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Enhanced depth and mass resolution with HIRBS
Nuclear Instruments & Methods in Physics Research
Nuclear Instruments and Methods in Physics Research B67 (1992) 98-102 North-Holland
Sechon B
Enhanced depth and mass resolution with HIRBS Q. Yang and D.J. O'Connor
Department of Physics, Universityof Newcastle, NSW 2308, Australia
The extension of Rutherford backscattering spectrometry (RBS) to heavier mass projectiles (HIRBS) has been limited, as these projectiles cause much more radiation damage in the detectors and curtail their lifetime. Despite this limitation interest in the use of heavier projectiles continues as there are several significant benefits which can accrue from their use. To properly understand the interaction of heavy ions with solids a systematic study of the energy loss and straggling of MeV heavy ions has been conducted and an empirical expression for these terms has been obtained. This expression has allowed the development of a realistic computer simulation which accurately predicts the energy spectra for a wide range of energies, projectiles and targets. In parallel with that study, measurements of the depth resolution of Si/Ge multilayer films using 4-6 MeV C projectiles have been used to verify the simulation.
1. Introduction
1.1. Advantages of HIRBS It has been recognized that heavy ion RBS (HIRBS) has several advantages over the conventional RBS using hydrogen or helium ions [1-4]. The principal advantage of HIRBS is that the mass resolution and sensitivity can be improved appreciably for heavy target isotopes, which has been studied extensively and applied Iio materials analysis [5-16]. The specific advantage of HIRBS is the combination of high mass and depth resolution. The advantages of HIRBS will be detailed more completely below. One disadvantage of this approach is the damage caused by heavy ions to the silicon surface barrier detectors (SSBD) which severely limits their useful lifetime; also the heavier mass ions induce greater damage in the target during analysis. As the scattering and damage cross sections result front the same repulsive potential, the relative effect can be easily estimated. The ratio of damage cross seclion to scattering cross section is proportional to the projectile mass. This additional damage may limit analysis in some applications. In addition, the energy resolution using SSBD is significantly poorer when using heavy projectiles. To overcome these difficulties other forms of energy analysis need to be used to properly realise the real benefits of the use of these ions. These methods of analysis may take the form of time-of-flight (TOF) or magnetic and electrostatic spectrometers. The advantages associated with the use of heavy ions are: 1) Improved mass resolution due to the better matching of the projectiles mass with that of the target
atoms. This allows the discrimination of small mass differences between target species at high mass values under conditions not possible with lighter projectiles. 2) Higher stopping power, which, under the right scattering conditions, can lead to equivalent or better depth resolution achievable with normal RBS. 3) The optimum depth resolution can be achieved at higher angles of incidence to the surface with HIRBS reducing the effect of surface roughness on the attainable depth resolution. The limitations to depth resolution involve not only the stopping power but also the energy loss straggling and the lateral spread of the projectiles. For heavy ions the relative contributions of these effects are such that the optimum depth resolution can be achieved at higher angles of incidence than for light projectiles. 4) The higher scattering cross section leads to a greater scattered particle yield per projectile. This feature combined with the reduced high energy tail from the leading edge of the substrate signal leads to an improved sensitivity to high mass surface impurities. By a suitable choice of projectile the scattering yield from a light substrate can be minimised or totally eliminated leading to an enhanced sensitivity to heavy mass surface impurities. With the combination of these effects it has been possible to demonstrate a detection limit for high mass impurities at the level of 10 "~ atoms cm - : [24].
1.2. Depth resolution contributions The depth resolution, St, is given by st = seas],
0168-583X/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
Q. Yang, D.J. O'Connor / Enhanced depth and mass resoh~tion with HIRBS ' . . . . . . . . . . . . . . . . .
(a) . . . . . . . . . . . . . . . . .
AI
Target
.......... •
Lindhard
H He i ° n
+
ion ,o. ion ion
¢2: --o
AA
÷
A
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,tx-~ ......... o
. . . . . . . .
l
. . . . . . . .
I
.01
001
.
,
,
....
. . . . . . .
.i
0.I
1.0
I0.
E/Z, =/' ( M e V / a m u ) .
.
.
.
.
.
.
.
!
.
.
.
.
.
.
.
.
!
.
.
.
.
.
.
.
.
(b)
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lr
~ E . F . ......
~.
Chu
.......... L i n d h n r d
on ֥ He ion A C] ion
--
c~o
~,
.,,.'
~
,s, ..'" ~:::~
~..... ~,....,. ~,,..' • .,e.,"..'~' ' •
o
.001
. . . . . . . .
|
. . . . . . .
.01 E / Z , '/*
II
O. 1
. . . . . . .
.0
(MeV/amu)
Fig, 1. Comparison of published measurements of heavy ion energy straggling with ihc empirical formula (E.F,) for (a) A I and (b) A t ,
I. EXCITATION,STOPPING
!00
Q. Yang, D.J. O'Connor / Enhanced depth and mass resolution with HIRBS
where [S] is the energy loss factor and ~E is the energy width, which has contributions from
~E~ = s e ~ + SE~s + ~Es~. + ~E~w + ~Ek~,+ ~E~s + ~E~s + ~E~ + ~E~. The terms BEBE (ion beam energy spread) and BEBs (ion beam angular divergence) are associated with the accelerator and are usually negligible while the contribution due to the beam area, ~iEBw, and the detector acceptance angle, ~iEAA, are variables at the discretion of the experiment. The term BEsR is associated with the surfaCe roughness, thus sample dependent. The lateral spread gELs is usually negligible and the detector contribution, 8E o, depends on the type of detector and the incident energy. The principal terms of interest are the energy loss straggling SEEs, and the multiple scattering gEMs. The lateral spread is well described by a model of Sigmund and Winterbon [17]. A more comprehensive description of the terms listed above is given elsewhere [3]. 1.3. Energy straggling
Although many experimental results of energy straggling have been reported, there are large discrepancies not only between experimental data and theoretical predictions but also between different measurements for the same combination of projectile and target. As energy straggling is one of the main factors limiting depth resolution, accurate information on energy straggling is important for the realistic modelling of HIRBS. An additional problem is that many of the projectile/target combinations of interest in HIRBS have not been measured for energy loss and straggling. A systematic literature search and analysis of all available measurements has lead to a reliable empirical description of the energy loss straggling [18]. The calculations by Chu [19,20] of the straggling of He ions in all elements were fitted to a functional form to simplify their use in the analysis: (/~CHU/K~B) 2 = (1 + aE b + cE d) - i, where /2 B is Bohr straggling and a, b, c, d are fitted coefficients which are Z 2 dependent. The extrapolation of this to heavy ions using an effective charge description reveals additional energy straggling contributions resulting from correlation effects [21] and charge state fluctuations: (J'~/[~B) 2 = ~2(Zl, Z 2, V)(~'~CHU/[~B) 2 +(Aa/nn)2,
35 a
g ?c g2~
100 nm
50 nm
20
10 nm O'Snm
15 ua m 5
• ~" i0" 1~" io" i f 3'o" ~s' go" i¢ ANGLE OF INCIDENCE
3st b
)
25 20 15 I
~
I
.
.
~
100 nm 50 nm J 10 nm| O'S nm|
o" ~" ~b" ~" 2"o" is" ~o" ~s" ~o" ~s" Angle of Incidence. Fig. 2. The depth resolution as a function of angle of incidence for (a) 2 M e V He and (b) C projectiles in silicon. A minimum in the depth resolution is seen with increasing angle if the analysis depth is greater than approximately 2 nm.
where 7(Z I, Z2, v ) = Zteff(Z I, Z2, u ) / Z 1 is the effective charge. The additional term has been fitted by the following expression:
(Aa/~B) 2 = (zV3/z~,/3)c,r/((~-
c2) 2 + r 2 ) ,
where r = c3(1 -exp~-C,O), and the form of ~c depends on the state of the target material [18]. This expression fits the observations accurately (fig. 1), and the universal nature of it has allowed its use in predicting the straggling for previously unstudied projectile/ target combinations. The resulting empirical formula describes the observations well for all projectiles measured so far, with the exception of Li. A more comprehensive discussion of the special case of Li is given elsewhere [18]. From simulations of the scattering of heavy ions from a surface it is clear that not only can the best oeoth resolution attainable with He at grazing incidence be also achieved with heavy ions, but that the depth resolution does not degrade as much at higher incidence angles when heavy ions are used (fig. 2).
2. Experiment The scattering of 4-6 MeV C from a series of $ i / G e multilayer samples with different layer thick-
IOl
Q. "tang, D.J. O'Connor / Enhanced depth and mass resolution with HIRBS
ncss has been used to test the estimates resulting from the empirical formula for the straggling of heavy ions and the computer simulation. The different multilayers have thickness ranging from 100 to 375 ,~ of alternating layers of Si and S i / G e (17%). The multilayers were chosen as a standard for their near-ideal interface sharpness allowing accurate measurement of energy width with minimum contribution from interface roughness. The abruptness of the interfaces have been determined by cross section TEM. The apparatus used to test the simulation was the 14UD tandem accelerator and an Enge magnetic spectrometer [22,23]. The primary beam was collimated to a spot size of 1 mm 2 and the detector acceptance angle set at 1° to minimise geometrical contributions to the energy width of the scattered particles. In all experiments described here the scattering angle was fixed at 70°. The projectile analysis energy was limited by the entrance window of the gas detector in the focal plane of the Enge magnetic spectrometer. The window would only transmit C projectiles with an energy greater than 2.5 MeV. For this reason the incident projectile energy was limited to 4 MeV, which is greater than the energy which would allow optimum depth resolution for the S i / G e multilayer samples.
3. Results and discussions
The energy spectra of 4 and 6 MeV C ions scattered from the multilayer samples of different thicknesses at various angles of beam incidence were analysed by the least squares fitting of the scattered projectile spectra to ideal profiles to determine the energy widths at the interfaces. From these widths the depth resolution was determined by dividing the energy width by the stopping power factor. The agreements between simulation and experiment are good for both 4 and 6 MeV C scattered off the S i / G e multilayers (fig. 3). There is agrez,nent concerning both the angle of incidence for the minimum depth resolution and the value of the depth resolution at the minimum. These two parameters are determined by a combination of the stopping power, the detector energy resolution, the lateral spread and the energy straggling. As the detector energy resolution for this analyser is well known and the lateral spread is also well characterised, the quality of agreement attests to the validity of the parameterisation described above for the energy straggling. A significant discrepancy is observed for the energy spread (and hence the depth resolution) at large angles of incidence. A typical example is the case of 6 MeV C at an incident angle of 35° for which the energy width is 80 keV, while the simulated width is only 44 keV. With respect to the contributions described in the introduction, the lateral spread and multiple scattering
a00. 4 MaV C Ion 7": + bcatteredf,om
#748 (275 A)
lal
"~- sel:Up~3tl::nt
~ 20( ~, o
o
~ 10c E
o °°m o
.........
Qca
/
I'o.........
~o .........
3'0.........
40
INCIDENTANGLE(degr~o)
a00
z 200
~_ ~ 10c
D~°° = experiment
0 ...................................... 10
20
30
40
INCIDENTANGLE(degrae) Fig. 3. Comparison between experiment and simulation for depth resolution attainable on Si/Ge muitilayers using (a) 4 and (b) 6 MeV carbon projectiles.
contributions to the total energy spread are negligible at large incident angles and the detector resolution for C ions at 4.8 MeV (the leading edge of first layer Ge signal for 6 MeV C) is less than 35 keV. Thus, as the principal angular dependent contribution to the energy straggling at high incidence is the energy straggling, there would appear to be a contradiction to the previously observed agreement. The energy straggling contribution is estimated to be only 21 keV and its contribution decreases with increasing angle, which is at variance with the observed behaviour. The level of disagreement has been observed to increase monotonically with increasing probing depth. The reason for this departure between simulation and experiment is believed to be caused by the crystalline structure of the target. The computer simulation models the interaction of a projectile with an amorphous target, while the target used is a single crystal multilayer sample. One possible explanation for the discrepancy, which could be a function of the probing depth, is that the additional width has been caused ~y partial planar channeling and dechanneling. The chanI. EXCITATION, STOPPING
102
Q. Yang, D.J. O'Connor / Enhanced depth and mass resohation with HIRBS
neling will influence the energy loss and the dcchanneling will contribute an additional energy spread. This hypcthesis is to be tested in a forthcoming series of experiments to he undertaken at different azimuths of the target to ascertain whether the widths depend on whether the incidence direction coincides with a low index or pseudo-random direction.
4. Conclusions An empirical formula has been developed which accurately describes the additional energy straggling from correlation and charge exchange effects observed for heavy ions. The use of this formula has significantly improved computer simulations of the scattering of high energy heavy ions from solid samples. This is verified by the good agreement observed for grazing incidence scattering of 4-6 MeV C ions from S i / G e nmltilayer samples. The angle for the optimum depth resolution and the value of the depth resolution agree well. A departure at larger incidence angles is believed to arise from dechannelling in the target.
Acknowledgements The au~thors thank Dr. T. Jackman of the Canadian National Research Council for the preparation and supply of the S i / G e multilayer samples used in this study, and Dr. T. Ophel of the Australian National University for assistance in making the measurements on the 14UD accelerator and Enge spectrometer possible.
References [1] W.K. Chu, J.W. Mayer and M.A. Nicolet, Backscattering Spectrometry (Academic Press, New York, 1978). [2] E. Schweikert, J. Radioanal. Chem. 78 (1983) 171. [3] DJ. O'Connor and Tan Chunyu, Nucl. Instr. and Meth. B36 (11989) 178.
[4l M. D6beli, P.C. Haubert, R.P. Livi, S.J. Spicklemire, D.L. Weathers and T.A. Tombrello, Nucl. Instr. and Meth. B47 (1990) 148. [5] P. Miiller, W. Szymczak and G. Ischenko, Nucl. Instr. and Meth. 149 (1978) 239. [6] R.T. Sullins, C.V. Barros Leite and E.A. Schweikert, IEEE Trans. Nucl. Sci. NS-28 (1981) 1831. [7] M. Ostling and C.S. Petersson, Nucl. Instr. and Meth. B4 (1984) 88. [8] E. Norbeck, L.W.Li, H.H. Lin and M.E. Anderson, Nucl. Instr. and Meth. B9 (1985) 197. [9] K.M. Yu, J.M. Jaklevic and E.E. Hailer, Nucl. Instr. and Meth. B10/! 1 (1985) 606. [10] K.M. Yu, S.K. Cheung, T. Sands, J.M. Jaklevic and E.E. Hailer, J. Appl. Phys. 61 (1987) 1099. [I I] K.M. Yu, W. Walukiewicz, J.M. Jaklevic and E.E. Hailer, Appl. Phys. Lett. 51 (1987) 189. [12] M.H. Mendenhall, Nucl. Instr. and Meth. BI0/I 1 (1985) 596. [13] T. Sands. J. Metals 38 (1986) 31. [14] A. Chevarier, N. Chevarier, M. Stern, D. Lamouche, P. Clechet, J.R. Martin and P. Person, Nucl. Instr. and Meth. BI3 (1976) 207. [15] P. Person, A. Chevarier, N. Chevarier, P. Clechet, D. Lamouche, J.R. Martin and M. Stern, Nucl. Instr. and Meth. B15 (1986) 425. [16] D.L. Weathers, T.A. Tombrello, M.H. Prior. R.G. Stokstad and R.E. Tribble, Nucl. Instr. and Meth. B42 (1989) 307. [17] P. Sigmund and K.B. Winterbon, Nucl. Instr. and Meth. 119 (1974) 541. [18] Q. Yang, D.J. O'Connor and Zhonglie Wang, Nucl. Instr. and Meth. B61 (1991) 149. [19] W.K. Chu, Phys. Rev. AI3 (1976) 2057. [20] W.K. Chu, in: Ion Beam Handbook for Material Analysis, eds. J.W. Mayer and E. Rimini (Academic Press, New York, 1977). [21] F. Besenbacher, J.U. Andersen and E. Bonderup, Nucl. Instr. and Meth. 168 (1980) 1, and references therein. [22] L.B. Bridwell, H.J. Hay, L.F. Pender, C.J. Sofield and P.B. Treacy, Aust. J. Phys. 41 (1988) 681. [23] L.K. Fifield, T.R. Ophel, G.L. Allan, J.R. Bird and R.F. Davie, Nucl. Irlstr. and Meth. B52 (1990) 233. [24] B.L. Doyle, J.A.Knapp and D.L. Bullet, Nucl. Instr. and Meth. B42 (1989) 295.
Nuclear Instruments and Methods in Physics Research B67 (1992) 98-102 North-Holland
Sechon B
Enhanced depth and mass resolution with HIRBS Q. Yang and D.J. O'Connor
Department of Physics, Universityof Newcastle, NSW 2308, Australia
The extension of Rutherford backscattering spectrometry (RBS) to heavier mass projectiles (HIRBS) has been limited, as these projectiles cause much more radiation damage in the detectors and curtail their lifetime. Despite this limitation interest in the use of heavier projectiles continues as there are several significant benefits which can accrue from their use. To properly understand the interaction of heavy ions with solids a systematic study of the energy loss and straggling of MeV heavy ions has been conducted and an empirical expression for these terms has been obtained. This expression has allowed the development of a realistic computer simulation which accurately predicts the energy spectra for a wide range of energies, projectiles and targets. In parallel with that study, measurements of the depth resolution of Si/Ge multilayer films using 4-6 MeV C projectiles have been used to verify the simulation.
1. Introduction
1.1. Advantages of HIRBS It has been recognized that heavy ion RBS (HIRBS) has several advantages over the conventional RBS using hydrogen or helium ions [1-4]. The principal advantage of HIRBS is that the mass resolution and sensitivity can be improved appreciably for heavy target isotopes, which has been studied extensively and applied Iio materials analysis [5-16]. The specific advantage of HIRBS is the combination of high mass and depth resolution. The advantages of HIRBS will be detailed more completely below. One disadvantage of this approach is the damage caused by heavy ions to the silicon surface barrier detectors (SSBD) which severely limits their useful lifetime; also the heavier mass ions induce greater damage in the target during analysis. As the scattering and damage cross sections result front the same repulsive potential, the relative effect can be easily estimated. The ratio of damage cross seclion to scattering cross section is proportional to the projectile mass. This additional damage may limit analysis in some applications. In addition, the energy resolution using SSBD is significantly poorer when using heavy projectiles. To overcome these difficulties other forms of energy analysis need to be used to properly realise the real benefits of the use of these ions. These methods of analysis may take the form of time-of-flight (TOF) or magnetic and electrostatic spectrometers. The advantages associated with the use of heavy ions are: 1) Improved mass resolution due to the better matching of the projectiles mass with that of the target
atoms. This allows the discrimination of small mass differences between target species at high mass values under conditions not possible with lighter projectiles. 2) Higher stopping power, which, under the right scattering conditions, can lead to equivalent or better depth resolution achievable with normal RBS. 3) The optimum depth resolution can be achieved at higher angles of incidence to the surface with HIRBS reducing the effect of surface roughness on the attainable depth resolution. The limitations to depth resolution involve not only the stopping power but also the energy loss straggling and the lateral spread of the projectiles. For heavy ions the relative contributions of these effects are such that the optimum depth resolution can be achieved at higher angles of incidence than for light projectiles. 4) The higher scattering cross section leads to a greater scattered particle yield per projectile. This feature combined with the reduced high energy tail from the leading edge of the substrate signal leads to an improved sensitivity to high mass surface impurities. By a suitable choice of projectile the scattering yield from a light substrate can be minimised or totally eliminated leading to an enhanced sensitivity to heavy mass surface impurities. With the combination of these effects it has been possible to demonstrate a detection limit for high mass impurities at the level of 10 "~ atoms cm - : [24].
1.2. Depth resolution contributions The depth resolution, St, is given by st = seas],
0168-583X/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
Q. Yang, D.J. O'Connor / Enhanced depth and mass resoh~tion with HIRBS ' . . . . . . . . . . . . . . . . .
(a) . . . . . . . . . . . . . . . . .
AI
Target
.......... •
Lindhard
H He i ° n
+
ion ,o. ion ion
¢2: --o
AA
÷
A
-
,tx-~ ......... o
. . . . . . . .
l
. . . . . . . .
I
.01
001
.
,
,
....
. . . . . . .
.i
0.I
1.0
I0.
E/Z, =/' ( M e V / a m u ) .
.
.
.
.
.
.
.
!
.
.
.
.
.
.
.
.
!
.
.
.
.
.
.
.
.
(b)
Target
lr
~ E . F . ......
~.
Chu
.......... L i n d h n r d
on ֥ He ion A C] ion
--
c~o
~,
.,,.'
~
,s, ..'" ~:::~
~..... ~,....,. ~,,..' • .,e.,"..'~' ' •
o
.001
. . . . . . . .
|
. . . . . . .
.01 E / Z , '/*
II
O. 1
. . . . . . .
.0
(MeV/amu)
Fig, 1. Comparison of published measurements of heavy ion energy straggling with ihc empirical formula (E.F,) for (a) A I and (b) A t ,
I. EXCITATION,STOPPING
!00
Q. Yang, D.J. O'Connor / Enhanced depth and mass resolution with HIRBS
where [S] is the energy loss factor and ~E is the energy width, which has contributions from
~E~ = s e ~ + SE~s + ~Es~. + ~E~w + ~Ek~,+ ~E~s + ~E~s + ~E~ + ~E~. The terms BEBE (ion beam energy spread) and BEBs (ion beam angular divergence) are associated with the accelerator and are usually negligible while the contribution due to the beam area, ~iEBw, and the detector acceptance angle, ~iEAA, are variables at the discretion of the experiment. The term BEsR is associated with the surfaCe roughness, thus sample dependent. The lateral spread gELs is usually negligible and the detector contribution, 8E o, depends on the type of detector and the incident energy. The principal terms of interest are the energy loss straggling SEEs, and the multiple scattering gEMs. The lateral spread is well described by a model of Sigmund and Winterbon [17]. A more comprehensive description of the terms listed above is given elsewhere [3]. 1.3. Energy straggling
Although many experimental results of energy straggling have been reported, there are large discrepancies not only between experimental data and theoretical predictions but also between different measurements for the same combination of projectile and target. As energy straggling is one of the main factors limiting depth resolution, accurate information on energy straggling is important for the realistic modelling of HIRBS. An additional problem is that many of the projectile/target combinations of interest in HIRBS have not been measured for energy loss and straggling. A systematic literature search and analysis of all available measurements has lead to a reliable empirical description of the energy loss straggling [18]. The calculations by Chu [19,20] of the straggling of He ions in all elements were fitted to a functional form to simplify their use in the analysis: (/~CHU/K~B) 2 = (1 + aE b + cE d) - i, where /2 B is Bohr straggling and a, b, c, d are fitted coefficients which are Z 2 dependent. The extrapolation of this to heavy ions using an effective charge description reveals additional energy straggling contributions resulting from correlation effects [21] and charge state fluctuations: (J'~/[~B) 2 = ~2(Zl, Z 2, V)(~'~CHU/[~B) 2 +(Aa/nn)2,
35 a
g ?c g2~
100 nm
50 nm
20
10 nm O'Snm
15 ua m 5
• ~" i0" 1~" io" i f 3'o" ~s' go" i¢ ANGLE OF INCIDENCE
3st b
)
25 20 15 I
~
I
.
.
~
100 nm 50 nm J 10 nm| O'S nm|
o" ~" ~b" ~" 2"o" is" ~o" ~s" ~o" ~s" Angle of Incidence. Fig. 2. The depth resolution as a function of angle of incidence for (a) 2 M e V He and (b) C projectiles in silicon. A minimum in the depth resolution is seen with increasing angle if the analysis depth is greater than approximately 2 nm.
where 7(Z I, Z2, v ) = Zteff(Z I, Z2, u ) / Z 1 is the effective charge. The additional term has been fitted by the following expression:
(Aa/~B) 2 = (zV3/z~,/3)c,r/((~-
c2) 2 + r 2 ) ,
where r = c3(1 -exp~-C,O), and the form of ~c depends on the state of the target material [18]. This expression fits the observations accurately (fig. 1), and the universal nature of it has allowed its use in predicting the straggling for previously unstudied projectile/ target combinations. The resulting empirical formula describes the observations well for all projectiles measured so far, with the exception of Li. A more comprehensive discussion of the special case of Li is given elsewhere [18]. From simulations of the scattering of heavy ions from a surface it is clear that not only can the best oeoth resolution attainable with He at grazing incidence be also achieved with heavy ions, but that the depth resolution does not degrade as much at higher incidence angles when heavy ions are used (fig. 2).
2. Experiment The scattering of 4-6 MeV C from a series of $ i / G e multilayer samples with different layer thick-
IOl
Q. "tang, D.J. O'Connor / Enhanced depth and mass resolution with HIRBS
ncss has been used to test the estimates resulting from the empirical formula for the straggling of heavy ions and the computer simulation. The different multilayers have thickness ranging from 100 to 375 ,~ of alternating layers of Si and S i / G e (17%). The multilayers were chosen as a standard for their near-ideal interface sharpness allowing accurate measurement of energy width with minimum contribution from interface roughness. The abruptness of the interfaces have been determined by cross section TEM. The apparatus used to test the simulation was the 14UD tandem accelerator and an Enge magnetic spectrometer [22,23]. The primary beam was collimated to a spot size of 1 mm 2 and the detector acceptance angle set at 1° to minimise geometrical contributions to the energy width of the scattered particles. In all experiments described here the scattering angle was fixed at 70°. The projectile analysis energy was limited by the entrance window of the gas detector in the focal plane of the Enge magnetic spectrometer. The window would only transmit C projectiles with an energy greater than 2.5 MeV. For this reason the incident projectile energy was limited to 4 MeV, which is greater than the energy which would allow optimum depth resolution for the S i / G e multilayer samples.
3. Results and discussions
The energy spectra of 4 and 6 MeV C ions scattered from the multilayer samples of different thicknesses at various angles of beam incidence were analysed by the least squares fitting of the scattered projectile spectra to ideal profiles to determine the energy widths at the interfaces. From these widths the depth resolution was determined by dividing the energy width by the stopping power factor. The agreements between simulation and experiment are good for both 4 and 6 MeV C scattered off the S i / G e multilayers (fig. 3). There is agrez,nent concerning both the angle of incidence for the minimum depth resolution and the value of the depth resolution at the minimum. These two parameters are determined by a combination of the stopping power, the detector energy resolution, the lateral spread and the energy straggling. As the detector energy resolution for this analyser is well known and the lateral spread is also well characterised, the quality of agreement attests to the validity of the parameterisation described above for the energy straggling. A significant discrepancy is observed for the energy spread (and hence the depth resolution) at large angles of incidence. A typical example is the case of 6 MeV C at an incident angle of 35° for which the energy width is 80 keV, while the simulated width is only 44 keV. With respect to the contributions described in the introduction, the lateral spread and multiple scattering
a00. 4 MaV C Ion 7": + bcatteredf,om
#748 (275 A)
lal
"~- sel:Up~3tl::nt
~ 20( ~, o
o
~ 10c E
o °°m o
.........
Qca
/
I'o.........
~o .........
3'0.........
40
INCIDENTANGLE(degr~o)
a00
z 200
~_ ~ 10c
D~°° = experiment
0 ...................................... 10
20
30
40
INCIDENTANGLE(degrae) Fig. 3. Comparison between experiment and simulation for depth resolution attainable on Si/Ge muitilayers using (a) 4 and (b) 6 MeV carbon projectiles.
contributions to the total energy spread are negligible at large incident angles and the detector resolution for C ions at 4.8 MeV (the leading edge of first layer Ge signal for 6 MeV C) is less than 35 keV. Thus, as the principal angular dependent contribution to the energy straggling at high incidence is the energy straggling, there would appear to be a contradiction to the previously observed agreement. The energy straggling contribution is estimated to be only 21 keV and its contribution decreases with increasing angle, which is at variance with the observed behaviour. The level of disagreement has been observed to increase monotonically with increasing probing depth. The reason for this departure between simulation and experiment is believed to be caused by the crystalline structure of the target. The computer simulation models the interaction of a projectile with an amorphous target, while the target used is a single crystal multilayer sample. One possible explanation for the discrepancy, which could be a function of the probing depth, is that the additional width has been caused ~y partial planar channeling and dechanneling. The chanI. EXCITATION, STOPPING
102
Q. Yang, D.J. O'Connor / Enhanced depth and mass resohation with HIRBS
neling will influence the energy loss and the dcchanneling will contribute an additional energy spread. This hypcthesis is to be tested in a forthcoming series of experiments to he undertaken at different azimuths of the target to ascertain whether the widths depend on whether the incidence direction coincides with a low index or pseudo-random direction.
4. Conclusions An empirical formula has been developed which accurately describes the additional energy straggling from correlation and charge exchange effects observed for heavy ions. The use of this formula has significantly improved computer simulations of the scattering of high energy heavy ions from solid samples. This is verified by the good agreement observed for grazing incidence scattering of 4-6 MeV C ions from S i / G e nmltilayer samples. The angle for the optimum depth resolution and the value of the depth resolution agree well. A departure at larger incidence angles is believed to arise from dechannelling in the target.
Acknowledgements The au~thors thank Dr. T. Jackman of the Canadian National Research Council for the preparation and supply of the S i / G e multilayer samples used in this study, and Dr. T. Ophel of the Australian National University for assistance in making the measurements on the 14UD accelerator and Enge spectrometer possible.
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