# Mechanical Behavior Investigation of 4H-SiC Single Crystal at the Micro–Nano Scale

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Procedure and Methods

#### 2.1. Materials and Preprocess

#### 2.2. Experimental Design

#### 2.3. Determination of Hardness and Modulus

_{f}refers to the depth of residual indentation after complete unloading, and S is the contact stiffness, which can be figured out by calculating the slope below a fifth from the top of the unloading curve (S = dF/dh).

_{max}is the peak indentation load, A

_{p}is projected contact area of the indenter and specimen, E

_{r}is the reduced elastic modulus, ν

_{s}is the Poisson’s ratio of the specimen, ν

_{i}is the Poisson’s ratio of the indenter, E

_{s}is the elasticity modulus of the specimen, and E

_{i}is the elasticity modulus of the indenter.

_{r}, is determined from the contact stiffness, S, and the projected contact area, A

_{p}, as follows:

_{p}, is calculated from:

_{1}through C

_{8}are constants accounting for tip rounding and other departures from the ideal shape.

_{c}, is calculated from:

_{max}is the peak indentation depth, and ε is a geometric constant (for the Berkovich indenter, ε = 0.75).

#### 2.4. Determination of the Critical Indentation Depth for the Plastic–Brittle Transition

_{m}is the uniform pressure. The critical condition of brittle materials for plastic–brittle transition during the nanoindentation process is:

## 3. Results Analysis and Discussion

#### 3.1. Elastic and Plastic Deformation of Nanoindentation

_{r}is determined in Section 3.3. The load versus indentation depth curves follow the Hertz contact theory in elastic deformation of 4H-SiC single crystal. Figure 5b shows that the unloading curve and loading curve are separated, and the residual indentation depth after removal of the force is 2.1 nm. It is demonstrated that irreversible plastic deformation happened on the sample surface. The loading curve follows the Hertz contact theory when the depth is less than 10 nm, but with the increase of depth, the loading curve no longer follows this theory. For one thing, the contact surface between the Berkovich indenter and sample become more complicated, and for another, the plastic deformation begins to play a major role. Furthermore, the smooth loading curves reveal good elastic and plastic deformations. Although the research by Han et al. [36] indicated that the load versus indentation strain curve over single crystal silicon would have pop-in point at the stage of plastic deformation, the load curves shown in Figure 5 have no obvious pop-in point. The reason is that the strain rate of the specimen above the reference is high, and the dislocation glide velocity is fast, but in contrast, these tests are quasi-static tests.

#### 3.2. Critical Indentation Depth for the Plastic–Brittle Transition

^{2}[38], the interplanar spacing of a is 0.3079 nm, the correlation coefficient a of material property based on fitting of the loading-displacement curve is 3.79 × 10

^{8}N/m

^{1.5}(average result of four curves), for which R-square is 0.9998, and the correlation coefficient n of the Berkovich indenter shape is 1.5. On this basis, the theoretical value of the critical indentation depth of 4H-SiC single crystal for the plastic–brittle transition is 20.8 to 64 nm, and the critical load is 1.1 to 6.1 mN. The test result is within the range of theoretical values, proving the feasibility of this method.

#### 3.3. The Influence of Cracks on the Modulus and Hardness

_{p}, and the reduced modulus and hardness decrease with the increase of the projected contact area. In order to obtain more accurate mechanical property values in nanoindentation tests for brittle materials like SiC, an appropriate load for avoiding surface cracks should be adopted.

## 4. Conclusions

- The stages of brittle material deformation (elastic, plastic, and brittle) can be characterized by the load versus indentation depth curves through the nanoindentation test. The curve of the elastic deformation stage follows the Hertz contact theory, and the plastic deformation occurs in nanoindentation at an indentation depth of up to 10 nm.
- The crackling mechanism of 4H-SiC single crystal is discussed and the theoretical models of critical indentation depth and critical force for the plastic–brittle transition are proposed using cleavage strength theory and contact theory. The test results were obtained through the occurrence of the pop-in point, and the theoretical results show good agreement with the test results.
- Both the values of elastic modulus and hardness decrease as the crack length increases, because the crack extension increases the projected contact area A
_{p}. In order to obtain more accurate mechanical property values in nanoindentation tests for brittle materials like SiC, an appropriate load for avoiding surface cracks should be adopted.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Microfracture model for brittle materials: (

**a**) Initial loading; (

**b**) Critical zone formation; (

**c**) Stable crack growth; (

**d**) Initial unloading; (

**e**) Residual-stress cracking; (

**f**) Complete unloading.

**Figure 5.**They are load versus indentation depth curves for elastic deformation and plastic deformation of indentations: (

**a**) the elastic deformation (maximum load of 0.4 mN) and (

**b**) the plastic deformation (maximum load of 1 mN).

**Figure 6.**The load versus indentation depth curves for brittle deformation of indentations: (

**a**) the maximum load of 6 mN, (

**b**) the maximum load of 7 mN, (

**c**) the maximum load of 8 mN, and (

**d**) the maximum load of 9 mN.

**Figure 7.**Load versus indentation depth curves with a maximum load range from 100–1000 mN for 4H-SiC single crystal samples (the small chart shows the crack length-load curve and the measuring method of the crack length is shown in the lower right corner).

**Figure 8.**Scanning electron microscopy (SEM) images of indentations at a peak load of 100 mN, 200 mN, 300 mN, 400 mN, 500 mN, 600 mN, 700 mN, 800 mN, 900 mN, and 1000 mN on the 4H-SiC single crystal sample surface.

**Figure 9.**Mechanical properties as a function of crack length: (

**a**) elastic modulus as a function of crack length and (

**b**) hardness as a function of crack length.

Max Load (mN) | Indentation Depth (nm) | First Pop-in Depth (nm) | First Pop-in Load (mN) |
---|---|---|---|

6 | 62 | 50.3 | 4.56 |

7 | 72 | 53.4 | 4.72 |

8 | 77 | 50.6 | 4.75 |

9 | 82 | 52.6 | 5.16 |

Average | - | 51.7 | 4.80 |

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**MDPI and ACS Style**

Chai, P.; Li, S.; Li, Y.; Liang, L.; Yin, X.
Mechanical Behavior Investigation of 4H-SiC Single Crystal at the Micro–Nano Scale. *Micromachines* **2020**, *11*, 102.
https://doi.org/10.3390/mi11010102

**AMA Style**

Chai P, Li S, Li Y, Liang L, Yin X.
Mechanical Behavior Investigation of 4H-SiC Single Crystal at the Micro–Nano Scale. *Micromachines*. 2020; 11(1):102.
https://doi.org/10.3390/mi11010102

**Chicago/Turabian Style**

Chai, Peng, Shujuan Li, Yan Li, Lie Liang, and Xincheng Yin.
2020. "Mechanical Behavior Investigation of 4H-SiC Single Crystal at the Micro–Nano Scale" *Micromachines* 11, no. 1: 102.
https://doi.org/10.3390/mi11010102