# 3-D SRIM Simulation of Focused Ion Beam
## 1 Introduction  
The Focused Ion Beam (FIB) instrument has been developing since developments in the liquid metal ion source (LMIS) during the 1970s [1; 2; 3; 4]. It has become one of the most important micro/nano manufacturing tools for its direct patterning, high resolution and its multi-role in the semiconductor field [5; 6]. It can be used for transmission electron microscopy (TEM) sample preparation [7; 8; 9; 10], direct and mask-less 3-D patterning [11; 12; 13], semiconductor integrated circuit failure analysis [14; 15], and solid oxide cell (SOC) fabrication [16]. Theories on ion-solid interaction and the relative simulation methods have developed rapidly along with the expansion of FIB application.  
Among all the methods to simulate ion-solid interaction, Monte-Carlo is popular and succeeds in forming software such as SRIM and TRIM [17], TRIDYN [18], SDTrimSP [19] and so forth. SRIM is based on TRIM (transaction of ions in matter) using short-range ZBL potential. TRIDYN is an improved version of TRIM code allowing dynamic simualtions with Krypton-Carbon interaction potential. SDTrimSP (SD for static-dynamic; SP for sequential and parallel processing) is based on TRIDYN code and used for sputtering process of low energy. [PERSON] et al. studied the angle-dependent sputter yields with SDTrimSP, TRIDYN and SRIM [20]. [PERSON] et al. combined SRIM and the thermal spike model to research the spatial and temperature evolution through the Gaussian profile beam of softmatter [21]. [PERSON] et al. analyzed the sputtering of 3-D rough samples with arbitrary 3-D surface morphologies [22]. [PERSON] et al. developed the mathematical model for sputtering sidewall with the beam radius, the substrate material properties and the supposed Gaussian beam current density [23], which is verified by the experiment of a single crystal (100) silicon [24]. In the above studies, sputtering objectives such as sputtering depth and radial range are mainly affected by parameters of the incident ion beam and samples. Normally, parameters of the incident ion beam include ion dose, ion energy, incident angle and Gaussian beam current density. However, these conclusions are not suitable for the FIB system as the Coulomb repulsion forces among ions make the incident beam different from the ideal Gaussian distribution and this change will influence the sputtering performance accordingly [25; 26]. Furthermore, FIB distributions are different under different beam energies and beam currents [27; 28]. In order to guarantee the precision in FIB fabrication under different beam energies and beam currents, a new application-oriented model including aberrations and Coulomb repulsion forces was brought forward in simulating ion-solid interaction.  
In this paper, the sputtering process of the high-energy ion beam on the sample was researched firstly under different beam energies, ion doses and incident angles. Ion-solid interaction was then simulated through the improved SRIM program with an application-oriented ion beam model, whose beam current distributions include aberrations and Coulomb repulsion forces among ions. In the end, the sputtering performance of this model and its comparison to the typical Gaussian incident beam were given in detail.