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Energy response of silicon surface-barrier particle detectors to slow heavy ions
NUCLEAR
INSTRUMENTS
AND
METHODS
[30
(1975) 533-538;
© NORTH-HOLLAND
PUBLISHING
CO
ENERGY R E S P O N S E OF S I L I C O N SURFACE-BARRIER P A R T I C L E D E T E C T O R S TO S L O W HEAVY IONS*
A. RATKOWSKIt Department of Physics, New York University, New York, New York 10003, U.S.A.
Received 18 September 1975 The energy deposited in electronic excitations was measured for It, He, El, N, Ne, Na, Ar, K, Rb, and Cs projectiles with initial ~elocities 0.3 v0
projectiles in matter. Energy straggling is consistently higher than predicted by theory. The locus of the data in reduced coordinates yields a nearly universal curve for such detectors and extends their applicability in charged-particle spectroscopy to low-velocityheavy ions.
I. Introduction This paper reports measurements of the response of silicon surface-barrier particle detectors to heavy charged particles stopping in the depletion region of the detector. The projectiles are all, 2He, 3Li, 7N, a0Ne, 11Na, 1BAr, 19K, 37Rb, and 5sCs in overlapping velocity ranges from 0.3 v0 to 3.75 v0, where Vo = e2/h = 2.18 × 108 cm/s is the atomic unit of velocity. The difference between the kinetic energy of the incident projectiles and the electronic energy losses measured through the detector pulse-height distribution of collected particle-hole pairs yields, to the extent that the division between electronic and screened Coulomb collisions is valid, the energy dissipated in elastic collisions with silicon target atoms. The detector response, therefore, can test the theory of the modes of energy deposition by heavy atomic projectiles in matter. Interpolations based on theory give reliable calibrations of the detector response for measuring the !kinetic energy of slow heavy ions. These experiments extend the first study made in this laboratory t) with slow projectiles, and make contact "with the large body of experimental evidence for the ,detector response at high projectile velocities, where practically all energy is lost in electronic excitations. The experimental details are discussed in section 2 and the data analysis and error discussion are given in section 3. The results are compared with theory in section 4.
New York University accelerator ranging in energy from 75 to 500 keV were stabilized in energy to ~< 0.2% by a crossed-field analyzer. The beams were isotopically pure and the most abundant isotope was selected as the projectile. The analyzed beam intensity was reduced to ~ 100 projectiles/s while being monitored with a Bendix M-306 electron multiplier. The particles impinged upon the target, Ortec detector model TB-022-050-200, serial number 14-009A, mounted in an aluminum housing fitted with a vapor trap. The aperture of the vapor trap, through which the projectiles passed, had an area smaller than the detector sensitive area and restricted the beam to a region of uniform depletion layer thickness. Within experimental error, bombarding the detector at different positions inside the active area produced identical detector response. The depletion depth of 190 pm exceeds the range in silicon of all projectiles investigated. The aluminum block holding the target was attached with a nylon screw to a dewar maintained at 78 K and electrically insulated from the dewar by a mica disc. A 10 cm Microdot coaxial cable connected the detector to a feedthrough in the wall of the target chamber. The output signal of an Ortec model 109A Col limotor ), ,(
Detector _ _
_
~ ~
i ~ P r e a m p lifier
[ I Electron
Col limotor
.Beam . Axis . .
XCrossed-Field Analyzer
:2. Experimental 1H, 2He, 7N, loNe, and 1BAr projectiles from the * Work supported by the United States Energy Research and Development Administration. ? Present address: lnstitut de Physique Nuel6aire, Universit6 Claude Bernard Lyon-l, Lyon, France.
533
G~r01or I
Fig. 1. Schematic representation of the experimental apparatus.
534
A.
RATKOWSKI
preamplifier, connected to the feedthrough by a BNC elbow, was then amplified by an Ortec model 435A amplifier located in the accelerator console room. The target chamber grounded through the amplifier acted as a Faraday cage for the detector. The output charge pulse of the amplifier was analyzed by a Northern Scientific NS-715 pulse-height analyzer. Energy calibration of the detection system, shown schematically in fig. 1, was performed before and after each set 41At n 57 of measurements with 295 ..... and 2vCo sources which emit gamma rays of energies 59.57 and 122.06 keV, respectively. The pressure in the target chamber was held at 2 × 10-7 torr by a turbomolecular pump. The vapor trap in front of the detector prevented carbon buildup from residual oil contamination in the system. Projectile energies were determined by measurements with a Rawson rotating-coil gaussmeter of the magnetic field required to produce a 90 ° deflection of the ion beam in a magnetic spectrometer. The gaussmeter was calibrated in terms of particle energies through the thick-target yield from (p, ~) and (p, 7) resonance reactions. Measurements with alkali ion projectiles, 3Li, 11Na, 19K, 37Rb, and ssCs, were performed at the 3 MeV Van de Graaff accelerator facility of the Carnegie Institution in Washington, D.C. For these experiments the apparatus and electronics were moved from New York to Washington without changes. The mass separation was performed with a magnet which deflected the ion beam through 7 ° . The projectile energies were determined by measuring the accelerating potential with a generating voltmeter calibrated through the yields of nuclear resonance reactions. Projectile energies are known within _+5x 10 - s MeV. Energy calibration of the analyzer was performed with a 241•m 4.7 MeV alpha source in addition to the 95 ..... and ~SWCogamma sources. The target in the alkali ion measurements was an Ortec detector, model A-016-025-100, serial number 10-401. The depletion depth of l l 5 / , m exceeds the range in silicon of the ions investigated. The collection efficiency of a detector for charge carriers produced in the sensitive volume by particlehole excitation was tested by substitution of an Ortec model 410 multimode amplifier for the 435A active filter amplifier so that the detection system time constants could be varied. The detector response was found to remain unchanged within experimental error for integration and differentiation time constants ranging between 1 and 5 l~s. In addition, the detector response to protons was equal to the proton energy in
the detector sensitive volume within experimental uncertainty.
3. Data analysis The amplitude of the output pulses from the amplifier ranged from 0 to 10 V. The pulse-height analyzer divided the voltage range into 512 equal intervals of width A V. The number of pulses, Ni, of amplitude between V i and V i + A V , were stored in channel number C~, forming a histogram of the pulse-height distribution. The position of the centroid of the distribution is proportional to the energy dissipated in electronic excitation by the projectile. The centroid, (7, was calculated numerically from the distributions, Ni Ci _
i
,
(1)
i
where the summation extended over the channel numbers. The pulse-height distributions were free of background. Statistical uncertainties in the numerical determinations of the centroids were < 0.2 %. The analyzer abscissa was calibrated in energy by fitting the centroids of the pulse-height distributions resulting from the detector response to monoenergetic alpha and gamma sources linearly to the corresponding energies by the method of least squares. The uncertainty in the energy calibration was < 0 . 1 % . The energy 0(E) calculated from the centroid is that part of the projectile energy, E, deposited in the sensitive detector volume in the form of particle-hole excitation. The remaining energy ~,(E) = E - ~ ( E )
(2)
is dissipated in elastic collisions. The variance, aa, of a pulse-height distribution was calculated numerically from the distribution,
?
i
l
It contains the contribution of electronic noise in the detection system. This was measured by injecting the output signal from an Ortec model 419 pulse generator into the preamplifier during the measurements, producing a known pulse-height distribution of variance %. Assuming the electronic noise contributes to the
ENERGY
RESPONSE
variance resulting from fluctuations in the stopping of the projectile, a, according to aa2 = a 2 + a p2,
(4)
the energy straggling, /2, is (5)
Q = ma,
where m is the slope of the analyzer calibration line and is; the energy equivalent of the channel width A V. Before entering the sensitive volume of the detector, the projectiles lose the energy AEA~ in penetrating the gold entrance electrode and the energy AEs~ in an insensitive silicon entrance layer. Measurements with protons revealed that, in addition to the gold electrode, quoted by the manufacturer to be of surface density 40pg/cm 2, detectors 14-009A and 10-401 had silicon entrance layers of (5.37 -t- 0.27) and (4.66 -+ 0.25) pg/cm 2, respectively. These values agree well with the findings of Siffert and his collaborators 2). The energy deposited in the sensitive volume of the detector is (6)
,
E = E,-AEAu-AEsl
where E 1 is the incident energy of the projectile. For H, He, and Li projectiles, AEAu and AEs~ were
TO SLOW
HEAVY
535
IONS
calculated from the stopping powers of Northcliffe and Schilling3), Whaling4), and ref. 5; the theory of Lindhard and his collaborators 6) was employed for all other projectiles. The uncertainty in E from the gold and silicon entrance layer corrections ranges from 0.2% at the highest to 0.5% at the lowest energy for the ~H, zHe, vN, loNe, and laAr projectiles and from 0.02% at the highest to 0.1% at the lowest energy for the aLl, ltNa, 19K, 37Rb, and 5sCs projectiles. In summary, it is estimated that for the measurements made from 0.075to0.5 MeV with 1H, 2He, 7N, 10Ne, and ~8Ar projectiles the uncertainty in f/is _+ 1%. The uncertainty in ~ is _+ 15 % at the lowest and +25 % at the highest energy. The error in -(2 is _+30% for vN, loNe, and ~sAr; for ~H and 2He the error is _+50 %. For the alkali ion measurements made from 0.5 to 3 MeV, the error in f/ is less than 1.6%. The uncertainty in ~ is _+20 % at the lowest and _+30 % at the highest energy. The error in .(2 is _+50% for 3Li and _+30 % for i l N a, 19K, 37 Rb, and 5s Cs projectiles. 4. Results
Following Lindhard's notation, we express the projectile energy E in terms of the reduced parameter, e,
I000
IOO
+ o o x o II
H He Li N Ne
a Mz
= Z!Z2(M
l+M2)e
E,
(7)
2
where (Z1, M1) and (Z2, M2) are the atomic number and mass of the projectile and target atoms, respectively, e is the electronic charge, and a is the T h o m a s - F e r m i screening length,
No ~t Ar K A Rb J~ Cs
(9~2) ~ a0 a = ~ 2 ± 2; ( Z [ + Z 2 ) ~'
I0
(8)
ao being the Bohr radius. For projectile velocities less than Z~r0, the electronic stopping cross-section, N - 1 (dE/dR), where N is the number of target atoms per unit volume and d E / d R is the electronic stopping power, in reduced variables is approximated by s. = ke ~, 0.[ ~ 0,1
I I
IO0
L
(9)
where
, I000
k = ~ Fig. 2. D e t e c t o r r e s p o n s e to h e a v y c h a r g e d p a r t i c l e s . T h e r e d u c e d v a r i a b l e s e a n d ~ are p r o p o r t i o n a l to the p r o j e c t i l e e a e r g y a n d the m e a n e n e r g y d e p o s i t e d in e l e c t r o n i c e x c i t a t i o n , respectively. T h e u p p e r solid line is ~ ( e ) = e, the l o w e r is ~'(e) c a l c u l a t e d for silicon p r o j e c t i l e s s t o p p i n g in silicon.
ZIZI2(M1+ M 2 ) ~ (Z~ + "~ 27J~ ~v* ~ 1 iv* ~ 2
0.0793
(~0)
and ~ ~ Z~. The experimental results are listed in reduced variables in table 1.
536
A. R A T K O W S K I TABLE 1
TABLE 1
T h e e x p e r i m e n t a l results. T h e r e d u c e d p r o j e c t i l e e n e r g y , e, t h e r e d u c e d e n e r g y d e p o s i t e d in e l e c t r o n i c e x c i t a t i o n s , ~(e), P ( e ) = e - ~ ( e ) , a n d t h e r e d u c e d e n e r g y s t r a g g l i n g , .(2(e), f o r t h e H , H e , Li, N , N e , N a , A r , K , R b , a n d C s p r o j e c t i l e s e m p l o y e d in this s t u d y . F o r t h e H , H e , a n d Li p r o j e c t i l e s , t h e r e d u c e d e n e r g y s t r a g g l i n g w a s f o u n d to be i n s e n s i t i v e to t h e p r o j e c t i l e e n e r g y a n d to h a v e t h e v a l u e 1.24-0.6.
Projectile
e
F/(e)
~ (e)
~Q(e)
84.83 102.70 106.41 124.85 144.75
85.51 102.63 106.37 125.26 144.16
-
-
145.14 168.51 191.55
145.23 168.43 190.99
-
-
~He
25.25 36.96 51.89 64.57 90.52
23.38 34,35 49.86 61.63 88.42
-
-
aVLi
104.71 104.71 158.84 158.84 213.51 213.51 213.51 213.51 213.51 268.43 268.43 323.49 323.49 378.66 378.66 433.88 433.88 489.11 489.11 544.35
104.24 104.38 158.23 158.00 213.11 213.30 213.29 213.36 213.26 268.17 268.43 323.00 323.26 377.75 377.34 432.15 432.40 489.59 490.17 544.07
-
-
5.90 7.73 9.86 12.72 12.73 12.99 13.07 15.80 15.88 18.14 18.15 19.52 26.08
4.01 5.49 7.39 9.87 9.90 10.31 10.34 12.59 12.74 14.72 14.76 16.03 22.04
1.89 2.24 2.47 2.85 2.84 2.68 2.73 3.21 3.14 3.42 3.39 3.49 4.04
0.664 0.714 0.747 0.904 0.994 0.922 0.780 0.898 1.072 1.139 1.126 1.127 1.162
3.07
1.81
1.26
0.307
,*H
17aN
zo loNe
Projectile
23 llNa
4o laAF
39
19 K
aS~Rb
e
(continued)
~ (e)
~ (e)
.(2 (e)
3.07 4.70 7.09 10.58 10.58 15.19 18.71 22.19
1.83 2.94 4.72 7.67 7.64 11.80 14.94 18.05
1.24 1.76 2.38 2.91 2.94 3.39 3.76 4.14
0.284 0.423 0.568 0.707 0.757 0.971 0.944 1.133
16.20 16.20 24.84 24.84 24.84 33.45 33.45 33.45 42.14 42.14 50.80 50.80 59.50 59.50
12.32 12.40 20.28 20.47 20.27 28.52 28.38 28.11 37.01 37.12 45.40 45.41 54.00 53.79
3.88 3.80 4.56 4.37 4.57 4.93 5.07 5.34 5.13 5.02 5.40 5.39 5.50 5.71
1.040 0.974 1.215 1.237 1.212 1.405 1.404 1.431 1.541 1.387 1.534 1.616 1.759 1.778
68.20 68.20 76.91 85.62
62.34 62.24 70.36 79.04
6.00 5.96 6.54 6.58
1.786 1.771 1.996 1.851
1.87 2.55 3.25 4.62
1.05 1.51 1.94 2.85
0.81 1.05 1.31 1.77
0.200 0.240 0.284 0.358
6.20 6.20 9.67 9.67 13.13 16.62 20.11 23.61 27.09
3.99 4.00 6.72 7.01 9.69 12.75 15.92 19.32 22.11
2.21 2.20 2.95 2.65 3.45 3.86 4.19 4.29 4.97
0.441 0.406 0.629 0.761 0.654 0.922 0.925 1.066 1.006
1.38 1.38 2.31 2.31 3.25 3.25 3.25 3.25 3.25 3.25 4.19 5.13 5.13
0.68 0.68 1.18 1.17 1.72 1.71 1.76 1.74 1.72 1.72 2.31 2.94 2.94
0.69 0.70 1.13 1.14 1.54 1.49 1.51 1.53 1.53 1.88 2.19 2.19
0,097 0.100 0.157 0.138 0.197 0.208 0.242 0,198 0.174 0.203 0.232 0.286 0.309
5.13 5.13
2.98 2.97
2.15 2.16
0.288 0.280
1.53
537
E N E R G Y R E S P O N S E TO S L O W H E A V Y I O N S TABLE 1 Projectile
133
55Cs
e
(continued)
~(e)
TABLE 2
~(e)
.Q(e)
6.07 6.07 6.07 6.07 6.07 6.07 7.01 7.01 7.01
3.60 3.58 3.54 3.51 3.60 3.63 4.24 4.26 4.25
2.47 2.49 2.52 2.56 2.47 2.44 2.77 2.75 2.76
0.321 0.313 0.372 0.345 0.312 0.307 0.373 0.368 0.355
0.45 0.45 0.65 0.65 0.65 0.85 0.85 0.85 1.26 1.26 1.26 1.26 1.26 1.26 1.26
0.20 0.20 0.27 0.27 0.28 0.37 0.37 0.37 0.56 0.55 0.55 0.55 0.55 0.56 0.56
0.25 0.25 0.38 0.38 0.37 0.49 0.48 0.48 0.70 0.70 0.70 0.71 0.70 0.70 0.70
0.033 0.036 0.049 0.045 0.045 0.067 0.054 0.061 0.080 0.085 0.084 0.086 0.074 0.070 0.092
The function g(e) employed to calculate the approximation 6) to 7(e), shown as the lower solid curve in fig. 3, from eq. (11).
e
g (e)
0.1 0.2 0.5 1 2 5 10 20 50 100
2.50 2.95 3.80 4.80 6.30 10.6 16.8 29.5 61.7 110
Fig. 2 shows ~/(e) as a function o f e. Comparison of the data with the straight line O(e)= e reveals that energy is dissipated via processes other than electronic excitation. The solid curve through the data is ~/(e) calculated f r o m the theory of Lindhard et al. for silicon projectiles stopping in silicon. The data f r o m ref. 1 are in essential agreement. Fig. 3 shows ~(e) as a function of e. The upper solid line is 9 ( e ) = e. The upper and lower dashed curves
10 I0 xN
i I
o Ne No Ar g K Rb Cs
/g¢(~,... ,Ax~x l Ix. I 0 I"
I
9.
0.I Na o Ne Ar
xK A Rb CS
,
,
ilO
100
E
0.01
Fig. 3. The complimentary function ~(e) = e - ~ ( e ) as a function of the reduced energy e. The upper solid curve is ~(e) = c, the upper and lower dashed curves are ~(e) calculated for Z1 = Z2 with k = 0.1 and 0.2, respectively, and the lower solid curve is an approximation ~ to 7(e) calculated from eq. (11), table 2, and with k = 0.14.
I
LI
I
llO
I00
Fig. 4. Reduced energy straggling,/2(e), in the detector response to heavy charged particles as a function of the reduced energy, e. The solid curve is £2 (e) calculated for silicon projectiles stopping in silicon.
538
A. RATKOWSKI
are ~(e) calculated for Z1 = Z2 with k = 0.1 a n d 0.2, respectively. The lower solid curve is an a p p r o x i m a tion 6) to ~(e) given by Fa(~) --
8
,
at velocities so low that the detector response is not linear in the projectile energy. T h e o r y provides a firm basis for the i n t e r p o l a t i o n o f the detector response for different projectiles o f widely varying energies.
(1 1)
l+kg(0 where k = 0.14 and #(~) is listed in table 2. F o r low values o f e, ~ ( e ) ~ ~. W h e n ~ is large, ~(e,) becomes nearly a constant and thus a decreasing fraction o f V/(~), as is a p p a r e n t from the a s y m p t o t i c a p p r o a c h of ~(~) to the line 0(~) = e in fig. I. The oscillations observed in the electronic stopping cross-section 7,8) are not reflected in these measurements o f the integral energy losses in the target. The d a t a do not permit differentiation to uncover such oscillations. The energy straggling, ,~2(~), is shown in fig. 4. The solid curve is calculated for silicon projectiles stopping in silicon. The energy straggling increases with ~ and is consistently higher than predicted by theory. F o r H, He, and Li, the energy straggling was f o u n d to be insensitive to the projectile energy and to have the value 1 . 2 ± 0 . 6 in reduced units. In conclusion, measurements of the modes of mean energy deposition by slow atomic projectiles in matter agree with the prediction o f the theory within the experimental uncertainties. The straggling in energy deposition is consistently higher by a factor two than predicted by theory, a discrepancy which needs to be resolved. The experiments show that surface barrier particle detectors can be employed reliably for heavy projectiles
i am grateful to W. Brandt for stimulating this investigation and for his help and e n c o u r a g e m e n t during its execution, to N. W o t h e r s p o o n for m a n y informative discussions, to L. Brown for his hospitality and assistance during my sojourn at the Carnegie Institution, and to C. A. Peterson for his diligence t h r o u g h o u t the measurements.
References 1) T. Karcher and N. Wotherspoon, Nucl. Instr. and Meth. 93
(1971) 519. 2) p. Sift'eft, G. Forcinal and A. Coche, IEEE Trans. Nucl. Sci. NS-15 (1968) 275. [Recent experiments 9) in aligned surface-barrier particle detectors reveal that the energy loss and straggling in the detector gold electrode and silicon entrance layer can be measured directly under axial channeling conditions.] :3) L. C. Northcliffe and R. F. Schilling, Atomic Data Tables A7 (1970) 233. 4) W. Whaling, Encyc, Phys. 34 (1958) 193. .5) Ortec Surfitce Barrier Detector Instruction Manual, Ortec, Oak Ridge, Tenn., U.S.A. ~) J. Lindhard, V. Nielsen, M. Scharff and P. V. Thomsen, Mat. Fys. Medd. Dan. Vid. Selsk. 33 no. 10 (1963). 7) j. H. Ormrod and H. E. Duckworth, Can. J. Phys. 41 (1963) 1424. 8) P. Hvelplund and B. Fastrup, Phys. Rev. 165 (1968) 408. ~) J. J. Grob, A. Grob, A. Pape and P. Siffert, Phys. Rev. BI1 (1975) 3273.
INSTRUMENTS
AND
METHODS
[30
(1975) 533-538;
© NORTH-HOLLAND
PUBLISHING
CO
ENERGY R E S P O N S E OF S I L I C O N SURFACE-BARRIER P A R T I C L E D E T E C T O R S TO S L O W HEAVY IONS*
A. RATKOWSKIt Department of Physics, New York University, New York, New York 10003, U.S.A.
Received 18 September 1975 The energy deposited in electronic excitations was measured for It, He, El, N, Ne, Na, Ar, K, Rb, and Cs projectiles with initial ~elocities 0.3 v0
projectiles in matter. Energy straggling is consistently higher than predicted by theory. The locus of the data in reduced coordinates yields a nearly universal curve for such detectors and extends their applicability in charged-particle spectroscopy to low-velocityheavy ions.
I. Introduction This paper reports measurements of the response of silicon surface-barrier particle detectors to heavy charged particles stopping in the depletion region of the detector. The projectiles are all, 2He, 3Li, 7N, a0Ne, 11Na, 1BAr, 19K, 37Rb, and 5sCs in overlapping velocity ranges from 0.3 v0 to 3.75 v0, where Vo = e2/h = 2.18 × 108 cm/s is the atomic unit of velocity. The difference between the kinetic energy of the incident projectiles and the electronic energy losses measured through the detector pulse-height distribution of collected particle-hole pairs yields, to the extent that the division between electronic and screened Coulomb collisions is valid, the energy dissipated in elastic collisions with silicon target atoms. The detector response, therefore, can test the theory of the modes of energy deposition by heavy atomic projectiles in matter. Interpolations based on theory give reliable calibrations of the detector response for measuring the !kinetic energy of slow heavy ions. These experiments extend the first study made in this laboratory t) with slow projectiles, and make contact "with the large body of experimental evidence for the ,detector response at high projectile velocities, where practically all energy is lost in electronic excitations. The experimental details are discussed in section 2 and the data analysis and error discussion are given in section 3. The results are compared with theory in section 4.
New York University accelerator ranging in energy from 75 to 500 keV were stabilized in energy to ~< 0.2% by a crossed-field analyzer. The beams were isotopically pure and the most abundant isotope was selected as the projectile. The analyzed beam intensity was reduced to ~ 100 projectiles/s while being monitored with a Bendix M-306 electron multiplier. The particles impinged upon the target, Ortec detector model TB-022-050-200, serial number 14-009A, mounted in an aluminum housing fitted with a vapor trap. The aperture of the vapor trap, through which the projectiles passed, had an area smaller than the detector sensitive area and restricted the beam to a region of uniform depletion layer thickness. Within experimental error, bombarding the detector at different positions inside the active area produced identical detector response. The depletion depth of 190 pm exceeds the range in silicon of all projectiles investigated. The aluminum block holding the target was attached with a nylon screw to a dewar maintained at 78 K and electrically insulated from the dewar by a mica disc. A 10 cm Microdot coaxial cable connected the detector to a feedthrough in the wall of the target chamber. The output signal of an Ortec model 109A Col limotor ), ,(
Detector _ _
_
~ ~
i ~ P r e a m p lifier
[ I Electron
Col limotor
.Beam . Axis . .
XCrossed-Field Analyzer
:2. Experimental 1H, 2He, 7N, loNe, and 1BAr projectiles from the * Work supported by the United States Energy Research and Development Administration. ? Present address: lnstitut de Physique Nuel6aire, Universit6 Claude Bernard Lyon-l, Lyon, France.
533
G~r01or I
Fig. 1. Schematic representation of the experimental apparatus.
534
A.
RATKOWSKI
preamplifier, connected to the feedthrough by a BNC elbow, was then amplified by an Ortec model 435A amplifier located in the accelerator console room. The target chamber grounded through the amplifier acted as a Faraday cage for the detector. The output charge pulse of the amplifier was analyzed by a Northern Scientific NS-715 pulse-height analyzer. Energy calibration of the detection system, shown schematically in fig. 1, was performed before and after each set 41At n 57 of measurements with 295 ..... and 2vCo sources which emit gamma rays of energies 59.57 and 122.06 keV, respectively. The pressure in the target chamber was held at 2 × 10-7 torr by a turbomolecular pump. The vapor trap in front of the detector prevented carbon buildup from residual oil contamination in the system. Projectile energies were determined by measurements with a Rawson rotating-coil gaussmeter of the magnetic field required to produce a 90 ° deflection of the ion beam in a magnetic spectrometer. The gaussmeter was calibrated in terms of particle energies through the thick-target yield from (p, ~) and (p, 7) resonance reactions. Measurements with alkali ion projectiles, 3Li, 11Na, 19K, 37Rb, and ssCs, were performed at the 3 MeV Van de Graaff accelerator facility of the Carnegie Institution in Washington, D.C. For these experiments the apparatus and electronics were moved from New York to Washington without changes. The mass separation was performed with a magnet which deflected the ion beam through 7 ° . The projectile energies were determined by measuring the accelerating potential with a generating voltmeter calibrated through the yields of nuclear resonance reactions. Projectile energies are known within _+5x 10 - s MeV. Energy calibration of the analyzer was performed with a 241•m 4.7 MeV alpha source in addition to the 95 ..... and ~SWCogamma sources. The target in the alkali ion measurements was an Ortec detector, model A-016-025-100, serial number 10-401. The depletion depth of l l 5 / , m exceeds the range in silicon of the ions investigated. The collection efficiency of a detector for charge carriers produced in the sensitive volume by particlehole excitation was tested by substitution of an Ortec model 410 multimode amplifier for the 435A active filter amplifier so that the detection system time constants could be varied. The detector response was found to remain unchanged within experimental error for integration and differentiation time constants ranging between 1 and 5 l~s. In addition, the detector response to protons was equal to the proton energy in
the detector sensitive volume within experimental uncertainty.
3. Data analysis The amplitude of the output pulses from the amplifier ranged from 0 to 10 V. The pulse-height analyzer divided the voltage range into 512 equal intervals of width A V. The number of pulses, Ni, of amplitude between V i and V i + A V , were stored in channel number C~, forming a histogram of the pulse-height distribution. The position of the centroid of the distribution is proportional to the energy dissipated in electronic excitation by the projectile. The centroid, (7, was calculated numerically from the distributions, Ni Ci _
i
,
(1)
i
where the summation extended over the channel numbers. The pulse-height distributions were free of background. Statistical uncertainties in the numerical determinations of the centroids were < 0.2 %. The analyzer abscissa was calibrated in energy by fitting the centroids of the pulse-height distributions resulting from the detector response to monoenergetic alpha and gamma sources linearly to the corresponding energies by the method of least squares. The uncertainty in the energy calibration was < 0 . 1 % . The energy 0(E) calculated from the centroid is that part of the projectile energy, E, deposited in the sensitive detector volume in the form of particle-hole excitation. The remaining energy ~,(E) = E - ~ ( E )
(2)
is dissipated in elastic collisions. The variance, aa, of a pulse-height distribution was calculated numerically from the distribution,
?
i
l
It contains the contribution of electronic noise in the detection system. This was measured by injecting the output signal from an Ortec model 419 pulse generator into the preamplifier during the measurements, producing a known pulse-height distribution of variance %. Assuming the electronic noise contributes to the
ENERGY
RESPONSE
variance resulting from fluctuations in the stopping of the projectile, a, according to aa2 = a 2 + a p2,
(4)
the energy straggling, /2, is (5)
Q = ma,
where m is the slope of the analyzer calibration line and is; the energy equivalent of the channel width A V. Before entering the sensitive volume of the detector, the projectiles lose the energy AEA~ in penetrating the gold entrance electrode and the energy AEs~ in an insensitive silicon entrance layer. Measurements with protons revealed that, in addition to the gold electrode, quoted by the manufacturer to be of surface density 40pg/cm 2, detectors 14-009A and 10-401 had silicon entrance layers of (5.37 -t- 0.27) and (4.66 -+ 0.25) pg/cm 2, respectively. These values agree well with the findings of Siffert and his collaborators 2). The energy deposited in the sensitive volume of the detector is (6)
,
E = E,-AEAu-AEsl
where E 1 is the incident energy of the projectile. For H, He, and Li projectiles, AEAu and AEs~ were
TO SLOW
HEAVY
535
IONS
calculated from the stopping powers of Northcliffe and Schilling3), Whaling4), and ref. 5; the theory of Lindhard and his collaborators 6) was employed for all other projectiles. The uncertainty in E from the gold and silicon entrance layer corrections ranges from 0.2% at the highest to 0.5% at the lowest energy for the ~H, zHe, vN, loNe, and laAr projectiles and from 0.02% at the highest to 0.1% at the lowest energy for the aLl, ltNa, 19K, 37Rb, and 5sCs projectiles. In summary, it is estimated that for the measurements made from 0.075to0.5 MeV with 1H, 2He, 7N, 10Ne, and ~8Ar projectiles the uncertainty in f/is _+ 1%. The uncertainty in ~ is _+ 15 % at the lowest and +25 % at the highest energy. The error in -(2 is _+30% for vN, loNe, and ~sAr; for ~H and 2He the error is _+50 %. For the alkali ion measurements made from 0.5 to 3 MeV, the error in f/ is less than 1.6%. The uncertainty in ~ is _+20 % at the lowest and _+30 % at the highest energy. The error in .(2 is _+50% for 3Li and _+30 % for i l N a, 19K, 37 Rb, and 5s Cs projectiles. 4. Results
Following Lindhard's notation, we express the projectile energy E in terms of the reduced parameter, e,
I000
IOO
+ o o x o II
H He Li N Ne
a Mz
= Z!Z2(M
l+M2)e
E,
(7)
2
where (Z1, M1) and (Z2, M2) are the atomic number and mass of the projectile and target atoms, respectively, e is the electronic charge, and a is the T h o m a s - F e r m i screening length,
No ~t Ar K A Rb J~ Cs
(9~2) ~ a0 a = ~ 2 ± 2; ( Z [ + Z 2 ) ~'
I0
(8)
ao being the Bohr radius. For projectile velocities less than Z~r0, the electronic stopping cross-section, N - 1 (dE/dR), where N is the number of target atoms per unit volume and d E / d R is the electronic stopping power, in reduced variables is approximated by s. = ke ~, 0.[ ~ 0,1
I I
IO0
L
(9)
where
, I000
k = ~ Fig. 2. D e t e c t o r r e s p o n s e to h e a v y c h a r g e d p a r t i c l e s . T h e r e d u c e d v a r i a b l e s e a n d ~ are p r o p o r t i o n a l to the p r o j e c t i l e e a e r g y a n d the m e a n e n e r g y d e p o s i t e d in e l e c t r o n i c e x c i t a t i o n , respectively. T h e u p p e r solid line is ~ ( e ) = e, the l o w e r is ~'(e) c a l c u l a t e d for silicon p r o j e c t i l e s s t o p p i n g in silicon.
ZIZI2(M1+ M 2 ) ~ (Z~ + "~ 27J~ ~v* ~ 1 iv* ~ 2
0.0793
(~0)
and ~ ~ Z~. The experimental results are listed in reduced variables in table 1.
536
A. R A T K O W S K I TABLE 1
TABLE 1
T h e e x p e r i m e n t a l results. T h e r e d u c e d p r o j e c t i l e e n e r g y , e, t h e r e d u c e d e n e r g y d e p o s i t e d in e l e c t r o n i c e x c i t a t i o n s , ~(e), P ( e ) = e - ~ ( e ) , a n d t h e r e d u c e d e n e r g y s t r a g g l i n g , .(2(e), f o r t h e H , H e , Li, N , N e , N a , A r , K , R b , a n d C s p r o j e c t i l e s e m p l o y e d in this s t u d y . F o r t h e H , H e , a n d Li p r o j e c t i l e s , t h e r e d u c e d e n e r g y s t r a g g l i n g w a s f o u n d to be i n s e n s i t i v e to t h e p r o j e c t i l e e n e r g y a n d to h a v e t h e v a l u e 1.24-0.6.
Projectile
e
F/(e)
~ (e)
~Q(e)
84.83 102.70 106.41 124.85 144.75
85.51 102.63 106.37 125.26 144.16
-
-
145.14 168.51 191.55
145.23 168.43 190.99
-
-
~He
25.25 36.96 51.89 64.57 90.52
23.38 34,35 49.86 61.63 88.42
-
-
aVLi
104.71 104.71 158.84 158.84 213.51 213.51 213.51 213.51 213.51 268.43 268.43 323.49 323.49 378.66 378.66 433.88 433.88 489.11 489.11 544.35
104.24 104.38 158.23 158.00 213.11 213.30 213.29 213.36 213.26 268.17 268.43 323.00 323.26 377.75 377.34 432.15 432.40 489.59 490.17 544.07
-
-
5.90 7.73 9.86 12.72 12.73 12.99 13.07 15.80 15.88 18.14 18.15 19.52 26.08
4.01 5.49 7.39 9.87 9.90 10.31 10.34 12.59 12.74 14.72 14.76 16.03 22.04
1.89 2.24 2.47 2.85 2.84 2.68 2.73 3.21 3.14 3.42 3.39 3.49 4.04
0.664 0.714 0.747 0.904 0.994 0.922 0.780 0.898 1.072 1.139 1.126 1.127 1.162
3.07
1.81
1.26
0.307
,*H
17aN
zo loNe
Projectile
23 llNa
4o laAF
39
19 K
aS~Rb
e
(continued)
~ (e)
~ (e)
.(2 (e)
3.07 4.70 7.09 10.58 10.58 15.19 18.71 22.19
1.83 2.94 4.72 7.67 7.64 11.80 14.94 18.05
1.24 1.76 2.38 2.91 2.94 3.39 3.76 4.14
0.284 0.423 0.568 0.707 0.757 0.971 0.944 1.133
16.20 16.20 24.84 24.84 24.84 33.45 33.45 33.45 42.14 42.14 50.80 50.80 59.50 59.50
12.32 12.40 20.28 20.47 20.27 28.52 28.38 28.11 37.01 37.12 45.40 45.41 54.00 53.79
3.88 3.80 4.56 4.37 4.57 4.93 5.07 5.34 5.13 5.02 5.40 5.39 5.50 5.71
1.040 0.974 1.215 1.237 1.212 1.405 1.404 1.431 1.541 1.387 1.534 1.616 1.759 1.778
68.20 68.20 76.91 85.62
62.34 62.24 70.36 79.04
6.00 5.96 6.54 6.58
1.786 1.771 1.996 1.851
1.87 2.55 3.25 4.62
1.05 1.51 1.94 2.85
0.81 1.05 1.31 1.77
0.200 0.240 0.284 0.358
6.20 6.20 9.67 9.67 13.13 16.62 20.11 23.61 27.09
3.99 4.00 6.72 7.01 9.69 12.75 15.92 19.32 22.11
2.21 2.20 2.95 2.65 3.45 3.86 4.19 4.29 4.97
0.441 0.406 0.629 0.761 0.654 0.922 0.925 1.066 1.006
1.38 1.38 2.31 2.31 3.25 3.25 3.25 3.25 3.25 3.25 4.19 5.13 5.13
0.68 0.68 1.18 1.17 1.72 1.71 1.76 1.74 1.72 1.72 2.31 2.94 2.94
0.69 0.70 1.13 1.14 1.54 1.49 1.51 1.53 1.53 1.88 2.19 2.19
0,097 0.100 0.157 0.138 0.197 0.208 0.242 0,198 0.174 0.203 0.232 0.286 0.309
5.13 5.13
2.98 2.97
2.15 2.16
0.288 0.280
1.53
537
E N E R G Y R E S P O N S E TO S L O W H E A V Y I O N S TABLE 1 Projectile
133
55Cs
e
(continued)
~(e)
TABLE 2
~(e)
.Q(e)
6.07 6.07 6.07 6.07 6.07 6.07 7.01 7.01 7.01
3.60 3.58 3.54 3.51 3.60 3.63 4.24 4.26 4.25
2.47 2.49 2.52 2.56 2.47 2.44 2.77 2.75 2.76
0.321 0.313 0.372 0.345 0.312 0.307 0.373 0.368 0.355
0.45 0.45 0.65 0.65 0.65 0.85 0.85 0.85 1.26 1.26 1.26 1.26 1.26 1.26 1.26
0.20 0.20 0.27 0.27 0.28 0.37 0.37 0.37 0.56 0.55 0.55 0.55 0.55 0.56 0.56
0.25 0.25 0.38 0.38 0.37 0.49 0.48 0.48 0.70 0.70 0.70 0.71 0.70 0.70 0.70
0.033 0.036 0.049 0.045 0.045 0.067 0.054 0.061 0.080 0.085 0.084 0.086 0.074 0.070 0.092
The function g(e) employed to calculate the approximation 6) to 7(e), shown as the lower solid curve in fig. 3, from eq. (11).
e
g (e)
0.1 0.2 0.5 1 2 5 10 20 50 100
2.50 2.95 3.80 4.80 6.30 10.6 16.8 29.5 61.7 110
Fig. 2 shows ~/(e) as a function o f e. Comparison of the data with the straight line O(e)= e reveals that energy is dissipated via processes other than electronic excitation. The solid curve through the data is ~/(e) calculated f r o m the theory of Lindhard et al. for silicon projectiles stopping in silicon. The data f r o m ref. 1 are in essential agreement. Fig. 3 shows ~(e) as a function of e. The upper solid line is 9 ( e ) = e. The upper and lower dashed curves
10 I0 xN
i I
o Ne No Ar g K Rb Cs
/g¢(~,... ,Ax~x l Ix. I 0 I"
I
9.
0.I Na o Ne Ar
xK A Rb CS
,
,
ilO
100
E
0.01
Fig. 3. The complimentary function ~(e) = e - ~ ( e ) as a function of the reduced energy e. The upper solid curve is ~(e) = c, the upper and lower dashed curves are ~(e) calculated for Z1 = Z2 with k = 0.1 and 0.2, respectively, and the lower solid curve is an approximation ~ to 7(e) calculated from eq. (11), table 2, and with k = 0.14.
I
LI
I
llO
I00
Fig. 4. Reduced energy straggling,/2(e), in the detector response to heavy charged particles as a function of the reduced energy, e. The solid curve is £2 (e) calculated for silicon projectiles stopping in silicon.
538
A. RATKOWSKI
are ~(e) calculated for Z1 = Z2 with k = 0.1 a n d 0.2, respectively. The lower solid curve is an a p p r o x i m a tion 6) to ~(e) given by Fa(~) --
8
,
at velocities so low that the detector response is not linear in the projectile energy. T h e o r y provides a firm basis for the i n t e r p o l a t i o n o f the detector response for different projectiles o f widely varying energies.
(1 1)
l+kg(0 where k = 0.14 and #(~) is listed in table 2. F o r low values o f e, ~ ( e ) ~ ~. W h e n ~ is large, ~(e,) becomes nearly a constant and thus a decreasing fraction o f V/(~), as is a p p a r e n t from the a s y m p t o t i c a p p r o a c h of ~(~) to the line 0(~) = e in fig. I. The oscillations observed in the electronic stopping cross-section 7,8) are not reflected in these measurements o f the integral energy losses in the target. The d a t a do not permit differentiation to uncover such oscillations. The energy straggling, ,~2(~), is shown in fig. 4. The solid curve is calculated for silicon projectiles stopping in silicon. The energy straggling increases with ~ and is consistently higher than predicted by theory. F o r H, He, and Li, the energy straggling was f o u n d to be insensitive to the projectile energy and to have the value 1 . 2 ± 0 . 6 in reduced units. In conclusion, measurements of the modes of mean energy deposition by slow atomic projectiles in matter agree with the prediction o f the theory within the experimental uncertainties. The straggling in energy deposition is consistently higher by a factor two than predicted by theory, a discrepancy which needs to be resolved. The experiments show that surface barrier particle detectors can be employed reliably for heavy projectiles
i am grateful to W. Brandt for stimulating this investigation and for his help and e n c o u r a g e m e n t during its execution, to N. W o t h e r s p o o n for m a n y informative discussions, to L. Brown for his hospitality and assistance during my sojourn at the Carnegie Institution, and to C. A. Peterson for his diligence t h r o u g h o u t the measurements.
References 1) T. Karcher and N. Wotherspoon, Nucl. Instr. and Meth. 93
(1971) 519. 2) p. Sift'eft, G. Forcinal and A. Coche, IEEE Trans. Nucl. Sci. NS-15 (1968) 275. [Recent experiments 9) in aligned surface-barrier particle detectors reveal that the energy loss and straggling in the detector gold electrode and silicon entrance layer can be measured directly under axial channeling conditions.] :3) L. C. Northcliffe and R. F. Schilling, Atomic Data Tables A7 (1970) 233. 4) W. Whaling, Encyc, Phys. 34 (1958) 193. .5) Ortec Surfitce Barrier Detector Instruction Manual, Ortec, Oak Ridge, Tenn., U.S.A. ~) J. Lindhard, V. Nielsen, M. Scharff and P. V. Thomsen, Mat. Fys. Medd. Dan. Vid. Selsk. 33 no. 10 (1963). 7) j. H. Ormrod and H. E. Duckworth, Can. J. Phys. 41 (1963) 1424. 8) P. Hvelplund and B. Fastrup, Phys. Rev. 165 (1968) 408. ~) J. J. Grob, A. Grob, A. Pape and P. Siffert, Phys. Rev. BI1 (1975) 3273.