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...
For applying focused ion beam technologies in fabrication of the predetermined structures it is essential to evaluate the ion dose delivered to the specimen by the beam and on this basis to predict the formed topography. In this article the authors obtain exact expressions for the ion dose distribution arising in the irradiated region when trenches and rectangular boxes are milled. Based on them the authors describe the surface shape of the structures under consideration when the constant sputtering yield conditions are realized during the milling process. The rather cumbersome analytical description can be transformed into the simple form for milled regions at the distance slightly exceeding the beam diameter from the structure boundaries. Within this region the milled surface shape can be represented as a sum of sinusoidal functions analogous to one- or two-dimensional Fourier series. For typical structure fabrication when the distance between neighboring beam stops is less than approximately two beam diameters the authors derive simple formulas for evaluating the mean depth and the peak-to-valley surface roughness. The authors also estimate when constant sputtering yield conditions can be utilized for the description of the actual milling process. To testify the theoretical considerations two trenches and four rectangular boxes were prepared. In addition, several deep and shallow dotlike structures were created for evaluating the ion flux density determining the beam shape, which was presented as the sum of two Gaussian functions. Peripheral regions of the deep dots cross-sections allow us to find the standard deviation of the second Gaussian function while the standard deviation of the first Gaussian function and the weight factor are retrieved using the milling profiles of the shallow dots. A set of parameters describing the ion flux density of the beam and milling process enables calculating the surface shapes and cross-sectional profiles of the fabricated structures. The authors show that the simulated shapes of the trench and the box and scanning electron microscope images of these structures are similar in appearance. Comparison of experiment and theoretical milling profiles demonstrates good agreement between them. Theoretically estimated mean depth and peak-to-valley surface roughness are consistent with experimental data.
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