Basal plane dislocations (BPDs) are a key factor influencing the advancement of the 4H-SiC semiconductor. In this paper, the effects of shear forces on the nucleation and movement of BPDs are revealed by employing molecular dynamics simulations. The stress–strain curves of 4H-SiC subjected to different shear forces at different temperatures are obtained. It is found that the decrease in mechanical properties of 4H-SiC is mainly due to the occurrence of dislocation. This study also delves into the complexities of dislocation entanglement and slip, unraveling the impact on the mechanical properties of 4H-SiC. Moreover, the causes of dislocation within the crystal lattice were clarified from a microscopic atomic vantage point, shedding light on the intricate mechanisms involving chemical bond rupture and regeneration. These findings not only enrich our understanding of BPDs nucleation but also provide invaluable insights for mitigating BPDs in 4H-SiC.

Taking advantage of high breakdown electric field strength, high carrier mobility, and high thermal conductivity, 4H-SiC has been widely used in the manufacturing of semiconductor devices in recent years.1–4 However, the use of 4H-SiC in high-temperature, high-power, and high-frequency fields is often limited by the hindrance of high-density extended defects within the single crystal.5–7 BPDs are the most common and significant form of defects in 4H-SiC, exerting a crucial influence on the lifespan of devices. The presence of BPDs can affect the performance of devices, mainly because it can be converted into Shockley stacking faults by electron–hole plasma, leading to unpredictable forward voltage drift during device operation. So, understanding the nucleation and slip of BPDs within the crystal is imperative.

Nowadays, a series of studies have shown that BPDs are often produced during production and processing.8–14 The formation mechanism of BPDs has been extensively studied.15 Thermal stress is the main cause of BPDs during the growth process. At a given annealing temperature, dislocation occurs when the temperature gradient exceeds a critical value. Gao and Kakimoto, employing an enhanced three-dimensional Alexander–-Haasen model, initially calculated the thermal stress in the primary slip direction and subsequently incorporated the solved shear stress to determine the distribution of BPDs.16 Besides, BPDs can also be formed during the grinding and polishing process of the 4H-SiC ingot. Akihiro Goryu et al. indicated that mechanical stress was an important factor for the formation of dislocations and proposed a formulation to explain the mechanism.17 Currently, to reduce the effects of BPDs, researchers studied and observed the nucleation and movement behavior of BPDs by experimental and theoretical approaches.18,19 For example, Ohtani et al. proposed that BPDs in 4H-SiC crystals nucleated first in the shoulder region of the ingot and slipped toward the growth front through the newly grown layer by analyzing the growth conditions at different stages of crystal growth.20 More recently, Liu et al. utilized nanoindentation testing and transmission electron microscopy (TEM) to investigate the nucleation of BPDs in 4H-SiC, finding that shear stress was greater than tensile stress, leading to the nucleation of BPDs in undoped 4H-SiC by low-load nanoindentation technology.21 However, the experimental methods have always failed to provide a clear elucidation of the nucleation mechanism of BPDs at the atomic level.

Recently, molecular dynamics (MD) simulation has emerged as a powerful tool for introducing stress and studying the generation and evolution of defects under different conditions.22,23 In this paper, in order to investigate the mechanical properties of 4H-SiC under realistic conditions, MD simulations were employed to examine the shear stress response along various slip systems for 4H-SiC crystals. The stress–strain curves of the 4H-SiC crystal under shear forces at different temperatures are obtained, and the significance of each inflection point on the curves is analyzed in detail. The results indicate that shear stress plays a dominant role in the nucleation of BPDs within 4H-SiC, and the generation of BPDs is the main cause for the degradation of material mechanical performance. These findings contribute to an enhanced understanding of BPD nucleation in 4H-SiC and the impact on improving the mechanical properties of semiconductors.

Figure 1(a) shows the structure of the 4H-SiC unit cell. A simulation box of 4H-SiC is constructed with a size of approximately 190 Å along all three dimensions, containing about 620 000 atoms (see Fig. S1 in the supplementary material). Two types of slip systems are considered for shear, as listed in Figs. 1(b) and Fig. S2 in the supplementary material, respectively. All shear molecular dynamics (MD) simulations are conducted using the Large-scale Atomic Molecular Massively Parallel Simulator (LAMMPS).24 Tersoff potential was chosen to describe the interactions of atoms in 4H-SiC.25 The equations of motion are integrated with a time step of 1 fs. Periodic boundary conditions are applied in all three directions to eliminate surface effects. All systems are relaxed under the isothermal–isobaric ensemble with an isotropic barostat set to 0 Pa and a Nose–Hoover thermostat at the simulated temperatures to equilibrate the system before applying the shear load. The shear load is applied every 1 fs with a shear strain rate of 1010 s−1 using the canonical ensemble with a Nose–Hoover thermostat at different temperatures until structural failure occurred. The effects of different strain rates are shown in Fig. S3 in the supplementary material. The strain rate used in molecular dynamics simulations is usually relatively high.26 Taking the simulated temperature of 2273 K as an example, when the strain rate decreases, the nucleation point of BPD (Point A) will advance, and the maximum stress value that the material can withstand will also decrease, but the change trend of the stress–strain curve is basically the same. Visualization and some post-processing procedures are performed using the OVITO package.26,27 Additionally, burger vectors and dislocation lines are identified using the Dislocation Extraction Algorithm (DXA).

FIG. 1.

Structure of 4H-SiC and shear stress response. (a) The structure of a 4H-SiC unit cell with a hexagonal system (red represents silicon atoms, blue represents carbon atoms). (b) The shear stress–strain curve of five different temperature systems. (c) The critical value of dislocation occurrence at different temperatures. The critical value: the stress value corresponding to the frame following the highest point of the stress–strain curve. The shear stress–strain curve of the [1 −2 1 0] lip system is partitioned into five stages: O–P: elastic stage; P–A: plastic stage. A–B: stress dropping stage; B–C: structural strengthening stage; C–D: structural failure stage.

FIG. 1.

Structure of 4H-SiC and shear stress response. (a) The structure of a 4H-SiC unit cell with a hexagonal system (red represents silicon atoms, blue represents carbon atoms). (b) The shear stress–strain curve of five different temperature systems. (c) The critical value of dislocation occurrence at different temperatures. The critical value: the stress value corresponding to the frame following the highest point of the stress–strain curve. The shear stress–strain curve of the [1 −2 1 0] lip system is partitioned into five stages: O–P: elastic stage; P–A: plastic stage. A–B: stress dropping stage; B–C: structural strengthening stage; C–D: structural failure stage.

Close modal

Researchers have found that no matter the thermal stress or the mechanical stress, the force acting on the crystal is mainly manifested as the shear action, so it is very critical and important to simulate the deformation of the crystal under the shear action when using molecular dynamics simulation to study the nucleation of BPD.2 So, first, the mechanical properties of flawless single crystal 4H-SiC are investigated by calculating the shear response along two plausible slip systems. Before simulation, the hexagonal crystal system of 4H-SiC is transformed into an orthogonal structure to satisfy the simulation system of LAMMPS, as depicted from Fig. S1(a) to S1(b) in the supplementary material. In order to investigate the anisotropy of crystal properties, the stress–strain behavior under different shear directions is compared. Fig. 1(b) and Fig. S2 in the supplementary material displayed the stress–strain curves for shear directions of [1 −2 1 0] and [1 0 −1 0], respectively. Through comparison, similar patterns of changes in the curves are shown in these two shear directions. Furthermore, taking the [1 −2 1 0] direction as an example, a detailed analysis of the mechanical properties of 4H-SiC is conducted. The internal stress within the crystal initially increases as the strain values on the x-axis ranged from 0 to the first extreme value, then rapidly decreases. This is followed by a subsequent rise and gradual decline until the end. Additionally, Fig. 1(b) illustrates the influence of temperature on the mechanical properties of 4H-SiC. It can be observed from the graph that the stress–strain curves of the crystal at different temperatures exhibit a similar pattern of variation. As the temperature increases, the maximum stress gradually decreases, and the corresponding strain value also decreases progressively. This is mainly attributed to molecular thermal motion.28 With increasing temperature, thermal motion intensified between silicon atoms and carbon atoms, leading to a weakening of intermolecular forces and consequently a gradual decrease in the maximum stress.29 The stress–strain pattern is categorized into four stages: O corresponds to the origin of the curve, while P, A, B, and C represent the extreme values during the curve evolution. Four distinct stages are defined: OP as the elastic stage, PA as the plastic stage, AB as the stage of sudden stress drop, BC as the stage of structural reinforcement, and CD as the stage of gradual structural damage. Figure 1(c) shows the extreme points of dislocation appearance at different temperatures (one frame after point A). It can be seen from the graph that it is more difficult for dislocation to form at low temperatures, while it is easier to form at high temperatures. In addition, it can also be seen from the figure that with the increase in temperature, small strain and stress values will lead to the generation of dislocations. In the following analysis, the characteristics displays in each stage are examined sequentially. To provide a more realistic perspective, the example of a temperature close to the growth temperature, especially 2273 K, is chosen for a detailed elucidation. In addition, the growth temperature of 2473 K for crystal growth is also shown in Fig. S4 in the supplementary material.

The first stage to consider is the OP stage when the crystal structure initially goes deformation. From the curve, it is apparent that the OP stage exhibits a nearly linear trend of change. Based on the principles governing the mechanical performance in the crystal structure, it is understood that the OP stage belongs to the elastic stage and the change pattern follows Hooke's law.30 In the elastic stage, when external forces act upon the internal structure of the 4H-SiC, the interior atoms deviate from their equilibrium positions. Since the applied forces do not exceed the interatomic bonding force, a temporary equilibrium is established. Upon removal of the external forces, the 4H-SiC atoms are promptly restored to the original equilibrium positions under the influence of the interatomic bonding force.31 From Fig. 1(b), it can be seen that the maximum stress that 4H-SiC can reach at 2200 °C is 37.5 GPa. This value is slightly higher than the value reported in the literature (34.7 GPa) using nanoindentation testing, primarily due to the fact that the established supercell structure represents a perfect crystal with no internal defects.21,32

With the increase in stress, the linear relationship between stress and strain is broken. When the external force exceeds the elastic limit of the material (P point), 4H-SiC begins to undergo plastic deformation. This deformation is permanent, that is, after the external force is eliminated, the material cannot be restored to its original shape. The characteristic of plastic deformation is that the relationship between stress and strain of 4H-SiC is no longer linear, but has obvious nonlinear characteristics. During the transition from elastic deformation to plastic deformation, the properties of 4H-SiC have undergone fundamental changes. In the elastic stage, 4H-SiC exhibits good reversibility, while in the plastic stage, the material exhibits irreversible deformation, which is the result of permanent changes in the internal structure of the material after stress.

Following the PA stage is the AB stage, during which 4H-SiC reaches the maximum stress value at point A, corresponding to a strain value of 0.245 [Fig. 2(a)]. In order to elucidate the abrupt decrease during the AB stage, the subsequent two points behind A point are selected for analysis with corresponding strain values of 0.250 and 0.255, respectively, as shown in Figs. 2(b) and 2(c). The boxed area indicates the location where the earliest structural changes occur within the crystal, with the color of the atoms representing the different strains during the shearing process.

FIG. 2.

Structural deformation during the stress dropping stage at 2273 K. Deformation of the whole structure at different shear strains: (a) 0.245, (b) 0.250, (c) 0.255. [(d), (g), and (j)] The cross sections of the first, second, and third stacks in (a). [(e), (h), and (k)] The cross sections of the first, second, and third stacks in (b). [(f), (i), and (l)] The sections of the first, second, and third stacks in (c). Atoms are color coded by the atomic shear strain.

FIG. 2.

Structural deformation during the stress dropping stage at 2273 K. Deformation of the whole structure at different shear strains: (a) 0.245, (b) 0.250, (c) 0.255. [(d), (g), and (j)] The cross sections of the first, second, and third stacks in (a). [(e), (h), and (k)] The cross sections of the first, second, and third stacks in (b). [(f), (i), and (l)] The sections of the first, second, and third stacks in (c). Atoms are color coded by the atomic shear strain.

Close modal

By comparison, it is evident that the deformation region within the 4H-SiC crystal (i.e., the area where atoms suffered higher strain values) gradually expands as the strain value increases. In order to clearly observe the patterns of internal structural changes occurring within the crystal, three cross sections of the region where deformation occurred first are selected to observe the changes in the structure of 4H-SiC. Figures 2(d)2(f) depict the trend of structural changes in the first cross section. It can be observed that the area of the red deformation region within each layer is gradually increasing, accompanied by the generation of dislocation cores. Figure S5 in the supplementary material is a magnified view, where the atomic structure at the location has undergone a misalignment and the dislocation cores appear. Figure S5(a) in the supplementary material shows the partial region that has not been deformed. Figures S5(b) and S5(c) in the supplementary material reveal the silicon and carbon cores appearing in the shear process of the cell, respectively. The silicon atoms in the local 4H-SiC are shifted in the direction [1 -1 0 0] as a whole. Similarly, the C atom also shows a similar change trend. Li et al. also established the relaxed supercell containing a typical BPD in 4H-SiC and proved that both the Si-core and C-core existed inside the crystal, which is consistent with the results reported in the literature.33 After reaching the second layer, the area of the red transition region gradually expands with the increase in the strain value. More dislocation cores can be observed in Fig. 2(g). When the strain value is 0.25, dislocation cores transform into two dislocation lines as shown in Fig. 2(h). Based on the positions of the dislocation lines located in the (0001) plane, it can be determined that the dislocation type present belongs to BPDs. However, the direction of the dislocation lines is not completely aligned with the [1 1 −2 0] direction. Dudley previously reported that BPD dislocations can be classified into two types: perfect BPD dislocations with Burgers vectors b = 1/3⟨1 1 −2 0⟩ (b = 0.31 nm) and BPD dislocation segment forms due to lattice slip.34 It is evident that the initially observed BPD dislocation during the MD simulations belongs to the latter category. Visual analysis of the dislocations using the OVITO software reveals that the actual Burgers vectors of these two dislocation lines are 1/3[1 1 −2 0] and 1/3[−1 −1 2 0]. Due to the opposite directions of the Burgers vectors, the subsequent frame shows a mutual annihilation between the dislocation lines, leading to the phenomenon of dislocation disappearance. Hirth et al. had previously reported that 1/3[1 1 −2 0] dislocation was evolved from 1/3[2 −1 −1 0] and 1/3[−1 2 −1 0] dislocation cores.35–37 Therefore, it can be supposed that the dislocation core forms in Fig. 2(g) belonged to 1/3[2 −1 −1 0] and 1/3[−1 2 −1 0] cores, which further transform and merge into a BPD core. The BPD core then extends into BPDs. At last, Figs. 2(j)2(l) illustrate the process of the formation of a new round of dislocations in a nearby location. With the expansion of the deformation region, dislocation cores are formed gradually. It leads to a gradual increase in the total number of dislocations. In conclusion, the aforementioned phenomena explain the sharp decrease in the 4H-SiC stress–strain curve under shear force, attributed to the formation of dislocations within the crystal structure, specifically BPDs. The formation of dislocations is a critical factor contributing to the decline in mechanical properties within the crystal.38 

In the following, the strengthening stage BC and the structural damage stage CD are further analyzed. Figure 3 presents a three-dimensional distribution of dislocation in 4H-SiC crystals under different strain conditions. Specifically, Fig. 3(a) represents the point at which dislocations occur, while Fig. 3(b) corresponds to point B where stress reaches its minimum value. Obviously, it is evident that there is a sharp increase in both the quantity and density of dislocations. The predominant dislocations observed, as indicated by the direction of the dislocation lines, belong to BPDs represented by the red lines, while a small portion belongs to threading mixed-type dislocations (TMDs) denoted by the green lines. The Burgers vectors of the TMDs mainly have components in the [0001], albeit relatively small, with the result that the direction of the dislocation lines is also arranged along the densely packed planes of 4H-SiC. The preceding description has already indicated that the sharp decrease after point A is primarily due to the generation of dislocations, and the stress value at point B reaches its minimum corresponding to a peak in both the quantity and density of dislocations. Figures 3(c) and 3(f) present statistical analysis data on dislocation length and density throughout the entire shearing process. Similarly, the stages of rapid increase in dislocation density and quantity are associated with the interval between 0.245 and 0.275, and the dislocation length is 3.38 × 10−7 m while the dislocation density is 4.4 × 1017 m−2. Going back to Fig. 3(d), the stress at point C on the stress–strain curve reaches a new peak. The interval from point B to point C corresponds to the structural strengthening stage observed in 4H-SiC during the shearing process. As the strain value increases from 0.275 to 0.340, the quantity and density of dislocation lines remains relatively constant. However, along with the increasing strain, the stress that acts on the 4H-SiC crystal gradually rises. To understand the underlying reasons for this phenomenon, a detailed analysis of the specific region is conducted and a localized area is selected for observation. As shown in Fig. S6(a) in the supplementary material, it is evident that entanglement occurs between different dislocation lines. Zhao et al. previously reported that the entanglement of dislocation lines can lead to a transient enhancement of the material's mechanical properties.38 In the same way, the main reason for the improvement in mechanical performance of the 4H-SiC crystal in the BC stage is the entanglement of dislocation lines, even though there are no significant changes in the quantity and density of dislocation lines. Furthermore, Fig. 3(e) represents the onset of gradual structural failure. As the strain increases in the CD stage, the stress underwent a slow decline. Figures 3(c) and 3(f) have indicated that there are minimal overall changes in dislocation density and quantity in the later stages. To clearly observe the variations in dislocations, a localized area is chosen for further analysis, like Fig. S6(b) in the supplementary material. From the distributions of dislocation in Fig. S6 in the supplementary material, it is found that a significant slip of local dislocations occurs in the 4H-SiC crystal, progressing interiorly. Lu's research on the evolution of dislocations within metals revealed that dislocation slip was the primary cause of stress reduction. For the semiconductor 4H-SiC, the gradual decrease in stress during the later stage of 4H-SiC structural failure is also attributed to dislocation slip.39 

FIG. 3.

Structural deformation under different strain values at 2273 K. [(a), (b), (d), and (e)] Dislocation distribution in 4H-SiC crystals under different strain conditions. (a) 0.250 (the dislocation first appeared), (b) 0.275 (point B), (d) 0.340 (point C), (e) 0.500 (point D). The red line represents BPDs and the green line represents threading mixed dislocations. (c) and (f) The distribution of dislocation length and dislocation density of 4H-SiC under different deformation conditions. (c) Dislocation length; (f) dislocation density.

FIG. 3.

Structural deformation under different strain values at 2273 K. [(a), (b), (d), and (e)] Dislocation distribution in 4H-SiC crystals under different strain conditions. (a) 0.250 (the dislocation first appeared), (b) 0.275 (point B), (d) 0.340 (point C), (e) 0.500 (point D). The red line represents BPDs and the green line represents threading mixed dislocations. (c) and (f) The distribution of dislocation length and dislocation density of 4H-SiC under different deformation conditions. (c) Dislocation length; (f) dislocation density.

Close modal

For a more in-depth understanding of the underlying reasons for the deformation of the 4H-SiC crystal, a series of explanations regarding the microscopic atomic arrangement is conducted, as shown in Fig. 4. Several frames near the key point A are selected for analysis, continuously magnifying the localized area. It can be observed that the fracture and regeneration of chemical bonds occur within the crystal structure with the increasing strain. In detail, it can be seen that when the strain value increases from 0.245 to 0.250, the covalent bond between the Si2 atom and C2 atom is significantly elongated, resulting in a weakening of the strength between the covalent bonds. As the strain value increases from 0.250 to 0.255, the covalent bonds between the Si-C atoms at number 2 and number 3 are broken due to the shear force. Furthermore, when the strain value reaches 0.26, the Si1 atom reconnects to form a new covalent bond due to its proximity to the atom C3. At the same time, the Si2 atom also combined with the surrounding carbon atom to form a new bond. As the modeling employs a perfect 4H-SiC crystal, the main cause of dislocation generation during the shearing process is formation of new nucleation rather than proliferation, for which the essence primarily involves the fracture and regeneration of chemical bonds. During the sudden decrease in the AB stage, the distance between Si–C bonds would increase, leading to gradual bond fracture. Subsequently, due to atomic misalignment, new chemical bonds would form between closely spaced atoms.36 Lu et al. simulated the shear deformation of InSb semiconductor compounds, which also attributed this deformation twinning to the “catching bond” involving breaking and re-formation of In–Sb bond in InSb. The concept of this paper is consistent with ours, which also proves the reliability of our conclusions.26 Besides, Liu et al. confirmed that the critical value of BPD formation in 4H-SiC was 29.45 GPa through nanoindentation experiments, which was also similar to our simulation results.21 

FIG. 4.

Local atomic configuration during the stress dropping stage at 2273 K. (a)–(d) Atomic structure at strain (a) 0.245, (b) 0.250, (c) 0.255, and (d) 0.260. The red atoms are Si and the blue atoms are C.

FIG. 4.

Local atomic configuration during the stress dropping stage at 2273 K. (a)–(d) Atomic structure at strain (a) 0.245, (b) 0.250, (c) 0.255, and (d) 0.260. The red atoms are Si and the blue atoms are C.

Close modal

The main cause of dislocation in 4H-SiC crystals is the unnecessary shear force caused by thermal stress and mechanical stress. In order to improve crystal quality, it is necessary to take applicable measures to reduce the influence of shear force. For example, before processing single crystals, adopt high-temperature annealing to reduce the impact of stress or optimize the structure of the equipment to reduce the impact of thermal stress during the growth process. In addition, some new methods also need to be further explored, such as irradiation technology, light treatment, and so on.40 

All in all, this discovery elucidates the nucleation mechanism of BPDs in 4H-SiC and visualizes the phenomena of dislocation movement and distribution under shear force. The findings of this study provide essential theoretical guidance to improve experimental processes related to the formation of BPDs. To reduce the formation of BPDs, several direct implications and measures should be highlighted: First, measures should be taken during crystal growth and processing to release excess stress and reduce BPDs, such as reducing thermal stress by lowering the radial temperature gradient on the crystal growth surface or performing high-temperature annealing after growth to eliminate residual stress in the crystal. Additionally, modifying the process parameters during cutting, grinding, and polishing can also reduce the shear stress. Second, this study provides stress–strain curve data at high temperatures, accurately reflecting the mechanical properties of 4H-SiC under high-temperature growth conditions. Combined with finite element thermal field simulation, it can more accurately reflect the nucleation and movement of BPDs in 4H-SiC at high temperatures. Third, the study points out that dislocations are mainly distributed along the close-packed planes. Therefore, considering the use of seed crystals with different off-angles for growing 4H-SiC can be beneficial. These measures are crucial for improving the overall quality and performance of 4H-SiC crystals in various applications.

In summary, we investigate the effect of shear on the nucleation and movement of BPDs in 4H-SiC. The shear stress of 4H-SiC is simulated by MD simulations. It is found that the appearance of BPDs is the main reason for the sudden drop of stress in 4H-SiC, and the entanglement and slip of dislocations will significantly affect the mechanical properties of 4H-SiC materials. Further, the change of dislocation morphology mainly involves the fracture and regeneration of chemical bonds within the crystal. This discovery is helpful for us to understand the mechanism of BPD nucleation and reduce the effect of BPD on crystal structure during production.

See the supplementary material for details on the transformation of the 4H-SiC crystal structure, the shear stress–strain curve along different slip directions, and the phenomenon of dislocation movement. Besides, stress–strain curves at different strain rates at 2273 K were compared. The partial enlarged view of dislocation cores was shown.

This study is mainly supported by the “Pioneer” and “Leading Goose” R&D Program of Zhejiang Province (Grant Nos. 2022C01021 and 2023C01010) and Natural Science Foundation of Zhejiang Province (No. LQ24F040001). Partial support is provided by the Natural Science Foundation of China for Innovative Research Groups (Grant No. 61721005) and the Fundamental Research Funds for the Central Universities (No. 226-2022-00200).

The authors have no conflicts to disclose.

Yanwei Yang: Conceptualization (equal); Data curation (equal); Investigation (equal); Writing – original draft (equal). Keqiang Li: Methodology (equal); Supervision (equal); Writing – review & editing (equal). Zhouyu Tong: Data curation (equal); Formal analysis (equal); Writing – review & editing (equal). Xiaodong Pi: Methodology (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal). Deren Yang: Funding acquisition (equal); Project administration (equal); Supervision (equal). Yuanchao Huang: Conceptualization (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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