# Investigation of Nanocutting Characteristics of Off-Axis 4H-SiC Substrate by Molecular Dynamics
## 2 Models and Methods  
The molecular-dynamics simulations in this paper were conducted with open-source software Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [11]. The Tersoff potential [12] was adopted to describe the interatomic interactions in the SiC workpiece and the diamond cutting tool. The Morse potential [9] was adopted to describe the interatomic interaction between the SiC workpiece and the diamond cutting tool. Simulation results were visualized with Open Visualization Tool (OVITO) [13]. The identify diamond structure module [14] in OVITO was used to analyze the structure transformation and inspect the defect propagation in the SiC workpiece.  
Figure 1 shows the nanocutting MD model of the off-axis 4H-SiC. The model consists of two parts, the diamond cutting tool and the SiC workpiece. The primary geometry parameters of the cutting tool are also shown in Figure 1. The cutting tool with a \(-30^{\circ}\) rake angle and a \(10^{\circ}\) clearance angle was used in this paper. Since the hardness of SiC is comparable with a diamond, the cutting tool was not treated as a rigid body [7]. The atoms marked in red in the SiC workpiece are the fixed layer atoms, which provide mechanical support for the workpiece to prevent it from translation motion. The red atoms in the cutting tool are the moving layer atoms that drive the cutting tool moving at a constant speed. The atoms in green are the thermostat layer atoms, which prevent the workpiece and cutting tool from melting. The Nose-Hoover thermostat method was applied. The thickness of the fixed and thermostat layers in the SiC workpiece was 1.0 nm for both, and the thickness of the moving and thermostat layers in the cutting tool was 0.35 nm for both. Periodic boundary conditions were applied in the directions of x- and y-axis. Figure 2 shows three different workpiece models used in the simulations. Figure 2b is the on-axis SiC model. The lattice directions were [11 - 20], [\(-\)1100] and [0001] along the positive x-axis, positive y-axis, and positive z-axis, respectively. The typical off-axis angles are \(4^{\circ}\) and \(8^{\circ}\). We chose a \(4^{\circ}\) off-axis angle in this paper, since a low off-axis angle is preferable to reduce cost, especially for large wafers. Figure 2a is the off-axis SiC model, where the c-axis rotates \(4^{\circ}\) toward [1 - 100]. Figure 2c is the off-axis SiC model, where the c-axis rotates \(4^{\circ}\) toward [\(-\)1100]. These models were used to investigate the influence of lattice orientation on nanocutting. Other parameters used in the simulations are listed in Table 1.  
The simulation started with the equilibrium of the system at 300 K for 10 ns. Then, the cutting tool moving along the negative z-axis pressed into the workpiece. Finally, the cutting tool moving along the negative y-axis direction finished the cutting process.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Dimensions** & 4.6 \(\times\) 70.2 \(\times\) 10.0 nm (on-axis), 4.6 \(\times\) 70.4 \(\times\) 10.0 nm (off-axis) \\
**Cutting speed** & 60, 80, 100, 120, and 140 m/s \\
**Cutting depth** & 0.5, 1.0, and 1.5 nm \\
**Cutting direction** & [1\(-\)100] \\
**Time step** & 0.5 fs \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters used in the simulations.  
Figure 1: Nanocutting molecular-dynamics (MD) model of off-axis 4H-SiC.  
Figure 2: Three different silicon carbide (SiC) workpiece models. (**a**) 4\({}^{\circ}\) Off-axis toward [1\(-\)100]. (**b**) On-axis. (**c**) 4\({}^{\circ}\) Off-axis toward [\(-\)1100].