**3. Experimental Setup**

A commercial wafer of 4H-SiC single crystal, grown using the physical vapor transport method, was supplied by Shanghai Institute of Optics and Mechanics Chinese Academy of Sciences. The 4H-SiC wafer was cut to the size of 10 mm × 10 mm by a laser cutting machine and its thickness was 0.5 mm. It was measured using a scanning electron microscope (SEM), and the surface roughness was found to be less than 1 nm after a polishing treatment. All experiments conducted in this paper were conducted on the (0001) plane. A diamond Berkovich indenter with an angle between the edge plane and the centerline of 65.27◦ was used in this study, and a standard fused quartz sample was employed to indirectly measure the nose radius of the indenter.

A laser cutting machine (HGLaser LCC0130-CO2, HGTECH, Wuhan, China) was used to prepare the sample used in this study. A nanomechanical test instrument (TI 950 Triboindenter, Hysitron, Minneapolis, MN, USA), with load sensitivity less than 30 nN and displacement sensitivity less than 0.2 nm, was used to scratch the sample surface and record the information of the scratching depth, tangential force, normal force, and time and to obtain in situ scanning probe microscopy (SPM) images. The instrument is shown in Figure 3. Scanning electron micrographs of the scratch were generated using a foucused ion beam-scanning electron microscope (FIB-SEM) system (Helios NanoLab 600i, FEI, Hillsboro, OR, USA).

**Figure 3.** Core components of the TI 950 Triboindenter.

The experiments consisted of two parts, namely, the indentation and scratch experiments. In order to determine the nose radius of the indenter, nine indents were made at maximum load capacity from 20 to 180 mN at a constant interval on the standard fused quartz sample surface, and a constant loading rate was used in the process of the experiment. All experiments were performed with a 10 s holding time at room temperature.

The scratch process on the commercial wafer of the 4H-SiC single crystal included three stages: (1) the pre-scan stage, (2) the scratching stage, and (3) the post-scan stage. In the first stage, the sample surface morphology information, such as surface roughness and sample inclination angle, were obtained when the indenter was scanned on the sample surface with a constant load of 0.1 mN. In the scratching stage, the indenter load was increased linearly from 0 to 80 mN while the sample table moved at a constant rate, and the length of the scratch on the sample surface was 250 μm. In the final stage, the indenter scanned backwards with a constant load of 0.1 mN to obtain the scratched surface morphology information. The scratch test parameters are shown in Table 1. The scratched surface topography imaging was delivered by dual piezo scanners in the in situ SPM imaging system.

A FIB-SEM system was used to measure and evaluate the deformation characteristics of scratches and cracks on the samples immediately after the nanoscratching tests.


**Table 1.** Scratch test parameters.

#### **4. Results, Analysis, and Discussion**

#### *4.1. Determination of the Indenter Nose Radius*

An indirect method to compare the theoretical projected area, which is a function of *R* and *d*, with the area function acquired through nanoindentation on the standard fused quartz sample was used to determine the numerical value of *R*. The hardness, *H*, can be expressed as [33]

$$H = \frac{F\_{\text{max}}}{A\_{\text{P}}} \tag{20}$$

where *F*max is the maximum load. For standard fused quartz, the hardness is 9.5 GPa. For the Berkovich indenter used in this study, α = 77.3◦, β = 57.64◦, θ = 65.27◦, and γ = 60◦. Table 2 shows the indenter height and projected area for a variety of maximum loads. Using least squares, the projected area was related to the indenter height by *Ap* = 25.58 × (123.8 + *d*) 2, as shown in Figure 4. The indenter nose radius was calculated as *R* = 4952 nm via Equation (8).

**Table 2.** Indenter height and contact area for di fferent loads.


**Figure 4.** Relationship between the projected area and indenter height.

## *4.2. Analytic Surface Morphology*

The surface morphology of the scratch is shown in Figure 5. It was observed in the enlarged image that material is removed but no cracks are formed in the surface at Position 1. There are cracks at the bottom of the scratch at Positions 2 to 4; these are perpendicular to the scratch motion and are the result of median crack closure and lateral crack growth due to the residual stress caused by the indenter. The size of the cracks was amplified with increasing scratching depth. Subsurface cracks were revealed with the scanning electron microscope. Therefore, the results show that the ductile–brittle transition of 4H-SiC is located before Position 2, as shown in Figure 5, and the corresponding scratch length ranges from 0 to 80 μm, with the scratching depth ranging from 0 to 120 nm.

**Figure 5.** Full view and enlarged image of a scratch using SEM.

#### *4.3. Comparison of the Critical Depth of Cut between Simulation and Experiments*

The experimental data were obtained using a two-dimensional three-plate capacitive sensor and a TI 950 piezoelectric ceramic. The experimental results are shown in Figure 6; Figure 7. Figure 6 shows the tangential force as a function of the lateral displacement. Figure 7 shows the scratching depth as a function of the lateral displacement.

According to the theory mentioned in Section 2.2, the whole scratch can be divided into three stages: I, standing for the elasticity leading stage; II, standing for the ductile leading stage; and III, standing for the brittleness leading stage, as shown in Figure 7. The minimum scratching depth is 40 nm and the elastic recovery depth/scratching depth ratio is 0.77 through an analysis of the scratching depth versus lateral displacement curve. In the elasticity leading stage, i.e., where the scratching depth is less than 40 nm, the experimental data were plugged into Equation (9), and we received a frictional and adhesive coefficient of μ = 0.31; this is much larger than the frictional coefficient, which is equal to 0.05 [34].

**Figure 6.** Tangential force as a function of lateral displacement.

**Figure 7.** Scratching depth as a function of lateral displacement.

In the ductile leading stage, i.e., where *d* ≥ 40 nm, the average contact pressure was computed via Equations (13) and (18) and is shown in Figure 8. The cleavage strength of silicon carbide is 26.7 Gpa [35]. The critical average contact pressure is 17.8 Gpa via Equation (19). According to the relationship between the average contact pressure and the scratching depth, the critical depth of cut of 4H-SiC was determined to be 92 nm. Extension of the crack can cause a drastic change in tangential force and the appearance of a pop-in phenomenon. The first pop-in point of the relation curve between tangential force and lateral displacement appears where the scratching depth is about 90 nm, and it is very close to the theoretical calculation results. The in situ SPM images where the lateral displacement ranged from 50 to 60 μm, including the critical depth of cut, indicate that the residual depth, when located in the critical depth of cut, is 20.8 nm, as shown in Figure 9. The two aforementioned scratch tests were repeated in order to exclude the contingency of a single-pass test. The same process was used to handle the test data, and the results are shown in Table 3. This result shows good agreemen<sup>t</sup> with other references, as shown in Table 4.

**Figure 8.** Average contact pressure as a function of scratching depth.

**Figure 9.** In situ SPM images.

**Table 3.** Repeated test results.


The sources of error in this study are as follows: (1) The frictional and adhesive coefficient between the indenter and sample surface is not a constant in the process of scratching when loaded linearly [41], but it was simplified to a constant in this study. (2) The wear of the indenter was ignored. (3) The

impact of defects in the crystal, such as microtubules, dislocations, and stacking faults, was also ignored. (4) Although the roughness of the sample surface was less than 1 nm, it still has a considerable influence in nanoscale experiments.


**Table 4.** Indenter height and contact area for different loads.

## **5. Summary and Conclusions**

A theoretical model of the critical depth of cut of nanoscratching on a 4H-SiC single crystal with a Berkovich indenter was proposed, and a scratch test in a nanomechanical test system was conducted. The following conclusions can be drawn from this study:

(1) Based on an analysis of the nanoindentation and typical scratch model, a new model of the critical depth of cut of nanoscratching on a 4H-SiC single crystal with a Berkovich indenter was established.

(2) The radius of the Berkovich indenter nose was indirectly confirmed by a nanoindentation experiment, and the range of cracks on the scratched surface was verified by SEM images.

(3) The change in the sample surface in the scratching process was revealed through the average contact pressure. The theoretical result of the critical depth of cut at the ductile–brittle transition for a 4H-SiC single crystal was obtained; it is close to the first obvious pop-in point of the relation curve between tangential force and lateral displacement, and this result shows good agreemen<sup>t</sup> with other references.

**Author Contributions:** Conceptualization, P.C. and S.L.; Data curation, P.C. and S.L.; Funding acquisition, S.L. and Y.L.; Investigation, P.C. and S.L.; Methodology, S.L.; Project administration, Y.L.; Writing—original draft, P.C.; Writing—review and editing, S.L. and Y.L.

**Funding:** This work is supported by the National Natural Science Foundation of China (Nos. 51575442) and Shaanxi Provincial Natural Science Foundation (2016JZ011).

**Acknowledgments:** The authors are grateful to the National Natural Science Foundation of China and Shaanxi Provincial Natural Science Foundation which enabled the research on the rails.

**Conflicts of Interest:** The authors declare no conflict of interest.
