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Energy loss and straggling of heavy ions by nuclear interactions in silicon
NUCLEAR
INSTRUMENTS
AND
METHODS
132 (1976) 273-279; ©
NORTH-HOLLAND
PUBLISHING
CO.
ENERGY L O S S AND STRAGGLING OF HEAVY IONS BY NUCLEAR INTERACTIONS IN SILICON A. G R O B , J . J . G R O B a n d P. S I F F E R T
Centre de Recherches Nucldaires, P R E N et Universitd Lou& Pasteur, 67037 Strasbourg Cedex, France Heavy ion channeling detection p e r f o r m e d in aligned silicon detectors (ion implanted a n d surface barrier) constitutes a procedure to determine energy loss a n d straggling in nuclear collisions when associated with r a n d o m oriented m e a s u r e m e n t s . Results for 12C+, 14N+, 160+, 2°Ne+, 28Si+, 32S+, 4°Ar+ in the energy range 300-3000 keV are presented. T h e y fit roughly L i n d h a r d ' s previsions but s h o w small discrepancies which are increasing with atomic n u m b e r Z1 o f the projectile and with energy. T h e total energy s p e n t by the ions o f the s a m e initial velocity does n o t oscillate as a function o f Z1 as does the electronic stopping power.
1. Introduction
Consider a heavy particle with initial energy Eo, which is stopped in a solid target, it creates charge carriers by electronic interactions and recoil atoms during nuclear collisions. These secondary species are able either to ionize or to displace other atoms which again, if they have sufficient energy, can continue the cascade. Finally, even if the different steps are not independent, a part v(Eo) of the ions initial energy is spent to the medium through nuclear collisions, whereas the other r/(Eo) through electronic interactions, so that E 0 = q(Eo)+ v(Eo). Theoretical estimations of this energy partition have been proposed by several authors 1'2) and especially by Lindhard et al.3). Experimentally, the situation is less satisfactory, mainly as a result of the absence of a suitable measurement procedure. Indeed, fission fragments have been mainly used in connection with semiconductor detectors4'5). Since only the electronic collisions lead to charge carrier creation in this kind of detectors, a "pulse height defect" (PHD) is observed (compared to ~t-particles) which is assumed to be equal to the energy spent in nuclear interactions. Unfortunately, other contributions to the P H D exist, which are generally neglected, especially: - the counter entrance window (dead layer) in which the charge carrier lifetime is too small to allow them to diffuse into the high field zone, - charge recombination along the track of the ion or trapping in deep levels, - a possible change in the energy necessary to create an electron-hole pair between light and heavy particles. in a previous paper6), we have presented a precise experimental method to evaluate the amount of energy lost through electronic and nuclear collisions during the slowing down of heavy ions in thick silicon targets.
In principle, this approach is valid for any ion (Z 1, M~) absorbed in a solid state detector (currently: silicon germanium, cadmium telluride, diamond). Here, we have studied, by this new method, the mean nuclear energy loss v ( E ) in silicon and the corresponding energy straggling A v ( E ) for 12C+, 14N+, 160+, 2°Ne+, 28Si+, 32S+, 4°Ar+ ions with energies ranging from 300 to 3000 keV. 2. Heavy ion detection in solid state counters in random and channeling conditions
The response of a solid state counter to a heavy ion beam depends strongly on its direction with respect to the detectors cristallographic axes or planes. Under random direction the counter presents a pulse height defect A E (with respect to protons of equivalent energy) given by 7. 8): A E = A E w + A E R + v[Eo - ( A E w + A E R ) ] ,
(1)
where A E w is the amount of energy lost in the counters dead layer, A E R a loss due to charge recombination and carrier trapping in the depletion region of the diode, v [ E o - ( A E w + A E R ) ] the energy lost through non-ionizing nuclear processes. When the beam enters the detector along a channelin9 direction it moves through low density regions without important nuclear interactions with the atoms forming the "walls" of the channel. In other words, the minimal approach of a particle focused between planes or strings is an impact parameter such that the transmitted energy to the stopping medium through elastic collisions is negligible. Thus, the channeled ions lose their energy only by electronic interactions. Consequently, the pulse height defect A E ' reduces to: AE' = A E w + A E R .
(2) V. D A M A G E
274
A. G R O B et al.
Eqs. (l) and (2) suppose that the charge collection is the same in random and aligned directions. Furthermore, they assume that the energy going into other processes (escaping X-rays for example) can be neglected in a first approximation. An illustration of the pulse distribution under random and aligned bombardment of a silicon detector by 2 MeV 160+ ions is given in fig. 1. In comparison to the energy reference peak given by 2 MeV 4He+ ions (fig. 2a), the random condition recorded 160+ distribution (fig. 2b) shows a P H D given by eq. (1). Along the (111) direction the recorded spectrum (fig. 2c) exhibits a higher energy "aligned" peak, with a P H D
a)
2000 keV
He +
b} 2000 keY 0 +
random detection
given by eq. (2). By neglecting the recombination A E R (discussed below) the nuclear losses v ( E o - A E w ) are given by the energy differences between the aligned and the random peaks. In the same way, we obtain the energy dispersion due to nuclear collisions. Under random bombardment, the peak width L is assumed to be given by:
L2
/?w+
=
(3)
L R2 + I S , ,
where L w, L R and L v are the energy straggling due, respectively, to detector window, recombination and nuclear interactions. When the ions are channeled, the term L 2 disappears in eq. (3) so that the nuclear collision energy straggling is given by the quadratic difference between the widths of the random and channeled peaks. This constitutes, to our knowledge, the first precise experimental procedure to evaluate these quantities. Without using channeling we would be obliged to evaluate theoretically the energy lost in the dead layer of detectors. But, even if much research has been devoted to this question s-t° ) it is presently not well understood, at least in the case of surface barrier counters. In the case of Schottky surface barrier diodes, the effective window is constituted first by the metallic layer used for the rectifying contact (mostly gold, with a minimum thickness of 80 A) and a more or less important silicon layer, contamined by oxygen, whose thickness depends on the surface chemical treatment,
I
l-
,¢,,Mam-~
~-
I c)
2000 keV
0+
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/
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V" 1700
1800
I \ 1900
t
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/
.~
.//s-/
detection
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"
.
/
..-7"
A,J J
...../7.,.'.,,-'-/ / /./
/'/-"
/
/
~oN,~,~,,o, ,N
...'/
20O0 ENERGY (keV)
Fig. I. Spectra recorded for (a) 4He+ ions, (b) u n c h a n n e l e d 160+ ions, a n d (c) 160+ penetrating the counter along the (11 I ) crystal axis. T h e ion energy in each case was 2000 keV. T h e detector used here was a 1 0 k e V b o r o n implanted 1 8 0 D c m resistivity silicon.
ENERGY I k*V I
Fig. 2. T h i c k n e s s o f the dead layer in front o f a boron implanted detector as a function o f ion energy a n d material base resistivity.
ENERGY
LOSS A N D S T R A G G L I N G
on the resistivity (more important in high resistivity) and on the applied voltage V (decrease with higher voltages). None of the models presented has been found by us to apply fully to evaluate the dead layer. In the case of implanted junctions, the thickness of
the window is essentially a function of the nature and energy of the implanted ions and on the starting material's resistivity. Fig. 2 shows the dead layer of boron implanted counters as a function of implant energy. The nature of the window in this kind of counter permits a better detection of heavy ions than surface barriers under channeling conditions. The absence of any metallic film reduces noticeably the beam divergence and then channeling is enhanced, as shown in fig. 3. Furthermore, this counter can hold a much higher dose than Schottky barriers, especially below room temperature, where the latter degrade very rapidly.
Eo 3200 keV Ar ++ on implanted detector m
275
channeling
o)
3. Experimental conditions 2200
2600
b)
2900
3000
In ref. 6 we have described in detail the experimental set-up and the method of alignment of the detectors with respect to the beam. This point will not be considered here; the main change was the moving of the apparatus to the 4 MeV Van de Graaff facilities of our Centre. The counters have been prepared either by a thin (80-200~,) gold layer evaporation on a correctly prepared silicon surface, or by implantation of boron or phosphorous in the energy range 5-15 keV into silicon. Choosing low resistivity starting material (<200 £2cm) and applying high bias voltages to the detectors, the electric field in the depletion zone is high enough to neglect the charge carrier recombination probability (so that AER ~ 0 and LR ~ 0). But even in the case where this assumption would not be valid,
3200
3200 keY Ar ++ on surface
barrier
ing
I 2/,00
2200
f 2600
I 2800
I N. 3000 3200 ENERGY ( keV}
Fig. 3. Spectra recorded for 3200 keV 4°Ar++ ions respectively with (a) an i m p l a n t e d detector a n d (b) a gold surface barrier counter.
0
#
bJ
•
o
@ o
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r~
II0
,(
[k. ~00000 • ~
0.2
we
/,0 0
detector resolution
20
I
i
1000
1
1500
I
2000 ENERGY ( keV )
F i g . 4 . Experimental values o f energy lost b y 1 4 N + ions into nuclear collisions in silicon. Solid line is the theoretical curve o f Lindhard et al. (ref. 3).
V. D A M A G E
276
A. GROB et al.
I*l
,;b
lie
•
~0
,,,
lSi+---Si I Ik
100
.
0.+.+I
[ detector resolution
I
0
1
5oo
I
1000
1
15oo
2000
ENERGY (keY)
Fig. 5. Experimental values of energy lost by zssi+ ions into nuclear collisions in silicon. Solid line is the theoretical curve of Lindhard et al. (ref. 3).
0 0 0
0
0 0o
0
o
0
0 0o
~
0
0
0
0
0 •
o
gIC
O
f
o
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o ~
O
•
LINDHARD it~_~r_+___.~
t Ar+--+Si k - 0.13
200
detector resotution
5~0
ENERGY (keY)
Fig. 6. Experimental values of energy lost by 4°Ar+ ions into nuclear collisions in silicon. Solid line is the theoretical curve of Lindhard et al. (ref. 3).
we verified that the energy difference between the aligned and random peak is not affected by a change in the voltage applied to the detector, demonstrating that this difference constitutes the " p u r e " nuclear energy loss. Furthermore, this result proves the accuracy of the above mentioned hypothesis, namely that the charge collection is the same for a random and aligned ion penetration direction. (This proof is possible only with implanted detectors, where the window thickness does not change with applied voltage, as in surface barriers.)
4.
Results
and discussion
4.1. ENERGY LOSSES IN NUCLEAR INTERACTIONS By using the experimental p r o c e d u r e described in ref. 6 we first studied the q u a n t i t y v(E) for the various ions previously mentioned. Fig. 4 shows our experimental results for t4N + ions between 200 and 2000 keV c o m p a r a t i v e to L i n d h a r d ' s theory. W i t h i n the experimental errors the agreement is satisfactory at higher energies, whilst u n d e r 900-1000 keV the experimental p o i n t s are b e l o w the theoretical
277
E N E R G Y LOSS A N D S T R A G G L I N G TABLE 1
ones. For heavier ions, like silicon (fig. 5), the saturation trend provided by theory does not appear at the foreseen energy, an increasing shift being observed with higher energies. This fact seems to be more pronounced for argon (fig. 6), for which the plateau is reached only around 4 MeV. Averaged curves for some of our experimental data are presented in fig. 7 together with the theoretical evaluations in the dimensionless units ~ of Lindhard. It appears that: 1) The quantity v(e) does not saturate as rapidly with increasing energy e as expected from theory; the difference between theoretical estimations and experimental points increases with the atomic number Z1 of the projectile. Using a different experimental approach, K a u f m a n et al.l~) observed the same trend for heavier ions. 2) On the low energy side, the energy going into nuclear interactions is probably overestimated by Lindhard. This assumption becomes even better visible in fig. 8, where our results for 12C+, 2ONe+ and
Energy-dependent correction factors for12C, 14N, 2°Ne, 28Si and 40Ar. Correction factor:
Energy (keV) 4oo 6oo 800 lOOO 12oo 1400 1600 1800 2000 3ooo 4000 5ooo
12C
14N
0.83 0.91 0.95 0.97 1.00 1.01 1.01 1.02
0.82 0.89 0.93 0.96 0.98 1.00 1.01 1.01
20N e
1.12 1.16 1.17 1.19 1.19 1.21 1.21 1.21 1.21 1.21 1.21
Pexp/~'th 28Si
1.05 1.08 1.12 1.17 1.19 1.21 1.23 1.24
4OAr
1.13 1.18 1.20 1.22 1.24 1.26 1.30 1.31 1.38 1.41 1.41
4°Ar+ ions are reported together with lower energy data from other authors 7' 12,13).
/ /
liAr
iO
I
I I I
I
I
I
/i
!
/
/
Si _At
I
/
~
//
/
/
.......0 I.-
.....~"~ ' / S i
/
N
......
. . - ' /
I //.t/,/ /
/
.,,
.._
///
/7/"
,/
7//¢//" 3 20
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."
/,'"
I
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i f ," ,-" , I~ 20
co,oo,o,.
_
----
",.c,or I r,--,"-- I I 40
I
I 60
I
I 80
I
I 100
Tr r I
I 120
I 140
Fig. 7. Review o f available data for energy lost by heavy ions into nuclear collisions in silicon in terms o f reduced variable e (ref. 3). Solid lines are the theoretical curves o f Lindhard et al. (ref. 3). Dashed curves are our averaged experimental results. V. D A M A G E
278
A. G R O B et al.
"F
Ar+
.~
I~
C ÷
-Si
p
.
..~
• • e ee°. + .. ~ a r
-L our results
Am
10
O
m llmmi
i
n
i
m t
m Ini
0.1
I
1
I
l
I
n ll~l
10
ENERGY (MmV) Fig. 8. Some o f o u r averaged results a b o u t energy lost by 12C+, 2°Ne+ a n d 40Ar+ in nuclear collisions in silicon c o m p a r e d with theoretical estimations (ref. 3) a n d lower energy results from other a u t h o r s (refs. 7, 12, 13).
Finally, our experimental results show that the theoretical predictions of Lindhard are verified in a rough approximation. But a more detailed analysis indicates that the theoretical estimations have to be corrected by the small factor given in table I to really fit our points.
/ AP+
35~
/// 1//
2.5
//f
/~ ~
~
N+
// fl ii / i / i// i/ //," /# /11 // / / / iii/ i /
15!
iiii// II / / ~ ~b 2'o io io s'o io 7'o 8'o 9'o ~'oo ~o
Fig. 9. Energy straggling for heavy ions in nuclear collisions in silicon in t e r m s o f reduced unity e c o m p a r a t i v e with L i n d h a r d et al. for 2ssi+ in silicon.
4 . 2 . ENERGY STRAGGLING DURING NUCLEAR PROCESSES
To our knowledge, the only experimental determination of nuclear straggling was made by Karcher et al. 7) who used a much less precise technique. The dispersion A v(e) was estimated for all the ions previously considered. Our averaged experimental results for C +, N + and Ar + ions are reported in fig. 9, together with Lindhard's estimations for silicon in silicon. If the general trend of the theoretical curve is verified, it seems that calculations underestimate the energy straggling due to nuclear interactions, C + and N + results being placed above the Si + in the silicon curve. 4.3. BEHAVIOUR OF ENERGY LOSS WITH Z 1 Recent experiments 14' 15) on energy losses of slow heavy ions passing through thin foils have shown the stopping power to be a periodic function of the atomic number Z~ of the projectile [and also of Z 2 of the stopping medium16)]. This effect was enhanced under channeling conditions where the nuclear contribution may be neglected. This demonstrates that these oscillations are related to electronic collisions. In our experimental procedure, we measured the electronic (and nuclear) stopping power integrated
ENERGY LOSS AND S T R A G G L I N G
279
5. Conclusion
In summary, our experimental data reported here about the quantity v(E) agree, in a first approximation, with theoretical estimates, but the precision of our procedure of channeling/random heavy ions detection allows us to observe small deviations which are a function of both incident particle atomic number and energy. The corresponding nuclear straggling is more clearly underestimated by the theories. Electronic stopping is shown not to oscillate with Z1 when integrated over the whole range. It should be interesting that other types of experiments verify our results.
~t
,~ 0.9
m o ~
0.8
INITIALVELOCITY
~
• Vo = 3610~cm/s iA Vo , =, 2"II108cm/s , I I
0.7
678910
~ ~
,
t
References ~"
I
14 16 18 ATONIC NUMBER Z1
Fig. 10. Fraction of incident energy E0 lost in electronic interactions as a function of the incident particle~atomic number Z1 for two different initial velocities (solid curves). Dashed lines were plotted from Lindhard et al. (ref. 3).
over the whole ion range. Using different projectiles Z~ of identical initial velocity (such as the ion ranges are nearly identical) we measured the ionized fraction of the energy lost over this range as a function of Z,. Our values reported in fig. 10 show, within the experimental precision that no oscillation with Z~ of the total energy lost in electronic collisions appears for the two values of the initial velocity. This result can be explained only by assuming one of the following statements: a) a relatively low stopping power is compensated, not by an increase in the nuclear stopping but by an increase of the ion range; b) the distribution of the energy deposited during electronic interactions along the path may change with Z,.
1) N. Bohr, Kgl. Dan. Vid. Selsk. Mat. Fys. Medd. 18, no. 8 (1954). 9) E. L. Haines and A. B. Whitehead, Rev. Sci. Instr. 37 (1966) 190. z) j. Lindhard, V. Nielsen, M. Scharff and P.V. Thomsen, Kgl. Dan. Vid. Selsk. Mat. Fys. Medd. 33, no. l0 (1963). 4) H. W. Schmitt, W. M. Gibson, J. H. Neiler, F. J. Walter and T. D. Thomas, Proc. Conf. on Physics and chemistry offission, Salzburg, Austria (I.A.E.A., Vienna, 1965). 5) E. Konecny and K. Hetwer, Nucl. Instr. and Meth. 36 (1965) 61. o) j . j . Grob, A. Grob, A. Pape and P. Siffert, Phys. Rev. B 11 (1975) 3273. 7) T. Karcher and N. Wotherspoon, Nucl. Instr. and Meth. 93, (1971) 519. 8) G. Forcinal, P. Siffert and A. Coche, IEEE Trans. Nucl. Sci. NS-15 (1968) 475. o) E. Elad, C . N . lnskeep, R. A. Sareen and P. Nestor, IEEE Trans. Nud. Sci. NS-20 (1973) 534. 10) C. Inskeep, E. Elad and R. A. Sareen, IEEE Trans. Nucl. Sci. NS-21 (1974) 379. 11) S. B. Kaufman, E. P. Steinberg, B. D. Wilkins, J. Unik, A. J. Gorski and M. J. Fluss, Nucl. Instr. and Meth. 115 (1974) 47. 12) R. Dean Campbell and R. P. Lin, Rev. Sci. Instr. 44 (1973) 1510. 13) H. Grahmann, Thesis, Heidelberg University (1974). 14) p. Hvelplund and B. Fastrup, Phys. Rev. 165 (1968) 408. 15) F. H. Eisen, Can. J. Phys. 46 (1968) 561. 1o) p. Hvelplund, Kgl. Dan. Vid. Selsk. Mat. Fys. Medd. 38, no. 4 (1971). 17) j. L. Whitton, Can. J. Phys. 52 (1974) 12.
V. DAMAGE
INSTRUMENTS
AND
METHODS
132 (1976) 273-279; ©
NORTH-HOLLAND
PUBLISHING
CO.
ENERGY L O S S AND STRAGGLING OF HEAVY IONS BY NUCLEAR INTERACTIONS IN SILICON A. G R O B , J . J . G R O B a n d P. S I F F E R T
Centre de Recherches Nucldaires, P R E N et Universitd Lou& Pasteur, 67037 Strasbourg Cedex, France Heavy ion channeling detection p e r f o r m e d in aligned silicon detectors (ion implanted a n d surface barrier) constitutes a procedure to determine energy loss a n d straggling in nuclear collisions when associated with r a n d o m oriented m e a s u r e m e n t s . Results for 12C+, 14N+, 160+, 2°Ne+, 28Si+, 32S+, 4°Ar+ in the energy range 300-3000 keV are presented. T h e y fit roughly L i n d h a r d ' s previsions but s h o w small discrepancies which are increasing with atomic n u m b e r Z1 o f the projectile and with energy. T h e total energy s p e n t by the ions o f the s a m e initial velocity does n o t oscillate as a function o f Z1 as does the electronic stopping power.
1. Introduction
Consider a heavy particle with initial energy Eo, which is stopped in a solid target, it creates charge carriers by electronic interactions and recoil atoms during nuclear collisions. These secondary species are able either to ionize or to displace other atoms which again, if they have sufficient energy, can continue the cascade. Finally, even if the different steps are not independent, a part v(Eo) of the ions initial energy is spent to the medium through nuclear collisions, whereas the other r/(Eo) through electronic interactions, so that E 0 = q(Eo)+ v(Eo). Theoretical estimations of this energy partition have been proposed by several authors 1'2) and especially by Lindhard et al.3). Experimentally, the situation is less satisfactory, mainly as a result of the absence of a suitable measurement procedure. Indeed, fission fragments have been mainly used in connection with semiconductor detectors4'5). Since only the electronic collisions lead to charge carrier creation in this kind of detectors, a "pulse height defect" (PHD) is observed (compared to ~t-particles) which is assumed to be equal to the energy spent in nuclear interactions. Unfortunately, other contributions to the P H D exist, which are generally neglected, especially: - the counter entrance window (dead layer) in which the charge carrier lifetime is too small to allow them to diffuse into the high field zone, - charge recombination along the track of the ion or trapping in deep levels, - a possible change in the energy necessary to create an electron-hole pair between light and heavy particles. in a previous paper6), we have presented a precise experimental method to evaluate the amount of energy lost through electronic and nuclear collisions during the slowing down of heavy ions in thick silicon targets.
In principle, this approach is valid for any ion (Z 1, M~) absorbed in a solid state detector (currently: silicon germanium, cadmium telluride, diamond). Here, we have studied, by this new method, the mean nuclear energy loss v ( E ) in silicon and the corresponding energy straggling A v ( E ) for 12C+, 14N+, 160+, 2°Ne+, 28Si+, 32S+, 4°Ar+ ions with energies ranging from 300 to 3000 keV. 2. Heavy ion detection in solid state counters in random and channeling conditions
The response of a solid state counter to a heavy ion beam depends strongly on its direction with respect to the detectors cristallographic axes or planes. Under random direction the counter presents a pulse height defect A E (with respect to protons of equivalent energy) given by 7. 8): A E = A E w + A E R + v[Eo - ( A E w + A E R ) ] ,
(1)
where A E w is the amount of energy lost in the counters dead layer, A E R a loss due to charge recombination and carrier trapping in the depletion region of the diode, v [ E o - ( A E w + A E R ) ] the energy lost through non-ionizing nuclear processes. When the beam enters the detector along a channelin9 direction it moves through low density regions without important nuclear interactions with the atoms forming the "walls" of the channel. In other words, the minimal approach of a particle focused between planes or strings is an impact parameter such that the transmitted energy to the stopping medium through elastic collisions is negligible. Thus, the channeled ions lose their energy only by electronic interactions. Consequently, the pulse height defect A E ' reduces to: AE' = A E w + A E R .
(2) V. D A M A G E
274
A. G R O B et al.
Eqs. (l) and (2) suppose that the charge collection is the same in random and aligned directions. Furthermore, they assume that the energy going into other processes (escaping X-rays for example) can be neglected in a first approximation. An illustration of the pulse distribution under random and aligned bombardment of a silicon detector by 2 MeV 160+ ions is given in fig. 1. In comparison to the energy reference peak given by 2 MeV 4He+ ions (fig. 2a), the random condition recorded 160+ distribution (fig. 2b) shows a P H D given by eq. (1). Along the (111) direction the recorded spectrum (fig. 2c) exhibits a higher energy "aligned" peak, with a P H D
a)
2000 keV
He +
b} 2000 keY 0 +
random detection
given by eq. (2). By neglecting the recombination A E R (discussed below) the nuclear losses v ( E o - A E w ) are given by the energy differences between the aligned and the random peaks. In the same way, we obtain the energy dispersion due to nuclear collisions. Under random bombardment, the peak width L is assumed to be given by:
L2
/?w+
=
(3)
L R2 + I S , ,
where L w, L R and L v are the energy straggling due, respectively, to detector window, recombination and nuclear interactions. When the ions are channeled, the term L 2 disappears in eq. (3) so that the nuclear collision energy straggling is given by the quadratic difference between the widths of the random and channeled peaks. This constitutes, to our knowledge, the first precise experimental procedure to evaluate these quantities. Without using channeling we would be obliged to evaluate theoretically the energy lost in the dead layer of detectors. But, even if much research has been devoted to this question s-t° ) it is presently not well understood, at least in the case of surface barrier counters. In the case of Schottky surface barrier diodes, the effective window is constituted first by the metallic layer used for the rectifying contact (mostly gold, with a minimum thickness of 80 A) and a more or less important silicon layer, contamined by oxygen, whose thickness depends on the surface chemical treatment,
I
l-
,¢,,Mam-~
~-
I c)
2000 keV
0+
LrtX
~.,o-,L_/ ~ W,
/
< 111> or ientation
•
| i
!
I
V" 1700
1800
I \ 1900
t
I
I
/
.~
.//s-/
detection
=F
"
.
/
..-7"
A,J J
...../7.,.'.,,-'-/ / /./
/'/-"
/
/
~oN,~,~,,o, ,N
...'/
20O0 ENERGY (keV)
Fig. I. Spectra recorded for (a) 4He+ ions, (b) u n c h a n n e l e d 160+ ions, a n d (c) 160+ penetrating the counter along the (11 I ) crystal axis. T h e ion energy in each case was 2000 keV. T h e detector used here was a 1 0 k e V b o r o n implanted 1 8 0 D c m resistivity silicon.
ENERGY I k*V I
Fig. 2. T h i c k n e s s o f the dead layer in front o f a boron implanted detector as a function o f ion energy a n d material base resistivity.
ENERGY
LOSS A N D S T R A G G L I N G
on the resistivity (more important in high resistivity) and on the applied voltage V (decrease with higher voltages). None of the models presented has been found by us to apply fully to evaluate the dead layer. In the case of implanted junctions, the thickness of
the window is essentially a function of the nature and energy of the implanted ions and on the starting material's resistivity. Fig. 2 shows the dead layer of boron implanted counters as a function of implant energy. The nature of the window in this kind of counter permits a better detection of heavy ions than surface barriers under channeling conditions. The absence of any metallic film reduces noticeably the beam divergence and then channeling is enhanced, as shown in fig. 3. Furthermore, this counter can hold a much higher dose than Schottky barriers, especially below room temperature, where the latter degrade very rapidly.
Eo 3200 keV Ar ++ on implanted detector m
275
channeling
o)
3. Experimental conditions 2200
2600
b)
2900
3000
In ref. 6 we have described in detail the experimental set-up and the method of alignment of the detectors with respect to the beam. This point will not be considered here; the main change was the moving of the apparatus to the 4 MeV Van de Graaff facilities of our Centre. The counters have been prepared either by a thin (80-200~,) gold layer evaporation on a correctly prepared silicon surface, or by implantation of boron or phosphorous in the energy range 5-15 keV into silicon. Choosing low resistivity starting material (<200 £2cm) and applying high bias voltages to the detectors, the electric field in the depletion zone is high enough to neglect the charge carrier recombination probability (so that AER ~ 0 and LR ~ 0). But even in the case where this assumption would not be valid,
3200
3200 keY Ar ++ on surface
barrier
ing
I 2/,00
2200
f 2600
I 2800
I N. 3000 3200 ENERGY ( keV}
Fig. 3. Spectra recorded for 3200 keV 4°Ar++ ions respectively with (a) an i m p l a n t e d detector a n d (b) a gold surface barrier counter.
0
#
bJ
•
o
@ o
n
r~
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,(
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i
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I
2000 ENERGY ( keV )
F i g . 4 . Experimental values o f energy lost b y 1 4 N + ions into nuclear collisions in silicon. Solid line is the theoretical curve o f Lindhard et al. (ref. 3).
V. D A M A G E
276
A. GROB et al.
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ENERGY (keY)
Fig. 5. Experimental values of energy lost by zssi+ ions into nuclear collisions in silicon. Solid line is the theoretical curve of Lindhard et al. (ref. 3).
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Fig. 6. Experimental values of energy lost by 4°Ar+ ions into nuclear collisions in silicon. Solid line is the theoretical curve of Lindhard et al. (ref. 3).
we verified that the energy difference between the aligned and random peak is not affected by a change in the voltage applied to the detector, demonstrating that this difference constitutes the " p u r e " nuclear energy loss. Furthermore, this result proves the accuracy of the above mentioned hypothesis, namely that the charge collection is the same for a random and aligned ion penetration direction. (This proof is possible only with implanted detectors, where the window thickness does not change with applied voltage, as in surface barriers.)
4.
Results
and discussion
4.1. ENERGY LOSSES IN NUCLEAR INTERACTIONS By using the experimental p r o c e d u r e described in ref. 6 we first studied the q u a n t i t y v(E) for the various ions previously mentioned. Fig. 4 shows our experimental results for t4N + ions between 200 and 2000 keV c o m p a r a t i v e to L i n d h a r d ' s theory. W i t h i n the experimental errors the agreement is satisfactory at higher energies, whilst u n d e r 900-1000 keV the experimental p o i n t s are b e l o w the theoretical
277
E N E R G Y LOSS A N D S T R A G G L I N G TABLE 1
ones. For heavier ions, like silicon (fig. 5), the saturation trend provided by theory does not appear at the foreseen energy, an increasing shift being observed with higher energies. This fact seems to be more pronounced for argon (fig. 6), for which the plateau is reached only around 4 MeV. Averaged curves for some of our experimental data are presented in fig. 7 together with the theoretical evaluations in the dimensionless units ~ of Lindhard. It appears that: 1) The quantity v(e) does not saturate as rapidly with increasing energy e as expected from theory; the difference between theoretical estimations and experimental points increases with the atomic number Z1 of the projectile. Using a different experimental approach, K a u f m a n et al.l~) observed the same trend for heavier ions. 2) On the low energy side, the energy going into nuclear interactions is probably overestimated by Lindhard. This assumption becomes even better visible in fig. 8, where our results for 12C+, 2ONe+ and
Energy-dependent correction factors for12C, 14N, 2°Ne, 28Si and 40Ar. Correction factor:
Energy (keV) 4oo 6oo 800 lOOO 12oo 1400 1600 1800 2000 3ooo 4000 5ooo
12C
14N
0.83 0.91 0.95 0.97 1.00 1.01 1.01 1.02
0.82 0.89 0.93 0.96 0.98 1.00 1.01 1.01
20N e
1.12 1.16 1.17 1.19 1.19 1.21 1.21 1.21 1.21 1.21 1.21
Pexp/~'th 28Si
1.05 1.08 1.12 1.17 1.19 1.21 1.23 1.24
4OAr
1.13 1.18 1.20 1.22 1.24 1.26 1.30 1.31 1.38 1.41 1.41
4°Ar+ ions are reported together with lower energy data from other authors 7' 12,13).
/ /
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I 140
Fig. 7. Review o f available data for energy lost by heavy ions into nuclear collisions in silicon in terms o f reduced variable e (ref. 3). Solid lines are the theoretical curves o f Lindhard et al. (ref. 3). Dashed curves are our averaged experimental results. V. D A M A G E
278
A. G R O B et al.
"F
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-L our results
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i
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ENERGY (MmV) Fig. 8. Some o f o u r averaged results a b o u t energy lost by 12C+, 2°Ne+ a n d 40Ar+ in nuclear collisions in silicon c o m p a r e d with theoretical estimations (ref. 3) a n d lower energy results from other a u t h o r s (refs. 7, 12, 13).
Finally, our experimental results show that the theoretical predictions of Lindhard are verified in a rough approximation. But a more detailed analysis indicates that the theoretical estimations have to be corrected by the small factor given in table I to really fit our points.
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~
N+
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15!
iiii// II / / ~ ~b 2'o io io s'o io 7'o 8'o 9'o ~'oo ~o
Fig. 9. Energy straggling for heavy ions in nuclear collisions in silicon in t e r m s o f reduced unity e c o m p a r a t i v e with L i n d h a r d et al. for 2ssi+ in silicon.
4 . 2 . ENERGY STRAGGLING DURING NUCLEAR PROCESSES
To our knowledge, the only experimental determination of nuclear straggling was made by Karcher et al. 7) who used a much less precise technique. The dispersion A v(e) was estimated for all the ions previously considered. Our averaged experimental results for C +, N + and Ar + ions are reported in fig. 9, together with Lindhard's estimations for silicon in silicon. If the general trend of the theoretical curve is verified, it seems that calculations underestimate the energy straggling due to nuclear interactions, C + and N + results being placed above the Si + in the silicon curve. 4.3. BEHAVIOUR OF ENERGY LOSS WITH Z 1 Recent experiments 14' 15) on energy losses of slow heavy ions passing through thin foils have shown the stopping power to be a periodic function of the atomic number Z~ of the projectile [and also of Z 2 of the stopping medium16)]. This effect was enhanced under channeling conditions where the nuclear contribution may be neglected. This demonstrates that these oscillations are related to electronic collisions. In our experimental procedure, we measured the electronic (and nuclear) stopping power integrated
ENERGY LOSS AND S T R A G G L I N G
279
5. Conclusion
In summary, our experimental data reported here about the quantity v(E) agree, in a first approximation, with theoretical estimates, but the precision of our procedure of channeling/random heavy ions detection allows us to observe small deviations which are a function of both incident particle atomic number and energy. The corresponding nuclear straggling is more clearly underestimated by the theories. Electronic stopping is shown not to oscillate with Z1 when integrated over the whole range. It should be interesting that other types of experiments verify our results.
~t
,~ 0.9
m o ~
0.8
INITIALVELOCITY
~
• Vo = 3610~cm/s iA Vo , =, 2"II108cm/s , I I
0.7
678910
~ ~
,
t
References ~"
I
14 16 18 ATONIC NUMBER Z1
Fig. 10. Fraction of incident energy E0 lost in electronic interactions as a function of the incident particle~atomic number Z1 for two different initial velocities (solid curves). Dashed lines were plotted from Lindhard et al. (ref. 3).
over the whole ion range. Using different projectiles Z~ of identical initial velocity (such as the ion ranges are nearly identical) we measured the ionized fraction of the energy lost over this range as a function of Z,. Our values reported in fig. 10 show, within the experimental precision that no oscillation with Z~ of the total energy lost in electronic collisions appears for the two values of the initial velocity. This result can be explained only by assuming one of the following statements: a) a relatively low stopping power is compensated, not by an increase in the nuclear stopping but by an increase of the ion range; b) the distribution of the energy deposited during electronic interactions along the path may change with Z,.
1) N. Bohr, Kgl. Dan. Vid. Selsk. Mat. Fys. Medd. 18, no. 8 (1954). 9) E. L. Haines and A. B. Whitehead, Rev. Sci. Instr. 37 (1966) 190. z) j. Lindhard, V. Nielsen, M. Scharff and P.V. Thomsen, Kgl. Dan. Vid. Selsk. Mat. Fys. Medd. 33, no. l0 (1963). 4) H. W. Schmitt, W. M. Gibson, J. H. Neiler, F. J. Walter and T. D. Thomas, Proc. Conf. on Physics and chemistry offission, Salzburg, Austria (I.A.E.A., Vienna, 1965). 5) E. Konecny and K. Hetwer, Nucl. Instr. and Meth. 36 (1965) 61. o) j . j . Grob, A. Grob, A. Pape and P. Siffert, Phys. Rev. B 11 (1975) 3273. 7) T. Karcher and N. Wotherspoon, Nucl. Instr. and Meth. 93, (1971) 519. 8) G. Forcinal, P. Siffert and A. Coche, IEEE Trans. Nucl. Sci. NS-15 (1968) 475. o) E. Elad, C . N . lnskeep, R. A. Sareen and P. Nestor, IEEE Trans. Nud. Sci. NS-20 (1973) 534. 10) C. Inskeep, E. Elad and R. A. Sareen, IEEE Trans. Nucl. Sci. NS-21 (1974) 379. 11) S. B. Kaufman, E. P. Steinberg, B. D. Wilkins, J. Unik, A. J. Gorski and M. J. Fluss, Nucl. Instr. and Meth. 115 (1974) 47. 12) R. Dean Campbell and R. P. Lin, Rev. Sci. Instr. 44 (1973) 1510. 13) H. Grahmann, Thesis, Heidelberg University (1974). 14) p. Hvelplund and B. Fastrup, Phys. Rev. 165 (1968) 408. 15) F. H. Eisen, Can. J. Phys. 46 (1968) 561. 1o) p. Hvelplund, Kgl. Dan. Vid. Selsk. Mat. Fys. Medd. 38, no. 4 (1971). 17) j. L. Whitton, Can. J. Phys. 52 (1974) 12.
V. DAMAGE