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Influence of the chemical state on the stopping of protons and He-ions in some oxides
BmamIntomotions MatarIa & Atoms
with ELSEVIER
Nuclear Instruments and Methods in Physics Research B 13&138 (1998) 103-108
Influence of the chemical state on the stopping of protons and He-ions in some oxides P. Bauer ‘.*, R. Golser b, D. Semrad a, P. Maier-Komor
‘, F. Aumayr d, A. Arnau e
a Institut jiir Experimentalphysik. Johannes-Kepler Universittit Linz. A-4040 Linz. Austria h Institut ftir Radiumjbrschung und Kernphysik. Universitiit Wien. A-1090 Wien. Austria ’ Target Lahorator): Technical University Munich. D-85748 Garching. German) ’ Institut .fiir Allgemeine Physik, Technische Universitiit Wien. A-1040 Wirn. Austria ’ Departamento de Fisica de Materiales. Universidud de1 Puis Vasw. Apartado 107 2. 20080 San Sehasticin. Spain
Abstract We present stopping cross section data of A&O3 and SiOz for hydrogen- and helium-ions in the energy range 2-1000 keV, measured in transmission and in backscattering geometry. To interpret the data, we discuss the high velocity and the low velocity limit of so-called chemical effects commonly defined as the difference in stopping of the compound and of a mixture of its constituents, as calculated by applying Bragg’s rule. At high velocities, the projectiles are point charges and only changes in the target electron states contribute to the chemical effect. In addition, at low velocities the charge states of the projectiles and the screening by the target valence electrons may differ in the compound and in 0 1998 Elsevier Science B.V. the mixture, due to different electron densities. PACS: 34.50 Bw; 61.82 MS; 61.80 AZ; 3450 Fa K~~~YNYIs:Protons; He ions; Insulators; Electronic
energy loss; Chemical
1. Introduction
This contribution deals with the energy loss of protons and helium ions in oxygen compounds (SiOz. A&03) and aims at the systematic investigation of the chemical effect in electronic stopping, i.e. the difference between the stopping cross section of a compound compared to a mixture of its constituents As = c,,,,,r - E,ix [1,2]. According
*Corresponding author. Tel.: +43 732 2468 516; fax: +43 732 2468 9677: e-mail: [email protected]. 0168-583X/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved PIISOl68-583X(97)00868-9
state effects; Bragg’s rule
to Bragg’s rule [3] this difference should be negligible. Amongst all compounds, oxides are of special interest because of both, their technical importance in many fields and the strength of the chemical bond, which on the one hand facilitates energy loss measurements and on the other hand results in large chemical effects [4]. Note that for oxygen not only the chemical environment but also the physical state changes when being incorporated into a solid oxide. We describe the electronic stopping in terms of the stopping cross section, E, in units of lOPI5 eV cm’, which includes all possible energy trans-
104
P. Bauer et al. I Nucl. Instr. and Meth. in Phys. Rex B 136-138 (1998) 103-108
fers weighted by the corresponding cross section [5]. In the literature, the chemical effects in oxides have been described by introducing a so-called ‘solid oxygen stopping cross section’ E~,~,,~ which for a compound X,0, is defined as follows (see Ref. [6] and references therein): QGIO”- m&X ~O.sol= (1) n with the stopping cross sections of the compound and the atom ‘X’ denoted by E~,~, and Ed, respectively. With this definition, the different behavior of the valence electrons in a metal and in an oxide is taken into account in a global way. An alternative description of chemical effects was given in [5] where the contribution of the valence electrons in the oxide was determined separately and was shown to be independent of details of the chemical bonds.
3. Chemical effects for protons In Fig. 1 we present our experimental results for proton stopping in A&O3 and SiOZ in the energy range 2-700 keV [4,7]. In order not to be confused by a large number of data points, where necessary we represent our data by fit curves with some error bars indicating the scatter of the indioidual measurements. In Fig. l(a), the results for the compounds are compared to &,,,ixof the corresponding mixtures, calculated using data from Refs. [8-121. The E values of the mixtures exceed 100,
H -> AI,O, and SiO, and mixtures .
....
. .... .
10
100
2. Experimental data Our investigation is based mainly on our own measurements of electronic stopping of protons and He ions in Si02 and A1203 [4,7] and in their solid constituents, Al and Si [8,9]; data for oxygen gas have been taken from Refs. [lo, 111, the data for low energy proton stopping in Al are taken from [12]. Our overall energy range is from 2 keV up to 1 MeV. The proton data for the oxides have been obtained in backscattering (RBS) and in transmission using an electrostatic analyzer (ESA) for ions at higher energies and time-of-flight (TOF) spectrometry for low energy ions. All experimental methods yield concordant results. This is the reason why we consider our data as being superior to data which are obtained in one lab by applying only one single method. As a consequence, we restrict our investigation of chemical effects to those data, where at least both, the stopping cross sections of the oxides and their solid constituents, were measured in one lab. For the oxides, our energy loss data for He ions have been obtained at the HMI in Berlin for the identical set of foils used for the measurements with protons, thus we could use the re-evaluated target thicknesses as described in 141.We estimate the accuracy of our data to be +5% (standard deviation).
1
a
1000
proton energy (keV) chemical effect for H -> AI,O, and SiO, rrrl 20
N-
b
15
(2Al+3/,0,
) - AI,O,
t
energy per nucleon (keV)
Fig. 1. (a) Stopping cross section of alumina and silica and of the corresponding mixtures for protons, as represented by fit curves. The error bars indicate our estimated experimental uncertainty of f5%. For comparison we have added the stopping cross section of an oxygen molecule from Refs. [lO.l I]. (b) Absolute chemical effect for alumina and silica for protons in terms of AE = &mix- ~,,p. Also shown are the high energy predictions by Bethe theory. The dotted lines assume velocity proportionality, see Eq. (3).
105
P. Baurr et al. I Nucl. Instr. and Meth. in Phys. Rex B 136-138 (1998)
those of the compounds in the whole energy range. The stopping maxima of the mixtures are higher and appear at lower energy compared to the oxides. In order to illustrate the chemical effect more clearly, we show As, in Fig. l(b). AE has its maximum value at a proton energy of about 30 keV which is shifted towards lower energies compared to both maxima, s,,,r and &mix;the exact energy position of ~~~~~is very sensitive to the detailed shape of the maxima -of s,,,r and &mix. That AE decreases when going to higher energies is easily understood in terms of Bethe theory. At high energies, where the projectiles are point charges, the only contribution to the chemical effect is due to a change in the states of the valence electrons when going from the mixture to the compound, the only quantity that might change is the ionization potential IYal of the valence electrons. Since the valence electrons are more strongly bound in a compound than in its constituents, l(?mp) Vdl is greater than Z$ix’. The chemical effect reads approximately.
Here, Z, and Z? are the atomic numbers of projectile and target, m, and e are mass and charge of an electron, v is the velocity of the ion and timi’) and ficomp)are the mean ionization potentials of the mixture and the compound, respectively. In Eq.. (2), the ratio I(comr)/l(mix) reflects the ratio Z$mp)/Z~~), since the inner shell contributions remain unaffected by the chemical bond and cancel each other out. It is worth to note that the Barkas term [13] is the only correction term to Bethe theory that is expected to contribute significantly to AE, too. According to Lindhard [14] the Bloch term takes account of modifying the stopping number for small impact parameters when increasing the projectile’s charge number. These close encounters are supposed to be less sensitive to changes in binding energy. In Fig. l(b), the Bethe result for the chemical effect using the Z values from Ref. [15] is included. The agreement with the experimental data is only qualitative, as a consequence of experimental uncertain-
103~1OX
ties: for our uncertainties of f5% for a,,, and E,,,~. respectively, and an assumed chemical effect AE x 0.1 E we obtain an uncertainty of N 70% for AE. Note that this is an inherent problem of investigations of chemical effects which leads to the consequence that investigations of the chemical effect suffer intrinsically from poor accuracy which results in widely spread data. At intermediate energies, i.e. in the velocity regime below N Zfi3v0 which is the mean velocity of projectile electrons within the Thomas-Fermi model, ions may carry bound electrons while traversing the target material. Here, capture and loss of electrons by the projectile will contribute to the energy loss and thus make the interpretation of the data more complex. At low velocities (o < rr = v. = c/137 with C’Fthe Fermi velocity and Do)the Bohr velocity) the ansatz dE/dx = Qtl
(3)
has a sound theoretical basis for a free electron gas. It has been found to be an appropriate description for metals [12] and insulators [7], independent of the magnitude of the gap. It also holds for gaseous targets, with the only exception of proton stopping in noble gases at very low proton velocities [16,17]. Thus, at low velocities, also the chemical effect is expected to be proportional to the ion velocity, AE 0~ u. As shown in Fig. l(b), our experimental results are within the experimental uncertainties in agreement with this behavior. We note that we cannot give a theoretical estimate of stopping cross sections for the gas phase or solid insulators which is as accurate as the one for solid metals in the low velocity regime, where the scattering of electrons at the Fermi level can be treated to all orders in the projectile charge and, consequently, it is not restricted to a perturbative description. However, the knowledge of the velocity dependence at low velocities may be used to extrapolate the chemical effect measured at 10 or 20 keV towards lower velocities.
4. Chemical effects for He ions In Fig. 2(a) we present our experimental results for He stopping in A&O3 and SiOr and the corre-
106
P. Bow 300
_
x0-
;
* 2
200-
?o
150-
et (11.I Nucl. Instr. and Meth. in Phys. Rex B 136-138 (1998)
,
,
,
,
,
200
400
600
800
1000
5 w 100. 501’ 0
a
1
1200
‘He energy (keV)
AI,O,,Santry& Werner
b Fig. 2. (a) Stopping cross section of alumina and silica for He ions. The data of the corresponding mixtures (solid lines) are represented by fit curves. The dashed lines represent the experimental results for the oxides from Santry [20.21]. (b) Absolute chemical effect for alumina and silica for He ions in terms of AE= s,,, - ~,,mp. The solid line and the dashed line represent our results for A1203 and for SiOz. respectively. The dotted line and the dashdotted line refer to the equivalent results from [20,2 I].
sponding mixtures in the energy range 15-800 keV [ 181.Our data for the compounds are compared to
&mixof the corresponding mixtures, which are calculated from Refs. [8,9,11]. Also shown are the experimental results for the oxides by Santry [21,22]. Compared to our data, Santry’s data are low in the whole energy range, by up to 10%. The maxima of the compounds again are found at a higher energy with a smaller height compared to the mixtures. Note that the E values are very large; in the case of alumina it corresponds to an energy loss per monolayer of up to 200 eV. Fig. 2(b) shows the chemical effect as a function of the He energy. Here, the behavior of the chemical effect deduced
103-108
from our data is in considerable contrast to that obtained from Santry’s work [2 1,221, corroborating our discussion of error propagation (see above). Our He data show the largest chemical effect at - 370 keV. Analogously to the case of proton stopping, this energy is below the stopping maxima of the compounds and the mixtures. In both cases, the relative chemical effect is up to B9% which is less than in the case of protons. Towards higher energies the chemical effect becomes smaller. similarly as for protons. Since in our energy range the He-ions are not point charges it does not make sense to compare these results to Bethe theory since charge state and screening effects will play an important role. At about IOO150 keV, i.e. at velocities L’z OF(OF of the oxides as calculated from plasmon energies is in the order of 1.2 uo), our data show no discernible (or even a negative) chemical effect. Finally we present the stopping ratio &H&Hfor our compounds and the corresponding mixtures in Fig. 3. For the oxides, the ratio .+JQ reaches a plateau at low energies, at values of 2.6 and 2.35 for A1203, and SiO,, respectively. The plateau values are quite large compared to the stopping ratios obtained for Al and Si [8,9] which are close to 2.0. Fig. 3 also includes the stopping ratio by Ziegler [23], which is a universal curve, independent of the target material. Ziegler’s curve is only in fair agreement with our experimental findings, with large deviations at the lowest energies. The findings of our investigation may be interpreted in terms of valence electron densities (in our regime the mean energy transfer is large compared to the energy gap): the plasmon energies of the oxides (- 24 eV) are considerably higher than that of Al and Si (15 and 16.5 eV, respectively), corresponding to considerably higher valence electron densities in the oxides. At low energies, a higher density of valence electrons leads to a larger stopping ratio E&E” [9], in qualitative agreement with density functional theory (DFT) which is a nonlinear model [ 19,201 to describe the stopping behavior of slow ions in an electron gas (see Fig. 3). The stopping ratio obtained from DFT fits our experimental findings nicely, but it yields the same plateau height for Si02 and for Al203, in contrast to the experimental findings. This shows again that
P. Buuer et ul. I Nucl. Instr. und Meth. in Phys. Rex B 136-138 (1998) 103-108
107
I
J
H, He -> AI,O,
0
50
100
.
150
200
fl
250
energy per nucleon (keV)
a
methods in three different labs which all contributed to a consistent set of data which gives our data special weight. For protons larger chemical effects have been observed than for He ions. As a consequence, in case the chemical effect cannot be taken into account properly, ion beam analysis by use of He beams will give lower systematic errors when simple additivity of the individual cross sections in the mixture is assumed according to Bragg’s rule. Acknowledgements We gratefully acknowledge the help of Peter Mertens in the course of performing the measurements with He ions and his continuous interest in the progress of this work. References
l,Bl;
0
b
h
50
100
h 150
J
200
energy per nucleon (keV)
Fig. 3. (a) Stopping ratio am/au for alumina (full circles) and the corresponding mixture (full line). For comparison we have added the universal curve from [23] (dashed line). (b) Stopping ratio E&Q for silica (full squares) and the corresponding mixture (full line). For comparison we have added the universal curve from [23] (dashed line).
the applicability of electron gas arguments for insulators is limited.
5. Conclusions We have presented experimental results for proton and He stopping in A1203 and SiO, and have compared the results to the equivalent mixtures. The information on chemical effects deduced from different sets of experiments is considerably at variance, as a consequence of experimental uncertainties and the well known misfit of data obtained in different labs. We therefore stress the point that our data are obtained by at least two independent
D.I. Thwaites. Nucl. Instr. and Meth. B I? (1985) 84. D.I. Thwaites, Nucl. Instr. and Meth. B 69 (1992) 53. [31 W.H. Bragg, R. Kleeman. Phil. Mag. 10 (1905) 318. [41 P. Bauer, W. Rossler. P. Mertens. Nucl. Instr. and Meth. B 69 (1992) 46. i51 P. Bauer. R. Golser. F. Aumayr. D. Semrad, A. Arnau. E. Zarate. R. Diez-Muitio. Nucl. Instr. and Meth. B 125 (1997) 102. PI J.F. Ziegler. in Stopping and Ranges of Ions in Matter. vol. 4. J.F. Ziegler (Ed.). Helium: Stopping Powers and Ranges in All Elemental Matter. Pergamon Press. New York. 1977. [71 K. Eder, D. Semrad, P. Bauer. R. Golser. P. MaierKomor. F. Aumayr. M. Peiialba. A. Arnau, J.M. Ugalde. P.M. Echenique, Phys. Rev. Lett. 79 (1997) 4112. PI Ch. Eppacher. Ph.D. Thesis. University of Linz. 1995. [91 Ch. Eppacher, D. Semrad. Nucl. Instr. Meth. B 69 (1992) 33. UOI V. Dose. G. Sele. Z. Phys. A 272 (1975) 237. [’ 11 G. Reiter. H. Baumgart, N. Kniest. E. Pfaff. G. Clausnitzer. Nucl. Instr. Meth. B 27 (1987) 280. J.E. Valdes. G. Martinez TdmayO. G.H. Lantschner. J.C. Eckardt. N.R. Arista. Nucl. Instr. and Meth. B 73 (1993) 313. u31 P. Sigmund, Nucl. Instr. Meth B (1998) in press. [I41 J. Lindhard. A. Sorensen. Phys. Rev. A 53 (1996) 2443. [I51 International commission on radiation units and measurements. Report 49, Stopping powers and ranges for protons and alpha particles. 1993. [I61 R. Golser. D. Semrad. Phys. Rev. Lett. 66 (1991) 1831. [I71 A. Schiefermueller. R. Golser. R. Stohl, D. Semrdd. Phys. Rev. A 48 (1993) 4467.
VI VI
108
P. Bauer et al. I Nucl. Instr.
and Meth.
W. Riissler. Diploma Thesis, University of Linz, 1992. [19] P.M. Echenique. R. Nieminen. R.H. Ritchie. Solid State Commun. 37 (1981) 779. [20] P.M. Echenique. F. Flores. R.H. Ritchie. in: H. Ehrenreich (Ed.). Solid State Physics: Advances in Research and Applications, vol. 43. Academic Press, New York, 1990, p. 229. [18]
in Phys. Res. B 136-138
[21] D.C. Santry. 169.
(1998)
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R.D. Werner.
Nucl. Instr. Meth. B 14 (1986)
[22] D.C. Santry, R.D. Werner, Nucl. Instr. and Meth. 178 (1980) 523. [23] J.F. Ziegler. J.P. Biersack. U. Littmark. The Stopping and Range of Ions in Solids, vol. 1. Pergamon Press. New York. 1985.
with ELSEVIER
Nuclear Instruments and Methods in Physics Research B 13&138 (1998) 103-108
Influence of the chemical state on the stopping of protons and He-ions in some oxides P. Bauer ‘.*, R. Golser b, D. Semrad a, P. Maier-Komor
‘, F. Aumayr d, A. Arnau e
a Institut jiir Experimentalphysik. Johannes-Kepler Universittit Linz. A-4040 Linz. Austria h Institut ftir Radiumjbrschung und Kernphysik. Universitiit Wien. A-1090 Wien. Austria ’ Target Lahorator): Technical University Munich. D-85748 Garching. German) ’ Institut .fiir Allgemeine Physik, Technische Universitiit Wien. A-1040 Wirn. Austria ’ Departamento de Fisica de Materiales. Universidud de1 Puis Vasw. Apartado 107 2. 20080 San Sehasticin. Spain
Abstract We present stopping cross section data of A&O3 and SiOz for hydrogen- and helium-ions in the energy range 2-1000 keV, measured in transmission and in backscattering geometry. To interpret the data, we discuss the high velocity and the low velocity limit of so-called chemical effects commonly defined as the difference in stopping of the compound and of a mixture of its constituents, as calculated by applying Bragg’s rule. At high velocities, the projectiles are point charges and only changes in the target electron states contribute to the chemical effect. In addition, at low velocities the charge states of the projectiles and the screening by the target valence electrons may differ in the compound and in 0 1998 Elsevier Science B.V. the mixture, due to different electron densities. PACS: 34.50 Bw; 61.82 MS; 61.80 AZ; 3450 Fa K~~~YNYIs:Protons; He ions; Insulators; Electronic
energy loss; Chemical
1. Introduction
This contribution deals with the energy loss of protons and helium ions in oxygen compounds (SiOz. A&03) and aims at the systematic investigation of the chemical effect in electronic stopping, i.e. the difference between the stopping cross section of a compound compared to a mixture of its constituents As = c,,,,,r - E,ix [1,2]. According
*Corresponding author. Tel.: +43 732 2468 516; fax: +43 732 2468 9677: e-mail: [email protected]. 0168-583X/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved PIISOl68-583X(97)00868-9
state effects; Bragg’s rule
to Bragg’s rule [3] this difference should be negligible. Amongst all compounds, oxides are of special interest because of both, their technical importance in many fields and the strength of the chemical bond, which on the one hand facilitates energy loss measurements and on the other hand results in large chemical effects [4]. Note that for oxygen not only the chemical environment but also the physical state changes when being incorporated into a solid oxide. We describe the electronic stopping in terms of the stopping cross section, E, in units of lOPI5 eV cm’, which includes all possible energy trans-
104
P. Bauer et al. I Nucl. Instr. and Meth. in Phys. Rex B 136-138 (1998) 103-108
fers weighted by the corresponding cross section [5]. In the literature, the chemical effects in oxides have been described by introducing a so-called ‘solid oxygen stopping cross section’ E~,~,,~ which for a compound X,0, is defined as follows (see Ref. [6] and references therein): QGIO”- m&X ~O.sol= (1) n with the stopping cross sections of the compound and the atom ‘X’ denoted by E~,~, and Ed, respectively. With this definition, the different behavior of the valence electrons in a metal and in an oxide is taken into account in a global way. An alternative description of chemical effects was given in [5] where the contribution of the valence electrons in the oxide was determined separately and was shown to be independent of details of the chemical bonds.
3. Chemical effects for protons In Fig. 1 we present our experimental results for proton stopping in A&O3 and SiOZ in the energy range 2-700 keV [4,7]. In order not to be confused by a large number of data points, where necessary we represent our data by fit curves with some error bars indicating the scatter of the indioidual measurements. In Fig. l(a), the results for the compounds are compared to &,,,ixof the corresponding mixtures, calculated using data from Refs. [8-121. The E values of the mixtures exceed 100,
H -> AI,O, and SiO, and mixtures .
....
. .... .
10
100
2. Experimental data Our investigation is based mainly on our own measurements of electronic stopping of protons and He ions in Si02 and A1203 [4,7] and in their solid constituents, Al and Si [8,9]; data for oxygen gas have been taken from Refs. [lo, 111, the data for low energy proton stopping in Al are taken from [12]. Our overall energy range is from 2 keV up to 1 MeV. The proton data for the oxides have been obtained in backscattering (RBS) and in transmission using an electrostatic analyzer (ESA) for ions at higher energies and time-of-flight (TOF) spectrometry for low energy ions. All experimental methods yield concordant results. This is the reason why we consider our data as being superior to data which are obtained in one lab by applying only one single method. As a consequence, we restrict our investigation of chemical effects to those data, where at least both, the stopping cross sections of the oxides and their solid constituents, were measured in one lab. For the oxides, our energy loss data for He ions have been obtained at the HMI in Berlin for the identical set of foils used for the measurements with protons, thus we could use the re-evaluated target thicknesses as described in 141.We estimate the accuracy of our data to be +5% (standard deviation).
1
a
1000
proton energy (keV) chemical effect for H -> AI,O, and SiO, rrrl 20
N-
b
15
(2Al+3/,0,
) - AI,O,
t
energy per nucleon (keV)
Fig. 1. (a) Stopping cross section of alumina and silica and of the corresponding mixtures for protons, as represented by fit curves. The error bars indicate our estimated experimental uncertainty of f5%. For comparison we have added the stopping cross section of an oxygen molecule from Refs. [lO.l I]. (b) Absolute chemical effect for alumina and silica for protons in terms of AE = &mix- ~,,p. Also shown are the high energy predictions by Bethe theory. The dotted lines assume velocity proportionality, see Eq. (3).
105
P. Baurr et al. I Nucl. Instr. and Meth. in Phys. Rex B 136-138 (1998)
those of the compounds in the whole energy range. The stopping maxima of the mixtures are higher and appear at lower energy compared to the oxides. In order to illustrate the chemical effect more clearly, we show As, in Fig. l(b). AE has its maximum value at a proton energy of about 30 keV which is shifted towards lower energies compared to both maxima, s,,,r and &mix;the exact energy position of ~~~~~is very sensitive to the detailed shape of the maxima -of s,,,r and &mix. That AE decreases when going to higher energies is easily understood in terms of Bethe theory. At high energies, where the projectiles are point charges, the only contribution to the chemical effect is due to a change in the states of the valence electrons when going from the mixture to the compound, the only quantity that might change is the ionization potential IYal of the valence electrons. Since the valence electrons are more strongly bound in a compound than in its constituents, l(?mp) Vdl is greater than Z$ix’. The chemical effect reads approximately.
Here, Z, and Z? are the atomic numbers of projectile and target, m, and e are mass and charge of an electron, v is the velocity of the ion and timi’) and ficomp)are the mean ionization potentials of the mixture and the compound, respectively. In Eq.. (2), the ratio I(comr)/l(mix) reflects the ratio Z$mp)/Z~~), since the inner shell contributions remain unaffected by the chemical bond and cancel each other out. It is worth to note that the Barkas term [13] is the only correction term to Bethe theory that is expected to contribute significantly to AE, too. According to Lindhard [14] the Bloch term takes account of modifying the stopping number for small impact parameters when increasing the projectile’s charge number. These close encounters are supposed to be less sensitive to changes in binding energy. In Fig. l(b), the Bethe result for the chemical effect using the Z values from Ref. [15] is included. The agreement with the experimental data is only qualitative, as a consequence of experimental uncertain-
103~1OX
ties: for our uncertainties of f5% for a,,, and E,,,~. respectively, and an assumed chemical effect AE x 0.1 E we obtain an uncertainty of N 70% for AE. Note that this is an inherent problem of investigations of chemical effects which leads to the consequence that investigations of the chemical effect suffer intrinsically from poor accuracy which results in widely spread data. At intermediate energies, i.e. in the velocity regime below N Zfi3v0 which is the mean velocity of projectile electrons within the Thomas-Fermi model, ions may carry bound electrons while traversing the target material. Here, capture and loss of electrons by the projectile will contribute to the energy loss and thus make the interpretation of the data more complex. At low velocities (o < rr = v. = c/137 with C’Fthe Fermi velocity and Do)the Bohr velocity) the ansatz dE/dx = Qtl
(3)
has a sound theoretical basis for a free electron gas. It has been found to be an appropriate description for metals [12] and insulators [7], independent of the magnitude of the gap. It also holds for gaseous targets, with the only exception of proton stopping in noble gases at very low proton velocities [16,17]. Thus, at low velocities, also the chemical effect is expected to be proportional to the ion velocity, AE 0~ u. As shown in Fig. l(b), our experimental results are within the experimental uncertainties in agreement with this behavior. We note that we cannot give a theoretical estimate of stopping cross sections for the gas phase or solid insulators which is as accurate as the one for solid metals in the low velocity regime, where the scattering of electrons at the Fermi level can be treated to all orders in the projectile charge and, consequently, it is not restricted to a perturbative description. However, the knowledge of the velocity dependence at low velocities may be used to extrapolate the chemical effect measured at 10 or 20 keV towards lower velocities.
4. Chemical effects for He ions In Fig. 2(a) we present our experimental results for He stopping in A&O3 and SiOr and the corre-
106
P. Bow 300
_
x0-
;
* 2
200-
?o
150-
et (11.I Nucl. Instr. and Meth. in Phys. Rex B 136-138 (1998)
,
,
,
,
,
200
400
600
800
1000
5 w 100. 501’ 0
a
1
1200
‘He energy (keV)
AI,O,,Santry& Werner
b Fig. 2. (a) Stopping cross section of alumina and silica for He ions. The data of the corresponding mixtures (solid lines) are represented by fit curves. The dashed lines represent the experimental results for the oxides from Santry [20.21]. (b) Absolute chemical effect for alumina and silica for He ions in terms of AE= s,,, - ~,,mp. The solid line and the dashed line represent our results for A1203 and for SiOz. respectively. The dotted line and the dashdotted line refer to the equivalent results from [20,2 I].
sponding mixtures in the energy range 15-800 keV [ 181.Our data for the compounds are compared to
&mixof the corresponding mixtures, which are calculated from Refs. [8,9,11]. Also shown are the experimental results for the oxides by Santry [21,22]. Compared to our data, Santry’s data are low in the whole energy range, by up to 10%. The maxima of the compounds again are found at a higher energy with a smaller height compared to the mixtures. Note that the E values are very large; in the case of alumina it corresponds to an energy loss per monolayer of up to 200 eV. Fig. 2(b) shows the chemical effect as a function of the He energy. Here, the behavior of the chemical effect deduced
103-108
from our data is in considerable contrast to that obtained from Santry’s work [2 1,221, corroborating our discussion of error propagation (see above). Our He data show the largest chemical effect at - 370 keV. Analogously to the case of proton stopping, this energy is below the stopping maxima of the compounds and the mixtures. In both cases, the relative chemical effect is up to B9% which is less than in the case of protons. Towards higher energies the chemical effect becomes smaller. similarly as for protons. Since in our energy range the He-ions are not point charges it does not make sense to compare these results to Bethe theory since charge state and screening effects will play an important role. At about IOO150 keV, i.e. at velocities L’z OF(OF of the oxides as calculated from plasmon energies is in the order of 1.2 uo), our data show no discernible (or even a negative) chemical effect. Finally we present the stopping ratio &H&Hfor our compounds and the corresponding mixtures in Fig. 3. For the oxides, the ratio .+JQ reaches a plateau at low energies, at values of 2.6 and 2.35 for A1203, and SiO,, respectively. The plateau values are quite large compared to the stopping ratios obtained for Al and Si [8,9] which are close to 2.0. Fig. 3 also includes the stopping ratio by Ziegler [23], which is a universal curve, independent of the target material. Ziegler’s curve is only in fair agreement with our experimental findings, with large deviations at the lowest energies. The findings of our investigation may be interpreted in terms of valence electron densities (in our regime the mean energy transfer is large compared to the energy gap): the plasmon energies of the oxides (- 24 eV) are considerably higher than that of Al and Si (15 and 16.5 eV, respectively), corresponding to considerably higher valence electron densities in the oxides. At low energies, a higher density of valence electrons leads to a larger stopping ratio E&E” [9], in qualitative agreement with density functional theory (DFT) which is a nonlinear model [ 19,201 to describe the stopping behavior of slow ions in an electron gas (see Fig. 3). The stopping ratio obtained from DFT fits our experimental findings nicely, but it yields the same plateau height for Si02 and for Al203, in contrast to the experimental findings. This shows again that
P. Buuer et ul. I Nucl. Instr. und Meth. in Phys. Rex B 136-138 (1998) 103-108
107
I
J
H, He -> AI,O,
0
50
100
.
150
200
fl
250
energy per nucleon (keV)
a
methods in three different labs which all contributed to a consistent set of data which gives our data special weight. For protons larger chemical effects have been observed than for He ions. As a consequence, in case the chemical effect cannot be taken into account properly, ion beam analysis by use of He beams will give lower systematic errors when simple additivity of the individual cross sections in the mixture is assumed according to Bragg’s rule. Acknowledgements We gratefully acknowledge the help of Peter Mertens in the course of performing the measurements with He ions and his continuous interest in the progress of this work. References
l,Bl;
0
b
h
50
100
h 150
J
200
energy per nucleon (keV)
Fig. 3. (a) Stopping ratio am/au for alumina (full circles) and the corresponding mixture (full line). For comparison we have added the universal curve from [23] (dashed line). (b) Stopping ratio E&Q for silica (full squares) and the corresponding mixture (full line). For comparison we have added the universal curve from [23] (dashed line).
the applicability of electron gas arguments for insulators is limited.
5. Conclusions We have presented experimental results for proton and He stopping in A1203 and SiO, and have compared the results to the equivalent mixtures. The information on chemical effects deduced from different sets of experiments is considerably at variance, as a consequence of experimental uncertainties and the well known misfit of data obtained in different labs. We therefore stress the point that our data are obtained by at least two independent
D.I. Thwaites. Nucl. Instr. and Meth. B I? (1985) 84. D.I. Thwaites, Nucl. Instr. and Meth. B 69 (1992) 53. [31 W.H. Bragg, R. Kleeman. Phil. Mag. 10 (1905) 318. [41 P. Bauer, W. Rossler. P. Mertens. Nucl. Instr. and Meth. B 69 (1992) 46. i51 P. Bauer. R. Golser. F. Aumayr. D. Semrad, A. Arnau. E. Zarate. R. Diez-Muitio. Nucl. Instr. and Meth. B 125 (1997) 102. PI J.F. Ziegler. in Stopping and Ranges of Ions in Matter. vol. 4. J.F. Ziegler (Ed.). Helium: Stopping Powers and Ranges in All Elemental Matter. Pergamon Press. New York. 1977. [71 K. Eder, D. Semrad, P. Bauer. R. Golser. P. MaierKomor. F. Aumayr. M. Peiialba. A. Arnau, J.M. Ugalde. P.M. Echenique, Phys. Rev. Lett. 79 (1997) 4112. PI Ch. Eppacher. Ph.D. Thesis. University of Linz. 1995. [91 Ch. Eppacher, D. Semrad. Nucl. Instr. Meth. B 69 (1992) 33. UOI V. Dose. G. Sele. Z. Phys. A 272 (1975) 237. [’ 11 G. Reiter. H. Baumgart, N. Kniest. E. Pfaff. G. Clausnitzer. Nucl. Instr. Meth. B 27 (1987) 280. J.E. Valdes. G. Martinez TdmayO. G.H. Lantschner. J.C. Eckardt. N.R. Arista. Nucl. Instr. and Meth. B 73 (1993) 313. u31 P. Sigmund, Nucl. Instr. Meth B (1998) in press. [I41 J. Lindhard. A. Sorensen. Phys. Rev. A 53 (1996) 2443. [I51 International commission on radiation units and measurements. Report 49, Stopping powers and ranges for protons and alpha particles. 1993. [I61 R. Golser. D. Semrad. Phys. Rev. Lett. 66 (1991) 1831. [I71 A. Schiefermueller. R. Golser. R. Stohl, D. Semrdd. Phys. Rev. A 48 (1993) 4467.
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