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N IM B
Beam Interactions with Materials & Atoms

Nuclear Instruments and Methods in Physics Research B 256 (2007) 21­23 www.elsevier.com/locate/nimb

Energy and charge distributions of fast nitrogen ions reflected from metal surface at grazing incidence
N.V. Novikov a, Ya.A. Teplova
a

a,* ,

V.V. Bondurko

b

D.V. Scobeltsin Institute of Nuclear Physics, Moscow State University, Moscow 119992, Russia b Moscow Engineering and Physics Institute, Moscow 115409, Russia Available online 12 January 2007

Abstract Energy and charge distributions of ions scattered under grazing incidence conditions from metallic surfaces are studied theoretically. The energy distribution of scattered ions with fixed charge is calculated by the energy distribution of reflected ions with equilibrium charge and charge fraction of these ions. The charge fractions of scattered ions are estimated by charge exchange cross sections. We calculated the energy and charge distributions of 1 MeV nitrogen ion scattered from platinum surface. The calculation results are in qualitative agreement with experimental data. ñ 2006 Elsevier B.V. All rights reserved.
PACS: 34.40.Dy Keywords: Ion-surface collision; Monte-Carlo method; Energy distribution

1. Introduction The processes of charge capture and electron loss in interaction of fast ions with a surface are important for understanding of the mechanism of ion-atomic collisions in solid [1­3]. The information on stopping power of ions in matter and charge exchange cross sections is required for the theoretical description of energy distribution of ions with charge i reflected from the surface. The complete information about charge exchange cross sections for ion­atom collisions is absent. The equilibrium charge distribution is determined from multiple change of ion charge. This distribution does not depend on initial charge of ions, incident angle a and scattering angle h Ïh > a÷ but depends on velocity of collision. There are empirical models for the dependence of the average equilibrium charge of ions from their velocity in gases [4] and solid [4­6]. For equilibrium charge distribution the charge fractions Fi or the relative amount of reflected ions with charge i are
*

determined by charge exchange cross sections rj;i where ion with charge j is converted to ion with charge i [4,7,8]. If the loss and capture of two and more electrons in one collision can be neglected it is possible to obtain Fi from electron loss ri;i×1 and capture ri;iþ1 cross sections and consequently to calculate the average ion charge [4]. i The theoretical description of electron loss and capture cross section requires complicated quantum mechanical calculations even for the analysis of collisions of ions and atoms with small number of electrons. On the other hand, there are experimental data about electron loss and capture cross sections in gases rj,i. This work is aimed at the theoretical description of energy and charge distributions of N+ ions reflected from metal surface under grazing incident angles and fixed scattering angle.

2. Theoretical method The angle-energy distribution of ions reflected from a surface can be calculated [9­11] by stopping power of ions

Corresponding author. E-mail address: teplova@anna19.npi.msu.su (Ya.A. Teplova).

0168-583X/$ - see front matter ñ 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.11.086


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with the equilibrium charge [12]. If the approximation of binary collisions is valid the Monte-Carlo simulation [13] can realize ion transport in the amorphous medium. The simulation [9­11] is based on the approximation of free ion motion between two collisions. The energy loss and the change of ion trajectory are taken into account in collision moment only. The ion loses a small part of energy in one collision. The ion slow down and stops because of the large number of collisions. The ion charge change is not taken into account in a collision. The applicability of the introduced model and the method of normalization of theoretical and experimental distributions of reflected ions were defined earlier [10,11]. There is a quality difference in the energy distribution of reflected ions between SRIM (stopping and range of ions in matter) [12,14] and the experimental data [10]. This code cannot describe the energy distribution of ions reflected under grazing incidence angles [10]. The estimation of the charge fractions Fi of reflected ions is based on the next approximations: · An initial energy E0 of ion and incident angle a are those that the charge of a reflected ion coincides with the average equilibrium charge. · A charge fractions Fi do not depend on incident angle a and scattered angle h. Fi are determined by the ratio of cross sections of loss and capture of one electron. · The charge exchange cross sections have similar dependence on charges i for the different media in fast collisions. The charge fractions Fi depend on the cross section ratio only but not depend on their absolute values. If the collision velocity is higher than orbital velocity of target atom electrons, the electron capture can be represented as a capture of free electron and the electronic structure of the target atom can be ignored. The electronic structure of neutral target atoms most strongly influences the differential cross section for electron loss at momentum transfer about 1 a.u. Its influence on a cross section diminishes for fast collisions, where the region of small transfer momentum is important. Therefore, there is a possibility to estimate Fi by the experimental data for interaction of this ion and atom of other medium [15]. In this estimation it is necessary to keep the proportionality between electron loss and capture cross sections so that the average charge of a scattered ion should be the equal to an averi age charge obtained experimentally or by the empirical relations [4­6]. In the present work, the experimental data about the cross sections of loss and capture of one electron by ions of nitrogen in helium are used to estimate the charge fractions of nitrogen ions in collisions with the platinum atoms. The energy dependence of rj;i determines Fi in a wide energy range. The energy distribution of ions with charge i can be obtained as a product of Fi and energy distribution of ions with equilibrium charge.

3. Calculation results The calculation of charge fractions of nitrogen ions in collisions with platinum atom is carried out using a charge exchange cross-sections in collisions of nitrogen ions and helium atoms normalizing an average charge to experimental value ¼ 2:2at a = 0.2°, h =1° [2]. The charge fractions i in total energy range can be determined by the energy dependence of the cross sections. The calculation results Fi for i = 0­5 and also the estimation Fi from ratio of amplitudes in the experimental spectrum [2] are shown in Fig. 1. The satisfactory agreement between the theoretical and experimental data is obtained for Fi (i = 1­4). The different dependence Fi on energy is the reason of decrease of amount of ions with the large charges (i = 3­5) at small energy of the reflected ions. The energy distributions of reflected ions with E0 = 1 MeV and charges i at a = 0.2°, h = 1° have the similar shape (i = 1­5) but the different amplitudes in maximum (Fig. 2). The different dependences of charge fractions on energy practically do not appear in narrow interval corresponding to the width of maximum. Both the theoretical and experimental distributions for different charges i are similar. There is a good agreement between the theoretical value of the amplitude for Ni+ (i = 1­4) and the experimental data. The amount of reflected ions diminishes more slowly in calculations than in experiment with decrease of energy. The experiment [2] was carried out on a single crystal of platinum while the considered theoretical model takes into account the interaction of ions with the amorphous medium. A depth of penetration of ions in a crystal can be larger than in amorphous medium. Therefore, an amount of reflected ions of low energy in the present calculation is more than in the experiment.

Fig. 1. The charge fractions Fi of Ni+ ions with equilibrium distribution of charges in platinum. The curves are the calculation results for different charge i. Numerals are values of charge i. The points are the estimation of a charge fraction of Ni+ ions from the ratio of amplitudes in the experimental distribution [2] at E0 = 1 MeV, a = 0.2°, h = 1°, (j) i =1, (d) i =2, (n) i =3, (h) i =4, (s) i =5.


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The calculations are carried out for the same incident angle a = 0.2° but for the greater scattered angle h = 2.7°. The calculations confirm the differences in energy dependence of amount of reflected ions with different charges. 4. Conclusion The theoretical model describing energy and charge distributions of ions reflected from a surface is proposed. The energy distribution of a reflected ion is calculated as a product of the energy distribution of ions with an equilibrium charge and the charge fraction Fi. The charge fraction depends on collision energy and is estimated by the relation between the charge exchange cross sections. The energy and charge distributions of nitrogen ions with energy 1 MeV, reflected from platinum surface are studied at incident angle a $ 0.2°. The calculation results are in qualitative agreement with the experimental data. References
[1] P. Sigmund, Stopping of Heavy Ions. A Theoretical Approach, Springer, Berlin, 2004, 153pp. [2] A. Robin, N. Hatke, A. Narmann, et al., Nucl. Inst and Meth. B 164­165 (2000) 566. [3] A. Robin, W. Heiland, J. Jensen, J.I. Juaristi, A. Arnau, Phys. Rev. A64 (2001) 052901. [4] V.S. Nikolaev, Uspekhi Fiz. Nauk 85 (N5) (1965) 679 (in Russian). [5] V.S. Nikolaev, I.S. Dmitriev, Phys. Lett. A 28 (1968) 277. [6] H.D. Betz, Rev. Mod. Phys. 44 (1972) 465. [7] Ya.A. Teplova, I.S. Dmitriev, Yu.A. Belkova, Izvestia RAN. Phys. 66 (N4) (2002) 565 (in Russian). [8] Yu.A. Belkova, Ya.A. Teplova, I.S. Dmitriev, Surface N4 (2003) 74 (in Russian). [9] N.V. Novikov, Ya.A. Teplova, Yu.A. Fainberg, V.A. Kurnaev, Nucl. Instr. and Meth. B 212 (2003) 96. [10] N.V. Novikov, Ya.A. Teplova, Yu.A. Fainberg, V.S. Kulikauskas, Nucl. Instr. and Meth. B 235 (2005) 448. [11] N.V. Novikov, Ya.A. Teplova, Yu.A. Fainberg, Surface N7 (2006) 45 (in Russian). [12] J.F. Ziegler, Stopping and range of ions in matter (SRIM2003.26), . [13] W. Eckstein, Computer Simulation of Ion Solid Interactions, Springer-Verlag, 1991, 254pp. [14] J.P. Biersack, L.G. Haggmark, Nucl. Instr. and Meth. B 174 (1980) 257. [15] I.S. Dmitriev, Ya.A. Teplova, Yu.A. Belkova, Vestnik MGU. Physics. Astronomy N4 (2000) 29 (in Russian).

Fig. 2. The dependence of energy distribution of Ni+ ions with energy E0 = 1 MeV reflected from a platinum surface at the incident angle a = 0.2° and scattering angle h =1° on E/i where E is the reflected ion energy. The curve is the calculation results. The points are the experimental data from [2].

Fig. 3. The dependence of the energy distribution of Ni+ ions with energy E0 = 1 MeV reflected from the platinum surface at the incident angle a = 0.2° and scattered angle h = 2.7° on the energy E. The numerals are charges of the reflected ion i.

The example of energy distribution of reflected ions with the greater full width at half maximum is shown in Fig. 3.