340 Nuclear lnstrumcnts and Methods in Physics Research B56/57 (1991) 340-344 North-Holland Stopping of swift projectiles in material thin films: hydrogen J.Z. Wu, Samuel B. Trickey, John R. Sabin and David E. Meltzer Quuntum Theory Project. Deportment of Physics, Umversify of Florida, Gainescille. FL 3261 I, LISA Pilot calculations of the stopping of swift protons by thin hydrogen films are reported. ‘The calculations are based on the kinetic theory of stopping. The requisite mean excitation energies are obtained from an energy band formulation of the local plasma approximation and velocity densities from an LCAO/local density calculation of a few atomic layers thick film. Results are reported for hydrogen l-, 2-, and 3-layer atomic- and molecular-like films. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG 1. Introduction The interpretation of experimental stopping data is generally based on the extrapolation of the data to zero thickness in order to avoid multiple scattering effects and complicated projectile trajectories. Such reduction produces properties of a film which is bulk-like, how- ever, rather than those of a more physical thin film, where one might expect quantum size effects to become evident when the film reaches a few atomic layers in thickness [l]. Similarly, theoretical treatments of stop- ping are generally applicable to either isolated atoms or molecules [2], which may represent vapor targets, or to bulk metals, if the standard electron gas theory is em- ployed 131. In neither case is the stopping of a thin film of arbitrary composition considered directly. In this communication we present a preliminary report of a developing scheme appropriate to treatment of ultrathin films of all compositions. and its applica- tion to some hydrogen films a few atomic layers thick. We consider an ultrathin film composed of several atomic layers (here taken to be homonuclear for con- venience), periodic in two dimensions, and with vacuum boundary conditions in the third (z) direction, compris- ing N,,, unit ceils, each containing n atoms of atomic number Z,, and with cell area A. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 2. Methodology One generally defines the linear energy loss as a function of projectile velocity of a massive projectile in a material target as -g =NS(r!), where N is the target number density. The stopping cross-section, S(o), is usually expressed in terms of the stopping number, L(u), given (in atomic units) by where 2, and Zz are projectile and target atom atomic numbers, respectively. Using classical conservation of energy and momentum. Sigmund [4] developed a formu- lation for I.( I)) which relates it to L,(u), the stopping number for the scattering particles (electrons) at rest. This formulation of the so-called kinetic theory of stop- ping has been implemented shell-wise for atoms [2,5], and has proved to be quite useful. Thus we adopt it for thin films. Experience shows [5] that in atoms the stopping must be considered on a shell-by-shell basis to get accurate values of stopping properties. Although the scattering electrons in atoms have an obvious segrega- tion by orbital energies, the analogous segregation in extended systems (by density of states) is a bit more subtle. The simplest numerical technique. which can be refined just as in the refinement of density of states beyond simple histograms, it to divide the scattering electron energy bands into M groups, each identified by energy I$, where zyxwvutsrqponmlkjihgfedcbaZYXWVU E,=E,,,,,+IAE, I=O,1,2 ,..., (3a) A.5 = (E, - E,,,,,)/M. (3b) Here E, is the Fermi energy of the system and .&, is the minimum energy of the band in question. We then formulate (see ref. [6] for details) the film stopping in the kinetic theory in terms of these energy sub-bands or regions, and for projectile velocities u normal to the film, as 0168-583X/91/$03.50 8 1991 - Elsevier Science Publishers B.V. (North-Holland)