Morphology change of the silicon surface induced by Ar ion beam sputtering

It is well known that low and medium energy ion sputtering may induce a fabrication of periodic nanoscale structures on an irradiated surface [1]. Depending on the sputtered substrate characteristics and sputtering conditions, different types of nanoscale structures such as ripples, nanoholes and nanodots can grow on a target during ion beam sputtering [2–6]. These patterns have been found on both amorphous and crystalline materials including insulators, semiconductors and metals (see reference [7] and citations therein). Main theoretical models describing ripple formation are based on the results of famous works by Bradley and Harper [4], Kardar et al. [8], Wolf and Villian [9], and Kuramoto et al. [10]. The main control parameters in these models reduced to surface tensions, tilt-dependent erosion rates and diffusion constants are determined by sputtered substrate characteristics and sputtering conditions (see for example [7]). Among theoretical investigations there are a lot of experimental data manifesting a large class of patterns formed due to the self-organization process. It was experimentally shown that the main properties of pattern formation processes depend on ion-beam parameters such as ion flux, energy of deposition, angle of incidence, and temperature of the substrate (target). Therefore, to study the ion beam sputtering processes theoretically one needs to determine the mentioned parameters of the model according to the physical conditions related to concrete materials. One of the most frequently used materials for ion beam sputtering is silicon because it is the mainstream material in modern microelectronic industry and it is readily available with high purity and quality. Nanostructuring of silicon has received much attention due to its potential application in developing the Si light sources [11]. Various techniques such as acid etching, ion implantation, reactive evaporation, chemical vapor deposition and molecular beam epitaxy have been used in developing the Si nanomaterials (porous Si, Si nanocrystal-doped dielectrics and Si quantum dots) (see reference [11] and citation therein). In this paper we study the properties of the formation of nanoscale patterns on a silicon target sputtered by Ar ions. To this end, we use a two-level scheme, based on Monte-Carlo simulations and the modified Bradley-Harper theory. In the first approach we compute the ion energy dependent penetration depth, widths of the ion energy distribution and sputtering yield. Next, we exploit these characteristics as input data for the continuum approach describing the evolution of the surface height field. We define the domains of values for the angle of incidence and ion energy where different nanoscale structures can be formed. The dynamics of nanoscale pattern formation is