- Email: [email protected]
Stopping power of He, C and O in GaN
Nuclear Instruments and Methods in Physics Research B 273 (2012) 26–29
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Stopping power of He, C and O in GaN Nuno P. Barradas a,⇑, E. Alves a, Z. Siketic´ b, I. Bogdanovic´ Radovic´ b a b
Instituto Tecnológico e Nuclear, E.N. 10, Sacavém 2686-953, Portugal - Boškovic´ Institute, P.O. Box 180, 10002 Zagreb, Croatia Ruder
a r t i c l e
i n f o
Article history: Available online 27 July 2011 Keywords: Stopping power Gallium nitride Heavy ions
a b s t r a c t GaN and other group III nitrides based alloys are important materials in optoelectronic and electronic devices, including high-brightness blue and white LEDs, multi-junction solar cells, high-frequency transistors, and THz emitters. Unintentional impurities can be present, with a strong influence in the properties of these materials. These impurities are often light elements such as H, C, or O, and an ion beam analysis technique such as heavy ion elastic recoil detection analysis can play a fundamental role in their quantification. However, to our knowledge stopping powers in GaN have not yet been measured, and data analysis relies on using the Bragg rule, which is often inaccurate. We have used a bulk method, previously developed by us and applied successfully to other systems, to determine experimentally the stopping power of 4He, 12C and 16O in GaN, in the energy ranges 0.6–2.3, 0.9–14.9, and 0.6–14.9 MeV, respectively. The results of our measurements and bulk method analysis are presented. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction GaN and other group III nitrides based alloys are important materials in optoelectronic and electronic devices, including high-brightness blue and white LEDs, multi-junction solar cells, high-frequency transistors, and THz emitters [1]. Unintentional impurities can be present, with a strong influence in the properties of these materials [2]. Heavy ion elastic recoil detection analysis (HI-ERDA) is ideally suited to determine the profile of light impurities in a heavy matrix such as GaN [3]. The accuracy of the depth profiles obtained depends on the stopping powers used in the analysis. Very often, the stopping powers are taken from interpolative schemes such as SRIM [4] or MSTAR [5], which however do not include any experimental data of stopping power of any heavy ion in GaN in their databases. The stopping of H in GaN has been reported by Ahlgren and Rauhala [6], and excellent agreement was found with SRIM-98 for energies above 1 MeV, while for energies below the measured values were slightly below the SRIM-98 prediction. Calculations and experiments for low velocity Au ions in GaN have been presented [7] and are about a factor of 2 lower than SRIM, but the energy range considered was much below the usual range useful for HI-ERDA experiments. In this case, lacking experimental data, the Bragg rule must be used, which may lead to large deviations around 10% or more, particularly for oxides, nitrides, and for heavy ions.
⇑ Corresponding author. E-mail address: [email protected] (N.P. Barradas). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.07.029
We have measured the stopping power of 4He, 12C and 16O in GaN thin films grown on sapphire, in the energy ranges 0.6–2.3, 0.9–14.9, and 0.6–14.9 MeV, respectively. These ions were selected because 4He is often used in Rutherford backscattering (RBS) studies, while C and O are, together with hydrogen, amongst the most common light impurities in GaN thin films. The samples we had available were too thin for measurements with H ions. For stopping power measurements we have applied a method previously developed by us and applied on other systems [8,9]. In the proposed method, several RBS spectra were collected at different ion energies and at several different backscattering angles. Spectra were fitted simultaneously, and the entire stopping power curve was taken as a fit parameter, using the effect it has on the height and width of the film signal, together with a well known marker layer to determine the solid-angle charge product. A Bayesian inference [10] Markov chain Monte Carlo (BI/MCMC) algorithm, included in the code NDF [11,12], was used, so the uncertainty of the stopping curve derived was also obtained. 2. Experimental details A GaN film with nominal thickness of 200 nm grown by molecular beam epitaxy on a sapphire substrate was used. A thin Au layer was evaporated on the top of the film in order to provide an absolute solid-angle charge calibration. The 4He RBS experiments were done at ITN at a 160° scattering angle with beam energies 1, 2 and 2.3 MeV. The 12C and 16O RBS experiments at 3, 6, 10 - Boškovic´ Institute using three and 15 MeV were done at the Ruder detectors simultaneously, at 118°, 150° and 165° scattering angles [9].
N.P. Barradas et al. / Nuclear Instruments and Methods in Physics Research B 273 (2012) 26–29
3. Calculations The objective of the data analysis is to retrieve the stopping power curve from the energy spectra collected. This can be done because the stopping power has an univocal influence in the data: considering a thin film, a larger stopping power leads to a larger observed energy width, accompanied by a smaller yield per channel. This effect is shown in Fig. 1, where simulations for 4He data are made considering SRIM stopping power, as well as stopping values 10% higher and 10% smaller than given by SRIM. It is clear that the effect of an incorrect stopping power cannot be compensated by changing the film thickness, because the signal height would still be incorrect. To analyse the data, we treated the entire stopping power curve as a free parameter, that is, we did not simply scale it by a constant factor, but the energy dependence could also change during the analysis. The stopping curve was constrained to reasonable shapes by using the ZBL85 parameterisation [13]. Note that it is the molecular stopping power in GaN that is determined, and not the elemental Ga and N stopping powers. Experimental parameters such as the energy calibration and the solid-angle charge product are also allowed to change within their uncertainties. We then perform a Bayesian inference analysis with the Markov chain Monte Carlo method (BI/MCMC). The details of the method have been given previously [8,9] and are beyond the scope of this paper. The final result is the stopping power together with its associated uncertainty.
Fig. 1. Spectra collected with 4He. Simulations using SRIM stopping, and with stopping 10% higher and 10% lower than SRIM, are shown.
27
This process relies on the quality of the simulations produced. NDF includes the effect of double scattering [14], pile-up [15], and we have analysed pulse-height spectra by taking into account the pulse height defect coming from the detector dead layer and non-ionising energy losses in the detector [16]. The thickness of the Au marker layer and of the GaN film was determined from the 4He data. In order to be able to do this, the measured molecular stopping power of 4He in the Al2O3 substrate was used [8], and its stated uncertainty was propagated to the final uncertainty quoted for the stopping power curves reported here. Finally, the process relies on the stoichiometry of the GaN film. GaN is a highly stoichiometric material, with vacancy concentrations usually between 1016 and 1018/cm3 [17], and departure from stoichiometry is only observed after annealing treatments above 500 °C [18]. The energy range covered by the experiment is given by the range of energies that the ion beam has while crossing the Ga, first on the way in, and then after scattering on the way out of the sample and towards the detector. In each stopping power curve presented here, we also show the energy regions effectively probed by the beam. We note that there are gaps in the energy ranges that are effectively probed. However, the stopping power in those gaps is effectively constrained by the parameterisation used, that forces the stopping power curve to have a reasonable shape. 4. Results and discussion Fig. 2 shows the stopping power curve obtained for 4He in GaN. What we show is actually the average value plus and minus one standard deviation, i.e., the determined uncertainty. For comparison, we also show the SRIM stopping calculated from the Ga and N elemental stopping powers assuming the Bragg rule. It is clear that the values determined by our method do not deviate strongly from the SRIM values. This can be also concluded from the data shown in Fig. 1, where SRIM stopping led to a reasonable fit of the spectra. Note that we also show in Fig. 2 the energy range of 4 He particles on their way in and out of the GaN film, considering for the way out scattering from the Ga. This is the energy range that is actually available from the Ga signal, and we consider the stopping power curve determined to be valid only between the lowest and the highest probed energies (0.6–2.3 MeV), and therefore, this is the range where we present the results. We could have used also the position of the Al edge, extending the limits of validity of the calculation to lower energies, but it is a well known
Fig. 2. Limits of confidence of the stopping power of 4He in GaN (average plus minus one standard deviation: solid lines; average: thick solid line). Stopping calculated with SRIM and the Bragg rule is also shown (dashed). The regions of energy covered by the Ga signal are shown.
28
N.P. Barradas et al. / Nuclear Instruments and Methods in Physics Research B 273 (2012) 26–29
fact that the RBS yield at low energies is extremely difficult to calculate, and therefore we preferred to take the conservative option of using the Ga signal only. The stopping power curve obtained for 12C in GaN is shown in Fig. 3. The uncertainty in the thickness of the Au marker layer and of the GaN film, as determined with the 4He beam, was propagated to the uncertainty shown. The energy ranges probed by the beam inside the GaN signal are also shown. For the way out, three sets of values are displayed, corresponding to the three detectors that were simultaneously used. The stopping power curve is determined within the minimum and maximum energies probed, that is, between 0.9 and 15 MeV. As for 4He, the obtained results follow closely SRIM stopping with the Bragg rule. This is different from what occurs in InN, where experimental values of the 12C stopping are almost 10% higher than those predicted by SRIM and Bragg rule [19]. We show in Fig. 4 the spectra collected at 150° with the 16O beam, together with simulations that were made using SRIM stopping values. For the two highest beam energies the difference is barely noticeable, indicating that the stopping power above 10 MeV must be very close to SRIM. At 6 MeV some slight difference can be seen, and a strong misfit when using SRIM stopping with the Bragg rule is observed at 3 MeV, showing that the stopping power must be larger than the SRIM prediction. Determined stopping power curve is shown in Fig. 5. The energy range probed is 0.6–15 MeV. Again and similar as for 12C, the determined values are close to SRIM but not in the low energy range, in contrast to InN where the experimental stopping power is above the SRIM prediction up to 15 MeV [19].
5. Summary We have determined the stopping of 4He, 12C and 16O in gallium nitride, in the energy ranges 0.6–2.3, 0.9–14.9, and 0.6–14.9 MeV, respectively. We used a Bayesian inference method that relies on a simple RBS spectra of thin film or bulk samples. The method leads not only to a stopping curve, but also to confidence limits on the results derived. These are, to our knowledge, the first measurements in this energy range of any ion in this important system for optoelectronic applications. These measurements are useful for heavy ion ERDA analysis of C and O as impurities in GaN, and also for RBS analysis of GaN with a 4He beam.
Fig. 4. Spectra collected with 16O. Simulations using SRIM stopping, and stopping determined using a Bayesian inference analysis with the Markov chain Monte Carlo method (BI/MCMC), are shown.
Fig. 5. Limits of confidence of the stopping power of 16O in GaN (average plus minus one standard deviation: solid lines; average: thick solid line). Stopping calculated with SRIM and the Bragg rule is also shown (dashed). The regions of energy covered by the Ga signal (short dashed) are also shown.
Acknowledgements Fig. 3. Limits of confidence of the stopping power of 12C in GaN (average plus minus one standard deviation: solid lines; average: thick solid line). Stopping calculated with SRIM and the Bragg rule is also shown (dashed). The regions of energy covered by the Ga signal are also shown.
We would like to thank the International Atomic Energy Agency for support under Research Contracts Nos. 14365 and 14580, Dr. Vanya Darakchieva for providing the sample, Micaela Fonseca for
N.P. Barradas et al. / Nuclear Instruments and Methods in Physics Research B 273 (2012) 26–29
the Au deposition, Katharina Lorenz for useful discussions, Filomena Baptista for technical help, and Prof. Helmut Paul for many useful discussions. References [1] L. Hsu, W. Walukiewicz, J. Appl. Phys. 104 (2008) 024507. [2] V. Darakchieva, N.P. Barradas, M.-Y. Xie, K. Lorenz, E. Alves, M. Schubert, P.O.A. Persson, F. Giuliani, F. Munnik, C.L. Hsiao, L.W. Tu, W.J. Schaff, Phys. B 404 (2009) 4476. [3] .K.S.A. Butcher, A.J. Fernandes, P.P-T. Chen, M. Wintrebert-Fouquet, H. Timmers, S.K. Shrestha, H. Hirshy, R.M. Perks, B.F. Usher, J. Appl. Phys. 181 (2007) 123702. [4] J.F. Ziegler, J.P. Biersack, M.D. Ziegler, SRIM – The Stopping and Range of Ions in Matter, Maryland, SRIM Co., 2008. [5] H. Paul, A. Schinner, Nucl. Instr. Meth. B B195 (2002) 166. [6] T. Ahlgren, E. Rauhala, J. Appl. Phys. 90 (2001) 4871.
29
[7] Yanwen Zhang, In-Tae Bae, K. Sun, C. Wang, M. Ishimaru, Z. Zhu, W. Jiang, W.J. Weber, J. Appl. Phys. 105 (2009) 104901. [8] C. Pascual-Izarra, N.P. Barradas, G. García, A. Climent Font, Nucl. Instr. Meth. B 239 (2005) 135. [9] N.P. Barradas, E. Alves, Z. Siketic´, I. Bogdanovic´ Radovic´, AIP CP 1099 (2009) 331. [10] T. Bayes, Philos. Trans. Royal Soc. London 53 (1763) 370. [11] N.P. Barradas, C. Jeynes, M.A. Harry, Nucl. Instr. Meth. B 13–138 (1998) 1163. [12] N.P. Barradas, C. Jeynes, K.P. Homewood, B.J. Sealy, M. Milosavljevic, Nucl. Instr. Meth. B 139 (1998) 235. [13] F. Ziegler, J.P. Biersack, U. Littmark, Stopping and Ranges of Ions in Solids, Pergamon, New York, 1985. [14] N.P. Barradas, Nucl. Instr. Meth. B 225 318 (2004). [15] S. Molodtsov, A.F. Gurbich, Nucl. Instr. Meth. B 267 (2010) 484. [16] C. Pascual-Izarra, N.P. Barradas, Nucl. Instr. Meth. B 266 (2008) 1866. [17] M.A. Reshchikov, H. Morkoç, J. Appl. Phys. 97 (2005) 061301. [18] M.A. Rana, T. Osipowicz, H.W. Choi, M.B.H. Breese, F. Watt, S.J. Chua, Appl. Phys. A 77 (2003) 103. [19] N.P. Barradas, E. Alves, Z. Siketic´, I. Bogdanovic´ Radovic´, AIP CP 1336 (2011).
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Stopping power of He, C and O in GaN Nuno P. Barradas a,⇑, E. Alves a, Z. Siketic´ b, I. Bogdanovic´ Radovic´ b a b
Instituto Tecnológico e Nuclear, E.N. 10, Sacavém 2686-953, Portugal - Boškovic´ Institute, P.O. Box 180, 10002 Zagreb, Croatia Ruder
a r t i c l e
i n f o
Article history: Available online 27 July 2011 Keywords: Stopping power Gallium nitride Heavy ions
a b s t r a c t GaN and other group III nitrides based alloys are important materials in optoelectronic and electronic devices, including high-brightness blue and white LEDs, multi-junction solar cells, high-frequency transistors, and THz emitters. Unintentional impurities can be present, with a strong influence in the properties of these materials. These impurities are often light elements such as H, C, or O, and an ion beam analysis technique such as heavy ion elastic recoil detection analysis can play a fundamental role in their quantification. However, to our knowledge stopping powers in GaN have not yet been measured, and data analysis relies on using the Bragg rule, which is often inaccurate. We have used a bulk method, previously developed by us and applied successfully to other systems, to determine experimentally the stopping power of 4He, 12C and 16O in GaN, in the energy ranges 0.6–2.3, 0.9–14.9, and 0.6–14.9 MeV, respectively. The results of our measurements and bulk method analysis are presented. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction GaN and other group III nitrides based alloys are important materials in optoelectronic and electronic devices, including high-brightness blue and white LEDs, multi-junction solar cells, high-frequency transistors, and THz emitters [1]. Unintentional impurities can be present, with a strong influence in the properties of these materials [2]. Heavy ion elastic recoil detection analysis (HI-ERDA) is ideally suited to determine the profile of light impurities in a heavy matrix such as GaN [3]. The accuracy of the depth profiles obtained depends on the stopping powers used in the analysis. Very often, the stopping powers are taken from interpolative schemes such as SRIM [4] or MSTAR [5], which however do not include any experimental data of stopping power of any heavy ion in GaN in their databases. The stopping of H in GaN has been reported by Ahlgren and Rauhala [6], and excellent agreement was found with SRIM-98 for energies above 1 MeV, while for energies below the measured values were slightly below the SRIM-98 prediction. Calculations and experiments for low velocity Au ions in GaN have been presented [7] and are about a factor of 2 lower than SRIM, but the energy range considered was much below the usual range useful for HI-ERDA experiments. In this case, lacking experimental data, the Bragg rule must be used, which may lead to large deviations around 10% or more, particularly for oxides, nitrides, and for heavy ions.
⇑ Corresponding author. E-mail address: [email protected] (N.P. Barradas). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.07.029
We have measured the stopping power of 4He, 12C and 16O in GaN thin films grown on sapphire, in the energy ranges 0.6–2.3, 0.9–14.9, and 0.6–14.9 MeV, respectively. These ions were selected because 4He is often used in Rutherford backscattering (RBS) studies, while C and O are, together with hydrogen, amongst the most common light impurities in GaN thin films. The samples we had available were too thin for measurements with H ions. For stopping power measurements we have applied a method previously developed by us and applied on other systems [8,9]. In the proposed method, several RBS spectra were collected at different ion energies and at several different backscattering angles. Spectra were fitted simultaneously, and the entire stopping power curve was taken as a fit parameter, using the effect it has on the height and width of the film signal, together with a well known marker layer to determine the solid-angle charge product. A Bayesian inference [10] Markov chain Monte Carlo (BI/MCMC) algorithm, included in the code NDF [11,12], was used, so the uncertainty of the stopping curve derived was also obtained. 2. Experimental details A GaN film with nominal thickness of 200 nm grown by molecular beam epitaxy on a sapphire substrate was used. A thin Au layer was evaporated on the top of the film in order to provide an absolute solid-angle charge calibration. The 4He RBS experiments were done at ITN at a 160° scattering angle with beam energies 1, 2 and 2.3 MeV. The 12C and 16O RBS experiments at 3, 6, 10 - Boškovic´ Institute using three and 15 MeV were done at the Ruder detectors simultaneously, at 118°, 150° and 165° scattering angles [9].
N.P. Barradas et al. / Nuclear Instruments and Methods in Physics Research B 273 (2012) 26–29
3. Calculations The objective of the data analysis is to retrieve the stopping power curve from the energy spectra collected. This can be done because the stopping power has an univocal influence in the data: considering a thin film, a larger stopping power leads to a larger observed energy width, accompanied by a smaller yield per channel. This effect is shown in Fig. 1, where simulations for 4He data are made considering SRIM stopping power, as well as stopping values 10% higher and 10% smaller than given by SRIM. It is clear that the effect of an incorrect stopping power cannot be compensated by changing the film thickness, because the signal height would still be incorrect. To analyse the data, we treated the entire stopping power curve as a free parameter, that is, we did not simply scale it by a constant factor, but the energy dependence could also change during the analysis. The stopping curve was constrained to reasonable shapes by using the ZBL85 parameterisation [13]. Note that it is the molecular stopping power in GaN that is determined, and not the elemental Ga and N stopping powers. Experimental parameters such as the energy calibration and the solid-angle charge product are also allowed to change within their uncertainties. We then perform a Bayesian inference analysis with the Markov chain Monte Carlo method (BI/MCMC). The details of the method have been given previously [8,9] and are beyond the scope of this paper. The final result is the stopping power together with its associated uncertainty.
Fig. 1. Spectra collected with 4He. Simulations using SRIM stopping, and with stopping 10% higher and 10% lower than SRIM, are shown.
27
This process relies on the quality of the simulations produced. NDF includes the effect of double scattering [14], pile-up [15], and we have analysed pulse-height spectra by taking into account the pulse height defect coming from the detector dead layer and non-ionising energy losses in the detector [16]. The thickness of the Au marker layer and of the GaN film was determined from the 4He data. In order to be able to do this, the measured molecular stopping power of 4He in the Al2O3 substrate was used [8], and its stated uncertainty was propagated to the final uncertainty quoted for the stopping power curves reported here. Finally, the process relies on the stoichiometry of the GaN film. GaN is a highly stoichiometric material, with vacancy concentrations usually between 1016 and 1018/cm3 [17], and departure from stoichiometry is only observed after annealing treatments above 500 °C [18]. The energy range covered by the experiment is given by the range of energies that the ion beam has while crossing the Ga, first on the way in, and then after scattering on the way out of the sample and towards the detector. In each stopping power curve presented here, we also show the energy regions effectively probed by the beam. We note that there are gaps in the energy ranges that are effectively probed. However, the stopping power in those gaps is effectively constrained by the parameterisation used, that forces the stopping power curve to have a reasonable shape. 4. Results and discussion Fig. 2 shows the stopping power curve obtained for 4He in GaN. What we show is actually the average value plus and minus one standard deviation, i.e., the determined uncertainty. For comparison, we also show the SRIM stopping calculated from the Ga and N elemental stopping powers assuming the Bragg rule. It is clear that the values determined by our method do not deviate strongly from the SRIM values. This can be also concluded from the data shown in Fig. 1, where SRIM stopping led to a reasonable fit of the spectra. Note that we also show in Fig. 2 the energy range of 4 He particles on their way in and out of the GaN film, considering for the way out scattering from the Ga. This is the energy range that is actually available from the Ga signal, and we consider the stopping power curve determined to be valid only between the lowest and the highest probed energies (0.6–2.3 MeV), and therefore, this is the range where we present the results. We could have used also the position of the Al edge, extending the limits of validity of the calculation to lower energies, but it is a well known
Fig. 2. Limits of confidence of the stopping power of 4He in GaN (average plus minus one standard deviation: solid lines; average: thick solid line). Stopping calculated with SRIM and the Bragg rule is also shown (dashed). The regions of energy covered by the Ga signal are shown.
28
N.P. Barradas et al. / Nuclear Instruments and Methods in Physics Research B 273 (2012) 26–29
fact that the RBS yield at low energies is extremely difficult to calculate, and therefore we preferred to take the conservative option of using the Ga signal only. The stopping power curve obtained for 12C in GaN is shown in Fig. 3. The uncertainty in the thickness of the Au marker layer and of the GaN film, as determined with the 4He beam, was propagated to the uncertainty shown. The energy ranges probed by the beam inside the GaN signal are also shown. For the way out, three sets of values are displayed, corresponding to the three detectors that were simultaneously used. The stopping power curve is determined within the minimum and maximum energies probed, that is, between 0.9 and 15 MeV. As for 4He, the obtained results follow closely SRIM stopping with the Bragg rule. This is different from what occurs in InN, where experimental values of the 12C stopping are almost 10% higher than those predicted by SRIM and Bragg rule [19]. We show in Fig. 4 the spectra collected at 150° with the 16O beam, together with simulations that were made using SRIM stopping values. For the two highest beam energies the difference is barely noticeable, indicating that the stopping power above 10 MeV must be very close to SRIM. At 6 MeV some slight difference can be seen, and a strong misfit when using SRIM stopping with the Bragg rule is observed at 3 MeV, showing that the stopping power must be larger than the SRIM prediction. Determined stopping power curve is shown in Fig. 5. The energy range probed is 0.6–15 MeV. Again and similar as for 12C, the determined values are close to SRIM but not in the low energy range, in contrast to InN where the experimental stopping power is above the SRIM prediction up to 15 MeV [19].
5. Summary We have determined the stopping of 4He, 12C and 16O in gallium nitride, in the energy ranges 0.6–2.3, 0.9–14.9, and 0.6–14.9 MeV, respectively. We used a Bayesian inference method that relies on a simple RBS spectra of thin film or bulk samples. The method leads not only to a stopping curve, but also to confidence limits on the results derived. These are, to our knowledge, the first measurements in this energy range of any ion in this important system for optoelectronic applications. These measurements are useful for heavy ion ERDA analysis of C and O as impurities in GaN, and also for RBS analysis of GaN with a 4He beam.
Fig. 4. Spectra collected with 16O. Simulations using SRIM stopping, and stopping determined using a Bayesian inference analysis with the Markov chain Monte Carlo method (BI/MCMC), are shown.
Fig. 5. Limits of confidence of the stopping power of 16O in GaN (average plus minus one standard deviation: solid lines; average: thick solid line). Stopping calculated with SRIM and the Bragg rule is also shown (dashed). The regions of energy covered by the Ga signal (short dashed) are also shown.
Acknowledgements Fig. 3. Limits of confidence of the stopping power of 12C in GaN (average plus minus one standard deviation: solid lines; average: thick solid line). Stopping calculated with SRIM and the Bragg rule is also shown (dashed). The regions of energy covered by the Ga signal are also shown.
We would like to thank the International Atomic Energy Agency for support under Research Contracts Nos. 14365 and 14580, Dr. Vanya Darakchieva for providing the sample, Micaela Fonseca for
N.P. Barradas et al. / Nuclear Instruments and Methods in Physics Research B 273 (2012) 26–29
the Au deposition, Katharina Lorenz for useful discussions, Filomena Baptista for technical help, and Prof. Helmut Paul for many useful discussions. References [1] L. Hsu, W. Walukiewicz, J. Appl. Phys. 104 (2008) 024507. [2] V. Darakchieva, N.P. Barradas, M.-Y. Xie, K. Lorenz, E. Alves, M. Schubert, P.O.A. Persson, F. Giuliani, F. Munnik, C.L. Hsiao, L.W. Tu, W.J. Schaff, Phys. B 404 (2009) 4476. [3] .K.S.A. Butcher, A.J. Fernandes, P.P-T. Chen, M. Wintrebert-Fouquet, H. Timmers, S.K. Shrestha, H. Hirshy, R.M. Perks, B.F. Usher, J. Appl. Phys. 181 (2007) 123702. [4] J.F. Ziegler, J.P. Biersack, M.D. Ziegler, SRIM – The Stopping and Range of Ions in Matter, Maryland, SRIM Co., 2008. [5] H. Paul, A. Schinner, Nucl. Instr. Meth. B B195 (2002) 166. [6] T. Ahlgren, E. Rauhala, J. Appl. Phys. 90 (2001) 4871.
29
[7] Yanwen Zhang, In-Tae Bae, K. Sun, C. Wang, M. Ishimaru, Z. Zhu, W. Jiang, W.J. Weber, J. Appl. Phys. 105 (2009) 104901. [8] C. Pascual-Izarra, N.P. Barradas, G. García, A. Climent Font, Nucl. Instr. Meth. B 239 (2005) 135. [9] N.P. Barradas, E. Alves, Z. Siketic´, I. Bogdanovic´ Radovic´, AIP CP 1099 (2009) 331. [10] T. Bayes, Philos. Trans. Royal Soc. London 53 (1763) 370. [11] N.P. Barradas, C. Jeynes, M.A. Harry, Nucl. Instr. Meth. B 13–138 (1998) 1163. [12] N.P. Barradas, C. Jeynes, K.P. Homewood, B.J. Sealy, M. Milosavljevic, Nucl. Instr. Meth. B 139 (1998) 235. [13] F. Ziegler, J.P. Biersack, U. Littmark, Stopping and Ranges of Ions in Solids, Pergamon, New York, 1985. [14] N.P. Barradas, Nucl. Instr. Meth. B 225 318 (2004). [15] S. Molodtsov, A.F. Gurbich, Nucl. Instr. Meth. B 267 (2010) 484. [16] C. Pascual-Izarra, N.P. Barradas, Nucl. Instr. Meth. B 266 (2008) 1866. [17] M.A. Reshchikov, H. Morkoç, J. Appl. Phys. 97 (2005) 061301. [18] M.A. Rana, T. Osipowicz, H.W. Choi, M.B.H. Breese, F. Watt, S.J. Chua, Appl. Phys. A 77 (2003) 103. [19] N.P. Barradas, E. Alves, Z. Siketic´, I. Bogdanovic´ Radovic´, AIP CP 1336 (2011).