Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://danp.sinp.msu.ru/LAS/Nimb235_05_448Teplova.pdf Äàòà èçìåíåíèÿ: Sun Oct 21 20:12:12 2007 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 22:05:35 2012 Êîäèðîâêà:

Nuclear Instruments and Methods in Physics Research B 235 (2005) 448­451 www.elsevier.com/locate/nimb

Reflection of nitrogen ions from copper surface: Experiment and calculations
N.V. Novikov, Ya.A. Teplova *, Yu.A. Fainberg, V.S. Kulikauskas
Institute of Nuclear Physics, Moscow State University, 119899 Moscow, Russia Available online 29 April 2005

Abstract The angular and energy distributions of nitrogen ions reflected from the Cu-surface are measured at the incident energy 300 keV. A theoretical model is proposed. A weak dependence of the yield of reflected particles is obtained at large scattering angles. This effect allows the normalization of experimental and theoretical data and the determination of the reflection coefficients. The calculation results for grazing angles 2° and 4° are in qualitative agreement with experimental data. ñ 2005 Elsevier B.V. All rights reserved.
PACS: 34.40.Dy Keywords: Angle-energy distributions; Grazing incidence angles; Ion­surface reflection

1. Introduction The big yield of reflected ions at small grazing angles provides statistical stability of experimental and theoretical results [1]. The projectiles interact not only with surface atoms but also with deeper target layers. Some scattered ions have energy close to the incident projectile energy E0 and the others lose almost all energy. There is a strong dependence of the energy distribution of scattered
Corresponding author. E-mail address: teplova@anna19.npi.msu.su (Ya.A. Teplova).
*

ions on the grazing angle a and on the reflecting angle h. A dependence on the surface relief is lacking in distribution of the scattered ions. Measurements of the angular and energy distributions by using method described in [2,3] were performed in the plane of incident beam and the normal to the target surface. Ions were accelerated by the cascade generator CG-500. The target was put in the chamber with three-axes goniometer. This allowed the sample rotation to an accuracy of 0.1°. Semiconductor detector with resolution 25 keV determined the energy of reflected particles. The solid angle of the detector was 1.3 · 10þ5 sr. The scanning step of detector was about 0.5°. The

0168-583X/$ - see front matter ñ 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.03.222


N.V. Novikov et al. / Nucl. Instr. and Meth. in Phys. Res. B 235 (2005) 448­451

449

yield of scattered particles was measured within accuracy better than 15­20%. If the approximation of binary collisions is valid the Monte-Carlo simulation [4] can realize a projectile transport in amorphous media. Usually it is possible to solve this problem using a potential of elastic interaction between incident ion and target atom [5­7]. This potential determines angular distribution of scattering ions. The impact parameter in ion­atom collisions does not exceed the distance between atoms [8]. This approximation excepts the extremely small scattering angles. The Coulomb part of the elastic potential increases the probability of the scattering at large angles. It causes the strong dependence of calculated distributions from the parameters describing the angular distributions of reflected ions [9]. The correction of the traditional model of angular distribution in ion­atom collisions is needed to describe the fast ion reflection at small grazing angles. Earlier it was made for proton scattering from metal surface [10,11]. The present work is aimed to measure the angular and energy distributions of fast N+ ions reflected from copper surface at small grazing angles and to test the theoretical model [10,11] for scattering of heavy ions.

tween two collisions without interaction with medium. The energy loss and the changing of the ion trajectory are taken into account in the moment of collision [10,11]. The ion loses the small part of energy in the collision. The ion is decelerated and stops because of the big number of collisions. The total cross section is determined by the stopping data [12]. These data take into account ion­atom and ion­free electron interactions. The angular distribution of scattering ions is described by one-parameter function [10,11]. The Monte-Carlo simulation allows the determination of the ratio of the number of reflected ions within the interval dE = 1 keV, dh = 1° and du = 1 rad and the total number of incident ions. Here h is the polar scattering angle (h P a), u is azimuth angle between incident and scattering planes. This ratio is described by the function f(E0, a, h, u, E). The energy distribution is determined by integration over u Z 2p F Ï E 0 ; a; h; E ÷ ¼ duf ÏE0 ; a; h; u; E÷. Ï1÷
0

2. Calculations Let us consider an incident ion moving with energy E in an amorphous medium. It undertakes a number of collisions with medium atoms, losing only a small part of its energy in each collision. The ion passing through the medium can interact with one or several atoms and with free electrons. It is possible to take into account the interaction with one medium atom in the case of fast ions or small density of medium. This binary approximation starts to be valid for proton­atom collisions at energies more than 20 eV [4]. In the present work the minimum of the energy of reflected ion E $ 1 keV is considerably higher than those values. Therefore this approximation can be used for fast ions reflected from the surface in range of energy E P 1 keV. The ion passing through the medium is simulated by the process when the ion is moving be-

This distribution has a maximum at the energy Emax(h) < E0 and full width at half maximum (FWHM) W(h). Angular distribution of reflected ions is written as Z E0 GÏE0 ; a; h÷ ¼ dEF ÏE0 ; a; h; E÷. Ï2÷
0

The reflection coefficient is determined by the integration Z 180 dhGÏE0 ; a; h÷. Ï3÷ RN Ï E 0 ; a ÷ ¼
0

3. Analysis of results Both calculated and experimental results (Fig. 1) demonstrate maximum in the angular distribution (2) when the reflecting angle (h þ a) is equal to the grazing angle a. The number of reflected ions decreases with increasing of scattering angle h > (h þ a) and the angular dependence becomes weak at h > 9°. It allows the normalization of the theoretical and experimental results. We obtained


450

N.V. Novikov et al. / Nucl. Instr. and Meth. in Phys. Res. B 235 (2005) 448­451

Fig. 1. Angular distribution (2) of nitrogen ions reflected from the copper surface for E = 300 keV: (j) experiment data at a = 2°, (d) experiment data at a =4°, solid and broken curves are the our theory results at a =2° and a = 4° respectively, (+) and (·) TRIM calculation results at a = 2° and a =4° respectively.

Fig. 2. The ratio of the energy corresponding to the maximum in energy spectra of reflected ions Emax (1) and projectile ion energy E0: (j) experiment data at a =2°, (d) experiment data at a =4°, solid and broken curves are the our theory results at a = 2° and a = 4° respectively, (+) TRIM calculation results at a = 2°.

theoretical RN(E0, a = 2°) = 0.490, RN(E0, a = 4°) = 0.291 and experimental RN(E0, a = 2°) = 0.417, RN(E0, a = 4°) = 0.294 coefficient (3). The experimental reflection coefficient (3) was determined using the theoretical data at h > 12°. TRIM calculations give RN(E0, a = 2°) = 0.703, RN(E0, a = 4°) = 0.610. When the grazing angle a increases the ion beam reaches deeper target layers. This phenomenon explains the decreasing of reflection coefficient RN(E0, a). The experiment and our theoretical calculations show that the number of reflected ions for a = 2° is more than the number of reflected ions for a = 4° for all scattering angles h. The TRIM calculations give an opposite relation at h > 9°. The ratio Emax(h)/E0 (Fig. 2) characterizes the maximum position in energy distribution F(E0, a, h, E) of reflected ions at fixed h. In each collision the ion can be scattered at a small angle. Therefore the track length of the scattered ion in the medium increases with increasing of h. Consequently, the maximum in energy distribution (1) of reflected ions shifts to smaller energies. There is the qualitative difference between TRIM [8] results and experimental data. It happens because of limitations of this code for ion­surface reflection at small incident angle. The experimental data and our calculation results demonstrate, that the maximum in energy distribution for a = 4°, h > 6°

takes place for smaller energies than the maximum for a = 2°. The ratio of FWHM and incident ion energy is presented in Fig. 3. FWHM increases and then decreases with increasing of a scattering angle. This dependence is stronger in the calculations than in the experiment. The decreasing of FWHM is caused by the diminishing of Emax in energy distribution (1) at large scattering angles. Low-energy part of distribution (1) degenerates for greater h. It reduces the FWHM.

Fig. 3. The ratio of the distribution of reflected (j) experiment data at solid and broken curves a = 4° respectively.

full width at half maximum in energy ions (1) and projectile ion energy E0: a =2°, (d) experiment data at a =4°, are the our theory results at a = 2° and


N.V. Novikov et al. / Nucl. Instr. and Meth. in Phys. Res. B 235 (2005) 448­451

451

4. Conclusion We studied the angular and energy distributions of fast nitrogen ions reflected from copper surface at small grazing angles. The Monte-Carlo simulation replaces the energy loss of ions between two collisions by energy loss in one collision with effective cross section proportional to the ion stopping in this medium. Our calculation results are in qualitative agreement with experimental data. This theoretical model can be used both for fast protons and heavy ions scattering from metal surface.

References
[1] A. Robin, W. Heiland, J. Jensen, J.I. Juaristi, A. Arnau, Phys. Rev. A 64 (2001) 052901. [2] Ya.A. Teplova, Yu.A. Fainberg, V.S. Kulikauskas, Poverkhnostó N3 (1997) 72 (in Russian), Surf. Invest. 13 (1998) 371.

[3] Yu.A. Fainberg, Ya.A. Teplova, V.S. Kulikauskas, Poverkhnostó N4 (2002) 43 (in Russian). [4] W. Eckstein, Computer Simulation of Ion Solid Interactions, Springer-Verlag, 1991, 254p. [5] A. Gras-Marti, H.M. Urbassek, N.R. Arista, F. Flores, Interaction of Charge Particles with Solid and Surfaces, Plenum Press, NY, 1991, 744p. [6] M. Vicanek, H.M. Urbassek, Nucl. Instr. and Meth. B 30 (1988) 507. [7] B. Rosner, S. Datz, W. Wu, et al., Phys. Rev. A 57 (1998) 2737. [8] J.P. Biersack, L.G. Haggmark, Nucl. Instr. and Meth. 174 (1980) 257. [9] V.A. Kurnaev, N.N. Trifonov, V.A. Urusov, Nucl. Instr. and Meth. B 212 (2003) 270. [10] N.V. Novikov, Ya.A. Teplova, Yu.A. Fainberg, Poverkhnostó N9 (2003) 47 (in Russian). [11] N.V. Novikov, Ya.A. Teplova, Yu.A. Fainberg, V.A. Kurnaev, Nucl. Instr. and Meth. B 212 (2003) 96. [12] H.H. Andersen, J.F. Ziegler, HydrogenStopping Power and Ranges in All Elements, Vol. 3, Pergamon Press, New York, 1977, 357p.