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Reduced electronic scattering in dechannelling
PHYSICS L E T T E R S
Volume 33A, number 7
by the X - r a y e x p e r i m e n t [4] and the r a t i o of stopping p o wer between for aligned and r a n d o m b e a m s , ~ = 0.61 [5], w e r e used. The r e s u l t shows that the dechanneling c o e f f i c i e n t is r e p r e sented by eq. (3) w h e r e A = 0.74 ,~-2 and B = 0.0076. The t h e o r e t i c a l value of A has been c a l c u l a t e d by Lindhard and we get A ~ 3.5 i - 2 in the p r e s ent cas e. The c a l c u l a t e d value i s f a i r l y l a r g e r than the o b s e r v e d one. We c a l c u l a t e d the e l e c t r o n i c p a r t and obtained B = B l n / l e , l e being the path length f o r which the b e a m d i v e r g e n c e b e c o m e s equal to the c r i t i c a l angle only by e l e c t r o n i c c o l l i s i o n in r a n d o m orientation. In the p r e s e n t c a s e , the e s t i m a t e d value of B is 0.0083 which a g r e e s v e r y well with o b s e r v e d one. The
REDUCED
ELECTRONIC
14 D e c e m b e r 1970
d e t a i l s of this work will be published e l s e w h e r e . We would like to thank P r o f e s s o r K. Hisatake of Tokyo Institute of Technology f o r his support and e n c o u r a g e m e n t of this work.
References
[1] J. Lindhard, Mat. Fys. Medd. Dan. Vid. Selsk. 34 no. 14 (1965). [2] C. Ellegaard and N. O. Lassen, Mat. Fys. Medd. Dan. Vid. Selsk. 35 no. 16 (1967). [3] F. Fujimoto, K. Komaki and H. Nakayama, to be published. [4] B. W. Batterman and D. R. Chipman, Phys. Rev. 127 (1962) 690. [5] B. R. Appelton, C. Erginsoy and W. M. Gibson, Phys. Rev. 161 (1967) 330.
SCATTERING
IN D E C H A N N E L L I N G
S. U. CAMPISANO, G. FOTI, F. GRASSO, R. QUATTROCCHI and E. RIMINI I s t i t u t o di S t r u t t u r a della M a t e r i a dell' Universittl, Catania Gruppo N a z i o n a l e di S t r u t t u r a della M a t e r i a del C. N. R. Istituto N a z i o n a l e di F i s i c a N u c l e a t e - Gruppo di Catania, Italy
Received 3 November 1970
Direct information on the contribution of electronic multiple scattering to dechanne[ling is obtained by measuring the H+ and D+ dechannelled fraction in Si. The experimental results are compared with the theory. The dechannelling, which c o n c e r n s with p a r t i c l e t r a n s i t o n s f r o m the aligned to the random b e a m , is a s e c o n d a r y channelling phenomenon; it i m p l i e s indeed the non c o n s e r v a t i o n of the t r a n s v e r s e e n e r g y of a channelled p a r t i c l e [1]. The i n c r e a s e in t r a n s v e r s e e n e r g y is mainly due to r e d u c e d n u c l e a r and e l e c t r o n i c multiple s c a t t e r i n g s . The f o r m e r is caused by the f o r c e field fluctuations p r o d u c e d by t h e r m a l v i b r a t i o n s of the c r y s t a l a t o m s ; it can be t h e r e f o r e i n v e s t i gated by changing the c r y s t a l t e m p e r a t u r e . As p r e v i o u s l y r e p o r t e d [2-4], the d e c h a n n e l l e d f r a c tion X c o m e s out to be independent of t e m p e r a t u r e if plotted v e r s u s zp 2, w h e r e z is the d e channelling depth and p2 is the m e a n s q u a r e v i b r a t i o n a l amplitude n o r m a l to the s t r in g . It has been r e m a r k e d h o w e v e r [1] that the e l e c t r o n i c s c a t t e r i n g f o r a channelled p a r t i c l e is not negligible c o m p a r e d with the n u c l e a r one: it
d e t e r m i n e s indeed the dechannelled f r a c t i o n at l a r g e z [5], acting as a "lift" for the i n i t i al l y w e l l channelled p a r t i c l e s , b r i n g i n g them to a suff i ci en t high t r a n s v e r s e e n e r g y to e x p e r i e n c e nuclear scattering. Although the e l e c t r o n i c contribution to d e channelling is a l m o s t independent of the t a r g e t t e m p e r a t u r e , the zp 2 dependence of the d e channelled f r a c t i o n r e m a i n s . This is r e l a t e d to the r e d u c t i o n , with i n c r e a s i n g t e m p e r a t u r e , of the c r i t i c a l angle and then of the m a x i m u m a l lowed t r a n s v e r s e e n e r g y [3,4] f o r a channelled particle. To obtain d i r e c t i n f o r m a t i o n on the e l e c t r o n i c s c a t t e r i n g the dechannelled f r a c t i o n s of H + and D + impinging along the (111) axis of Si have been m e a s u r e d by the b a c k - s c a t t e r i n g [4] technique. Some typical r e s u l t s a r e r e p o r t e d in fig. 1 f o r d i f f e r e n t ion e n e r g i e s and c r y s t a l t e m p e r a t u r e s . 433
Volume 33A, number 7
PHYSICS
I
I
'
A X
0.3
0.3 MeV
z o ~,
423OK ~' 0.2
77"
+.,
. o
y
.
o o H;//
. ° .
m, - / nl
,.,z z
o
D+ "
/
~ ,,./" •
/
a 6 M,v
I
i
I
2
i
I
3
, [~m] Fig. 1. Dechannelled fraction for protons a n d d e u t o n s on Si {111} v e r s u s penetration depth. Dots and full lines are experimental and theoretieal r e s u l t s for deutons, while c i r e l e s and dashed lines r e f e r to protons.
T h e d e c h a n n e l l e d f r a c t i o n s f o r p r o t o n s and d e u t o n s d i f f e r b e y o n d e x p e r i m e n t a l e r r o r s ; the m e a s u r e d f r a c t i o n at t h e s a m e d e p t h i s l o w e r f o r D + t h a n f o r H +. I n f o r m a t i o n on t h e e l e c t r o n i c s c a t t e r i n g c a n not b e o b t a i n e d e x p e r i m e n t a l l y by v a r y i n g t h e a t o m i c n u m b e r s of p r o j e c t i l e a n d t a r g e t a t o m s , b e c a u s e t h i s p r o d u c e s c h a n g e s in b o t h e l e c t r o n i c a n d n u c l e a r s c a t t e r i n g . It h a s b e e n o b t a i n e d h e r e by v a r y i n g only the v e l o c i t y of the p r o j e c t i l e i o n s i . e . u s i n g p r o t o n s and d e u t o n s of t h e s a m e e n e r g y ; in f a c t the n u c l e a r s c a t t e r i n g d e p e n d s on the e n e r gy, w h i l e the e l e c t r o n i c c r o s s s e c t i o n d e p e n d s a l s o on the ion v e l o c i t y t h r o u g h t h e f a c t o r L e = log(2mv2/I): w h e r e m i s the e l e c t r o n i c m a s s , v t h e p r o j e c t i l e v e l o c i t y and I the a v e r a g e e x c i t a t i o n p o t e n t i a l of t h e t a r g e t . F i g . 1 s h o w s t h a t the e x p e r i m e n t a l p o i n t s a r e a l m o s t c o i n c i d e n t f o r low p e n e t r a t i o n , w h i l e t h e y d i v e r g e w i t h i n c r e a s i n g z. T h e r e s u l t s a g r e e w i t h t h e a b o v e d e s c r i p t i o n b e c a u s e of the r o l e p l a y e d by e l e c t r o n i c s c a t t e r i n g at l a r g e d e p t h ,
434
H +
D+/H +
0.3 0.6
0.85 1.54
1.52 2.21
0.56 0.70
~+
/
1
D~
.a-.
~
o
I
E ne rgy
(MeV)
i.J Q
0
Table 1 l e values
•
/o H+
~ ,y/
14 D e c e m b e r 1970
I
si (111>
r./
Q L,J
I
LETTERS
a n d of the s t r o n g v a r i a t i o n in t h e c o r r e s p o n d i n g c a l c u l a t e d L e v a l u e s ( s e e t a b l e 1). The e x p e r i m e n t a l r e s u l t s a r e c o m p a r e d in fig. 1 w i t h t h o s e c a l c u l a t e d f o r p r o t o n s a c c o r d i n g to r e f . [4] in t e r m s of a s t e a d y i n c r e a s e in t h e transverse energy, accounting for both electronic and n u c l e a r s c a t t e r i n g . The c a l c u l a t i o n s f o r d e u t o n s h a v e b e e n c a r r i e d out in t h e s a m e way c h a n g i n g only the e l e c t r o n i c c o n t r i b u t i o n a c c o r d ing to L e v a l u e s of t a b l e 1. The a g r e e m e n t b e t w e e n e x p e r i m e n t s and t h e o r y , b o t h in g e n e r a l t r e n d and in m a g n i t u d e s e e m s to g i v e a s i g n i f i c a n t t e s t of the p r o p o s e d interpretation. The a u t h o r s a r e i n d e b t e d to P r o f s . J. L i n d h a r d a n d J. A. D a v i e s f o r u s e f u l d i s c u s s i o n s d u r i n g the last Aarhus Meeting.
References [1] J. Lindhard, Dan. Vid. Selsk. Mat. Fys. Medd. 34, no. 1 (1965). [2] G. Foti, F . G r a s s o and E. Rimini, Lett. N.C. 1 {1969) 941. [3] G. Foti, F . G r a s s o , R. Quattrocchi, I . F . Q u e r e i a and E. Rimini, P , o c . Fifth Yugoslav Syrup. and Summer School on the P h y s i c s of ionized gases. Herceg Novi July 1970, p. 47. [4] G. Foti, F . G r a s s o . R. Quattrocchi a n d E . Rimini, T e m p e r a t u r e and energy dependence of proton dechannelling in silicon, submitted to Phys. Rev. [5] G. Foti, F . G r a s s o . R. Quattroechi, I . F . Q u e r c i a and E, Rimini, Lett. N.C. 4 (1970) 707.
Volume 33A, number 7
by the X - r a y e x p e r i m e n t [4] and the r a t i o of stopping p o wer between for aligned and r a n d o m b e a m s , ~ = 0.61 [5], w e r e used. The r e s u l t shows that the dechanneling c o e f f i c i e n t is r e p r e sented by eq. (3) w h e r e A = 0.74 ,~-2 and B = 0.0076. The t h e o r e t i c a l value of A has been c a l c u l a t e d by Lindhard and we get A ~ 3.5 i - 2 in the p r e s ent cas e. The c a l c u l a t e d value i s f a i r l y l a r g e r than the o b s e r v e d one. We c a l c u l a t e d the e l e c t r o n i c p a r t and obtained B = B l n / l e , l e being the path length f o r which the b e a m d i v e r g e n c e b e c o m e s equal to the c r i t i c a l angle only by e l e c t r o n i c c o l l i s i o n in r a n d o m orientation. In the p r e s e n t c a s e , the e s t i m a t e d value of B is 0.0083 which a g r e e s v e r y well with o b s e r v e d one. The
REDUCED
ELECTRONIC
14 D e c e m b e r 1970
d e t a i l s of this work will be published e l s e w h e r e . We would like to thank P r o f e s s o r K. Hisatake of Tokyo Institute of Technology f o r his support and e n c o u r a g e m e n t of this work.
References
[1] J. Lindhard, Mat. Fys. Medd. Dan. Vid. Selsk. 34 no. 14 (1965). [2] C. Ellegaard and N. O. Lassen, Mat. Fys. Medd. Dan. Vid. Selsk. 35 no. 16 (1967). [3] F. Fujimoto, K. Komaki and H. Nakayama, to be published. [4] B. W. Batterman and D. R. Chipman, Phys. Rev. 127 (1962) 690. [5] B. R. Appelton, C. Erginsoy and W. M. Gibson, Phys. Rev. 161 (1967) 330.
SCATTERING
IN D E C H A N N E L L I N G
S. U. CAMPISANO, G. FOTI, F. GRASSO, R. QUATTROCCHI and E. RIMINI I s t i t u t o di S t r u t t u r a della M a t e r i a dell' Universittl, Catania Gruppo N a z i o n a l e di S t r u t t u r a della M a t e r i a del C. N. R. Istituto N a z i o n a l e di F i s i c a N u c l e a t e - Gruppo di Catania, Italy
Received 3 November 1970
Direct information on the contribution of electronic multiple scattering to dechanne[ling is obtained by measuring the H+ and D+ dechannelled fraction in Si. The experimental results are compared with the theory. The dechannelling, which c o n c e r n s with p a r t i c l e t r a n s i t o n s f r o m the aligned to the random b e a m , is a s e c o n d a r y channelling phenomenon; it i m p l i e s indeed the non c o n s e r v a t i o n of the t r a n s v e r s e e n e r g y of a channelled p a r t i c l e [1]. The i n c r e a s e in t r a n s v e r s e e n e r g y is mainly due to r e d u c e d n u c l e a r and e l e c t r o n i c multiple s c a t t e r i n g s . The f o r m e r is caused by the f o r c e field fluctuations p r o d u c e d by t h e r m a l v i b r a t i o n s of the c r y s t a l a t o m s ; it can be t h e r e f o r e i n v e s t i gated by changing the c r y s t a l t e m p e r a t u r e . As p r e v i o u s l y r e p o r t e d [2-4], the d e c h a n n e l l e d f r a c tion X c o m e s out to be independent of t e m p e r a t u r e if plotted v e r s u s zp 2, w h e r e z is the d e channelling depth and p2 is the m e a n s q u a r e v i b r a t i o n a l amplitude n o r m a l to the s t r in g . It has been r e m a r k e d h o w e v e r [1] that the e l e c t r o n i c s c a t t e r i n g f o r a channelled p a r t i c l e is not negligible c o m p a r e d with the n u c l e a r one: it
d e t e r m i n e s indeed the dechannelled f r a c t i o n at l a r g e z [5], acting as a "lift" for the i n i t i al l y w e l l channelled p a r t i c l e s , b r i n g i n g them to a suff i ci en t high t r a n s v e r s e e n e r g y to e x p e r i e n c e nuclear scattering. Although the e l e c t r o n i c contribution to d e channelling is a l m o s t independent of the t a r g e t t e m p e r a t u r e , the zp 2 dependence of the d e channelled f r a c t i o n r e m a i n s . This is r e l a t e d to the r e d u c t i o n , with i n c r e a s i n g t e m p e r a t u r e , of the c r i t i c a l angle and then of the m a x i m u m a l lowed t r a n s v e r s e e n e r g y [3,4] f o r a channelled particle. To obtain d i r e c t i n f o r m a t i o n on the e l e c t r o n i c s c a t t e r i n g the dechannelled f r a c t i o n s of H + and D + impinging along the (111) axis of Si have been m e a s u r e d by the b a c k - s c a t t e r i n g [4] technique. Some typical r e s u l t s a r e r e p o r t e d in fig. 1 f o r d i f f e r e n t ion e n e r g i e s and c r y s t a l t e m p e r a t u r e s . 433
Volume 33A, number 7
PHYSICS
I
I
'
A X
0.3
0.3 MeV
z o ~,
423OK ~' 0.2
77"
+.,
. o
y
.
o o H;//
. ° .
m, - / nl
,.,z z
o
D+ "
/
~ ,,./" •
/
a 6 M,v
I
i
I
2
i
I
3
, [~m] Fig. 1. Dechannelled fraction for protons a n d d e u t o n s on Si {111} v e r s u s penetration depth. Dots and full lines are experimental and theoretieal r e s u l t s for deutons, while c i r e l e s and dashed lines r e f e r to protons.
T h e d e c h a n n e l l e d f r a c t i o n s f o r p r o t o n s and d e u t o n s d i f f e r b e y o n d e x p e r i m e n t a l e r r o r s ; the m e a s u r e d f r a c t i o n at t h e s a m e d e p t h i s l o w e r f o r D + t h a n f o r H +. I n f o r m a t i o n on t h e e l e c t r o n i c s c a t t e r i n g c a n not b e o b t a i n e d e x p e r i m e n t a l l y by v a r y i n g t h e a t o m i c n u m b e r s of p r o j e c t i l e a n d t a r g e t a t o m s , b e c a u s e t h i s p r o d u c e s c h a n g e s in b o t h e l e c t r o n i c a n d n u c l e a r s c a t t e r i n g . It h a s b e e n o b t a i n e d h e r e by v a r y i n g only the v e l o c i t y of the p r o j e c t i l e i o n s i . e . u s i n g p r o t o n s and d e u t o n s of t h e s a m e e n e r g y ; in f a c t the n u c l e a r s c a t t e r i n g d e p e n d s on the e n e r gy, w h i l e the e l e c t r o n i c c r o s s s e c t i o n d e p e n d s a l s o on the ion v e l o c i t y t h r o u g h t h e f a c t o r L e = log(2mv2/I): w h e r e m i s the e l e c t r o n i c m a s s , v t h e p r o j e c t i l e v e l o c i t y and I the a v e r a g e e x c i t a t i o n p o t e n t i a l of t h e t a r g e t . F i g . 1 s h o w s t h a t the e x p e r i m e n t a l p o i n t s a r e a l m o s t c o i n c i d e n t f o r low p e n e t r a t i o n , w h i l e t h e y d i v e r g e w i t h i n c r e a s i n g z. T h e r e s u l t s a g r e e w i t h t h e a b o v e d e s c r i p t i o n b e c a u s e of the r o l e p l a y e d by e l e c t r o n i c s c a t t e r i n g at l a r g e d e p t h ,
434
H +
D+/H +
0.3 0.6
0.85 1.54
1.52 2.21
0.56 0.70
~+
/
1
D~
.a-.
~
o
I
E ne rgy
(MeV)
i.J Q
0
Table 1 l e values
•
/o H+
~ ,y/
14 D e c e m b e r 1970
I
si (111>
r./
Q L,J
I
LETTERS
a n d of the s t r o n g v a r i a t i o n in t h e c o r r e s p o n d i n g c a l c u l a t e d L e v a l u e s ( s e e t a b l e 1). The e x p e r i m e n t a l r e s u l t s a r e c o m p a r e d in fig. 1 w i t h t h o s e c a l c u l a t e d f o r p r o t o n s a c c o r d i n g to r e f . [4] in t e r m s of a s t e a d y i n c r e a s e in t h e transverse energy, accounting for both electronic and n u c l e a r s c a t t e r i n g . The c a l c u l a t i o n s f o r d e u t o n s h a v e b e e n c a r r i e d out in t h e s a m e way c h a n g i n g only the e l e c t r o n i c c o n t r i b u t i o n a c c o r d ing to L e v a l u e s of t a b l e 1. The a g r e e m e n t b e t w e e n e x p e r i m e n t s and t h e o r y , b o t h in g e n e r a l t r e n d and in m a g n i t u d e s e e m s to g i v e a s i g n i f i c a n t t e s t of the p r o p o s e d interpretation. The a u t h o r s a r e i n d e b t e d to P r o f s . J. L i n d h a r d a n d J. A. D a v i e s f o r u s e f u l d i s c u s s i o n s d u r i n g the last Aarhus Meeting.
References [1] J. Lindhard, Dan. Vid. Selsk. Mat. Fys. Medd. 34, no. 1 (1965). [2] G. Foti, F . G r a s s o and E. Rimini, Lett. N.C. 1 {1969) 941. [3] G. Foti, F . G r a s s o , R. Quattrocchi, I . F . Q u e r e i a and E. Rimini, P , o c . Fifth Yugoslav Syrup. and Summer School on the P h y s i c s of ionized gases. Herceg Novi July 1970, p. 47. [4] G. Foti, F . G r a s s o . R. Quattrocchi a n d E . Rimini, T e m p e r a t u r e and energy dependence of proton dechannelling in silicon, submitted to Phys. Rev. [5] G. Foti, F . G r a s s o . R. Quattroechi, I . F . Q u e r c i a and E, Rimini, Lett. N.C. 4 (1970) 707.