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The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal
Nuclear Instruments and Methods in Physics Research B xxx (2017) xxx–xxx
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal R. Mikšová a,b,⇑, A. Macková a,b, P. Malinsky´ a a b
Nuclear Physics Institute of the Academy of Sciences of the Czech Republic, v. v. i., 250 68 Rez, Czech Republic Department of Physics, Faculty of Science, J. E. Purkinje University, Ceske Mladeze 8, 400 96 Usti nad Labem, Czech Republic
a r t i c l e
i n f o
Article history: Received 30 July 2016 Received in revised form 30 December 2016 Accepted 24 February 2017 Available online xxxx Keywords: Energy-loss measurement SOI material RBS-channelling
a b s t r a c t We have measured the electronic stopping powers of helium and lithium ions in the channelling direction of the Sih1 0 0i crystal. The energy range used (2.0–8.0 MeV) was changed by 200 and 400-keV steps. The ratio a between the channelling and random stopping powers was determined as a function of the angle for 2, 3 and 4 MeV 4He+ ions and for 3 and 6 MeV 7Li+,2+ ions. The measurements were carried out using the Rutherford backscattering spectrometry in the channelling mode (RBS-C) in a silicon-oninsulator material. The experimental channelling stopping-power values measured in the channelling direction were then discussed in the frame of the random energy stopping predictions calculated using SRIM-2013 code and the theoretical unitary convolution approximation (UCA) model. The experimental channelling stopping-power values decrease with increasing ion energy. The stopping-power difference between channelled and randomly moving ions increases with the enhanced initial ion energy. The ratio between the channelling and random ion stopping powers a as a function of the ion beam incoming angle for 2, 3 and 4 MeV He+ ions and for 3 and 6 MeV Li+,2+ ions was observed in the range 0.5–1. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction When energetic ions pass through an investigated material, they lose their energy due to the energy transferred by the ion to the target nuclei and the energy transferred by the ion to the target electrons, which mostly depends on the target atom, on the ion velocity and on the ion charge state [1]. The knowledge of the stopping powers in random and channelling directions in the amorphous and crystal materials [2–4] is important for many theoretical and practical applications dependent on the transport of ions in matter. Particularly ion implantation and ion beam analysis techniques such as Rutherford backscattering spectrometry or experimental data can be used as input values of analytical or simulation programs that calculate depth distributions and the damage produced by ions implanted in channelling and random directions [5,6]. When an ion beam affects a crystal near the crystal’s major symmetry direction, the incident ions carry out a range of correlated small angular deflections along the channel [5]. This range has the effect of steering the incident ions near the centre of the
⇑ Corresponding author at: Nuclear Physics Institute of the Academy of Sciences of the Czech Republic, v. v. i., 250 68 Rez, Czech Republic. E-mail address: [email protected] (R. Mikšová).
channel, which results in the ion flux with a peak in the centre of the channel, whose magnitude is dependent on the beam incident angle [6]. The ion stopping power can be reduced unlike the one along a random direction [7]. Measurements of the energy loss as a function of the incidence angle provide information important in studies of the dopant positioning in a crystalline matrix [8], atomic surfaces [9], and distributions of the defect in the depth [10,11]. Many research groups have measured energy loss mainly for He+ ions in the comparable energy range in Si under channelling conditions as is reported in [6,26,30]. Nevertheless, very few measurements of the electronic stopping power as a function of the ion incoming angle under channelling conditions are available as well as for the higher energy range used in our experiment [5,28]. In the last years, a first-principles calculation method has been developed that makes it possible to determine the energy loss. The method, called perturbative convolution approximation, and the more modern unitary convolution approximation (UCA) [12] take into account non-perturbative effect on the energy loss, with no need to perform heavy computational work (in contrast to, for instance, the coupled-channel method [13]). This model has been implemented in a computer code called convolution approximation for swift particles (CasP) [14].
http://dx.doi.org/10.1016/j.nimb.2017.02.065 0168-583X/Ó 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: R. Mikšová et al., The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal, Nucl. Instr. Meth. B (2017), http://dx.doi.org/10.1016/j.nimb.2017.02.065
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R. Mikšová et al. / Nuclear Instruments and Methods in Physics Research B xxx (2017) xxx–xxx
The electronic energy stopping in amorphous and semicrystalline material are most commonly measured using the ion beam transmission technique [15,16], where energetic ions pass through the extremely thin foil of the single crystalline investigated material. This technique has many advantages – mainly the calculation of the mean energy is very simple, but the precise energy loss evaluation strongly depends on the preparation of homogeneous thin single crystals in the case of ion energy stopping in channelling mode studies. Due to this fact was suggested the experimental set-up using a detailed analysis of the random/ channelling RBS spectra, described by Azevedo [6]. This method was invented to avoid this problem as an alternative method for the electronic energy-loss measurement in channelling directions [6] and can be used only for channelled electronic energy-loss determination. For these purposes, silicon-on-insulator (SOI) materials are usually used [17,18]. In the present work, the electronic stopping powers of helium and lithium ions in the channelling direction of the Sih1 0 0i crystal and the energy range of 2.0–8.0 MeV were measured using the standard Rutherford backscattering spectrometry-channelling (RBS-C) method. The measured channelling stopping powers were compared to the predicted random values of the electronic energy loss using semi-empirical approaches implemented in the SRIM [19] code and the theoretical UCA model in CasP [14]. Subsequently, the angular-dependence energy loss was measured for 2, 3, 4 MeV 4He+ ions and since 3, 6 MeV 7Li+, 2+ ions as a function of the ion incident angle. Experimental FWHM of the channels was compared with the theoretical prediction. 2. Experimental details 2.1. Material characterisation For our experiment, we have used the silicon-on-insulator (SOI) material, which was prepared at the Shin-Etsu Chemical Co., Ltd. in Japan using thermal oxidation and chemical etching [20]. The SOI material contains a 200 ± 12-nm Sih1 0 0i crystal layer on top of a buried 380 ± 20-nm SiO2 layer produced in a Sih1 0 0i wafer. Silicon crystallises in a diamond cubic crystal structure with a lattice constant of 0.54 nm. Along this crystalline direction h1 0 0i, the lattice atoms form channels with a diameter of approximately 0.16 nm (0.3 of the lattice constant). These channels can be used by implanted ions to penetrate rather deep into the target (channelling effect), because the scattering probability is reduced for an ion moving along a channel [21]. 2.2. Measurement setup The experiments were carried out on a Tandetron MC 4130 accelerator at the Nuclear Physics Institute in Rez near Prague. The measurement using the Rutherford backscattering spectrometry in the channelling mode (RBS-C) was performed using the 4He+ and 7Li+, 2+ ion beams in the channelling direction of the Sih1 0 0i crystal. The energy was changed by 200 and 400-keV steps in the incident energy range of 2.0–8.0 MeV (the charge states of ions were chosen according the limitation ion current production from the Tandetron accelerator; 7Li+ ions for the energy range of 2.0– 6.0 MeV and above ion energy 6 MeV 7Li2+ ions were used). For some energies (2, 3 and 4 MeV for 4He+ ions and 3 and 6 MeV for 7 +, 2+ Li ions), the ratio a between the channelling and random stopping powers was determined as a function of the ion incoming angle. After determining the channelling direction, RBS spectra were recorded in aligned direction and for different values of the H angle in the range of 0.9° to 0.9° to perform the fine scan around the axis of the channel. The backscattered ions were
detected by a partially depleted PIPS detector at 170° placed below the incident ion beam. The typical energy resolution of the ion spectroscopic system was mainly given by the detector energy resolution, which has been determined for 241Am, 5.486 MeV alphas and lithium determined as 12 keV and 35 keV (FWHM – Full width at half maximum) [22].
2.3. Data analysis The RBS random and channelling spectra, taken using 2.4 and 2.8 MeV 4He+ ions, are shown in Fig. 1a,b; they were analysed using the SIMNRA 6.06 code [23]. The energy difference between the Si/ SiO2 interface positions in the random and channelling spectra provides differences in the energy lost in the path of the ions backscattered from the crystalline and amorphous interface. The RBS method simultaneously provides information about the ions traversing the sample in the random direction. The edges Er and Ec are ascribed to the backscattered helium ion energies at the Si/SiO2 interface in channelling and random directions, respectively. From these parameters, one can deduce the channelled elecc of the incoming tronic stopping power Sc using the mean energy E in particle described by the relation suggested by Santos in [24]
c Þ ¼ Sc ð E in
KE0 Ec cos Hc r r b b þ 1 2 S ðEin Þ KE0 Er cos Hr
ð1Þ
where K is the kinematic factor, E0 is the incident ion energy, and parameters b1 and b2 are given by
b1
r Þ cos Hc Sr ðE out r r KS ðEin Þ cos Wr
ð2Þ
b2
c Þ cos Hc Sr ðE out r r KS ðEin Þ cos Wc
ð3Þ
The upper indices r and c of the parameters in the relations (1) (3) indicate that the given parameter was taken in random or chanin nelled measurement. For the calculation of the mean energy E out , we have used the mean-energy approximation described andE in [25], where the energy is expressed using the relations
in ¼ E0 1 DE E 4
ð4Þ
and
out ¼ E1 þ 1 DE E 4
ð5Þ
The angles H and W are the angles between the directions of the ion beam and the sample’s normal and between the sample’s normal and the direction of the detector (see Fig. 2). out Þ in the relations (2) and (3) are in Þ and SðE The values of the SðE the stopping powers at the mean energy in the inward and outward paths, which were taken from the SRIM-2013 code [19]. The RBS spectra were recorded for several H angles around the channelling direction taking 0.1° steps. Typical RBS energy spectra taken with 3-MeV 7Li+ ions at H = 0.0°, 0.3° and 0.4° angles are shown in Fig. 3 together with the RBS spectra for a random direction. We have determined the ratio a between the channelling and random stopping powers, whereas the theoretical value of the random stopping powers has been taken from SRIM [19].
Please cite this article in press as: R. Mikšová et al., The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal, Nucl. Instr. Meth. B (2017), http://dx.doi.org/10.1016/j.nimb.2017.02.065
R. Mikšová et al. / Nuclear Instruments and Methods in Physics Research B xxx (2017) xxx–xxx
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Fig. 1. The RBS spectra obtained in random and channelling directions in Si using 2.4 MeV (a) and 2.8 MeV (b) 4He+ ions. The energy edges appropriate to the random (Er ) and channelling (Ec ) ions back-scattered in the Si/SiO2 are indicated.
3. Results and discussions 3.1. Stopping-power data
Fig. 2. A scheme of the experimental geometry with the angles H and W.
Fig. 3. The random and channelling RBS spectra at 3 MeV for 7Li+ at 0.0°, 0.3° and 0.4° along the Sih1 0 0i direction of a SOI target.
The channelling electronic stopping-power values Sc in the Si/ SiO2 for helium and lithium ions as a function of the mean energy c are presented in Fig. 4a,b, respectively. The channelling stopE in ping powers of helium and lithium ions is compared to the semiempirical stopping powers in the random direction Sr predicted by SRIM-2013 and the results of the theoretical UCA model. The random energy stopping experimentally determined by other groups is also provided for comparison in Fig. 4. The uncertainties associated with the measured energy-loss values have been analysed by considering the propagated errors derived from the different quantities in the calculation formula (1) and were obtained by a standard manner, i.e. as square root of the sum of the squares of all particular errors. The energy stopping power uncertainties is influenced by the energy detector resolution, the energy edge extraction uncertainty from the random and channelled spectra and by the uncertainty of the SRIM-2013 code (accuracy of SRIM stopping power calculation is taken from [19]), which was used in Þ and SðE out Þ values in the relations (2) for calculation of the SðE and (3). The total relative uncertainties determined for energy stopping powers of 4He+ ions are evaluated as 3.8% and 4.5% for 7Li+,2+ ions. As expected, the ion stopping powers are lower in the channelling direction than in the random direction of penetrating ions. For helium ions, the differences between the channelling stopping power and the predicted random energy stopping determined by SRIM are below 30% in the whole investigated energy region. For lithium ions, in the energy range of 6.8–8.0 MeV, a comparison between the measured stopping-power values and the values calculated by SRIM showed larger differences. An inspection of the error bars reveals, we can see that the stopping power of lithium ions tend to become constant at energies of about 6.8 MeV. This change in the curve could be related to an increasing contribution of the silicon L inner shell to the channelling stopping power at higher energies observed earlier in [26]. A comparison with the theoretical UCA model, which uses the fast numerical calculations of the mean electronic energy transfer (due to excitation and ionization of target atoms). The UCA stopping power is subsequently calculated for a selected predefined projectile-screening function. UCA predictions for the theoretical random energy stopping powers are lower, about 9–18% for 4He+ ions and about 8–28% for
Please cite this article in press as: R. Mikšová et al., The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal, Nucl. Instr. Meth. B (2017), http://dx.doi.org/10.1016/j.nimb.2017.02.065
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Fig. 4. The experimental stopping powers for helium (a) and lithium (b) ions along the h1 0 0i direction in Si (points) and the calculated random stopping powers using SRIM2013 (solid line), the UCA model from the CasP code (dash-dot line) and the experimental random stopping powers from literature for comparison (points).
7 n+ Li compared to SRIM predictions. The experimental random stopping powers found in the literature show values very close to the SRIM predictions for both ion species see Fig. 4a,b, thus we have used SRIM theoretical random stopping powers for the a ratio calculation (the ratio between the channelling stopping power and the random ones) (see Section 3.2.). It may be concluded that the channelling stopping power decreases with increasing energy, which is a general trend of the Sc values for both ion species. At higher ion energy, the differences between the channelling and random stopping powers of helium ions are quite similar to those obtained for lithium ions, so that for both ion species at higher energy the channelling stopping powers are close to 50% of the random stopping powers. This confirms the basic theory suggested in [27], namely that the best channelling ions have a stopping power in the order of one-half of the stopping power in the corresponding random direction.
3.2. Angular-dependent data The ratio between the channelling and the random stoppingpower values a as a function of the H angle closely around the channelling direction of Si is shown in Fig. 5a–c together with a Gaussian fit applied on the energy stopping angular scans. It is evident that the ratio a between the channelling stopping powers and random stopping powers determined by SRIM reaches its lowest value under well-channelled conditions (H = 0°). The random stopping powers from SRIM were taken into account because in our experiment we did not have random values of electronic energy loss from independent measurement available. We deduced the minimum values of a and the experimental values of the FWHM. The minimum values for a, the experimental and calculated values for the FWHM obtained from angulardependent data for 4He+ ions at 2, 3 and 4 MeV and for 7Li+,2+ ions at 3 and 6 MeV are summarized in Table 1. The minima at H = 0° decrease linearly for 4He+ ions from the value 0.73 ± 0.08 at 2 MeV to 0.58 ± 0.06 at 4 MeV. It is in good agreement with the results in [28,2], reporting the value 0.64 for 2 MeV. In the case higher energies (3 and 4 MeV) for 4He+ ions, appropriate data for comparison are not available. The minimum values for a between the channelling and random stopping powers as a function of the angle for 7Lin+ ions (Fig. 6a,b) is 0.81 ± 0.14 for the energy of 3.0 MeV and 0.61 ± 0.10 for 6 MeV, it is in good agreement with the results in [26]. The experimentally determined value of FWHM for 4He+ ions is 0.47° ± 0.02° and the theoretical value of FWHM calculated using
the relation in [9,29] using main crystal parameters are presented in Table 1 also. The experimentally determined FWHMs are descending function of the ion energy from 0.47° ± 0.02° at 2 MeV to 0.39° ± 0.01° at 4 MeV. For 7Lin+ ions a FWHM decrease from 0.47° ± 0.02° at 3 MeV to 0.42° ± 0.01° at 6 MeV was identified. It arises from Figs. 5 and 6 that in some cases, for large angles of incidence, the ratio a reaches values above unity, which implies that the stopping power of channelling ions under certain conditions can exceed the random one because of the inaccuracy of the SRIM calculation. We have compared our experimental results with SRIM-calculated values and not with experimental results in a random direction, which was discussed above. It can be concluded that our measurement confirms the trend from previous measurements performed by other groups [5,28] and the theoretical approach [1,27], where the ratio between channelling and random energy loss at the angle H = 0° decreases with increasing energy. Our measurement also shows that FWHMs decrease with increasing energy and in the case of some energy and different ion species (3 MeV for 4He+ and 7Li+), FWHM is higher for heavier ions. This is connected with the theoretical prediction where the FWHM value increases with higher Z of ions and for the same Z of ions, it decreases with the increasing energy of the pffiffiffi ions as 1= E.
4. Conclusion In summary, the paper presents the electronic stopping powers of helium and lithium ions in the channelling direction of the Si 100 crystal in the energy range of 2.0–8.0 MeV using the standard Rutherford backscattering spectrometry in the channelling mode (RBS-C) and the silicon-on-insulator (SOI) material and angular dependence of the energy loss at different values of the energies. This method allows for measurements in a wide energy range without using thin single crystalline layers for the transmission experiments. The experimentally determined the channelling energy loss are lower than the values calculated using the SRIM code and the UCA model, which provide random energy loss. This is in accordance with the theory, which assumes that for well-channelled ions, the energy losses are reduced to a half [27]. The measurement showed a decrease in the ratio a between channelling and random energy loss with increasing energy for both ion species and FWHMs as a descending function of the ion energy. The new data of the channelling energy losses were presented in energy region
Please cite this article in press as: R. Mikšová et al., The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal, Nucl. Instr. Meth. B (2017), http://dx.doi.org/10.1016/j.nimb.2017.02.065
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Fig. 5. The ratio a between the channelling (Sc) and random (Sr) stopping powers of incident 2 MeV (a), 3 MeV (b) and 4 MeV (c) 4He+ ions as a function of the angle H and a Gaussian fit to the data (solid line).
Table 1 The minimum values for a, the experimental and calculated values for the FWHM obtained from angular-dependent data. Energy [MeV]
2 3 4 6
4
He+ ions
7
Li+,
2+
ions
a
FWHM [°] – experimental
FWHM [°] – calculated
Α
FWHM [°] – experimental
FWHM [°] – calculated
0.73 ± 0.08 0.67 ± 0.07 0.58 ± 0.06
0.47° ± 0.02° 0.44° ± 0.02° 0.39° ± 0.01°
0.49° 0.45° 0.36°
0.81 ± 0.14
0.47° ± 0.02°
0.49°
0.61 ± 0.10
0.42° ± 0.01°
0.35°
Fig. 6. The ratio between the channelling (Sc) and random (Sr) stopping powers of incident 3 MeV (a) and 6 MeV (b) 7Li+,
2+
ions as a function of the angle H.
Please cite this article in press as: R. Mikšová et al., The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal, Nucl. Instr. Meth. B (2017), http://dx.doi.org/10.1016/j.nimb.2017.02.065
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2.8–4.0 MeV for helium ions, where data are rare as well as energy stopping angular dependence for energy above 3 and 4 MeV is missing. Acknowledgement
[11] [12] [13] [14]
[15]
The research was realised at the CANAM (Center of Accelerators and Nuclear Analytical Methods) infrastructure LM 2015056 and has been supported by the project of the Czech Science Foundation GACR 15-01602S and the SGS UJEP (J. E. Purkinje University Student Grant Competition) project.
[16] [17]
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Please cite this article in press as: R. Mikšová et al., The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal, Nucl. Instr. Meth. B (2017), http://dx.doi.org/10.1016/j.nimb.2017.02.065
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal R. Mikšová a,b,⇑, A. Macková a,b, P. Malinsky´ a a b
Nuclear Physics Institute of the Academy of Sciences of the Czech Republic, v. v. i., 250 68 Rez, Czech Republic Department of Physics, Faculty of Science, J. E. Purkinje University, Ceske Mladeze 8, 400 96 Usti nad Labem, Czech Republic
a r t i c l e
i n f o
Article history: Received 30 July 2016 Received in revised form 30 December 2016 Accepted 24 February 2017 Available online xxxx Keywords: Energy-loss measurement SOI material RBS-channelling
a b s t r a c t We have measured the electronic stopping powers of helium and lithium ions in the channelling direction of the Sih1 0 0i crystal. The energy range used (2.0–8.0 MeV) was changed by 200 and 400-keV steps. The ratio a between the channelling and random stopping powers was determined as a function of the angle for 2, 3 and 4 MeV 4He+ ions and for 3 and 6 MeV 7Li+,2+ ions. The measurements were carried out using the Rutherford backscattering spectrometry in the channelling mode (RBS-C) in a silicon-oninsulator material. The experimental channelling stopping-power values measured in the channelling direction were then discussed in the frame of the random energy stopping predictions calculated using SRIM-2013 code and the theoretical unitary convolution approximation (UCA) model. The experimental channelling stopping-power values decrease with increasing ion energy. The stopping-power difference between channelled and randomly moving ions increases with the enhanced initial ion energy. The ratio between the channelling and random ion stopping powers a as a function of the ion beam incoming angle for 2, 3 and 4 MeV He+ ions and for 3 and 6 MeV Li+,2+ ions was observed in the range 0.5–1. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction When energetic ions pass through an investigated material, they lose their energy due to the energy transferred by the ion to the target nuclei and the energy transferred by the ion to the target electrons, which mostly depends on the target atom, on the ion velocity and on the ion charge state [1]. The knowledge of the stopping powers in random and channelling directions in the amorphous and crystal materials [2–4] is important for many theoretical and practical applications dependent on the transport of ions in matter. Particularly ion implantation and ion beam analysis techniques such as Rutherford backscattering spectrometry or experimental data can be used as input values of analytical or simulation programs that calculate depth distributions and the damage produced by ions implanted in channelling and random directions [5,6]. When an ion beam affects a crystal near the crystal’s major symmetry direction, the incident ions carry out a range of correlated small angular deflections along the channel [5]. This range has the effect of steering the incident ions near the centre of the
⇑ Corresponding author at: Nuclear Physics Institute of the Academy of Sciences of the Czech Republic, v. v. i., 250 68 Rez, Czech Republic. E-mail address: [email protected] (R. Mikšová).
channel, which results in the ion flux with a peak in the centre of the channel, whose magnitude is dependent on the beam incident angle [6]. The ion stopping power can be reduced unlike the one along a random direction [7]. Measurements of the energy loss as a function of the incidence angle provide information important in studies of the dopant positioning in a crystalline matrix [8], atomic surfaces [9], and distributions of the defect in the depth [10,11]. Many research groups have measured energy loss mainly for He+ ions in the comparable energy range in Si under channelling conditions as is reported in [6,26,30]. Nevertheless, very few measurements of the electronic stopping power as a function of the ion incoming angle under channelling conditions are available as well as for the higher energy range used in our experiment [5,28]. In the last years, a first-principles calculation method has been developed that makes it possible to determine the energy loss. The method, called perturbative convolution approximation, and the more modern unitary convolution approximation (UCA) [12] take into account non-perturbative effect on the energy loss, with no need to perform heavy computational work (in contrast to, for instance, the coupled-channel method [13]). This model has been implemented in a computer code called convolution approximation for swift particles (CasP) [14].
http://dx.doi.org/10.1016/j.nimb.2017.02.065 0168-583X/Ó 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: R. Mikšová et al., The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal, Nucl. Instr. Meth. B (2017), http://dx.doi.org/10.1016/j.nimb.2017.02.065
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R. Mikšová et al. / Nuclear Instruments and Methods in Physics Research B xxx (2017) xxx–xxx
The electronic energy stopping in amorphous and semicrystalline material are most commonly measured using the ion beam transmission technique [15,16], where energetic ions pass through the extremely thin foil of the single crystalline investigated material. This technique has many advantages – mainly the calculation of the mean energy is very simple, but the precise energy loss evaluation strongly depends on the preparation of homogeneous thin single crystals in the case of ion energy stopping in channelling mode studies. Due to this fact was suggested the experimental set-up using a detailed analysis of the random/ channelling RBS spectra, described by Azevedo [6]. This method was invented to avoid this problem as an alternative method for the electronic energy-loss measurement in channelling directions [6] and can be used only for channelled electronic energy-loss determination. For these purposes, silicon-on-insulator (SOI) materials are usually used [17,18]. In the present work, the electronic stopping powers of helium and lithium ions in the channelling direction of the Sih1 0 0i crystal and the energy range of 2.0–8.0 MeV were measured using the standard Rutherford backscattering spectrometry-channelling (RBS-C) method. The measured channelling stopping powers were compared to the predicted random values of the electronic energy loss using semi-empirical approaches implemented in the SRIM [19] code and the theoretical UCA model in CasP [14]. Subsequently, the angular-dependence energy loss was measured for 2, 3, 4 MeV 4He+ ions and since 3, 6 MeV 7Li+, 2+ ions as a function of the ion incident angle. Experimental FWHM of the channels was compared with the theoretical prediction. 2. Experimental details 2.1. Material characterisation For our experiment, we have used the silicon-on-insulator (SOI) material, which was prepared at the Shin-Etsu Chemical Co., Ltd. in Japan using thermal oxidation and chemical etching [20]. The SOI material contains a 200 ± 12-nm Sih1 0 0i crystal layer on top of a buried 380 ± 20-nm SiO2 layer produced in a Sih1 0 0i wafer. Silicon crystallises in a diamond cubic crystal structure with a lattice constant of 0.54 nm. Along this crystalline direction h1 0 0i, the lattice atoms form channels with a diameter of approximately 0.16 nm (0.3 of the lattice constant). These channels can be used by implanted ions to penetrate rather deep into the target (channelling effect), because the scattering probability is reduced for an ion moving along a channel [21]. 2.2. Measurement setup The experiments were carried out on a Tandetron MC 4130 accelerator at the Nuclear Physics Institute in Rez near Prague. The measurement using the Rutherford backscattering spectrometry in the channelling mode (RBS-C) was performed using the 4He+ and 7Li+, 2+ ion beams in the channelling direction of the Sih1 0 0i crystal. The energy was changed by 200 and 400-keV steps in the incident energy range of 2.0–8.0 MeV (the charge states of ions were chosen according the limitation ion current production from the Tandetron accelerator; 7Li+ ions for the energy range of 2.0– 6.0 MeV and above ion energy 6 MeV 7Li2+ ions were used). For some energies (2, 3 and 4 MeV for 4He+ ions and 3 and 6 MeV for 7 +, 2+ Li ions), the ratio a between the channelling and random stopping powers was determined as a function of the ion incoming angle. After determining the channelling direction, RBS spectra were recorded in aligned direction and for different values of the H angle in the range of 0.9° to 0.9° to perform the fine scan around the axis of the channel. The backscattered ions were
detected by a partially depleted PIPS detector at 170° placed below the incident ion beam. The typical energy resolution of the ion spectroscopic system was mainly given by the detector energy resolution, which has been determined for 241Am, 5.486 MeV alphas and lithium determined as 12 keV and 35 keV (FWHM – Full width at half maximum) [22].
2.3. Data analysis The RBS random and channelling spectra, taken using 2.4 and 2.8 MeV 4He+ ions, are shown in Fig. 1a,b; they were analysed using the SIMNRA 6.06 code [23]. The energy difference between the Si/ SiO2 interface positions in the random and channelling spectra provides differences in the energy lost in the path of the ions backscattered from the crystalline and amorphous interface. The RBS method simultaneously provides information about the ions traversing the sample in the random direction. The edges Er and Ec are ascribed to the backscattered helium ion energies at the Si/SiO2 interface in channelling and random directions, respectively. From these parameters, one can deduce the channelled elecc of the incoming tronic stopping power Sc using the mean energy E in particle described by the relation suggested by Santos in [24]
c Þ ¼ Sc ð E in
KE0 Ec cos Hc r r b b þ 1 2 S ðEin Þ KE0 Er cos Hr
ð1Þ
where K is the kinematic factor, E0 is the incident ion energy, and parameters b1 and b2 are given by
b1
r Þ cos Hc Sr ðE out r r KS ðEin Þ cos Wr
ð2Þ
b2
c Þ cos Hc Sr ðE out r r KS ðEin Þ cos Wc
ð3Þ
The upper indices r and c of the parameters in the relations (1) (3) indicate that the given parameter was taken in random or chanin nelled measurement. For the calculation of the mean energy E out , we have used the mean-energy approximation described andE in [25], where the energy is expressed using the relations
in ¼ E0 1 DE E 4
ð4Þ
and
out ¼ E1 þ 1 DE E 4
ð5Þ
The angles H and W are the angles between the directions of the ion beam and the sample’s normal and between the sample’s normal and the direction of the detector (see Fig. 2). out Þ in the relations (2) and (3) are in Þ and SðE The values of the SðE the stopping powers at the mean energy in the inward and outward paths, which were taken from the SRIM-2013 code [19]. The RBS spectra were recorded for several H angles around the channelling direction taking 0.1° steps. Typical RBS energy spectra taken with 3-MeV 7Li+ ions at H = 0.0°, 0.3° and 0.4° angles are shown in Fig. 3 together with the RBS spectra for a random direction. We have determined the ratio a between the channelling and random stopping powers, whereas the theoretical value of the random stopping powers has been taken from SRIM [19].
Please cite this article in press as: R. Mikšová et al., The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal, Nucl. Instr. Meth. B (2017), http://dx.doi.org/10.1016/j.nimb.2017.02.065
R. Mikšová et al. / Nuclear Instruments and Methods in Physics Research B xxx (2017) xxx–xxx
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Fig. 1. The RBS spectra obtained in random and channelling directions in Si using 2.4 MeV (a) and 2.8 MeV (b) 4He+ ions. The energy edges appropriate to the random (Er ) and channelling (Ec ) ions back-scattered in the Si/SiO2 are indicated.
3. Results and discussions 3.1. Stopping-power data
Fig. 2. A scheme of the experimental geometry with the angles H and W.
Fig. 3. The random and channelling RBS spectra at 3 MeV for 7Li+ at 0.0°, 0.3° and 0.4° along the Sih1 0 0i direction of a SOI target.
The channelling electronic stopping-power values Sc in the Si/ SiO2 for helium and lithium ions as a function of the mean energy c are presented in Fig. 4a,b, respectively. The channelling stopE in ping powers of helium and lithium ions is compared to the semiempirical stopping powers in the random direction Sr predicted by SRIM-2013 and the results of the theoretical UCA model. The random energy stopping experimentally determined by other groups is also provided for comparison in Fig. 4. The uncertainties associated with the measured energy-loss values have been analysed by considering the propagated errors derived from the different quantities in the calculation formula (1) and were obtained by a standard manner, i.e. as square root of the sum of the squares of all particular errors. The energy stopping power uncertainties is influenced by the energy detector resolution, the energy edge extraction uncertainty from the random and channelled spectra and by the uncertainty of the SRIM-2013 code (accuracy of SRIM stopping power calculation is taken from [19]), which was used in Þ and SðE out Þ values in the relations (2) for calculation of the SðE and (3). The total relative uncertainties determined for energy stopping powers of 4He+ ions are evaluated as 3.8% and 4.5% for 7Li+,2+ ions. As expected, the ion stopping powers are lower in the channelling direction than in the random direction of penetrating ions. For helium ions, the differences between the channelling stopping power and the predicted random energy stopping determined by SRIM are below 30% in the whole investigated energy region. For lithium ions, in the energy range of 6.8–8.0 MeV, a comparison between the measured stopping-power values and the values calculated by SRIM showed larger differences. An inspection of the error bars reveals, we can see that the stopping power of lithium ions tend to become constant at energies of about 6.8 MeV. This change in the curve could be related to an increasing contribution of the silicon L inner shell to the channelling stopping power at higher energies observed earlier in [26]. A comparison with the theoretical UCA model, which uses the fast numerical calculations of the mean electronic energy transfer (due to excitation and ionization of target atoms). The UCA stopping power is subsequently calculated for a selected predefined projectile-screening function. UCA predictions for the theoretical random energy stopping powers are lower, about 9–18% for 4He+ ions and about 8–28% for
Please cite this article in press as: R. Mikšová et al., The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal, Nucl. Instr. Meth. B (2017), http://dx.doi.org/10.1016/j.nimb.2017.02.065
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Fig. 4. The experimental stopping powers for helium (a) and lithium (b) ions along the h1 0 0i direction in Si (points) and the calculated random stopping powers using SRIM2013 (solid line), the UCA model from the CasP code (dash-dot line) and the experimental random stopping powers from literature for comparison (points).
7 n+ Li compared to SRIM predictions. The experimental random stopping powers found in the literature show values very close to the SRIM predictions for both ion species see Fig. 4a,b, thus we have used SRIM theoretical random stopping powers for the a ratio calculation (the ratio between the channelling stopping power and the random ones) (see Section 3.2.). It may be concluded that the channelling stopping power decreases with increasing energy, which is a general trend of the Sc values for both ion species. At higher ion energy, the differences between the channelling and random stopping powers of helium ions are quite similar to those obtained for lithium ions, so that for both ion species at higher energy the channelling stopping powers are close to 50% of the random stopping powers. This confirms the basic theory suggested in [27], namely that the best channelling ions have a stopping power in the order of one-half of the stopping power in the corresponding random direction.
3.2. Angular-dependent data The ratio between the channelling and the random stoppingpower values a as a function of the H angle closely around the channelling direction of Si is shown in Fig. 5a–c together with a Gaussian fit applied on the energy stopping angular scans. It is evident that the ratio a between the channelling stopping powers and random stopping powers determined by SRIM reaches its lowest value under well-channelled conditions (H = 0°). The random stopping powers from SRIM were taken into account because in our experiment we did not have random values of electronic energy loss from independent measurement available. We deduced the minimum values of a and the experimental values of the FWHM. The minimum values for a, the experimental and calculated values for the FWHM obtained from angulardependent data for 4He+ ions at 2, 3 and 4 MeV and for 7Li+,2+ ions at 3 and 6 MeV are summarized in Table 1. The minima at H = 0° decrease linearly for 4He+ ions from the value 0.73 ± 0.08 at 2 MeV to 0.58 ± 0.06 at 4 MeV. It is in good agreement with the results in [28,2], reporting the value 0.64 for 2 MeV. In the case higher energies (3 and 4 MeV) for 4He+ ions, appropriate data for comparison are not available. The minimum values for a between the channelling and random stopping powers as a function of the angle for 7Lin+ ions (Fig. 6a,b) is 0.81 ± 0.14 for the energy of 3.0 MeV and 0.61 ± 0.10 for 6 MeV, it is in good agreement with the results in [26]. The experimentally determined value of FWHM for 4He+ ions is 0.47° ± 0.02° and the theoretical value of FWHM calculated using
the relation in [9,29] using main crystal parameters are presented in Table 1 also. The experimentally determined FWHMs are descending function of the ion energy from 0.47° ± 0.02° at 2 MeV to 0.39° ± 0.01° at 4 MeV. For 7Lin+ ions a FWHM decrease from 0.47° ± 0.02° at 3 MeV to 0.42° ± 0.01° at 6 MeV was identified. It arises from Figs. 5 and 6 that in some cases, for large angles of incidence, the ratio a reaches values above unity, which implies that the stopping power of channelling ions under certain conditions can exceed the random one because of the inaccuracy of the SRIM calculation. We have compared our experimental results with SRIM-calculated values and not with experimental results in a random direction, which was discussed above. It can be concluded that our measurement confirms the trend from previous measurements performed by other groups [5,28] and the theoretical approach [1,27], where the ratio between channelling and random energy loss at the angle H = 0° decreases with increasing energy. Our measurement also shows that FWHMs decrease with increasing energy and in the case of some energy and different ion species (3 MeV for 4He+ and 7Li+), FWHM is higher for heavier ions. This is connected with the theoretical prediction where the FWHM value increases with higher Z of ions and for the same Z of ions, it decreases with the increasing energy of the pffiffiffi ions as 1= E.
4. Conclusion In summary, the paper presents the electronic stopping powers of helium and lithium ions in the channelling direction of the Si 100 crystal in the energy range of 2.0–8.0 MeV using the standard Rutherford backscattering spectrometry in the channelling mode (RBS-C) and the silicon-on-insulator (SOI) material and angular dependence of the energy loss at different values of the energies. This method allows for measurements in a wide energy range without using thin single crystalline layers for the transmission experiments. The experimentally determined the channelling energy loss are lower than the values calculated using the SRIM code and the UCA model, which provide random energy loss. This is in accordance with the theory, which assumes that for well-channelled ions, the energy losses are reduced to a half [27]. The measurement showed a decrease in the ratio a between channelling and random energy loss with increasing energy for both ion species and FWHMs as a descending function of the ion energy. The new data of the channelling energy losses were presented in energy region
Please cite this article in press as: R. Mikšová et al., The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal, Nucl. Instr. Meth. B (2017), http://dx.doi.org/10.1016/j.nimb.2017.02.065
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Fig. 5. The ratio a between the channelling (Sc) and random (Sr) stopping powers of incident 2 MeV (a), 3 MeV (b) and 4 MeV (c) 4He+ ions as a function of the angle H and a Gaussian fit to the data (solid line).
Table 1 The minimum values for a, the experimental and calculated values for the FWHM obtained from angular-dependent data. Energy [MeV]
2 3 4 6
4
He+ ions
7
Li+,
2+
ions
a
FWHM [°] – experimental
FWHM [°] – calculated
Α
FWHM [°] – experimental
FWHM [°] – calculated
0.73 ± 0.08 0.67 ± 0.07 0.58 ± 0.06
0.47° ± 0.02° 0.44° ± 0.02° 0.39° ± 0.01°
0.49° 0.45° 0.36°
0.81 ± 0.14
0.47° ± 0.02°
0.49°
0.61 ± 0.10
0.42° ± 0.01°
0.35°
Fig. 6. The ratio between the channelling (Sc) and random (Sr) stopping powers of incident 3 MeV (a) and 6 MeV (b) 7Li+,
2+
ions as a function of the angle H.
Please cite this article in press as: R. Mikšová et al., The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal, Nucl. Instr. Meth. B (2017), http://dx.doi.org/10.1016/j.nimb.2017.02.065
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2.8–4.0 MeV for helium ions, where data are rare as well as energy stopping angular dependence for energy above 3 and 4 MeV is missing. Acknowledgement
[11] [12] [13] [14]
[15]
The research was realised at the CANAM (Center of Accelerators and Nuclear Analytical Methods) infrastructure LM 2015056 and has been supported by the project of the Czech Science Foundation GACR 15-01602S and the SGS UJEP (J. E. Purkinje University Student Grant Competition) project.
[16] [17]
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Please cite this article in press as: R. Mikšová et al., The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal, Nucl. Instr. Meth. B (2017), http://dx.doi.org/10.1016/j.nimb.2017.02.065