e l a r g e r t h e
h i g h e r t h e e n e r g y , and by a r e g i o n between E = 0.02 and t h e h i g h e s t
e n e r g y where d a t a e x i s t s , which p r e s e n t s a broad maximun.
A t h e r m a l s p i k e model h a s been d e v e l o p e d t o p r e d i c t t h e e n e r g y range
.
where t h e n o n l i n e a r
e f f e c t s should a f f e c t
15
the sputtering yield
I
1
I
.
1
UT
z
E!
L
T h i s model h a s been a p -
i,
W
m-
plied f o r X e incident
on A u , and e x t e n d e d f o r
X e 2 on Au by assuming
t h a t t h e energy p e r m i t
volume i n t h e c a s c a d e
i s t w i c e t h a t of t h e
a t o m i c case, which cor-
[L
Q
U
I
0.001
0.01
r e s p o n d s t o assuming a
100% overlap i n t h e cas
0.1
ENERGY PER ATOM ( E UNITS)
w
r!
U
3
z
c a d e s of t h e i n d i v i d u a l
p r o j e c t i l e s , and t h u s
Figure 2
The molecular-to atomic y i e l d r a t i o s of Au
r e p r e s e n t s a n upper bud as a f u n c t i o n of t h e reduced energy14, for: 0 Xe,
t o t h e n o n l i n e a r effects t h i s work; 0 Te, Andersen and Bay3;
Sb, Thompson
e x p e c t e d from t h i s mkiel. and J o h a r 4 .
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6
A. R. OLIVA-FLORIA, E. V. ALONSO, R. A. BARAGIOLA, J. FERRON and M. M. JAKAS
I n t h i s case, t h e h e a t c o n d u c t i o n equation s u p p l i e s u s w i t h t h e s c a l i n g
f a c t o r T ~ ~ ~ T~~~~
= J Zf o r t h e t i m e c o n s t a n t o f t h e c a s c a d e , w h i l e t h e
slowing down t i m e o f t h e p r o j e c t i l e , T,, and r e c o i l atoms, T', a r e
t a k e n t o b e t h e same f o r a t o m i c and m o l e c u l a r p r o j e c t i l e s .
The r e s u l t s o f t h e s e c a l c u l a t i o n s a r e p l o t t e d i n F i g . 3 , where w e
c a n see t h a t t h e mean energyper atom
i n t h e c a s c a d e e x c e e d s U, for energies
l e s s t h a n 9 2 KeV f o r X e and 1 7 5 KeV/
atom f o r X e 2 ( ~ = 0 . 0 7 4 and 0.14 res p e c t i v e l y ) and t h e time c o n s t a n t o f
t h e cascade exceeds both
and T'
f o r e n e r g i e s h i g h e r t h a n 1 6 and 1 3
K e V / a t o m ( E = 0.13 and 0 . 0 1 0 ) f o r X e
T,
and X e 2 r e s p e c t i v e l y . T h u s , a c c o r d i n g
-10
t o t h i s model, w e s h o u l d e x p e c t a
s i g n i f i c a n t c o n t r i b u t i o n o f mnlinear
-13
effects to the sputtering yield i n
t h e r a n g e between 1 3 and 1 7 5 KeV/
atom f o r X e 2 , and 1 6 and 9 2 KeV f o r
X e . F o r atomic X e , t h e r e i s no clear
i n c r e a s e o r d e v i a t i o n on t h e e n e r g y
dependence t h a t e n a b l e s u s t o d e f i n e
a t h r e s h o l d f o r t h e a p p e a r a n c e of
n o n l i n e a r e f f e c t s , and f u r t h e r m o r e ,
as w a s mentioned b e f o r e , t h e r e i s
good agreement in the absolute values
of o u r measured d a t a and c a l c u l a t e d
yields.
Examining F i g . 2 i t i s e v i d e n t
t h a t f o r m o l e c u l a r p r o j e c t i l e s non-
-15
1
10
100
10
E IKEV)
Figure 3 Energy d e n s i t y and time c o n s t a n t
i n t h e thermal spike15 vs i n c i d e n t atom
t
energy f o r Au bombarded with Xe' and Xe2.
To is t h e slowing down t i m e of t h e p r o j e c
t i l e and U, t h e s u r f a c e binding energy.
l i n e a r e f f e c t s t a k e p l a c e a t e n e r g i e s which a r e w e l l o u t s i d e t h e r a n g e
p r e d i c t e d by t h e t h e r m a l s p i k e model. W e a t t r i b u t e t h i s f a i l u r e of t h e
model t o t h e no c o n s i d e r a t i o n of d e n s e s u b c a s c a d e s 1 6 , which a r e c o n n e c
t e d w i t h f l u c t u a t i o n s i n t h e d e p o s i t i o n o f e n e r g y , whose m a g n i t u d e a t
t h e surface, according t o a recent c a l ~ u l a t i o n ~
would
~ , b e of t h e same
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ENERGY DEPENDENCE OF THE MOLECULAR EFFECTS ON SPUlTERINC
I
order as the mean value of the deposited energy, as well as to the
small number of atoms involved in the cascade at low energies, which
makes the applicability of the thermal approach questionable.
Acknowledgements
This work was supported in part by the Multinational Program in
Physics of the Organization of American States.
We thank Dr.E.P.EerNisse for providing us with the crystals used
in this work.
References
*
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t Comisidn Nacional de Energfa Atemica
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