Probing the limitations of Sigmund's model of spatially resolved sputtering using Monte Carlo simulations

Abstract

Sigmund's model of spatially resolved sputtering is the underpinning of many models of nanoscale pattern formation induced by ion bombardment. It is based on three assumptions: (i) the number of sputtered atoms is proportional to the nuclear energy deposition (NED) near the surface, (ii) the NED distribution is independent of the orientation and shape of the solid surface and is identical to the one in an infinite medium, and (iii) the NED distribution in an infinite medium can be approximated by a Gaussian. We test the validity of these assumptions using Monte Carlo simulations of He, Ar, and Xe impacts on Si at energies of 2, 20, and 200 keV with incidence angles from perpendicular to grazing. We find that for the more commonly-employed beam parameters (Ar and Xe ions at 2 and 20 keV and non-grazing incidence), the Sigmund model's predictions are within a factor of 2 of the Monte Carlo results for the total sputter yield and the first two moments of the spatially resolved sputter yield. This is partly due to a compensation of errors introduced by assumptions (i) and (ii). The Sigmund model, however, does not describe the skewness of the spatially resolved sputter yield, which is almost always significant. The approximation is much poorer for He ions and/or high energies (200 keV). All three of Sigmund's assumptions break down at grazing incidence angles. In all cases, we discuss the origin of the deviations from Sigmund's model.

Physical mechanisms affecting critical angle for nanopatterning in irradiated thin films: II. Collision cascade details

“…The indication of power deposition "above the bulk" is a quirk of the Gaussian ellipsoid model and has been noted elsewhere [60,59,6]. Indeed, such a "re-averaging" would obscure the well-known Bradley-Harper instability [11,30], as the instability is driven precisely by spatial variation.…”

“…It is also possible, in principle, that our derivation of the shape of the amorphous-crystalline interface is no longer valid for systems that are poorly-approximated by Gaussian ellipsoidal power deposition. Indeed, as has been discussed in [59], power deposition within the irradiated film may not perfectly follow a Gaussian distribution near grazing incidence. There may also be significant errors in the Gaussian approximation for films with large variations in their density [60].…”

Sputtering of SicGe1−c nanospheres

“…For details on the selection of collision partners and the treatment of the surface we refer the reader to our recent publications [34,35]. For the surface binding energies of Si and Ge atoms in the Si c Ge 1−c alloy we use a simple model based on a pair-interaction picture [36,37]:…”

“…The atomic density of the Si c Ge 1−c alloy is calculated assuming constant atomic volumes of Si and Ge consistent with atomic densities of pure Si and Ge of 4.994 × 10 22 cm −3 and 4.428×10 22 cm −3 , respectively. The lower surface binding energy of Ge requires that the trajectory cutoff-energy and the displacement energy are also set to this value; for a discussion see [34]. An extension of IMSIL required for this work was the implementation of a spherical geometry.…”

Влияние кривизны поверхности на процессы физического распыления кремния ионами Ar низкой энергии

“…Однако эта модель не позволяет предсказать особенности физического распыления при низких энергиях ионов. Например, в [4,5] было показано, что при низких энергиях ионов нарушается линейная связь между коэффициентом распыления и энергией, передаваемой налетающей частицей атомам мишени, причем пространственное распределение этой энергии оказывается зависящим не только от параметров ионов, но и от материала мишени. В [6,7] аналитически было продемонстрировано, что в случае наноразмерных объектов коэффициент распыления в существенной степени зависит от кривизны поверхности.…”