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Simulation of RBS spectra with known 3D sample surface roughness
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
Simulation of RBS spectra with known 3D sample surface roughness Petr Malinsky´ a,b,⇑, Jakub Siegel c, Vladimir Hnatowicz a, Anna Macková a,b, Václav Švorcˇík c a
Nuclear Physics Institute of the Czech Academy of Sciences, v. v. i., 250 68 Rez, Czech Republic Department of Physics, Faculty of Sciences, J.E. Purkinje University, 400 96 Usti nad Labem, Czech Republic c Department of Solid State Engineering, University of Chemistry and Technology, 166 28 Prague, Czech Republic b
a r t i c l e
i n f o
Article history: Received 4 August 2016 Received in revised form 9 December 2016 Accepted 8 February 2017 Available online xxxx Keywords: Computer simulation Rutherford Backscattering Spectroscopy Surface roughness AFM
a b s t r a c t The Rutherford Backscattering Spectrometry (RBS) is a technique for elemental depth profiling with a nanometer depth resolution. Possible surface roughness of analysed samples can deteriorate the RBS spectra and makes their interpretation more difficult and ambiguous. This work describes the simulation of RBS spectra which takes into account real 3D morphology of the sample surface obtained by AFM method. The RBS spectrum is calculated as a sum of the many particular spectra obtained for randomly chosen particle trajectories over sample 3D landscape. The spectra, simulated for different ion beam incidence angles, are compared to the experimental ones measured with 2.0 MeV 4He+ ions. The main aim of this work is to obtain more definite information on how a particular surface morphology and measuring geometry affects the RBS spectra and derived elemental depth profiles. A reasonable agreement between the measured and simulated spectra was found and the results indicate that the AFM data on the sample surface can be used for the simulation of RBS spectra. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction The Rutherford Backscattering Spectroscopy (RBS), Elastic Recoil Detection Analysis (ERDA) and Medium Energy Ion Scattering (MEIS) are well established IBA (Ion Beam Analysis) techniques for quantitative analyses of the near-surface regions of various materials and determination of elemental depth profiles with nanometer depth resolution which can be achieved by tilting the sample with respect to an incoming and/or outgoing ion beam [1]. The depth resolution may adversely be affected by the surface roughness occurring on real samples. The sample roughness deteriorates depth resolution and precludes the elemental depth profiling in a worst case. The roughness effects become extremely important in glancing-angle measuring geometry used in the case when a high depth resolution is required. Neglecting the effects of surface roughness may result in a serious misinterpretation of the RBS data. The effects of roughness on RBS spectra have been addressed in several theoretical and experimental studies published since the early 1980s. Metzner et al. [2,3] have measured RBS spectra from samples comprising thin surface layers of different roughness and suggested a simple technique for the evaluation of RBS spectra ⇑ Corresponding author at: Nuclear Physics Institute of the Czech Academy of Sciences, v. v. i., 250 68 Rez, Czech Republic. E-mail address: [email protected] (P. Malinsky´).
from such samples measured under specific geometry. In previously published papers [4–7] the statistical weights of surface non-uniformities were determined from the TEM or AFM data and the final RBS spectrum was obtained as a sum of weighted particular RBS spectra calculated by standard codes. Procedures for the evaluation of RBS spectra from rough samples are included in some standard codes for the evaluation of IBA spectra. In the SIMNRA code [8,9], the RBS spectra of the surface film with specific thickness distribution are obtained as a sum of several particular spectra each calculated for a specific thickness and summed according to expected thickness distribution. In the NDF code [10,11], the effect of roughness is included as an extra contribution to energy straggling, calculated for smooth sample. Specific procedures for the elimination of adverse effects of surface roughness are included in the code RBS-MAST [12–16]. Among the most recent publications, the studies of samples with rough surface performed by MEIS [17–19] and RBS techniques [20,21] should be mentioned too. The effects of top-layer roughness on the RBS spectra of a submerged marker were examined in [7]. The surface roughness could be well included in codes based on the Monte Carlo (MC) technique, but standard MC calculations are too slow for the routine RBS analysis. In the MC code Corteo for the simulation of RBS spectra [22], the computational time is reduced substantially, and the version of the program taking into account sample roughness has been published recently [23]. Despite of ever increasing interest in the roughness effects in IBA analyses the
http://dx.doi.org/10.1016/j.nimb.2017.02.020 0168-583X/Ó 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: P. Malinsky´ et al., Simulation of RBS spectra with known 3D sample surface roughness, Nucl. Instr. Meth. B (2017), http:// dx.doi.org/10.1016/j.nimb.2017.02.020
2
´ et al. / Nuclear Instruments and Methods in Physics Research B xxx (2017) xxx–xxx P. Malinsky
works comparing the spectra, measured on the samples with a well-defined surface morphology, with simulated ones are rather scarce. In this work, the RBS spectra from the samples comprising a thin gold layer sputtered onto a polymer backing with a periodically patterned surface are measured and compared to those simulated by the F95-Rough code, which takes into account a real three-dimensional surface relief of the analysed samples determined by the AFM. 2. Experimental details The samples with a periodically patterned surface (see below in Fig. 3) were prepared by the laser irradiation of polyethylene terephthalate (PET) foils and coated by a thin gold layer (for details see [24]). Oriented PET foils, 50 mm in thickness (supplied by Goodfellow Ltd., United Kingdom), were scanned with a KrF laser light (COMPexPro 50 F, Coherent Inc., operational wavelength 248 nm, pulse duration 20–40 ns, and repetition rate 10 Hz). The laser light was polarized linearly with a UV-grade fused silica prism (model PBSO-248-100). An aperture of 10 5 mm2 was used for a homogeneous illumination of the sample. The irradiation fluences were 6.6 mJ cm 2.The PET samples were irradiated with 6000 pulses per area in ambient atmosphere. The angles of 0°, 22.5° and 45° between the sample surface normal and the laser beam were chosen to prepare samples with different surface reliefs [25,26]. The patterned PET foils were sputtered with an approximately 35 nm thick Au layer from a gold target (99.99%) by diode sputtering (BAL-TEC SCD 050). The deposition was performed at room temperature under following conditions: deposition time of 600 s, discharge current of 40 mA, total argon pressure of about 4 Pa and electrode distance of 50 mm. The thickness of the sputtered gold layer was determined from RBS measurement performed on a smooth part of the PET foils and verified by AFM scratch test on Si substrate sputtered simultaneously with PET samples [27,28]. The data from RBS measurement were converted into nm using a bulk gold density (19.3 g cm 3). The surface morphology and roughness were examined by AFM using a Bruker Corp. (Veeco CP II) scanner with a Veeco oxidesharpened P-doped silicon probe RTESPA-CP (a tip radius of 8 nm, tip angles of about 20°, a tip height of 17.5 lm) attached to a flexible micro-cantilever near its resonant frequency of 300 kHz and a spring constant of 40 N/m. All AFM measurements were carried out in the tapping mode in the ambient atmosphere and at room temperature. A new AFM tip was used for each sample. The RBS spectra were measured on a 3 MV Tandetron MC 4130 accelerator of the Nuclear Physics Institute of the Czech Academy
Fig. 2. Evolution of the final RBS spectrum with increasing number of particular spectra. The simulation was performed for the sample prepared by laser irradiation under 0° incident beam angle and analysed with 2.0 MeV 4He+ ions (incoming beam angle 75° and 170° laboratory scattering angle).
of Sciences (NPI CAS) using 2.0 MeV 4He+ ions in the Cornell geometry at laboratory scattering angle of 170°. The angle between the incidence beam and the sample surface normal was changed from 0° to 75° to examine the effects of surface roughness on the RBS spectra measured in different geometries. The Ultra-Ortec PIPS detector solid angle was 2.612 mSr, the spectrometer energy resolution for 2.0 MeV 4He+ ions was FWHM = 12 keV and the beam spot area on the sample was 1 1 mm2. The typical beam current was 5 nA. The sample was oriented so that the ridges of the ripple pattern were oriented parallel to the plane of the incident and output ion beam (see Fig. 1).
3. RBS spectrum simulation
Fig. 1. A schematic view of the RBS measuring geometry with respect to the orientation of surface ripple patterns.
RBS spectra were simulated using the F95-Rough code, written in FORTRAN 95, for simulation of RBS spectra from samples with known 2D or 3D surface roughness [29,30]. The basic idea of the code is to use AFM data on surface morphology of a real sample and simulate large number of particular RBS spectra for the ion beam impinging the sample surface at different randomly chosen
Please cite this article in press as: P. Malinsky´ et al., Simulation of RBS spectra with known 3D sample surface roughness, Nucl. Instr. Meth. B (2017), http:// dx.doi.org/10.1016/j.nimb.2017.02.020
´ et al. / Nuclear Instruments and Methods in Physics Research B xxx (2017) xxx–xxx P. Malinsky
3
Fig. 3. Images of the AFM input data for the simulation of RBS spectra. The data were obtained by cutting off and rotating of the original AFM data. The samples were prepared by irradiation of PET foil with laser beam coming under the angles 0° (a), 22.5° (b) and 45° (c) and subsequent coating with 35 nm thick gold film.
entrance points and scattered under identical measuring geometry (incident and laboratory scattering angle). The sum of all particular spectra represents the RBS spectrum from the real sample with rough surface. Present calculation was performed using the three-dimensional AFM data on the surface morphology of rough PET samples with sputtered gold layer (see Fig. 3). The position of the interface between the gold layer and the patterned PET backing was obtained simply by subtracting gold layer thickness of 35 nm, measured perpendicularly to the local surface, from the sample surface determined by AFM. The sample surface/interface is represented by polygon mesh consisting of vertices and quadrilateral faces. The gold layer and PET substrate bulk densities 19.3 g cm 3 and 1.35 g cm 3 respectively were used in simulation. The trajectories of the incident and back-scattered ions are approximated by straight lines and the ion energy slowing down process is separated from the scattering events. Multiple and plural scattering are not taken into account for the sake of simplicity. The ion trajectory is incremented by a small, constant step (can be liberally chosen as an input parameter) and the current ion energy is changed accordingly using the appropriate stopping power at the immediate ion position. At each incremental step the coordinates of the current ion position are tested with respect to the local position of the sample surface or gold-PET backing interface in order to decide what physical parameters as cross sections, kinematic factors and related parameters should be used for the spectrum simulation. At each incident ion position virtual scattering into the direction to the detector is considered with the probability proportional to the appropriate Rutherford cross section multiplied by L’Écuyer correction factor [31]. The ingoing ion is removed from the simulation as the ion reaches the predefined depth or the ion energy falls below some predefined value. The outgoing trajectory of the backscattered ion is treated in the same manner. SRIM stopping powers [32] and Bohr straggling [33] are used in the course of calculation. In such way for each ion trajectory a full RBS spectrum is obtained, respecting ion entrance point coordinates and the local sample properties. The calculation is repeated many times with randomly generated ion entrance points spread over a representative sample area and particular spectra are stored in a virtual multichannel analyser. The final RBS spectrum, obtained as a sum of all particular spectra, is convoluted with a Gaussian function the width of which combines detector resolution with energy spread estimated with the code DEPTH [34] for the mean layer thickness. To take into account the fine features of the sample surface properly, typically several hundred ion trajectories have to be generated. Evolution of the simulated final RBS spectrum with increasing number of particular spectra, generated for randomly chosen ion trajectories is shown in Fig. 2. One can see that already after summing about 300 particular spectra required simulated spectrum is reached.
4. Results and discussion The RBS spectra were simulated using the F95-Rough code with the data obtained by the AFM examination of the real samples. From these original AFM data, taken under casual direction, a relevant part was cut-off and slightly rotated in order to match present experimental arrangement shown in Fig. 1 and described above. AFM images of the samples (laser patterned PET with sputtered gold layer) used for the RBS spectra simulation, are shown in the Fig. 3. One can see the periodic ripple patterns whose height, width and frequency depend on the laser irradiation angle. The root-mean-square wavelength of the structure increases from 240 to 420 nm and the root-mean-square undulation of the ridges increases from 80 to 110 nm when the irradiation angle increased from 0° to 45°. The relevant parts of the experimental RBS spectra arising from the gold layer deposited on the patterned PET are shown in Fig. 4 together with the spectra simulated using the F95-Rough code. Constant 35 nm thickness of the gold layer over all sample surfaces was assumed in the simulation. It is evident that the shape of the gold peak in the RBS spectrum varies strongly as a function of increasing angle of incoming ion beam measured with respect to sample surface normal. While for low incident angles the RBS spectrum comprises dominant Gaussian-like component. At larger incidence angles a low energy component arises and relative area of this component increases rapidly with increasing incident angle. The appearance and growth of the low energy component is explained by the fact that the ions incoming at glancing angle scan penetrate the gold layer and the underlying PET several times before being scattered to the detector. So that, in glancing angle measuring geometry the gold signal is expected to comprise one or a few side peaks shifted to lower energy. The simulation performed under the assumption of constant thickness of the gold layer reproduces at least qualitatively the main features of the measured RBS spectra. The simulated spectra for ion beam incident angles below 45° are in very good agreement with experimental ones. For larger incident angles the increasing discrepancies between the experimental and simulated spectra are seen, which may be attributed to the possible non-uniformity of the sputtered gold layer. To test of the effect of the gold layer thickness and thickness non-uniformity, the RBS spectra were first simulated for different but constant thickness of gold layer. The results of these simulations are shown in the Fig. 5, from which one can see the development of the spectra simulated for constant thickness of the gold layer varying from 25 to 45 nm. It is evident that a significantly better agreement between simulated and measured RBS spectra cannot be achieved only by changing of the gold layer thickness. With a particular layer thickness it is possible to achieve better agreement in some part of the spectrum but at the cost of worsen-
Please cite this article in press as: P. Malinsky´ et al., Simulation of RBS spectra with known 3D sample surface roughness, Nucl. Instr. Meth. B (2017), http:// dx.doi.org/10.1016/j.nimb.2017.02.020
4
´ et al. / Nuclear Instruments and Methods in Physics Research B xxx (2017) xxx–xxx P. Malinsky
Fig. 4. Comparison of the RBS experimental spectra from rough samples, measured under different incident angle, with those simulated by the F95-Rough code (smooth lines). The simulations were performed under the assumption of constant gold layer thickness of 35 nm.
Fig. 5. The simulated RBS spectra development in dependence on the thickness of the gold layer used in simulation. The simulations were performed for samples of PET backing, patterned by the laser beam at incident angle 22.5° and coated with homogenous gold layers of different thicknesses. The RBS spectra were measured under ion beam incident angle of 75°.
ing in other ones. In particular best simulation at high energy peak (between channels from 760 to 800) is obtained for layer thickness 25 nm and for the peak at lowest energy for the layer thickness above 40 nm. In the next step the effect of the gold layer thickness nonuniformity was examined on the simulated sample with the gold layer thickness which was assumed to change linearly between
Fig. 6. Comparison of the RBS experimental spectra from rough samples, measured under different incident angles, with those simulated by the F95-Rough code (smooth lines). The simulations were performed with assumption of linearly changing gold layer thickness between top (20 nm) and bottom (75 nm) of the ripple patterns. The simulations were performed for sample with PET backing patterned by the laser beam with incident angle 22.5°.
the top (20 nm) and the bottom (75 nm) of the ripple patterns. The simulations were performed on the sample prepared by PET laser patterning under laser beam incident angle 22.5° and for RBS analysis with ion beam incident angles changed from 0° to 75°. The results are shown in Fig. 6. One can see that the simulated spectra reproduce the experimental ones much better for all used
Please cite this article in press as: P. Malinsky´ et al., Simulation of RBS spectra with known 3D sample surface roughness, Nucl. Instr. Meth. B (2017), http:// dx.doi.org/10.1016/j.nimb.2017.02.020
´ et al. / Nuclear Instruments and Methods in Physics Research B xxx (2017) xxx–xxx P. Malinsky
incident angles compare with the spectra simulated with constant gold layer thickness. It is evident, that there are still some small discrepancies between simulation and experiment that can be attributed to the ad-hoc chosen linear thickness dependence of the gold layer which can differ from real one. Another reason may lie in finite dimension of the AFM tip which may corrupt AFM images of the gold coated samples. Probably the best way to avoid doubts would be to use AFM data of the laser patterned samples without gold layer along with AFM data of sample after deposition of gold. 5. Conclusion The feasibility of the code F95-rough for the simulation of the RBS spectra from the samples with a definite surface roughness was demonstrated on the RBS spectra measured on real samples with regular roughness, the parameters of which were determined by AFM method. The samples were prepared by the sputtering of a 35-nm-thick gold layer on the surface of the PET substrate periodically patterned by laser irradiation. It was shown that required simulated spectrum can be obtained already after summing of about 300 randomly generated particular spectra. The RBS spectra measured at glancing angles exhibit a more complex gold signal comprising the main peak and low-energy components corresponding to ion scattering from gold layers on the neighboring ripples. The relative intensity of the low-energy components is an increasing function of the incoming ion-beam incidence angle. For lower ion beam incident angles the measured gold signal is well reproduced by computer simulation. For larger incident angles the evolution of the gold signal is reproduced rather qualitatively. The effects of varying gold layer thickness and gold layer non-uniformity on simulated RBS spectra was examined. It was shown that the agreement between measured and simulated spectra for different ion beam incident angles cannot be improved with uniform gold layer thickness. On the other hand the simulations assuming gold layer thickness linearly varying between top and bottom of the ripple patterns reproduce the experimental RBS spectra fairly. Present results show that the data of surface roughness obtained from AFM analysis of the sample surface can be used for the simulation of RBS spectra and that the RBS measurements accomplished at glancing angle may indicate the presence of a periodic structure on the sample surface.
5
(LM2015056) and has been supported by the project P108/12/ G108. References [1] Y. Wang, M. Nastasi, Handbook of Modern Ion-Beam Materials Analysis, Materials Research Society, Pittsburgh, 2009. [2] H. Metzner, M. Gossla, Th. Hahn, Nucl. Instr. Meth. B 124 (1997) 567–574. [3] H. Metzner, Th. Hahn, M. Gossla, J. Conrad, J.-H. Bremer, Nucl. Instr. Meth. B 134 (1998) 249–261. [4] M. Marin, Y. Serruys, P. Calmon, Nucl. Instr. Meth. B 108 (1996) 179–187. [5] J. Slotte, A. Laakso, T. Ahlgren, E. Rauhala, R. Salonen, J. Räisänen, A. Simon, I. Uzonyi, Á.Z. Kiss, E. Somorjai, J. Appl. Phys. 87 (2000) 140–143. [6] M.J.F. Healy, M. Torres, J.D. Painter, Nucl. Instr. Meth. B 249 (2006) 789–791. [7] H. Langhuth, M. Mayer, S. Lindig, Nucl. Instr. Meth. B 269 (2011) 1811–1817. [8] M. Mayer, AIP Conf. Proc. 475 (1999) 541–544. [9] M. Mayer, Nucl. Instr. Meth. B 194 (2002) 177–186. [10] N.P. Barradas, J. Phys. D Appl. Phys. 34 (2001) 2109–2116. [11] N.P. Barradas, C.G. Núñez, A. Redondo-Cubero, G. Shen, P. Kung, J.L. Pau, Nucl. Instr. Meth. B 371 (2016) 116–120. [12] Z. Hajnal, E. Szilágyi, F. Pászti, G. Battistig, Nucl. Instr. Meth. B 118 (1996) 617– 621. [13] F. Pászti, E. Szilágyi, Z.E. Horváth, A. Manuaba, G. Battistig, Z. Hajnal, É. Vázsonyi, Nucl. Instr. Meth. B 136–138 (1998) 533–539. [14] Z. Zolnai, A. Deák, N. Nagy, A.L. Tóth, E. Kótai, G. Battistig, Nucl. Instr. Meth. B 268 (2010) 79–86. [15] Z. Zolnai, N. Nagy, A. Deák, G. Battistig, E. Kótai, Phys. Rev. B 83 (2011) 233302. [16] Z. Zolnai, Appl. Surf. Sci. 281 (2013) 17–23. [17] M.A. Sortica, P.L. Grande, G. Machado, L. Miotti, J. Appl. Phys. 106 (2009) 114320. [18] M.A. Sortica, P.L. Grande, C. Radtke, L.G. Almeida, R. Debastiani, J.F. Dias, A. Hentz, Appl. Phys. Lett. 101 (2012) 023110. [19] J. Gustafson, A.R. Haire, C.J. Baddeley, Surf. Sci. 605 (2011) 220–224. [20] A. Tunyogi, F. Tanczikó, Cs. Bogdán, Z.E. Horváth, E. Szilágyi, Nucl. Instr. Meth. B 268 (2010) 1972–1975. [21] S.L. Molodtsov, A.F. Gurbich, C. Jeynes, J. Phys. D Appl. Phys. 41 (2008) 205303. [22] F. Schiettecate, Nucl. Instrum. Meth. B 266 (2008) 1880–1885. [23] F. Schiettecate, M. Chicoine, Nucl. Instr. Meth. B 371 (2016) 106–110. [24] J. Siegel, P. Slepicka, J. Heitz, Z. Kolska, P. Sajdl, V. Svorcik, Appl. Surf. Sci. 256 (2010) 2205–2209. [25] J. Siegel, J. Heitz, V. Švorcˇík, Surf. Coat. Technol. 206 (2012) 517–521. [26] P. Slepicˇka, E. Rebollar, J. Heitz, V. Švorcˇík, Appl. Surf. Sci. 254 (2008) 3585– 3590. [27] V. Švorcˇík, J. Zehentner, V. Rybka, P. Slepicˇka, V. Hnatowicz, Appl. Phys. A 75 (2002) 541–544. [28] P. Slepicˇka, Z. Kolská, J. Náhlík, V. Hnatowicz, V. Švorcˇík, Surf. Interf. Anal. 41 (2009) 741–745. [29] P. Malinsky, V. Hnatowicz, A. Mackova, Nucl. Instr. Meth. B 371 (2016) 101– 105. [30] M. Mayer, P. Malinsky´, F. Schiettekatte, Z. Zolnai, Nucl. Instr. Meth. B 385 (2016) 65–73. [31] J. L’Ecuyer, J.A. Davies, N. Matsunami, Nucl. Instr. Meth. 160 (1979) 337–346. [32] J.F. Ziegler, Nucl. Instr. Meth. B 219–220 (2004) 219–220. [33] N. Bohr, Philos. Mag. 30 (1915) 581–612. [34] E. Szilágyi, F. Pászti, G. Amsel, Nucl. Instr. Meth. B 100 (1995) 103–121.
Acknowledgements The research has been carried out at the CANAM (Center of Accelerators and Nuclear Analytical Methods) infrastructure
Please cite this article in press as: P. Malinsky´ et al., Simulation of RBS spectra with known 3D sample surface roughness, Nucl. Instr. Meth. B (2017), http:// dx.doi.org/10.1016/j.nimb.2017.02.020
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Simulation of RBS spectra with known 3D sample surface roughness Petr Malinsky´ a,b,⇑, Jakub Siegel c, Vladimir Hnatowicz a, Anna Macková a,b, Václav Švorcˇík c a
Nuclear Physics Institute of the Czech Academy of Sciences, v. v. i., 250 68 Rez, Czech Republic Department of Physics, Faculty of Sciences, J.E. Purkinje University, 400 96 Usti nad Labem, Czech Republic c Department of Solid State Engineering, University of Chemistry and Technology, 166 28 Prague, Czech Republic b
a r t i c l e
i n f o
Article history: Received 4 August 2016 Received in revised form 9 December 2016 Accepted 8 February 2017 Available online xxxx Keywords: Computer simulation Rutherford Backscattering Spectroscopy Surface roughness AFM
a b s t r a c t The Rutherford Backscattering Spectrometry (RBS) is a technique for elemental depth profiling with a nanometer depth resolution. Possible surface roughness of analysed samples can deteriorate the RBS spectra and makes their interpretation more difficult and ambiguous. This work describes the simulation of RBS spectra which takes into account real 3D morphology of the sample surface obtained by AFM method. The RBS spectrum is calculated as a sum of the many particular spectra obtained for randomly chosen particle trajectories over sample 3D landscape. The spectra, simulated for different ion beam incidence angles, are compared to the experimental ones measured with 2.0 MeV 4He+ ions. The main aim of this work is to obtain more definite information on how a particular surface morphology and measuring geometry affects the RBS spectra and derived elemental depth profiles. A reasonable agreement between the measured and simulated spectra was found and the results indicate that the AFM data on the sample surface can be used for the simulation of RBS spectra. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction The Rutherford Backscattering Spectroscopy (RBS), Elastic Recoil Detection Analysis (ERDA) and Medium Energy Ion Scattering (MEIS) are well established IBA (Ion Beam Analysis) techniques for quantitative analyses of the near-surface regions of various materials and determination of elemental depth profiles with nanometer depth resolution which can be achieved by tilting the sample with respect to an incoming and/or outgoing ion beam [1]. The depth resolution may adversely be affected by the surface roughness occurring on real samples. The sample roughness deteriorates depth resolution and precludes the elemental depth profiling in a worst case. The roughness effects become extremely important in glancing-angle measuring geometry used in the case when a high depth resolution is required. Neglecting the effects of surface roughness may result in a serious misinterpretation of the RBS data. The effects of roughness on RBS spectra have been addressed in several theoretical and experimental studies published since the early 1980s. Metzner et al. [2,3] have measured RBS spectra from samples comprising thin surface layers of different roughness and suggested a simple technique for the evaluation of RBS spectra ⇑ Corresponding author at: Nuclear Physics Institute of the Czech Academy of Sciences, v. v. i., 250 68 Rez, Czech Republic. E-mail address: [email protected] (P. Malinsky´).
from such samples measured under specific geometry. In previously published papers [4–7] the statistical weights of surface non-uniformities were determined from the TEM or AFM data and the final RBS spectrum was obtained as a sum of weighted particular RBS spectra calculated by standard codes. Procedures for the evaluation of RBS spectra from rough samples are included in some standard codes for the evaluation of IBA spectra. In the SIMNRA code [8,9], the RBS spectra of the surface film with specific thickness distribution are obtained as a sum of several particular spectra each calculated for a specific thickness and summed according to expected thickness distribution. In the NDF code [10,11], the effect of roughness is included as an extra contribution to energy straggling, calculated for smooth sample. Specific procedures for the elimination of adverse effects of surface roughness are included in the code RBS-MAST [12–16]. Among the most recent publications, the studies of samples with rough surface performed by MEIS [17–19] and RBS techniques [20,21] should be mentioned too. The effects of top-layer roughness on the RBS spectra of a submerged marker were examined in [7]. The surface roughness could be well included in codes based on the Monte Carlo (MC) technique, but standard MC calculations are too slow for the routine RBS analysis. In the MC code Corteo for the simulation of RBS spectra [22], the computational time is reduced substantially, and the version of the program taking into account sample roughness has been published recently [23]. Despite of ever increasing interest in the roughness effects in IBA analyses the
http://dx.doi.org/10.1016/j.nimb.2017.02.020 0168-583X/Ó 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: P. Malinsky´ et al., Simulation of RBS spectra with known 3D sample surface roughness, Nucl. Instr. Meth. B (2017), http:// dx.doi.org/10.1016/j.nimb.2017.02.020
2
´ et al. / Nuclear Instruments and Methods in Physics Research B xxx (2017) xxx–xxx P. Malinsky
works comparing the spectra, measured on the samples with a well-defined surface morphology, with simulated ones are rather scarce. In this work, the RBS spectra from the samples comprising a thin gold layer sputtered onto a polymer backing with a periodically patterned surface are measured and compared to those simulated by the F95-Rough code, which takes into account a real three-dimensional surface relief of the analysed samples determined by the AFM. 2. Experimental details The samples with a periodically patterned surface (see below in Fig. 3) were prepared by the laser irradiation of polyethylene terephthalate (PET) foils and coated by a thin gold layer (for details see [24]). Oriented PET foils, 50 mm in thickness (supplied by Goodfellow Ltd., United Kingdom), were scanned with a KrF laser light (COMPexPro 50 F, Coherent Inc., operational wavelength 248 nm, pulse duration 20–40 ns, and repetition rate 10 Hz). The laser light was polarized linearly with a UV-grade fused silica prism (model PBSO-248-100). An aperture of 10 5 mm2 was used for a homogeneous illumination of the sample. The irradiation fluences were 6.6 mJ cm 2.The PET samples were irradiated with 6000 pulses per area in ambient atmosphere. The angles of 0°, 22.5° and 45° between the sample surface normal and the laser beam were chosen to prepare samples with different surface reliefs [25,26]. The patterned PET foils were sputtered with an approximately 35 nm thick Au layer from a gold target (99.99%) by diode sputtering (BAL-TEC SCD 050). The deposition was performed at room temperature under following conditions: deposition time of 600 s, discharge current of 40 mA, total argon pressure of about 4 Pa and electrode distance of 50 mm. The thickness of the sputtered gold layer was determined from RBS measurement performed on a smooth part of the PET foils and verified by AFM scratch test on Si substrate sputtered simultaneously with PET samples [27,28]. The data from RBS measurement were converted into nm using a bulk gold density (19.3 g cm 3). The surface morphology and roughness were examined by AFM using a Bruker Corp. (Veeco CP II) scanner with a Veeco oxidesharpened P-doped silicon probe RTESPA-CP (a tip radius of 8 nm, tip angles of about 20°, a tip height of 17.5 lm) attached to a flexible micro-cantilever near its resonant frequency of 300 kHz and a spring constant of 40 N/m. All AFM measurements were carried out in the tapping mode in the ambient atmosphere and at room temperature. A new AFM tip was used for each sample. The RBS spectra were measured on a 3 MV Tandetron MC 4130 accelerator of the Nuclear Physics Institute of the Czech Academy
Fig. 2. Evolution of the final RBS spectrum with increasing number of particular spectra. The simulation was performed for the sample prepared by laser irradiation under 0° incident beam angle and analysed with 2.0 MeV 4He+ ions (incoming beam angle 75° and 170° laboratory scattering angle).
of Sciences (NPI CAS) using 2.0 MeV 4He+ ions in the Cornell geometry at laboratory scattering angle of 170°. The angle between the incidence beam and the sample surface normal was changed from 0° to 75° to examine the effects of surface roughness on the RBS spectra measured in different geometries. The Ultra-Ortec PIPS detector solid angle was 2.612 mSr, the spectrometer energy resolution for 2.0 MeV 4He+ ions was FWHM = 12 keV and the beam spot area on the sample was 1 1 mm2. The typical beam current was 5 nA. The sample was oriented so that the ridges of the ripple pattern were oriented parallel to the plane of the incident and output ion beam (see Fig. 1).
3. RBS spectrum simulation
Fig. 1. A schematic view of the RBS measuring geometry with respect to the orientation of surface ripple patterns.
RBS spectra were simulated using the F95-Rough code, written in FORTRAN 95, for simulation of RBS spectra from samples with known 2D or 3D surface roughness [29,30]. The basic idea of the code is to use AFM data on surface morphology of a real sample and simulate large number of particular RBS spectra for the ion beam impinging the sample surface at different randomly chosen
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Fig. 3. Images of the AFM input data for the simulation of RBS spectra. The data were obtained by cutting off and rotating of the original AFM data. The samples were prepared by irradiation of PET foil with laser beam coming under the angles 0° (a), 22.5° (b) and 45° (c) and subsequent coating with 35 nm thick gold film.
entrance points and scattered under identical measuring geometry (incident and laboratory scattering angle). The sum of all particular spectra represents the RBS spectrum from the real sample with rough surface. Present calculation was performed using the three-dimensional AFM data on the surface morphology of rough PET samples with sputtered gold layer (see Fig. 3). The position of the interface between the gold layer and the patterned PET backing was obtained simply by subtracting gold layer thickness of 35 nm, measured perpendicularly to the local surface, from the sample surface determined by AFM. The sample surface/interface is represented by polygon mesh consisting of vertices and quadrilateral faces. The gold layer and PET substrate bulk densities 19.3 g cm 3 and 1.35 g cm 3 respectively were used in simulation. The trajectories of the incident and back-scattered ions are approximated by straight lines and the ion energy slowing down process is separated from the scattering events. Multiple and plural scattering are not taken into account for the sake of simplicity. The ion trajectory is incremented by a small, constant step (can be liberally chosen as an input parameter) and the current ion energy is changed accordingly using the appropriate stopping power at the immediate ion position. At each incremental step the coordinates of the current ion position are tested with respect to the local position of the sample surface or gold-PET backing interface in order to decide what physical parameters as cross sections, kinematic factors and related parameters should be used for the spectrum simulation. At each incident ion position virtual scattering into the direction to the detector is considered with the probability proportional to the appropriate Rutherford cross section multiplied by L’Écuyer correction factor [31]. The ingoing ion is removed from the simulation as the ion reaches the predefined depth or the ion energy falls below some predefined value. The outgoing trajectory of the backscattered ion is treated in the same manner. SRIM stopping powers [32] and Bohr straggling [33] are used in the course of calculation. In such way for each ion trajectory a full RBS spectrum is obtained, respecting ion entrance point coordinates and the local sample properties. The calculation is repeated many times with randomly generated ion entrance points spread over a representative sample area and particular spectra are stored in a virtual multichannel analyser. The final RBS spectrum, obtained as a sum of all particular spectra, is convoluted with a Gaussian function the width of which combines detector resolution with energy spread estimated with the code DEPTH [34] for the mean layer thickness. To take into account the fine features of the sample surface properly, typically several hundred ion trajectories have to be generated. Evolution of the simulated final RBS spectrum with increasing number of particular spectra, generated for randomly chosen ion trajectories is shown in Fig. 2. One can see that already after summing about 300 particular spectra required simulated spectrum is reached.
4. Results and discussion The RBS spectra were simulated using the F95-Rough code with the data obtained by the AFM examination of the real samples. From these original AFM data, taken under casual direction, a relevant part was cut-off and slightly rotated in order to match present experimental arrangement shown in Fig. 1 and described above. AFM images of the samples (laser patterned PET with sputtered gold layer) used for the RBS spectra simulation, are shown in the Fig. 3. One can see the periodic ripple patterns whose height, width and frequency depend on the laser irradiation angle. The root-mean-square wavelength of the structure increases from 240 to 420 nm and the root-mean-square undulation of the ridges increases from 80 to 110 nm when the irradiation angle increased from 0° to 45°. The relevant parts of the experimental RBS spectra arising from the gold layer deposited on the patterned PET are shown in Fig. 4 together with the spectra simulated using the F95-Rough code. Constant 35 nm thickness of the gold layer over all sample surfaces was assumed in the simulation. It is evident that the shape of the gold peak in the RBS spectrum varies strongly as a function of increasing angle of incoming ion beam measured with respect to sample surface normal. While for low incident angles the RBS spectrum comprises dominant Gaussian-like component. At larger incidence angles a low energy component arises and relative area of this component increases rapidly with increasing incident angle. The appearance and growth of the low energy component is explained by the fact that the ions incoming at glancing angle scan penetrate the gold layer and the underlying PET several times before being scattered to the detector. So that, in glancing angle measuring geometry the gold signal is expected to comprise one or a few side peaks shifted to lower energy. The simulation performed under the assumption of constant thickness of the gold layer reproduces at least qualitatively the main features of the measured RBS spectra. The simulated spectra for ion beam incident angles below 45° are in very good agreement with experimental ones. For larger incident angles the increasing discrepancies between the experimental and simulated spectra are seen, which may be attributed to the possible non-uniformity of the sputtered gold layer. To test of the effect of the gold layer thickness and thickness non-uniformity, the RBS spectra were first simulated for different but constant thickness of gold layer. The results of these simulations are shown in the Fig. 5, from which one can see the development of the spectra simulated for constant thickness of the gold layer varying from 25 to 45 nm. It is evident that a significantly better agreement between simulated and measured RBS spectra cannot be achieved only by changing of the gold layer thickness. With a particular layer thickness it is possible to achieve better agreement in some part of the spectrum but at the cost of worsen-
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´ et al. / Nuclear Instruments and Methods in Physics Research B xxx (2017) xxx–xxx P. Malinsky
Fig. 4. Comparison of the RBS experimental spectra from rough samples, measured under different incident angle, with those simulated by the F95-Rough code (smooth lines). The simulations were performed under the assumption of constant gold layer thickness of 35 nm.
Fig. 5. The simulated RBS spectra development in dependence on the thickness of the gold layer used in simulation. The simulations were performed for samples of PET backing, patterned by the laser beam at incident angle 22.5° and coated with homogenous gold layers of different thicknesses. The RBS spectra were measured under ion beam incident angle of 75°.
ing in other ones. In particular best simulation at high energy peak (between channels from 760 to 800) is obtained for layer thickness 25 nm and for the peak at lowest energy for the layer thickness above 40 nm. In the next step the effect of the gold layer thickness nonuniformity was examined on the simulated sample with the gold layer thickness which was assumed to change linearly between
Fig. 6. Comparison of the RBS experimental spectra from rough samples, measured under different incident angles, with those simulated by the F95-Rough code (smooth lines). The simulations were performed with assumption of linearly changing gold layer thickness between top (20 nm) and bottom (75 nm) of the ripple patterns. The simulations were performed for sample with PET backing patterned by the laser beam with incident angle 22.5°.
the top (20 nm) and the bottom (75 nm) of the ripple patterns. The simulations were performed on the sample prepared by PET laser patterning under laser beam incident angle 22.5° and for RBS analysis with ion beam incident angles changed from 0° to 75°. The results are shown in Fig. 6. One can see that the simulated spectra reproduce the experimental ones much better for all used
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incident angles compare with the spectra simulated with constant gold layer thickness. It is evident, that there are still some small discrepancies between simulation and experiment that can be attributed to the ad-hoc chosen linear thickness dependence of the gold layer which can differ from real one. Another reason may lie in finite dimension of the AFM tip which may corrupt AFM images of the gold coated samples. Probably the best way to avoid doubts would be to use AFM data of the laser patterned samples without gold layer along with AFM data of sample after deposition of gold. 5. Conclusion The feasibility of the code F95-rough for the simulation of the RBS spectra from the samples with a definite surface roughness was demonstrated on the RBS spectra measured on real samples with regular roughness, the parameters of which were determined by AFM method. The samples were prepared by the sputtering of a 35-nm-thick gold layer on the surface of the PET substrate periodically patterned by laser irradiation. It was shown that required simulated spectrum can be obtained already after summing of about 300 randomly generated particular spectra. The RBS spectra measured at glancing angles exhibit a more complex gold signal comprising the main peak and low-energy components corresponding to ion scattering from gold layers on the neighboring ripples. The relative intensity of the low-energy components is an increasing function of the incoming ion-beam incidence angle. For lower ion beam incident angles the measured gold signal is well reproduced by computer simulation. For larger incident angles the evolution of the gold signal is reproduced rather qualitatively. The effects of varying gold layer thickness and gold layer non-uniformity on simulated RBS spectra was examined. It was shown that the agreement between measured and simulated spectra for different ion beam incident angles cannot be improved with uniform gold layer thickness. On the other hand the simulations assuming gold layer thickness linearly varying between top and bottom of the ripple patterns reproduce the experimental RBS spectra fairly. Present results show that the data of surface roughness obtained from AFM analysis of the sample surface can be used for the simulation of RBS spectra and that the RBS measurements accomplished at glancing angle may indicate the presence of a periodic structure on the sample surface.
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Acknowledgements The research has been carried out at the CANAM (Center of Accelerators and Nuclear Analytical Methods) infrastructure
Please cite this article in press as: P. Malinsky´ et al., Simulation of RBS spectra with known 3D sample surface roughness, Nucl. Instr. Meth. B (2017), http:// dx.doi.org/10.1016/j.nimb.2017.02.020