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Backscattered electrons from surface films deposited on bulk targets: A comparison between computational and experimental results
Nuclear Instruments and Methods in Physics Research B 269 (2011) 1672–1674
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Backscattered electrons from surface films deposited on bulk targets: A comparison between computational and experimental results Maurizio Dapor a,b,⇑, Nicola Bazzanella c, Laura Toniutti c, Antonio Miotello c, Stefano Gialanella b a
Interdisciplinary Laboratory for Computational Science (LISC), FBK-CMM and University of Trento, via Sommarive 18, I-38123 Povo, Trento, Italy Department of Materials Engineering and Industrial Technologies, University of Trento, via Mesiano 77, I-38123, Trento, Italy c Department of Physics, University of Trento, via Sommarive 14, I-38123 Povo, Trento, Italy b
a r t i c l e
i n f o
Article history: Received 12 July 2010 Received in revised form 8 October 2010 Available online 9 November 2010 Keywords: Applications of Monte Carlo methods Other electron-impact emission phenomena
a b s t r a c t A Monte Carlo code is described, validated, and utilized to calculate the backscattering coefficient from surface layers of Pd deposited on bulk targets of Si. A quantitative evaluation of the backscattering coefficient as a function of the over-layer thickness is provided, as well as a comparison of the simulated results with experimental data concerning Pd thin films with known thicknesses. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Palladium is an interesting material for particle accelerator and vacuum chambers applications. Pd is known for its high hydrogen solubility and diffusivity. Thin film coatings of Pd were found to pump H2 and CO, even without activation by heating [1]. Thin Pd layers can also be used for protecting a getter film from oxidation in vacuum chambers [1]. Filters of Pd and Pd based alloys exhibit extremely high selectivity for hydrogen [2]. Measurement of the presence of traces of hydrogen gas is also a challenging technological problem, and Pd thin films have important sensor applications, as well. Actually many kinds of hydrogen sensors which use different mechanism for detecting H2 are known. Pd is often used in these sensors, due to its ability of selectively absorbing H2 and to form palladium hydride. Since, as a function of hydrogen concentration, optical properties of palladium change when in contact with H2, Pd can be used as the active sensing layer of the sensor [3,4]. In general Pd, due to its extremely high diffusivity and absorption capacity for H2, is used in hydride batteries, optical switching devices, hydrogen purification membranes, and hydrogen sensors [5]. This paper addresses the problem of the thickness determination of thin Pd over-layers using a joint experimental/theoretical approach. It is well known that over-layer films affect the electron backscattering coefficient of bulk targets. The experimental data available in the literature for backscattering coefficient are rather scattered and, sometimes, difficulties arise in their interpretation ⇑ Corresponding author at: Interdisciplinary Laboratory for Computational Science (LISC), FBK-CMM and University of Trento, via Sommarive 18, I-38123 Povo, Trento, Italy. E-mail address: [email protected] (M. Dapor). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.11.016
due to the lack of knowledge of the thickness, uniformity, and nature of the surface layers. In particular, a quantitative treatment of the effect of surface films deposited on bulk targets and a systematic comparison with experimental data are currently lacking. In this work, a Monte Carlo code is described and utilized to calculate the backscattering coefficient from surface layers deposited on bulk targets. A simple experimental set up, using a conventional Scanning Electron Microscope (SEM) without the necessity of any further equipment, is demonstrated to be sufficient to establish the supported film thickness. A quantitative evaluation of the backscattering coefficient as a function of the over-layer thickness is provided, as well as a comparison of the simulated results with experimental data concerning Pd thin films with known thicknesses. Excellent agreement between Monte Carlo and experimental results has been found.
2. Experimental Palladium thin films, 10–270 nm thick, were deposited at a rate of 0.03 nm/s by electron beam evaporation in a vacuum apparatus with background pressure better than 105 Pa. The sample substrate was a 0.7 mm thick silicon wafer. The Pd film thickness was measured during deposition by means of an INFICON thickness monitor and verified further using a Dektak 3 stylus profilometer. For analysis with Scanning Electron Microscopy (SEM), all samples with different thickness were mounted on a single stub (as shown in Fig. 1) and Backscattered Electron Images (BEI) were acquired using a JEOL JSM7001F FEG-SEM (some selected pictures are reported in Fig. 1). To compare experimental data with Monte Carlo simulations, experimental curves were obtained by analysing
M. Dapor et al. / Nuclear Instruments and Methods in Physics Research B 269 (2011) 1672–1674
1673
Fig. 1. SEM micrographs of the Pd on Si films, of different thicknesses, used for the experimental determination of the backscattering coefficient.
the grey level scale of images at different electron beam energies and making normalization to the corresponding Pd bulk signal. The values of the backscattered electron (BSE) efficiency are estimated from the ratio of the BSE emission from thin samples divided by the emission from a bulk sample. In this respect, the absolute BSE emission current is not critical for our calculations. Owing to the much reduced grain size of all analysed samples, as compared to the investigated sample areas, possible channeling effects would affect contrast in very much the same way in all cases, and as such it can be disregarded. 3. The Monte Carlo scheme A Monte Carlo simulation is an idealized experiment. As it is statistical, the accuracy of its results depends on the number of simulated trajectories and on the used pseudo-random number generator. Owing to recent evolution in computer calculation capability, we are now able to obtain statistically meaningful results in reasonably short times of calculation. The accuracy of a Monte Carlo simulation also depends on the approximations introduced in the scheme. For the present application, the elastic scattering computations have been obtained by the relativistic partial wave expansion method. It corresponds to the (numerical) solution of the Dirac equation in a central field. For an excellent review about the subject, see Ref. [6]. For the present calculation of the differential elastic scattering cross section see Refs. [7–10]. Concerning the energy loss mechanisms, as the measurements were performed in the primary energy range 10–30 keV, the semi-empirical equation proposed by Kanaya and Okayama [11] can be safely used, as demonstrated in Ref. [12]. The details of the present Monte Carlo scheme have been described elsewhere: see for example, Refs. [10,12,13]. A similar approach can also be found in Ref. [14]. We will give here just a brief description of the main characteristics of the scheme. The present Monte Carlo scheme is based on the continuous slowing down approximation. Let us adopt spherical coordinates (r,h,/) and assume that a stream of mono-energetic electrons irradiates a solid target in the +z direction. The path-length distribution is assumed to follow a Poisson-type law. The step-length Ds is then given by
Ds ¼ kel lnðr 1 Þ;
ð1Þ
where r1 is a random number uniformly distributed in the range [0,1] and kel = 1/Nrel is the elastic mean free path. Note that here N is the number of atoms per unit of volume in the target and rel
is the elastic scattering cross section calculated by the relativistic partial expansion method. The energy loss DE along the segment of trajectory Ds is approximated as follows
DE ¼ ðdE=dsÞDs;
ð2Þ
where dE/ds is the Kanaya and Okayama’s stopping power [11]. The polar scattering angle h after an elastic collision is calculated assuming that the probability P(h) of elastic scattering within an angular range from 0 to h is a random number r2 uniformly distributed in the range [0,1]. The azimuth angle / can take on any value in the range [0,2p] selected by a random number r3 uniformly distributed in that range. Both the h and / angles are calculated relative to the last direction in which the particle was moving before the impact. The direction h0z in which the particle is moving after the last deflection, relative to the z direction, is given by
cos h0z ¼ cos hz cos h þ sin hz sin h cos /;
ð3Þ
where hz is the angle relative to the z direction before the impact. The motion Dz along the z direction is then calculated by
Dz ¼ Ds cos h0z :
ð4Þ
The new angle h0z then becomes the incident angle hz for the next path step. For surface films we have taken into account the changes in the scattering probabilities per unit length in passing from the film to the substrate and vice versa (for technical details about this problem see, for example, Ref. [13]). The particles are followed in their trajectories until their energies become lower than 50 eV or until they leave the solid target. 4. Results and discussion The backscattering coefficient is defined as the fraction of electrons of the primary beam that emerge from the surface of an electron-irradiated target. Secondary electrons are not included in the definition of the backscattering coefficient: the energy cut-off is typically 50 eV. Our experimental approach is represented in Fig. 1: the grey levels of the investigated samples (Pd/Si films with different thicknesses and a bulk of Pd) were acquired simultaneously and under the same experimental conditions; the ratio of the values, at the same primary energy, between the grey levels of the film and that of the bulk of palladium is equal to the ratio between the backscattering coefficient of the Pd/Si system, gPd/Si, and that of the bulk of Pd, gPd. For a description of a similar method of measurement of the thickness of thin films from backscattered electron image contrast, also see Refs. [15–17]. Fig. 1 even shows a Pd film having
1674
M. Dapor et al. / Nuclear Instruments and Methods in Physics Research B 269 (2011) 1672–1674
tively. As the thickness of the substrate was greater than the maximum range of penetration in Si for all the primary energy considered in this study (3–30 keV), the substrate can be considered as a bulk. The Pd over-layers were deposited and their thicknesses measured before their introduction in the analysis chamber. In such a way we were able to predict, on the basis of the Monte Carlo code, the behavior of the backscattering coefficient as a function of the primary electron energy. Taking into account that the selected thicknesses are in the range 100–300 nm, the backscattering coefficient should decrease from the value corresponding to a bulk of Pd (when the primary energy is lower than 10–15 keV) toward the value of a bulk of Si. This prediction is confirmed by both the experimental data and the Monte Carlo results (see Figs. 2 and 3). Furthermore, the Monte Carlo simulated data are in very good agreement with the experimental ones (also taking into account the experimental errors, not represented in the figures for the sake of clarity, which have been estimated to be about 10–15%). Fig. 2. Comparison between the experimental and the Monte Carlo backscattering coefficient, as a function of the primary electron energy, of a Pd thin film deposited on a Si substrate. The Pd film thickness in this case is 110 nm.
5. Conclusion A Monte Carlo code was utilized to calculate the backscattering coefficient from two surface layers of Pd – whose thicknesses were measured before the introduction of the sample in the analysis chamber – that were deposited on bulk targets of Si. A quantitative evaluation of the backscattering coefficient as a function of the over-layer thickness was provided, as well as a comparison of the simulated results with experimental data. An excellent agreement was found between simulated and experimental data in the Pd film thicknesses range between 110 and 270 nm, and in the primary energy range between 3 and 30 keV. As expected, layers that were too thin (in the 10 nm range or less) did not show any change in the grey level upon changing the primary electron energy as the backscattered electrons signal from the substrate is paramount. Acknowledgement The authors wish to thank the colleague Mirco D’Incau (University of Trento) for his help with the profilometer measurements. References
Fig. 3. Comparison between the experimental and the Monte Carlo backscattering coefficient, as a function of the primary electron energy, of a Pd thin film deposited on a Si substrate. The Pd film thickness in this case is 270 nm.
a nominal thickness of 10 nm. This value is too low to provide any detectable change in the grey scale contrast as a function of the primary electron energy. Indeed, even at the lowest energy that has been employed (3 keV) the main contribution to backscattered electron emission is provided by the substrate(s). Therefore, even though this over-layer cannot be profitably used in for the calculation of the backscattering coefficient, nonetheless provides an indication on the applicability limit of this approach to the evaluation of the thickness of thin layers. It is worth saying that when thickness is so small, the film can actually be granular, with portions directly exposed to the incoming electron beam, that in this case is not interacting at all with the over-layer material. The Monte Carlo code was thus utilized to study the backscattering coefficient of the two Pd supported thin films deposited on Si, whose thicknesses were 110 and 270 nm, respec-
[1] C. Benvenuti, P. Chiggiato, F. Cicoira, Y. L’Aminot, V. Ruzinov, Vacuum 73 (2004) 139. [2] R. Checchetto, N. Bazzanella, B. Patton, A. Miotello, Surf. Coat. Technol. 177–178 (2004) 73. [3] M.A. Butler, Sens. Actuators B 22 (1994) 166. [4] K. Gleeson, E. Lewis, J. Phys.: Conf. Ser. 76 (2007) 012004. [5] M. Krishna Kumar, M.S. Ramachandra Rao, S. Ramaprabhu, J. Phys. D: Appl. Phys. 39 (2006) 2791. [6] A. Jablonski, F. Salvat, C.J. Powell, J. Phys. Chem. Ref. Data 33 (2004) 409. [7] F. Salvat, R. Mayol, Comput. Phys. Commun. 74 (1993) 358. [8] M. Dapor, J. Appl. Phys. 79 (1996) 8406. [9] R. Mayol, F. Salvat, At. Data Nucl. Data Tables 65 (1997) 55. [10] M. Dapor, Electron-beam interactions with solids: application of the monte carlo method to electron scattering problems, Springer Tracts in Modern Physics, vol. 186, Springer, Berlin, 2003. [11] K. Kanaya, S. Okayama, J. Phys. D 5 (1972) 43. [12] M. Dapor, Phys. Rev. B 46 (1992) 618. [13] M. Dapor, Surf. Interface Anal. 40 (2008) 714. [14] M.M. El Gomati, C.G. Walker, A.M.D. Assa’d, M. Zadrazˇil, Scanning 30 (2008) 2. [15] O.S. Rayora, A.E. Curzon, Thin Solid Film 123 (1985) 235. [16] O.S. Rayora, A.E. Curzon, Thin Solid Film 199 (1991) 313. [17] O.S. Rayora, A.E. Curzon, Phys. Stat. Sol. A. Appl. Res. 193 (1994) 319.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Backscattered electrons from surface films deposited on bulk targets: A comparison between computational and experimental results Maurizio Dapor a,b,⇑, Nicola Bazzanella c, Laura Toniutti c, Antonio Miotello c, Stefano Gialanella b a
Interdisciplinary Laboratory for Computational Science (LISC), FBK-CMM and University of Trento, via Sommarive 18, I-38123 Povo, Trento, Italy Department of Materials Engineering and Industrial Technologies, University of Trento, via Mesiano 77, I-38123, Trento, Italy c Department of Physics, University of Trento, via Sommarive 14, I-38123 Povo, Trento, Italy b
a r t i c l e
i n f o
Article history: Received 12 July 2010 Received in revised form 8 October 2010 Available online 9 November 2010 Keywords: Applications of Monte Carlo methods Other electron-impact emission phenomena
a b s t r a c t A Monte Carlo code is described, validated, and utilized to calculate the backscattering coefficient from surface layers of Pd deposited on bulk targets of Si. A quantitative evaluation of the backscattering coefficient as a function of the over-layer thickness is provided, as well as a comparison of the simulated results with experimental data concerning Pd thin films with known thicknesses. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Palladium is an interesting material for particle accelerator and vacuum chambers applications. Pd is known for its high hydrogen solubility and diffusivity. Thin film coatings of Pd were found to pump H2 and CO, even without activation by heating [1]. Thin Pd layers can also be used for protecting a getter film from oxidation in vacuum chambers [1]. Filters of Pd and Pd based alloys exhibit extremely high selectivity for hydrogen [2]. Measurement of the presence of traces of hydrogen gas is also a challenging technological problem, and Pd thin films have important sensor applications, as well. Actually many kinds of hydrogen sensors which use different mechanism for detecting H2 are known. Pd is often used in these sensors, due to its ability of selectively absorbing H2 and to form palladium hydride. Since, as a function of hydrogen concentration, optical properties of palladium change when in contact with H2, Pd can be used as the active sensing layer of the sensor [3,4]. In general Pd, due to its extremely high diffusivity and absorption capacity for H2, is used in hydride batteries, optical switching devices, hydrogen purification membranes, and hydrogen sensors [5]. This paper addresses the problem of the thickness determination of thin Pd over-layers using a joint experimental/theoretical approach. It is well known that over-layer films affect the electron backscattering coefficient of bulk targets. The experimental data available in the literature for backscattering coefficient are rather scattered and, sometimes, difficulties arise in their interpretation ⇑ Corresponding author at: Interdisciplinary Laboratory for Computational Science (LISC), FBK-CMM and University of Trento, via Sommarive 18, I-38123 Povo, Trento, Italy. E-mail address: [email protected] (M. Dapor). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.11.016
due to the lack of knowledge of the thickness, uniformity, and nature of the surface layers. In particular, a quantitative treatment of the effect of surface films deposited on bulk targets and a systematic comparison with experimental data are currently lacking. In this work, a Monte Carlo code is described and utilized to calculate the backscattering coefficient from surface layers deposited on bulk targets. A simple experimental set up, using a conventional Scanning Electron Microscope (SEM) without the necessity of any further equipment, is demonstrated to be sufficient to establish the supported film thickness. A quantitative evaluation of the backscattering coefficient as a function of the over-layer thickness is provided, as well as a comparison of the simulated results with experimental data concerning Pd thin films with known thicknesses. Excellent agreement between Monte Carlo and experimental results has been found.
2. Experimental Palladium thin films, 10–270 nm thick, were deposited at a rate of 0.03 nm/s by electron beam evaporation in a vacuum apparatus with background pressure better than 105 Pa. The sample substrate was a 0.7 mm thick silicon wafer. The Pd film thickness was measured during deposition by means of an INFICON thickness monitor and verified further using a Dektak 3 stylus profilometer. For analysis with Scanning Electron Microscopy (SEM), all samples with different thickness were mounted on a single stub (as shown in Fig. 1) and Backscattered Electron Images (BEI) were acquired using a JEOL JSM7001F FEG-SEM (some selected pictures are reported in Fig. 1). To compare experimental data with Monte Carlo simulations, experimental curves were obtained by analysing
M. Dapor et al. / Nuclear Instruments and Methods in Physics Research B 269 (2011) 1672–1674
1673
Fig. 1. SEM micrographs of the Pd on Si films, of different thicknesses, used for the experimental determination of the backscattering coefficient.
the grey level scale of images at different electron beam energies and making normalization to the corresponding Pd bulk signal. The values of the backscattered electron (BSE) efficiency are estimated from the ratio of the BSE emission from thin samples divided by the emission from a bulk sample. In this respect, the absolute BSE emission current is not critical for our calculations. Owing to the much reduced grain size of all analysed samples, as compared to the investigated sample areas, possible channeling effects would affect contrast in very much the same way in all cases, and as such it can be disregarded. 3. The Monte Carlo scheme A Monte Carlo simulation is an idealized experiment. As it is statistical, the accuracy of its results depends on the number of simulated trajectories and on the used pseudo-random number generator. Owing to recent evolution in computer calculation capability, we are now able to obtain statistically meaningful results in reasonably short times of calculation. The accuracy of a Monte Carlo simulation also depends on the approximations introduced in the scheme. For the present application, the elastic scattering computations have been obtained by the relativistic partial wave expansion method. It corresponds to the (numerical) solution of the Dirac equation in a central field. For an excellent review about the subject, see Ref. [6]. For the present calculation of the differential elastic scattering cross section see Refs. [7–10]. Concerning the energy loss mechanisms, as the measurements were performed in the primary energy range 10–30 keV, the semi-empirical equation proposed by Kanaya and Okayama [11] can be safely used, as demonstrated in Ref. [12]. The details of the present Monte Carlo scheme have been described elsewhere: see for example, Refs. [10,12,13]. A similar approach can also be found in Ref. [14]. We will give here just a brief description of the main characteristics of the scheme. The present Monte Carlo scheme is based on the continuous slowing down approximation. Let us adopt spherical coordinates (r,h,/) and assume that a stream of mono-energetic electrons irradiates a solid target in the +z direction. The path-length distribution is assumed to follow a Poisson-type law. The step-length Ds is then given by
Ds ¼ kel lnðr 1 Þ;
ð1Þ
where r1 is a random number uniformly distributed in the range [0,1] and kel = 1/Nrel is the elastic mean free path. Note that here N is the number of atoms per unit of volume in the target and rel
is the elastic scattering cross section calculated by the relativistic partial expansion method. The energy loss DE along the segment of trajectory Ds is approximated as follows
DE ¼ ðdE=dsÞDs;
ð2Þ
where dE/ds is the Kanaya and Okayama’s stopping power [11]. The polar scattering angle h after an elastic collision is calculated assuming that the probability P(h) of elastic scattering within an angular range from 0 to h is a random number r2 uniformly distributed in the range [0,1]. The azimuth angle / can take on any value in the range [0,2p] selected by a random number r3 uniformly distributed in that range. Both the h and / angles are calculated relative to the last direction in which the particle was moving before the impact. The direction h0z in which the particle is moving after the last deflection, relative to the z direction, is given by
cos h0z ¼ cos hz cos h þ sin hz sin h cos /;
ð3Þ
where hz is the angle relative to the z direction before the impact. The motion Dz along the z direction is then calculated by
Dz ¼ Ds cos h0z :
ð4Þ
The new angle h0z then becomes the incident angle hz for the next path step. For surface films we have taken into account the changes in the scattering probabilities per unit length in passing from the film to the substrate and vice versa (for technical details about this problem see, for example, Ref. [13]). The particles are followed in their trajectories until their energies become lower than 50 eV or until they leave the solid target. 4. Results and discussion The backscattering coefficient is defined as the fraction of electrons of the primary beam that emerge from the surface of an electron-irradiated target. Secondary electrons are not included in the definition of the backscattering coefficient: the energy cut-off is typically 50 eV. Our experimental approach is represented in Fig. 1: the grey levels of the investigated samples (Pd/Si films with different thicknesses and a bulk of Pd) were acquired simultaneously and under the same experimental conditions; the ratio of the values, at the same primary energy, between the grey levels of the film and that of the bulk of palladium is equal to the ratio between the backscattering coefficient of the Pd/Si system, gPd/Si, and that of the bulk of Pd, gPd. For a description of a similar method of measurement of the thickness of thin films from backscattered electron image contrast, also see Refs. [15–17]. Fig. 1 even shows a Pd film having
1674
M. Dapor et al. / Nuclear Instruments and Methods in Physics Research B 269 (2011) 1672–1674
tively. As the thickness of the substrate was greater than the maximum range of penetration in Si for all the primary energy considered in this study (3–30 keV), the substrate can be considered as a bulk. The Pd over-layers were deposited and their thicknesses measured before their introduction in the analysis chamber. In such a way we were able to predict, on the basis of the Monte Carlo code, the behavior of the backscattering coefficient as a function of the primary electron energy. Taking into account that the selected thicknesses are in the range 100–300 nm, the backscattering coefficient should decrease from the value corresponding to a bulk of Pd (when the primary energy is lower than 10–15 keV) toward the value of a bulk of Si. This prediction is confirmed by both the experimental data and the Monte Carlo results (see Figs. 2 and 3). Furthermore, the Monte Carlo simulated data are in very good agreement with the experimental ones (also taking into account the experimental errors, not represented in the figures for the sake of clarity, which have been estimated to be about 10–15%). Fig. 2. Comparison between the experimental and the Monte Carlo backscattering coefficient, as a function of the primary electron energy, of a Pd thin film deposited on a Si substrate. The Pd film thickness in this case is 110 nm.
5. Conclusion A Monte Carlo code was utilized to calculate the backscattering coefficient from two surface layers of Pd – whose thicknesses were measured before the introduction of the sample in the analysis chamber – that were deposited on bulk targets of Si. A quantitative evaluation of the backscattering coefficient as a function of the over-layer thickness was provided, as well as a comparison of the simulated results with experimental data. An excellent agreement was found between simulated and experimental data in the Pd film thicknesses range between 110 and 270 nm, and in the primary energy range between 3 and 30 keV. As expected, layers that were too thin (in the 10 nm range or less) did not show any change in the grey level upon changing the primary electron energy as the backscattered electrons signal from the substrate is paramount. Acknowledgement The authors wish to thank the colleague Mirco D’Incau (University of Trento) for his help with the profilometer measurements. References
Fig. 3. Comparison between the experimental and the Monte Carlo backscattering coefficient, as a function of the primary electron energy, of a Pd thin film deposited on a Si substrate. The Pd film thickness in this case is 270 nm.
a nominal thickness of 10 nm. This value is too low to provide any detectable change in the grey scale contrast as a function of the primary electron energy. Indeed, even at the lowest energy that has been employed (3 keV) the main contribution to backscattered electron emission is provided by the substrate(s). Therefore, even though this over-layer cannot be profitably used in for the calculation of the backscattering coefficient, nonetheless provides an indication on the applicability limit of this approach to the evaluation of the thickness of thin layers. It is worth saying that when thickness is so small, the film can actually be granular, with portions directly exposed to the incoming electron beam, that in this case is not interacting at all with the over-layer material. The Monte Carlo code was thus utilized to study the backscattering coefficient of the two Pd supported thin films deposited on Si, whose thicknesses were 110 and 270 nm, respec-
[1] C. Benvenuti, P. Chiggiato, F. Cicoira, Y. L’Aminot, V. Ruzinov, Vacuum 73 (2004) 139. [2] R. Checchetto, N. Bazzanella, B. Patton, A. Miotello, Surf. Coat. Technol. 177–178 (2004) 73. [3] M.A. Butler, Sens. Actuators B 22 (1994) 166. [4] K. Gleeson, E. Lewis, J. Phys.: Conf. Ser. 76 (2007) 012004. [5] M. Krishna Kumar, M.S. Ramachandra Rao, S. Ramaprabhu, J. Phys. D: Appl. Phys. 39 (2006) 2791. [6] A. Jablonski, F. Salvat, C.J. Powell, J. Phys. Chem. Ref. Data 33 (2004) 409. [7] F. Salvat, R. Mayol, Comput. Phys. Commun. 74 (1993) 358. [8] M. Dapor, J. Appl. Phys. 79 (1996) 8406. [9] R. Mayol, F. Salvat, At. Data Nucl. Data Tables 65 (1997) 55. [10] M. Dapor, Electron-beam interactions with solids: application of the monte carlo method to electron scattering problems, Springer Tracts in Modern Physics, vol. 186, Springer, Berlin, 2003. [11] K. Kanaya, S. Okayama, J. Phys. D 5 (1972) 43. [12] M. Dapor, Phys. Rev. B 46 (1992) 618. [13] M. Dapor, Surf. Interface Anal. 40 (2008) 714. [14] M.M. El Gomati, C.G. Walker, A.M.D. Assa’d, M. Zadrazˇil, Scanning 30 (2008) 2. [15] O.S. Rayora, A.E. Curzon, Thin Solid Film 123 (1985) 235. [16] O.S. Rayora, A.E. Curzon, Thin Solid Film 199 (1991) 313. [17] O.S. Rayora, A.E. Curzon, Phys. Stat. Sol. A. Appl. Res. 193 (1994) 319.