The method of material sputtering with a focused ion beam (FIB), which is based on scanning the target surface with a sharply focused ion beam, typically of gallium ions with energies up to 30 keV, allows the material to be locally removed from the surface with high precision. This technology is finding increasing application for the creation and modification of micro and nanostructures [1, 2], formation and anal ysis of separate transverse sections (e.g., ion integrated circuits) and series of such sections for three dimen sional imaging of inhomogeneous material (FIB tomography) [3,4], and preparation of samples for transmission electron microscopy [5,6].The rapid progress of the FIB method and its numerous applications are prompting investigations aimed at detailed description of the interaction between incident ions and a target material and the development of approaches to quantitative simulation of micro and nanostructures formed by FIBs. For example, calculations based on simple models assumed that the depth of craters formed by FIBs was linearly dependent on the ion dose [7]. A more realis tic two dimensional (2D) modeling of structures pos sessing circular symmetry with allowance for the angular dependence of sputtering coefficients and the secondary deposition (redeposition) of sputtered atoms was reported in [8]. The use of a 3D modeling based on the nonstructured grid method ensured qual itative agreement with experimental data, although the application of this approach encountered a num ber of technical difficulties [9]. Possibilities of using the modern highly effective level set method [10] for description of the evolution of a sample surface under the action of ion beam have been demonstrated for the first time by Ertl et al. [11].The present work was aimed at further develop ment of approaches to 3D modeling of FIB sputtered samples using the level set method. After determining the real FIB beam shape and refining the model for secondary sputtering of redeposited atoms, this method was used to simulate FIB produced cavities with comparison of the results to experimental data.Let us describe the surface relief formed under the effect of an FIB by the function S(x, y, t), the value of which at an arbitrary point (x, y) gives coordinate z characterizing the distance from the surface at current time t to plane x0y corresponding to the sample sur face position at t = 0. In the framework of the level set method, S(x, y, t) is implicitly set using function Φ(x, y, z, t). By calculating its zero level Φ(x, y, z, t) = 0, we can determine the surface z = S(x, y, t) at each moment of time. According to [11], the function Φ(x, y, z, t) is a solution of the differential equation (1) where r = (x, y, z) and V N (r, t) is the velocity at which each elementary region of the surface shifts in the nor mal direction under the effect of the FIB. This velocity depends on the fluxes of atoms sputtered from the sur face (F sp ) and those redeposited onto the surface (F r ). After numerical integration of Eq. (1), the f...
