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Chapter 1. Introduction
The study of atomic collisions covers a broad range of phenomena. There is a vast literature on this subject. During the collision of two atoms a wide range of processes can occur. A+B A+B A*+B A+B A++B A+B* A+BC A+B+C etc. A+B A+B* A+B A++B+eA+B+ A*+B AB+C AB+C elastic scattering excitation de-excitation ionization (electron loss) charge transfer (electron capture and loss) transfer of excitation re-arrangement reaction

Often these processes are studied by observing collisions of atoms or ions with dilute gases. The subject of this series of lectures is the interaction of ions with atoms embedded in a solid. It is to be expected that the electronic excitations during atomic collisions in a solid differ in many details from those in a gas, because the electronic structure of the embedded atoms is different. An energetic ion propagating in a solid has a high frequency of collisions, and cannot decay to the ground state in the short time interval between collisions. Also the electronic excitations of atoms in a solid cannot be measured in detail. Inner shell excitations may be measured by observing the emitted X-rays or electrons. In most materials the lower-energy excitations giving rise to emission of photons in the optical range or low-energy electrons escape observation. It may be clear that detailed knowledge and understanding of electronic interactions during atomic collisions in solids is still lacking. A theoretical approach including all the excitations mentioned above is not possible yet, and details of these processes are not accessible to observation. A fairly complete theoretical description containing a number of approximations can be given for the electronic interactions evoked by bare ions. As soon as the electronic excitations of the ion itself must be taken into account, the problems are too complicated for a detailed theoretical description. In ion-solid interactions the ion as a whole is deflected by the ion-atom potential. This deflection is accompanied by electronic excitation. It is customary to treat the deflection and excitation as separate problems. This is a reasonable approach if the ion energy is in the keV range or higher, because the impulse transferred to electrons is only a small fraction of the total transferred impulse. For deflection angles of a few degrees or less of light ions the disentanglement of the deflection by the atomic potential and electronic excitations is not fully justified. Also the energy lost in electronic excitations is ignored in the calculation of the deflection angle. In other words: the deflections of an ion propagating in a solid are treated as elastic collisions of isolated atoms. The binding energy of the atom in the solid ( 5 eV) is neglected. Also the deflection is calculated using a classical (versus quantum mechanical) approximation. As will be shown, this is a good approximation for ions with energies of keV's, or higher. Atomic collisions in solids play an important role in a number of processes in materials science that can be summarized as ion beam modifications of materials. These include ion implantation, sputtering, sputter deposition, sputter cleaning of surfaces, radiation damage, ion beam mixing. The application of these processes is widespread, so that practically each materials scientist gets involved in it. Also scattering of ions with keV-MeV energies is applied for ion beam analysis.of surfaces and of thin layers. For instance, by high-energy ion scattering (HEIS) the concentration of elements in a thin layer (up to some µm's) of a solid can be determined on an absolute scale as a function of depth. Also the position of atoms can be determined with a high precision in thin layers of mono-crystalline material. The structure and composition of surfaces and of shallow interfaces can be determined with mediumenergy ion scattering (MEIS), or with low-energy ion scattering (LEIS), using the channeling or


channeling + blocking technique. A different form of analysis is secondary ion mass spectrometry (SIMS), whereby the mass spectrum of sputtered ions is measured to probe the composition of samples as a function of depth. Also the use of ion beam analysis methods is widespread, and it is in some form available in many research laboratories. In this series of lectures the fundamental processes underlying ion-solid interactions are treated. The electronic interactions are described using simple theories. The validity of the approximations used is discussed. The use of quantum mechanics is limited to some basic considerations. A brief description of computer simulations of ion-solid interactions is given. In the last chapters the applications of the theory to ion-beam analysis and modification of materials are treated. A number of examples of these applications is given. LITERATURE General [1] H.W. Massey, Atomic and molecular collisions, (Halsted Press N.Y. (1979)) Chapter 1. [2] M.R.C. McDowell and J.P. Coleman, Introduction to the theory of ion-atom collisions, North Holland, Amsterdam (1970). [3] E.W. McDaniel, Collision phenomena in ionised gases, Wiley, N.Y. (1964). [4] H. Goldstein, Classical mechanics, Addison-Wesley, Cambridge (1959). Stopping Power calculations [5] J.D. Jackson, Classical electrodynamics, 2nd. ed. Wiley, N.Y. (1975) Chapter 13. [6] N. Bohr, K. Danske Vidensk. Selsk. Mat. Fys. Medd. 18 (1948). [7] W.K. Chu, Meth. of Exp. Phys. 17 (1980) 25, Ac. Press (ed. P. Richard). [8] U. Littmark and J.F. Ziegler, Handbook of range distributions in all elements, Vol. 6: The stopping and ranges of ions in matter. (Pergamon Press, N.Y., 1980). [9] D.K. Brice, K.B. Winterbon, Ion implantation range and energy deposition distributions. Vol. 1 and Vol. 2 (Plenum Press, N.Y. 1975). Radiation damage, modification of materials by ion beam irradiation [10] I. Auciello and R. Kelly, eds. Ion bombardment modification of surfaces (Elsevier, 1984). [11] J.W. Mayer, L. Eriksson and J.A. Davies, Ion implantation in semi-conductors (Academic Press, N.Y., 1970). [12] N.L. Peterson and S.D. Harkness, eds. Radiation damage in metals (Ac. Soc. for Metals, Ohio, 1975). [13] Ch. SteinbrЭchel, A simple formula for low-energy sputtering yields, Appl. Phys. A36 (1985) 37. [14] J.P. Biersack and W. Eckstein, Sputtering studies with the Monte Carlo program TRIM.SP, Appl. Phys. A34 (1984) 73. Shadowing and blocking, Channeling [15] J. Lindhard, K. Danske Vidensk. Selsk. Mat. Fys. Medd. 34 (1965) 14. [16] L.C. Feldman, J.W. Mayer, S.T. Picraux, Materials analysis by ion channeling, Academic Press, N.Y. (1982). [17] W.K. Chu, J.W. Mayer and M.A. Nicolet, Backscattering spectrometry, Acedemic Press, N.Y. (1978). [18] D.S. Gemmel, Rev. Mod. Phys. 46 (1974) 129. [19] J.F. van der Veen, Surf. Sci. Reports 5 (1985) no. 5,6. [20] W. Heiland and E. Taglauer, Surface Sci. 68 (1977) 96. [21] O.S. Oen, Surf. Sci. 131 (1983) L407. [22] B. Poelsema, L.K. Verhey and A.L. Boers, Surf. Sci. 30 (1972) 134. [23] D.O. Boerma, in: Nuclear physics applications on materials science. Edited by: E. Recknagel and J.C. Soares. NATO ASL Series E Vol. 144 (Kluwer, Dordrecht) 1988.


[25] [26]

J.W. Mayer and E. Rimini, eds. Ion beam handbook for materials analysis (Ac. Press, N.Y., 1977). D.O. Boerma, Nucl. Instr. and Meth. in Phys. Res. B50 (1990) 77.

Units and constants 1 еngstrЖm = 1 е = 10-10 m 1 Femtometer = 1 fm = 10-15 m 1 barn = 10-28 m2 = 100 fm2 Velocity of light c = 2,99792 x 108 m/s Bohr radius a0 = 0.53 x 10-10 m Bohr velocity v0 = 2,2 x 106 m/s Screening radius a5 = 0,8853 a0 (Z11/2 + Z21/2)-3/2 Lading electron e = 1,60206 x 10-19 C 1 eV = 1,60206 x 10-19 J MeV = 1,60206 x 10-13 J h/2 = 1,055 x 10-34 J x s (Plank constant) = 0,6582 x 10-15 eV x s = Ke2/hc = 7,29729 x 10-3 (fine structure constant) -1 = 137,0373 e2 = hc = 1,43987 Mev x fm = 1,43987 x 101 eVе me= electron mass = 9,10956 x 10-31 kg = 5,48580 x 10-4 AMU mp= proton mass = 1,67261 x 10-27 kg 1 AMU = 1 atomic mass unit = 1/12 x mass 12C atom = 1,6597 x 10 1 AMU = 1822 electron masses K = constant in Coulomb potential in the M Kg S system = 9 x 109 Nm2C-2 (K = 1/4 0) 0 = 107/4c2 = 8,844 x 1012 N-1m-2C2 Number of Avogadro: NA = 6,02217 x 1023 mole-1 KB = Bolzman constant = 1,38054 x 10-23 J/K = 8,6173 x 10-5 eV/K Greek alphabet A B E Z H I K M µ alpha beta gamma delta epsilon zХta Хta thХta iota kappa lambda mu N O P T X o nu xi omicron pi rho sigma tau upsilon phi chi psi omega

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kg