Prediction of crystalline properties from ultrathin layered systems: Energy deposition

Abstract

mThe stopping of energetic ions by ultrathin films is of interest, as such films are mesoscopic structures which comprise the delamination limit of crystals, and as they are of practical interest because of their connection to microelectronics. A matter of special interest is the effect of the number of target layers on the stopping. Here we show that the stopping cross-section, S( N, u), of a system of N layers for projectiles with velocity u is a linear function of N-' for small N. Such behavior would be expected for N + m, in which case the constant term would be the bulk crystalline cross section at the specified projectile velocity and the coefficient of the linear term would be the lowest-order surface correction. Surprisingly, the constant coefficient from a small N fit is reasonably consistent (within limits of imprecision) with the crystalline cross section. This linear scaling of S with N-' for small N tracks the scaling behavior of the cohesive energy of the films. We discuss the physics and provide some illustrations. 0 1995 John Wiley & Sons, Inc.

Extracting convergent surface formation energies from slab calculations

“…A recent paper by Fiorentini and Methfessel [1] discussed two important aspects of the determination of surface energies E s from slab (or more precisely, ordered film) calculations. Unfortunately, all of the conceptual and procedural issues discussed in [1] had been treated previously [2][3][4][5][6][7] in work ignored in [1]. The only original physics in [1] is the finding that the linear divergence in calculated E s values discussed originally by Boettger [3] becomes significant for very thick slabs even after taking care to obviate potential inconsistencies between the calculated bulk and film total energies per cell.…”

Momentum-density effects upon the electronic stopping of elemental solids

“…None of the published conclusions is altered by the differences. In particular, the 1/N linear scaling for convergence of the layers toward the bulk value [37]…”

Shape‐dependent molecular polarizabilities

“…Studies of the energy deposition processes by swift ions in materials now have an accuracy that makes more detailed effects of the target electronic structure amenable to investigation at the 5–10% level 1. In several papers 2–8 we have concentrated on an understanding, within a simple framework, of target shape and geometry effects upon the energy deposition (stopping power) in terms of Bethe theory. Thus we have found a way of extracting crystalline (bulk) cross sections from ultra‐thin layered systems 2, as well as isolating a pure surface contribution in the energy loss, depending on the shape of the surface electronic profile 3.…”

“…In several papers 2–8 we have concentrated on an understanding, within a simple framework, of target shape and geometry effects upon the energy deposition (stopping power) in terms of Bethe theory. Thus we have found a way of extracting crystalline (bulk) cross sections from ultra‐thin layered systems 2, as well as isolating a pure surface contribution in the energy loss, depending on the shape of the surface electronic profile 3. Furthermore, the main features of the anisotropic stopping in oriented molecules have been delineated using a simple jellium blob‐like description 4.…”