Dislocation Analysis of Nanoindentation on Different Crystal Planes of 6H-SiC Based on Molecular Dynamics Simulation

Abstract

In order to explore the deformation law of nanoindentation dislocation on different crystal planes of 6H-SiC by cube indenter at high temperature, the (0001), (1$\overline{1}$00) and (2$\overline{1}\overline{1}$0) crystal planes were simulated by molecular dynamics, and changes of dislocation and shear stress under different crystal planes were analyzed. With the deepening of indentation depth, the formation of dislocations on different indentation surfaces has a certain repeatability. The crystal plane (0001) continuously generates horizontal dislocations around the indentation, (1$\overline{1}$00) the crystal plane generates two square dislocation rings moving downward at a time, and (2$\overline{1}\overline{1}$0) the crystal plane generates one square dislocation ring moving downward at a time.

1. Introduction

6H-SiC has excellent comprehensive properties of high strength, high hardness, corrosion resistance, high temperature resistance and a small dielectric constant [1,2,3], and is widely used in aerospace, weapons and equipment, biomedicine, integrated circuits, and other sophisticated fields [4,5,6]. In the actual indentation process, it is difficult to measure the changes in dislocation, shear strain and other values in the whole process and thus they cannot be systematically analyzed [7,8,9]. When the indentation surface is different, the atoms in the crystal are arranged in different directions, which has different influences on the indentation experiment [10,11,12]. By using the molecular dynamics simulation of 6H-SiC nanoindentation, the dislocation deformation and shear strain distribution of 6H-SiC nanoindentation on different crystal surfaces can be analyzed effectively and in real-time.

Molecular dynamics simulation has become a common method to study the mechanical properties of materials, which can effectively simulate the whole process of nanoindentation and allow for the conduction of data analysis [13,14,15]. Nawaz et al. [16] studied the elastic-plastic deformation of 6H-SiC single crystal on the nanoscale by using the Burkovich indentation machine. It was found that, under the condition of 0.54 mN indentation load and 20 μN/s loading rate, the elastic-plastic transformation is shown by stable pop-in events. In the load-independent region, the hardness is 33 ± 2 GPa, and the elastic modulus is stable at 393 ± 8 GPa. ZW A et al. [17] systematically studied the mechanism of amorphous and dislocation evolution of single crystal 6H-SiC crystals using nanoindentation, high-resolution transmission electron microscopy, molecular dynamics simulation, and generalized superimposed fault energy surface analysis. It is revealed that the amorphous process is realized through the transformation of wurtzite structure to intermediate structure, and then through further amorphous processing. XG Ma et al. [18] used acoustic emission (AE) to characterize in-situ deformation, micro-fracture, and phase transformation induced by nanoindentation, and explained the scale dependence of the indenting head radius and applied normal load on plastic deformation and micro-fracture through the types and intensity of AE events revealed by displacement mutation in a loading response. Zta B et al. [19] obtained through molecular dynamics studies that both the C and Si planes of 4H-sic show greater normal resistance than 6H-SiC, and for 4H and 6H-SiC, the C plane may be easier to process than the Si plane. Scholars have carried out detailed molecular dynamics simulation analysis of nanoindentation on 6H-SiC and analyzed its elastic-plastic deformation mechanism and mechanical properties but did not carry out dislocation change and shear strain analysis for the nanoindentation of different crystal planes by cubic indenters at high temperatures.

On the basis of the above research on nanoindentation, the molecular dynamics method was adopted to explore the changes of dislocation and shear strain during nanoindentation of different crystal faces by the cubic indenting head at high temperatures. The research results have guiding significance for the dislocation-forming law and crystal face processing research in the nanoindentation process.

2. Silicon Carbide Indentation Process Physical Model

2.1. Establishment of the MD Model

The physical model of nanoindentation constructed by LAMMPS based on molecular dynamics is shown in Figure 1. Figure 1a–c are three physical nanoindentation models of the (0001), (1$\overline{1}$00) and (2$\overline{1}\overline{1}$0) crystal planes in 6H-SiC crystal with indentation surfaces, respectively. In order to effectively analyze the effect of different 6H-SiC crystal planes on its properties, different sizes of 6H-SiC substrates with different indentation surfaces were adopted. All 6H-SiC substrates are equipped with a boundary layer, constant temperature layer and Newtonian layer, respectively, from bottom to top. The thickness of the boundary layer and constant temperature layer is 1 nm, and the rest is the Newtonian layer. The boundary layer is used to fix the boundary, prevent the outward diffusion of atoms and reduce the boundary effect. The constant temperature layer can transfer heat to keep the temperature stable. The Newton layer follows Newton’s law of motion as the main compression and analysis parts. The diamond indenter is a cube with a side length of 3 nm. The four sides of the indenter are parallel to the corresponding side of the 6H-SiC substrate, and the center of gravity of the diamond indenter is in a vertical line with the center of gravity of the 6H-SiC substrate. In order to ensure the reliability and accuracy of molecular dynamics simulation results of nanoindentation, the indenter is divided into the boundary layer, constant temperature layer and Newtonian layer from top to bottom. The thickness of the boundary layer and constant temperature layer is 0.5 nm. The distance between the indentation surface and the bottom surface of the indenter is 1 nm, and the indentation movement of the indenter is carried out towards the 6H-SiC substrate along the negative direction of the Z-axis.

The simulation parameters are partly different due to the change in the indentation surface, and the atomic number of the 6H-SiC substrate is greatly different due to the change in volume. The 6H-SiC substrate with (1$\overline{1}$00) indentation surface has the most atoms (623,610), and the 6H-SiC substrate with (0001) indentation surface has the least atoms (223,212). The atomic numbers of (0001) crystal plane, (1$\overline{1}$00) crystal plane and (2$\overline{1}\overline{1}$0) crystal plane are 4913, 4633 and 4768, respectively. During the indentation process, the environmental parameters have a certain influence on the simulation results. The simulation temperature of different crystal planes is 900 K, the indenting head drop rate is 50 m/s, and the time step is 1 fs. Specific simulation parameters are shown in

Table 1. Molecular dynamics simulation parameters.

Parameters	Value
Sample indentation surface	(0001)	(1$\overline{1}$00)	(2$\overline{1}\overline{1}$0)
Crystal plane group	{1000}	{1$\overline{1}$00}	{2$\overline{1}$$\overline{1}$0}
Numbers of atoms in substrate	223,212	623,610	447,928
Dimensions of substrate	12 nm × 12 nm × 16 nm	20 nm × 20 nm × 16 nm	12 nm × 12 nm × 32 nm
Dimensions of indenter	3 nm × 3 nm × 3 nm
Numbers of indenter	4913	4633	4768
Equilibration temperature	900 K
Indenting speed	50.00 m/s
Time step	1 fs

.

2.2. Selection of Potential Functions

Since silicon nitride and diamond are both high hardness materials, in order to make simulation results more reliable, the diamond indenter is set as a non-rigid body, and an appropriate potential function is selected. In the nanoindentation process, there are three kinds of atom interactions: carbon atoms in diamond, silicon atoms in silicon carbide, and carbon atoms, and there are altogether six kinds of atom interactions. The analytic bond order action potential (ABOP) function is suitable for the interaction between C atoms in the diamond indenter, C atoms in silicon carbide crystal and Si atoms [20]. The ABOP potential function can more accurately describe the atomic collision between diamond and silicon carbide, and its expression is as follows:

$${\rm E}=\frac{1}{2}{\displaystyle \sum _{i>j}{f}_C}(r_{ij})[2V_R(r_{ij})-(b_{ij}+b_{ji})V_A(r_{ij})]$$

(1)

$$V_R(r)=\frac{D_0}{S-1}\exp [-\beta \sqrt{2S}(r-r_0)]$$

(2)

$$V_A(r)=\frac{S{D}_0}{S-1}\exp [-\beta \sqrt{2/S}(r-r_0)]$$

(3)

where E is the total energy in the system, f_C is the smooth truncation function, V_R is the repulse duality, V_A is the attraction duality, b_ij is the bond order function, r_ij is the distance between atom i and atom j, D₀ is the dimer energy quantity, r₀ is the dimer bond length and β and S are parameters.

Vasishta potential functions are used for interactions between C atoms, Si atoms and between C atoms and Si atoms in silicon carbide crystals [21]. Vahishta potential function can accurately describe the collisions between atoms in silicon carbide crystals, and its expression is as follows:

$$V={\displaystyle \sum _{i>j}{V}_{ij}^{(2)}}(r_{ij})+{\displaystyle \sum _{i,j<k}{V}_{ijk}^{(3)}}(r_{ij},r_{ik})$$

(4)

$$V_{ij}^{(2)}(r)=\frac{H_{ij}}{r^{\eta ij}}+\frac{Z_i{Z}_j}{r}{e}^{-r/\lambda }-\frac{D_i{}_j}{2r^4}{e}^{-r/\xi }-\frac{W_{ij}}{r^6}$$

(5)

$$V_{jik}^{(3)}(r_{ij},r_{ik})=R^{(3)}(r_{ij},r_{ik})P^{(3)}({\theta }_{jik})$$

(6)

where V is the total energy in the system, V_ij is the two-body potential, V_ijk is the three-body potential, H_ij is the spatial repulsive force strength, Z is the effective charge, D_ij charge-dipole gravitational strength, W_ij is the van der Waals interaction strength, ƞ_ij is the spatial repulsive term index, and P⁽³⁾ is the angular three-body interaction potential.

In order to reduce the boundary effect, the X and Y axis directions are set as periodic boundary conditions, and the Z axis direction is set as free boundary conditions with contraction. In order to keep the indentation system in a stable state, the relaxation stage uses the constant-pressure ensemble (NPT) to eliminate the influence of particle number, pressure and temperature on the system. After the system tends to be stable, it enters the indentation stage, and atomic collisions bring about a mutual conversion of energy. Micro-canonical ensemble (NVE) is used in the indentation stage to achieve stable energy equilibrium.

2.3. Simulation Calculation

Through analyzing the indentation defects by various methods, the relative information of atom movement in the process of defect formation can be obtained. Through coordination analysis, the internal structure of the crystal changes can be analyzed, so as to determine whether defects are generated. Dislocation analysis (DXA) is used in conjunction with crystal structure identification (IDS) to automatically extract dislocated atoms and dislocation lines and identify their Bergdahl vectors. Atomic strain allows for the analysis of the von Mises shear strain distribution in crystal.

3. Results and Analysis

3.1. Influence of Different Crystal Planes on Dislocation

Figure 2 shows the initial deformation process of dislocation atoms during 6H-SiC (0001) crystal surface nanoindentation at different indentation depths. To facilitate the observation of the dislocation atoms, the region of the sic substrate at a height of 70 to 150 Å was color stratified. The basal model of the X, Y and Z axes have [$\overline{1}$00$\overline{1}$], [$\overline{1}$2$\overline{1}$0] and [0001] orientation, respectively. When the indentation depth is 1.8 nm, as shown in Figure 2a, more and more atoms slip below the indentation defect, and the region of atomic slip appears as a large cube. In the process of atomic slip, the first total dislocation is generated on one side of the big cube, which is a screw dislocation, and the Burr vector is b = 1/3 [1$\overline{2}$10]. When the indentation depth is 2.3 nm, as shown in Figure 2b, the atoms gradually slip outward, the dislocation region transforms from cube to ellipsoid, and the dislocation ring keeps getting larger. When the indentation depth is 2.8 nm, as shown in Figure 2c, a new layer of dislocation atoms is formed, in which the dislocation generated is edge dislocation, and its Burr vector is b = 1/3 [$\overline{1}\overline{1}$20]. With the increase of indentation depth, when atoms slip along [$\overline{1}\overline{1}$20] crystal direction, the direction of atomic slip changes after encountering atoms sliding along other crystal directions. The edge dislocation was combined with other non-total dislocations to form a large screw dislocation, as shown in Figure 2d. When the indentation depth is 3.8 nm, as shown in Figure 2e, the third layer dislocation atom is formed, and a non-total dislocation is generated in the second layer atom, and its Burr vector is b = 1/6 [2$\overline{2}$0$\overline{3}$]. During the indentation process, the incomplete dislocations are constantly merged with other dislocations and are constantly changing. When the indentation depth is 4.3 nm, as shown in Figure 2f, atoms in the third layer keep increasing, and dislocation rings are generated. The Burr vectors are the same as those in the second layer when dislocation is just formed, both of which are b = 1/3 [$\overline{1}\overline{1}$20], and the dislocation is roughly the same. In the whole indentation process, the dislocation produced is horizontal dislocation: dislocation combined with each other, but dislocation around the indentation defect is a perpendicular line. When an atom at the bottom reaches saturation with increasing indentation depth, it will slip down to the next layer.

Figure 3 shows the initial deformation process of the dislocation of atoms in nanoindentation of 6H-SiC (1$\overline{1}$00) crystal face at different indentation depths. When the indentation surface is (1$\overline{1}$00) crystal plane, the X-axis direction is [000$\overline{1}$] crystal direction, the Y axis direction is [11$\overline{2}$0] crystal direction and the Z axis direction is [1$\overline{1}$00] crystal direction. When the indentation depth is 0.8 nm, as shown in Figure 3a, the first dislocation ring is generated under a right angle of the square indentation defect, and the indentation depth is much smaller than when the indentation surface is (0001), and the first dislocation ring is generated. When the depth of the indentation is 1.0 nm, as shown in Figure 3b, a second dislocation ring is rapidly formed under another right angle of the indentation defect, and its Burr vector is b = 1/3 [$\overline{1}\overline{1}$20]. One end of the two dislocation rings is connected to a pair of non-adjacent right angles of the square indentation defect, and the other end is converged below the center of the square defect. With increasing indentation depth, the atoms at the two ends of the dislocation ring slip in the direction of [11$\overline{2}\overline{3}$] and [$\overline{1}\overline{1}$20], respectively, and the atoms at the center of the intersection of the defect are gradually separated. When the indentation depth is 1.2 nm, as shown in Figure 3c, the two dislocation rings are basically separated, but not disconnected from the main dislocation part. With a further increase in the indentation depth, the dislocation ring is gradually disconnected from the main part, and atomic diffusion causes the main part to regenerate a small dislocation ring whose Burr vector is b = 1/3 [11$\overline{2}\overline{3}$], as shown in Figure 3d,e. When the indentation depth is 1.8 nm, as shown in Figure 3f, the two dislocation rings move to both sides. During the movement, the shape of the dislocation rings keeps changing and eventually becomes stable after forming a square. During the indentation process, atoms slip mainly in two crystal directions. The dislocation is mainly divided into two parts: one is the dislocation ring moving down independently from the main body, and the other is the dislocation ring that has not formed a separate dislocation ring and is still on the main body.

Figure 4 shows the initial deformation process of dislocation atoms in nanoindentation of 6H-SiC (2$\overline{1}\overline{1}$0) crystal surface at different indentation depths. When the indentation is (2$\overline{1}\overline{1}$0) crystal, the X-axis direction for the [01$\overline{1}$0] crystal, Y direction, for the [0001] crystal Z axis is in the [2$\overline{1}\overline{1}$0] to the silicon wafer. When the indentation depth is 0.5 nm, as shown in Figure 4a, the atom slips towards the crystal direction of [03$\overline{3}\overline{1}$]. The indentation depth required to produce the first dislocation ring is the smallest among the three different indentation surfaces, and no atoms have accumulated beneath the indentation defect. The indentation depth required to produce the first dislocation ring is the smallest among the three different indentation surfaces, and no atoms have accumulated beneath the indentation defect. When the indentation depth is 0.7 nm, as shown in Figure 4b, the dislocation ring keeps expanding, and both ends of the dislocation ring move to the same right angle of the square defect at the same time, but no other dislocation rings are generated, and the Burr vector is still b = 1/3 [03$\overline{3}\overline{1}$]. When the indentation depth is 0.9 nm, as shown in Figure 4c, both ends of the dislocation ring converge under a right angle of the square defect. With increasing depth of indentation, dislocation cutting occurs, and the dislocation ring is separated from the main part of the dislocation. The shape of the separated dislocation ring is square, as shown in Figure 4d. When the indentation depth is 1.3 nm, as shown in Figure 4e after the first dislocation ring breaks away from the main part, the atom continues to slip towards the crystal direction of [03$\overline{3}\overline{1}$], and a second dislocation ring is generated at the location where the first dislocation ring is generated, with the same Burr vector as the first one, b = 1/3 [03$\overline{3}\overline{1}$]. When the indentation depth is 1.5 nm, as shown in Figure 4f, the second dislocation ring is about to be disconnected from the main part, and the disconnection position is roughly the same as the last one, but the formation speed is faster than that of the first dislocation ring. During the indentation process, the resulting dislocation ring moves continuously in the same crystal direction. After dislocation severing occurs, a new dislocation will be generated in the main part of the dislocation, and the motion of the first one will be repeated, but the time required is different.

3.2. Effect of Different Crystal Planes on the Shear Stress of Nanoindentation

To observe the shear strain inside the silicon carbide substrate, the silicon carbide was sectioned and colored according to the strain degree. As shown in Figure 5, von Mises shear strain distributions in different directions were observed when the indentation surface was 6H-SiC (0001) crystal plane at different indentation depths. In Figure 5a–c are the sections perpendicular to the X-axis at the indentation depth of 3 nm, 6 nm and 9 nm, respectively. In Figure 5d–f are the sections perpendicular to the Y-axis at the indentation depth of 3 nm, 6 nm and 9 nm, respectively. In Figure 5g–i are the slices perpendicular to the z-axis silicon carbide substrate height of 12 nm when the indentation depth is 3 nm, 6 nm and 9 nm, respectively. When sliced perpendicular to the X axis, the silicon carbide atomic bonds show a zigzag vertical arrangement. In the indentation process, the shear strain mainly concentrated below the indentation defect and formed a serrated shear strain on both sides of the defect, and the shear stress on the left was less than that on the right. The serrated shear deformation increases with increasing depth of indentation. During the indentation process, the atoms slip and gradually stratify, and the shear strain concentrated under the indentation defect releases the shear strain outward when a new layer of dislocated atoms is formed. However, hindered by the arrangement and combination structure of atoms, atoms cannot slip outwards indefinitely, and the release of shear strain is hindered. When sliced perpendicular to the Y axis, the atomic bond is hexagonal and rectangular. The distribution of shear deformation is similar to that of the slice perpendicular to the X-axis, and the shear deformation is mainly concentrated below the indentation defect. The number of shear strains on both sides is roughly the same and more obvious. Shear should be easily released along the atomic bond structure and weaken more slowly. During the indentation process, the shear strain distribution of sic substrate height of 12 nm is constantly changing. When the indentation depth is 3 nm, as shown in Figure 5g, the bottom of the diamond indenter does not reach 12 nm. The shear strain did not distribute like a circle but concentrated in three directions with an angle of 120 degrees in two directions. When the indentation depth is 6 nm, as shown in Figure 5h, the shape of the region with a strong shear strain shows a rough triangle, and multiple shear strain closed loops are formed on the triangle. When the indentation depth is 9 nm, as shown in Figure 5i, the closed-loop shear strain changes. As atoms slip, the dislocation rings continue to decompose and fuse to form new ones, but they all change around the central position. When the indentation surface is crystal plane, the shear strain is concentrated mainly below the indentation defect, which is difficult to release in the negative direction of the Z axis, and only a small part is released around it.

As shown in Figure 6, von Mises shear strain distributions in different directions were observed when the indentation surface was 6H-SiC (1$\overline{1}$00) crystal plane at different indentation depths. In Figure 6a–c are the sections perpendicular to the X-axis at the indentation depth of 3 nm, 6 nm and 9 nm, respectively. In Figure 6d–f are the sections perpendicular to the Y-axis at the indentation depth of 3 nm, 6 nm and 9 nm, respectively. In Figure 6g–i are the slices perpendicular to the z-axis silicon carbide substrate height of 7.5 nm when the indentation depth is 3 nm, 6 nm and 9 nm, respectively. When sliced perpendicular to the X-axis, the silicon carbide atomic bonds show a zigzag transverse alignment. In the nanoindentation process, the shear strain is effectively concentrated below the indentation defect and does not release in the Y-axis direction. When sliced perpendicular to the Y-axis, the atomic bonds combine to form a hexagonal cross-section with an angle of the hexagon at the top. When the tip is subjected to pressure, it is easy to decompose into two pressures perpendicular to its adjacent sides. When the indentation depth is 3 nm, as shown in Figure 6d, two shear strain chains are released below and on both sides of the indentation defect, one extending to the lower left, and the other extending to the lower right. Shear strain chains on the same side form a strong shear strain closed loop with a similar shape to a square, as shown in Figure 6g. When the indentation depth is 6 nm, as shown in Figure 6e, two new shear strain chains are formed under the indentation defect, and the length of the shear strain chain formed first increases. Four square closed loops are formed on the slice perpendicular to the Z-axis, as shown in Figure 6h. When the indentation depth is 9 nm, as shown in Figure 6f, as the shear strain chain in the middle is about to touch the constant temperature layer at the bottom, the strong shear strain region concentrated below the defect is released to both sides, including the shear strain chain at the bottom. As shown in Figure 6i, the center is an expanded region of strong shear strain. When the indentation surface is (1$\overline{1}$00) crystal plane, the shear strain is concentrated mainly below the indentation defect, and the shear strain is mainly released diagonally to both sides of the X-axis, but difficult to release to both sides of the Y-axis. As the atom slips along the X-axis, it forms a square dislocation ring.

As shown in Figure 7, von Mises shear strain distributions in different directions were observed when the indentation surface was 6H-SiC (2$\overline{1}\overline{1}$0) crystal plane at different indentation depths. In Figure 7a–c are the sections perpendicular to the X-axis at the indentation depth of 3 nm, 6 nm and 9 nm, respectively. In Figure 7d–f are the sections perpendicular to the Y-axis at the indentation depth of 3 nm, 6 nm and 9 nm, respectively. In Figure 7g–i are the slices perpendicular to the z-axis silicon carbide substrate height of 23 nm when the indentation depth is 3 nm, 6 nm, and 9 nm, respectively. When sliced perpendicular to the X-axis, the atomic bonds combine to form a hexagonal cross section with one edge of the hexagon as the top. When the atoms on the top of the hexagon are stressed, the stress is transmitted to the atoms on the bottom. When the indentation depth is 3 nm, as shown in Figure 7a, two long strong shear strain chains are generated below the indentation defect. As the atoms continue to slip, the shear stress chain continues to extend downward. The shear strain is mainly concentrated around and at the bottom of the indentation defect. When the side is stressed, the tip is decomposed into two stresses through atomic bonds, as shown in Figure 7c. When sliced perpendicular to the Y-axis, the atomic bond is hexagonal and rectangular. The area of strong shear deformation is mainly under the indentation defect and less around the defect. With increasing indentation depth, the two shear stress chains under the indentation defect also grow. The two shear strains perpendicular to the X-axis slice, and the shear strains perpendicular to the Y-axis slice together form a square shear strain closed-loop, as shown in Figure 7g. The strong shear strain region decreases with the depth of the indenter head, and the shear strain inside the square closed-loop gradually increases and releases in the Y-axis direction after reaching saturation inside, as shown in Figure 7h,i. When the indentation surface is (2$\overline{1}\overline{1}$0), the shear strain is mainly concentrated below the indentation defect, which is released mainly in the negative direction of the Z-axis and generates a square dislocation ring in the negative direction of the Z-axis.

3.3. Influence of Different Crystal Planes on Plastic Deformation of Nanoindentation

Dislocations and dislocation curves are shown in Figure 8 when the indentation depth is larger at different 6H-SiC nanoindentation plastic deformation stages. In Figure 8a–c are the atomic dislocations of 6H-SiC with (0001), (1$\overline{1}$00) and (2$\overline{1}\overline{1}$0) indentation surfaces at the plastic deformation stage, respectively. In Figure 8d–f, respectively, (0001), (1$\overline{1}$00) and (2$\overline{1}\overline{1}$0) crystal 6H-SiC are in the plastic deformation phase of dislocation from the curve. In Figure 8g–i are the top views of dislocation curves of (0001), (1$\overline{1}$00) and (2$\overline{1}\overline{1}$0) crystal plane 6H-SiC at the stage of plastic deformation, respectively. When the indentation surface is (0001) crystal plane, a large number of horizontal dislocations are formed around the indentation defect in the center. From its dislocation curve, the location and shape of the fault can be more clearly observed. There is a small difference between the dislocation depth and the indentation depth at the bottom, and the downward slip distance of atoms is small. When the indentation surface is (1$\overline{1}$00) crystal plane, the atomic slip will continue to produce a square dislocation ring moving diagonally downward toward both ends of the X-axis. The dislocation depth at the bottom is deeper than the indentation depth, and the indentation has a greater impact on the vertical plane parallel to the X-axis where the defect is located but has less impact on other parts. When the indentation surface is (2$\overline{1}\overline{1}$0) crystal plane, square dislocation rings moving towards the Y-axis will be formed continuously during the plastic deformation stage. The depth of the bottom dislocation is much deeper than the depth of the indentation, which has a great influence on the vertical axis where the defect is located. Different indentation surfaces have different dislocation results, and the rules of dislocation formation are also different.

Coordination number analysis was used to analyze dislocation structures in 6H-SiC substrates with different crystal faces and different indentation depths. RDF analysis of C-Si bonds in substrates is shown in Figure 9. In the three different crystal planes, the values of g(r) are the largest and have multiple peaks when the indentation depth is 1 nm. When the indentation depth is 3 nm, the curves of the three crystal planes at the truncation radius r > 2 Å tend to be horizontal, and the number and value of g(r) peaks decrease, indicating that the partial structure of the dislocation has changed. RDF analysis of different crystal faces without nanoindentation is shown in Figure 9d. As shown in Figure 9d, the g(r) curves of three different crystal faces coincide, and the internal crystal structures of 6H-SiC with different crystal faces are basically the same. The g(r) curve after the indentation is quite different from that before the indentation; there are more peaks before the indentation, and the curve after the indentation is gentler. In the nanoindentation process, the crystalline structure of the C-Si bond on the 6H-SiC substrate is destroyed by the diamond indenters, and amorphous silicon carbide is formed.

Figure 10 is the broken line diagram of the number of 6H-SiC nanoindentation dislocations in different crystal planes at different indentation depths. When the indentation surface is (0001) crystal plane, the number of dislocations increases greatly from the indentation depth of 2.5 nm, and the number of full dislocation b = 1/3 <1$\overline{2}$10> increases the fastest, while the number of incomplete dislocations b = 1/3 <1$\overline{1}$00> increases slowly. The main dislocations in the plastic deformation stage are total dislocations. When the indentation surface is (1$\overline{1}$00), the total dislocation begins to grow at the beginning of the indentation, but the growth is slow. When the indentation depth is deep, the number of total dislocations increases unstably and decreases, while the number of incomplete dislocations increases slightly. When the indentation surface is (2$\overline{1}\overline{1}$0) crystal plane, the number of dislocations increases slightly from the indentation depth of 1.5 nm, and incomplete dislocations begin to appear at an indentation depth of 3.5 nm. In the nanoindentation process, full dislocation appears at the initial stage of the indentation and increases with increasing indentation depth, while the incomplete dislocation occurs mainly with the severe plastic deformation of sic and begins to form when the indentation depth is large.

4. Conclusions

(1)

Through the simulation of 6H-SiC nanoindentation based on molecular dynamics, the effect of indentation depth on atomic slip and dislocation deformation at 900 K at different indentation surfaces is analyzed. In the nanoindentation process, when the indentation surface is in the crystal plane, the dislocation occurs closely around the indentation defect, no independent dislocation ring will be generated and the dislocation ring is deep. When the indentation surface is (1$\overline{1}$00) crystal plane, two square dislocation rings will be generated that move in different directions, and the indentation depth of the dislocation ring is smaller than that of the crystal plane. When the indentation surface is (2$\overline{1}\overline{1}$0), a square dislocation ring will be generated, and the indentation depth of the dislocation ring is the smallest.

(2)

In the nanoindentation process, different indentation surfaces will eventually lead to different shear strains in the crystal when the atoms slip. When the indentation surface is crystal plane, and when the crystal surface is subjected to the pressure of the diamond indentation, shear strain is gathered at the bottom of the indentation defect but is released from the side of the defect, making it difficult to machine it in the actual indentation process. When the indentation surface is (1$\overline{1}$00) crystal plane, the shear strain is effectively concentrated at the bottom of the defect in the section perpendicular to the X-axis and is not released in the section perpendicular to the Y-axis, which makes the substrate easier to process than when the indentation surface is (0001) crystal plane. When the indentation surface is (2$\overline{1}\overline{1}$0) crystal plane, the shear stress on each cutting plane will be released vertically downward. When the indentation surface is (2$\overline{1}\overline{1}$0) crystal plane, it is the easiest to process.

(3)

When the nanoindentation depth is deep, the formation of dislocation has a certain regularity with the deepening of the indentation depth. When the indentation surface is (0001), the dislocation expands to a new layer every time it reaches saturation. When the indentation surface is (1$\overline{1}$00) plane and (2$\overline{1}\overline{1}$0) plane, dislocation rings moving in the same direction will be generated continuously.