Influence of Temperature and Incidence Angle on the Irradiation Cascade Effect of 6H-SiC: Molecular Dynamics Simulations

SiC devices have been typically subjected to extreme environments and complex stresses during operation, such as intense radiation and large diurnal amplitude differences on the lunar surface. Radiation displacement damage may lead to degradation or failure of the performance of semiconductor devices. In this paper, the effects of temperature and incidence angle on the irradiation cascade effect of 6H-SiC were investigated separately using the principles of molecular dynamics. Temperatures were set to 100 K, 150 K, 200 K, 250 K, 300 K, 350 K, 400 K and 450 K. The incidence direction was parallel to the specified crystal plane, with angles of 8°, 15°, 30°, 45°, 60° and 75° to the negative direction of the Z-axis. In this paper, the six types of defects were counted, and the microscopic distribution images and trajectories of each type of defect were extracted. The results show a linear relationship between the peak of the Frenkel pair and temperature. The recombination rate of Frenkel pairs depends on the local temperature and degree of aggregation at the center of the cascade collision. Increasing the angle of incidence first inhibits and then promotes the production of total defects and Frenkel pairs. The lowest number of total defects, Frenkel pairs and antisite defects are produced at a 45° incident angle. At an incidence angle of 75°, larger size hollow clusters and anti-clusters are more likely to appear in the 6H-SiC.


Introduction
SiC material is a typical third-generation semiconductor material.It has been used in space exploration, nuclear reactions and electrical equipment at high altitudes on plateaus.3C-SiC is mainly used in photovoltaic applications [1].4H-SiC materials are mainly used to fabricate high-frequency and high-power devices [2].6H-SiC materials are mainly used for the manufacture of photoconductive detectors [3].Researchers typically use Rutherford Backscattering Spectroscopy (RBS) and Transmission Electron Microscope (TEM) to probe the irradiation damage of SiC materials [4].Wenhui Dong et al. studied different doses of Si, H ion injection experiments using Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy.The results show that the irradiation damage effect of 6H-SiC is highly dependent on the type of irradiated ions, the amount of ion injection and the irradiation sequence [5,6].W. J. Weber investigated defect clusters and amorphization induced by high-dose neutron irradiation in SiC materials [7].The generation and recrystallization behavior of SiC amorphous crystals has been achieved by low-energy He and Fe ion injection [8,9].C. Hemmingsson et al. conducted an investigation into the deep-level defects induced by electron irradiation in 4H-SiC using deep-level transient spectroscopy.They observed multiple electron traps and a single hole trap [10].Concurrently, A. Castaldini et al. identified that among the five defect levels introduced by irradiation, three exhibited similar electrical characteristics [11].Katoh et al. investigated the composite materials of SiC fibers and pyrocarbon under neutron irradiation conditions.They found that the density of defects significantly influences the post-neutron irradiation electrical properties of SiC semiconductors [12].Wang Pengfei et al. found that the type and structure of irradiation-induced defects in 6H-SiC materials affect the extent of neutron irradiation damage.They observed that annealing temperature affects the recombination of defects and lattice recovery, ultimately influencing the resistivity of 6H-SiC materials [13].Other researchers also found that the radiation damage caused by P ion injection partially recovered or even disappeared at different annealing temperatures and annealing times [14].In addition, several researchers have investigated the displacement threshold energies and the laws of defect aggregation in SiC lattice atoms [15,16].
Silicon vacancies in silicon carbide (SiC) have been proposed as attractive candidates for quantum technology applications, such as quantum sensing and quantum repeaters [17].As the use of 6H-SiC becomes more widespread, the complex environment poses new challenges for the application of 6H-SiC materials.Further understanding of the defect formation mechanism in 6H-SiC will help broaden the application fields of 6H-SiC.For example, in SiC device manufacturing technology, proton irradiation can be used to create localized regions of high resistance in a semiconductor [18].Based on the principles of molecular dynamics (MD), this paper simulated the cascade effect of 6H-SiC at different temperatures and incidence directions.The evolution of point defects and clusters in 6H-SiC materials was studied under specific stress conditions.

Methods
In this paper, irradiation experiments on 6H-SiC targets are modelled and simulated using the Large-scale Atomic\Molecular Massive Parallel Simulator (LAMMPS) [19].6H-SiC is a hexagonal crystal.The lattice constants are a = b = 3.08101 Å and c = 15.1248Å.Table 1 shows the atomic coordinates of the unit cell of 6H-SiC [20].Figure 1a,b show the unit cell and the supercell of the model for 6H-SiC, respectively.The supercell is obtained by expanding the unit cell.When low-energy particles irradiate materials, the main mode of energy loss is elastic collisions between atoms.Displacement cascades from cascade collisions are the main form of displacement damage.Figure 2 shows an irradiation model with fully periodic boundary conditions.Periodic boundary conditions ensure the integrity of the forces on the simulated system boundary atoms.The blue area in the model is a 1.5 nm thick constant temperature area.The temperature of the thermostatic area is controlled by the velocity rescaling (temp/rescale) method.The method is used to simulate the dissipation of energy.Collision area, the red area of the model, can be used to simulate the cascade collision effect of 6H-SiC.The Si-PKA is set in the inner part of the collision area, and the place is 2 nm from the thermostatic area on the upper surface.The aim is to avoid displaced atoms from cascade collisions entering the thermostat area.The incident direction of the PKA is parallel to the x-z plane and at an angle of 8 • along the negative direction of the Z-axis.When low-energy particles irradiate materials, the main mode of energy loss collisions between atoms.Displacement cascades from cascade collisions are th form of displacement damage.Figure 2 shows an irradiation model with fully boundary conditions.Periodic boundary conditions ensure the integrity of the fo the simulated system boundary atoms.The blue area in the model is a 1.5 nm th stant temperature area.The temperature of the thermostatic area is controlled by locity rescaling (temp/rescale) method.The method is used to simulate the dissip energy.Collision area, the red area of the model, can be used to simulate the casc lision effect of 6H-SiC.The Si-PKA is set in the inner part of the collision area, place is 2 nm from the thermostatic area on the upper surface.The aim is to av placed atoms from cascade collisions entering the thermostat area.The incident d of the PKA is parallel to the x-z plane and at an angle of 8° along the negative dire the Z-axis.The potential function describes the potential energy of the atoms in a mate function of the positions of the atoms, i.e., it describes the forces between the ato accuracy of the potential function parameters determines the accuracy of the sim results.The potential function used in this paper is the Tersoff/ZBL potential f whose parameters were confirmed in the experiments of Erhart et al. [21,22].Ac to molecular dynamics, the atoms in the system obey the classical mechanics.The of motion of each atom can be derived from the definition of velocity, i.e., the atom system satisfy the set of Equations (1).As shown in Table 2, the simulation syst first relaxed by constant-pressure, constant-temperature ensemble (NPT) for 30 the micro-canonical ensemble (NVE) was used during the irradiation process.shows the experimental design.Experiment 1 parameters are kept constant exce perature.Experiment 2 parameters are kept constant except for the angle of incid is the force on particle i at time . ,  and  are the mass, velocity and nates of particle i, respectively.The potential function describes the potential energy of the atoms in a material as a function of the positions of the atoms, i.e., it describes the forces between the atoms.The accuracy of the potential function parameters determines the accuracy of the simulation results.The potential function used in this paper is the Tersoff/ZBL potential function, whose parameters were confirmed in the experiments of Erhart et al. [21,22].According to molecular dynamics, the atoms in the system obey the classical mechanics.The velocity of motion of each atom can be derived from the definition of velocity, i.e., the atoms in the system satisfy the set of Equations (1).As shown in Table 2, the simulation system was first relaxed by constant-pressure, constant-temperature ensemble (NPT) for 30 ps.And the micro-canonical ensemble (NVE) was used during the irradiation process.Table 3 shows the experimental design.Experiment 1 parameters are kept constant except temperature.Experiment 2 parameters are kept constant except for the angle of incidence.
F i (t) is the force on particle i at time t.m i , ν i and r i are the mass, velocity and coordinates of particle i, respectively.The dimensions of the model are 65a × 38b × 13c.Total atomic number is 770,640. 2 The velocity component of the x-axis is 0.

Validation of the Model
The density, radial distribution function, atomic angular distribution fu coordination number of the model are calculated in this section.In addition, t reliability of the model, the experimental data from other researchers are com following content.
Table 4 shows that the lattice constants after NPT optimization are not s different from the experimental values.Figure 4a shows that the bond lengt 1.8645 Å in the simulated system.Figure 4b shows that the coordination nu 6H-SiC crystal is 12, consistent with the coordination number of the actual hex tal structure.Figure 4c shows angles of 109.5° and 109.2° for C-Si-C and Si-C tively.

Validation of the Model
The density, radial distribution function, atomic angular distribution function and coordination number of the model are calculated in this section.In addition, to verify the reliability of the model, the experimental data from other researchers are compared in the following content.
Table 4 shows that the lattice constants after NPT optimization are not significantly different from the experimental values.Figure 4a shows that the bond length of C-Si is 1.8645 Å in the simulated system.Figure 4b shows that the coordination number of the 6H-SiC crystal is 12, consistent with the coordination number of the actual hexagonal crystal structure.Figure 4c shows angles of 109.5 • and 109.2 • for C-Si-C and Si-C-Si, respectively.Table 5 shows the error statistics information.Compared with the experimental value [20], the density error of the model in this paper is about 3.302%.The error of the Si-C bond length is about −1.3388%.The atomic angle errors of Si-C-Si and C-Si-C are about −0.2439% and 0.0759%, respectively.109.417(C-Si-C) 0.0759 1 The temperature is 300 K. 2 ± indicates that the value in this paper is greater or less than the experimental value.

Effect of Temperature on 6H-SiC Cascade Collisions
In the field of space exploration, extreme environments pose a severe impact on equipment.For example, the temperature on the lunar surface can reach −183 °C or 127 °C.This subsection focuses on the variation in the 6H-SiC irradiation cascade effect at ambient temperatures of 100 K, 150 K, 200 K, 250 K, 300 K, 350 K, 400 K and 450 K.
Figure 5a shows that different temperatures have no effect on the overall trend of defect evolution in 6H-SiC.The peak formation times of the Frenkel pairs are basically the same.The duration of cascade collisions becomes longer with increasing temperature.Figure 5b shows that the fitted curve between the peak of the Frenkel pair and the temperature satisfies a linear relationship, which can be expressed by Equation (2).The reason is that the transition from low to high temperatures enhances the thermal motion of the atoms.The energy of the lattice atoms is more likely to meet the displacement threshold energy.The permanent Frenkel pairs and their recombination rates have no obvious Table 5 shows the error statistics information.Compared with the experimental value [20], the density error of the model in this paper is about 3.302%.The error of the Si-C bond length is about −1.3388%.The atomic angle errors of Si-C-Si and C-Si-C are about −0.2439% and 0.0759%, respectively.109.417(C-Si-C) 0.0759 1 The temperature is 300 K. 2 ± indicates that the value in this paper is greater or less than the experimental value.

Effect of Temperature on 6H-SiC Cascade Collisions
In the field of space exploration, extreme environments pose a severe impact on equipment.For example, the temperature on the lunar surface can reach −183 • C or 127 • C.This subsection focuses on the variation in the 6H-SiC irradiation cascade effect at ambient temperatures of 100 K, 150 K, 200 K, 250 K, 300 K, 350 K, 400 K and 450 K.
Figure 5a shows that different temperatures have no effect on the overall trend of defect evolution in 6H-SiC.The peak formation times of the Frenkel pairs are basically the same.The duration of cascade collisions becomes longer with increasing temperature.Figure 5b shows that the fitted curve between the peak of the Frenkel pair and the temperature satisfies a linear relationship, which can be expressed by Equation (2).The reason is that the transition from low to high temperatures enhances the thermal motion of the atoms.The energy of the lattice atoms is more likely to meet the displacement threshold energy.The permanent Frenkel pairs and their recombination rates have no obvious regularity.The paper further explains this phenomenon through the temperature nephogram.
where N max is the peak of the Frenkel pair, a is the intercept (a = 111.94048± 2.99957).k is the slope (k = 0.00976 ± 0.01007), and T is the temperature in Kelvin.
Figure 6 shows the nephogram at different temperatures.A peak represents a cascade collision centre, corresponding to a recombination centre.As the temperature increases from 100 to 200 K, the number of recombination centres increases and the dispersion decreases.The result is an increase in the recombination rate of Frenkel pairs.As the temperature rises from 200 K to 350 K, the dispersion of the recombination centre increases, leading to a decrease in the recombination rate of Frenkel pairs.A larger cascade of atomic collisions occurs when the temperature is raised from 350 K to 450 K, corresponding to a local temperature of over 1000 K. Further, high temperature annealing promotes the recombination of defects [14].
where  is the peak of the Frenkel pair,  is the intercept ( = 111.94048± 2.99957). is the slope ( = 0.00976 ± 0.01007), and  is the temperature in Kelvin.
Figure 6 shows the nephogram at different temperatures.A peak represents a cascade collision centre, corresponding to a recombination centre.As the temperature increases from 100 to 200 K, the number of recombination centres increases and the dispersion decreases.The result is an increase in the recombination rate of Frenkel pairs.As the temperature rises from 200 K to 350 K, the dispersion of the recombination centre increases, leading to a decrease in the recombination rate of Frenkel pairs.A larger cascade of atomic collisions occurs when the temperature is raised from 350 K to 450 K, corresponding to a local temperature of over 1000 K. Further, high temperature annealing promotes the recombination of defects [14].The barrier potential for various types of point defects in SiC is given in Table 6 [25][26][27].Figure 7 shows that the irradiation defect types are mainly in the form of point defects at different temperatures.These clusters are mainly vacancy clusters and antisite clusters.The reason is that I C and I Si have relatively low migration potential.It is not easy to form interstitial clusters.

Effect of Incidence Angle on 6H-SiC Cascade Collisions
The incident angle of irradiated ions affects the particle deposition trajectory and hence the transient current of the device, a phenomenon that has been reported [28,29].The 6H-SiC is an anisotropic crystal.Irradiated particles with different incidence angles may form different cascade collisions in 6H-SiC, leading to different levels of irradiation damage.Therefore, this section focuses on the effect of different incidence angles on 6H-SiC cascade collisions.
Figure 8a shows that the number of permanent defects produced by cascade collisions tends to decrease and then increase as the angle of incidence increases.When the incidence angles are 8 • and 15 • , the total number of defects is roughly the same.The number of total defects, Si C and C Si , are the least at the 45 • incident angle.Among them, the total defect consists of V C , V Si , I C , I Si , Si C and C Si .Figure 8b shows a similar regularity for the number of permanent Frenkel pairs generated by cascade collisions.Figure 8c indicates that the number of permanent C Si tends to decrease and then increase as the angle of incidence increases.When the incidence angle is 15 • and 30 • , the difference in C Si quantity is very small.Figure 8d shows that there is no obvious regularity in the number of Si C. To further explain the differences in the number of defects in each category, we provide reactions between the various types of point defects studied and their reaction barrier (E Re ) and reaction distances (r) [27,30].In Table 7, the reaction barriers for C C and Si Si are smaller than those of the other forms.Therefore, during the defective recombination phase, a large number of recombination occurs between V C and I C and between V Si and I Si .This leads to a large reduction in Frenkel pairs as shown in Figure 8b.However, by comparison with Figure 8b,c, it can be observed that the amount of C Si does not change significantly during the defect recombination phase.The recombination of Si atoms in Si C and V Si is the reason for the decrease in the amount of Si C in Figure 8d.This also suggests that the Si C produced at the beginning of irradiation is not stable Si C , but a combination of V C and I Si .As shown in Table 8 [26,27], the formation energy of Si C is lower than that of C Si , so the peak defects in Figure 8c are lower than those in Figure 8d.The results in Figure 8e,f show that the variation in the incidence angle has no significant effect on the final percentage of vacancy defects and antisite defects.This shows that the effect of the variation in the PKA incidence angle on the electrical properties of the electronic devices is more in the regional distribution of defect clusters of vacancy defects and interstitial atomic defects generated within the material.The barrier potential for various types of point defects in SiC is given in Table 6 [25][26][27].Figure 7 shows that the irradiation defect types are mainly in the form of point defects at different temperatures.These clusters are mainly vacancy clusters and antisite clusters.The reason is that IC and ISi have relatively low migration potential.It is not easy to form interstitial clusters.Figure 9 shows the microscopic distribution of various defect types.The trajectories in the figure are produced by atoms with displacements greater than 4 Å.Defects are distributed in the shape of grape bunches near the PKA trajectory.As the angle of incidence increases, local cascade collisions become more intense, and the aggregation of defects becomes more pronounced at the end of the PKA trajectory.Consistent with the above results, the local amorphization is more obvious within the 6H-SiC material.A distinct region characterized by the aggregation of vacancy defects and interstitial atomic defects emerges irrespective of alterations in the incident angle.Furthermore, this region undergoes modifications as the incident angle varies.

Effect of Incidence Angle on 6H-SiC Cascade Collisions
The incident angle of irradiated ions affects the particle deposition trajectory and hence the transient current of the device, a phenomenon that has been reported [28,29].The 6H-SiC is an anisotropic crystal.Irradiated particles with different incidence angles may form different cascade collisions in 6H-SiC, leading to different levels of irradiation damage.Therefore, this section focuses on the effect of different incidence angles on 6H-SiC cascade collisions.
Figure 8a shows that the number of permanent defects produced by cascade collisions tends to decrease and then increase as the angle of incidence increases.When the incidence angles are 8° and 15°, the total number of defects is roughly the same.The number of total defects, SiC and CSi, are the least at the 45° incident angle.Among them, the total defect consists of VC, VSi, IC, ISi, SiC and CSi. Figure 8b shows a similar regularity for the number of permanent Frenkel pairs generated by cascade collisions.Figure 8c indicates that the number of permanent CSi tends to decrease and then increase as the angle of incidence increases.When the incidence angle is 15° and 30°, the difference in CSi quantity is very small.Figure 8d shows that there is no obvious regularity in the number of SiC.To further explain the differences in the number of defects in each category, we provide reactions between the various types of point defects studied and their reaction barrier (ERe) and reaction distances (r) [27,30].In Table 7, the reaction barriers for CC and SiSi are smaller than those of the other forms.Therefore, during the defective recombination phase, a large number of recombination occurs between VC and IC and between VSi and ISi.This leads to a large reduction in Frenkel pairs as shown in Figure 8b.However, by comparison with Figure 8b,c, it can be observed that the amount of CSi does not change significantly during the defect recombination phase.The recombination of Si atoms in SiC and VSi is the reason for the decrease in the amount of SiC in Figure 8d.This also suggests that the SiC produced at the beginning of irradiation is not stable SiC, but a combination of VC and ISi.As shown in Table 8 [26,27], the formation energy of SiC is lower than that of CSi, so the peak defects in Figure 8c are lower than those in Figure 8d.The results in Figure 8e,f show that the Figure 10 shows that vacancy clusters and antisite clusters with an atomic number of two are the most common.The largest size of vacancy clusters and antisite clusters appear at a 75 • incident angle.At an incident angle of 60 • , there are no antisite clusters and no vacancy clusters greater than two.However, it can be concluded from Table 6 that the migration potentials of vacancy and antisite defects are much higher than those of interstitial defects, and therefore the clusters formed are mainly vacancy and antisite clusters.Figure 10 shows that vacancy clusters and antisite clusters with an atomic number of two are the most common.The largest size of vacancy clusters and antisite clusters appear at a 75° incident angle.At an incident angle of 60°, there are no antisite clusters and no vacancy clusters greater than two.However, it can be concluded from Table 6 that the migration potentials of vacancy and antisite defects are much higher than those of interstitial defects, and therefore the clusters formed are mainly vacancy and antisite clusters.

Conclusions
During irradiation of 6H-SiC crystals, there is a monotonically increasing linear rela tionship between the peak of the Frenkel pair and temperature.The peak of the Frenke pair increases with increasing temperature, but the amount of change is small.The recom bination rate of Frenkel pairs depends on the local temperature and the degree of defective recombination center aggregation.As the temperature increases from 300 K to 450 K, the cascade collision distribution tends to concentrate, and local high temperatures are more likely to occur.As the angle of incidence increases, the number of both total defects and Frenkel pairs exhibits a trend of first decreases and then increases.Among them, the num

Conclusions
During irradiation of 6H-SiC crystals, there is a monotonically increasing linear relationship between the peak of the Frenkel pair and temperature.The peak of the Frenkel pair increases with increasing temperature, but the amount of change is small.The recombination rate of Frenkel pairs depends on the local temperature and the degree of defective recombination center aggregation.As the temperature increases from 300 K to 450 K, the cascade collision distribution tends to concentrate, and local high temperatures are more

Figure 2 .
Figure 2. Schematic diagram of the irradiation model.

Figure 2 .
Figure 2. Schematic diagram of the irradiation model.

Figure 3
Figure 3 is a schematic representation of the Wiger-Seitz method.The Open Visualisation Tool (OVITO) is used to identify and count the types and clusters of defects [23].Frenkel pairs, silicon vacancy (V Si ), carbon vacancy (V C ), silicon interstitial (I Si ), carbon interstitial (I C ), silicon antisite (Si C ), carbon antisite (C Si ) and cluster can be shown in the OVITO.Among them, clusters have a search radius of 0.22 nm [16,24].

Figure 3
Figure 3 is a schematic representation of the Wiger-Seitz method.The Op sation Tool (OVITO) is used to identify and count the types and clusters of Frenkel pairs, silicon vacancy (VSi), carbon vacancy (VC), silicon interstitial (ISi terstitial (IC), silicon antisite (SiC), carbon antisite (CSi) and cluster can be sh OVITO.Among them, clusters have a search radius of 0.22 nm [16,24].

Figure 4 .
Figure 4. Structural data for the models in this paper.(a) Radial distribution function; (b) coordination number; (c) atomic angle distribution function.

Figure 4 .
Figure 4. Structural data for the models in this paper.(a) Radial distribution function; (b) coordination number; (c) atomic angle distribution function.

Figure 5 .
Figure 5. Production of a Frenkel pair at different temperatures.(a) Number of Frenkel pairs versus time; (b) Peak number of Frenkel pairs and permanent defects at different temperatures.

Figure 5 .
Figure 5. Production of a Frenkel pair at different temperatures.(a) Number of Frenkel pairs versus time; (b) Peak number of Frenkel pairs and permanent defects at different temperatures.

Figure 8 .
Figure 8.(a) Number of total defects versus time curves; (b) Number of Frenkel pairs versus time curves; (c) Number of CSi versus time curves; (d) Number of SiC versus time curves; (e) Percentage of vacancy; (f) Percentage of antisite.

Figure 8 .Figure 9 .
Figure 8.(a) Number of total defects versus time curves; (b) Number of Frenkel pairs versus time curves; (c) Number of C Si versus time curves; (d) Number of Si C versus time curves; (e) Percentage of vacancy; (f) Percentage of antisite.

Table 2 .
Parameters related to the time step.

Table 3 .
The design of the experiment.

Table 3 .
The design of the experiment.

Table 4 .
Lattice constants.The hexagonal lattice constants in the table were all converted to orthogonal lattice constants.
1The hexagonal lattice constants in the table were all converted to orthogonal lattice constants.

Table 5 .
Error statistics table.

Table 5 .
Error statistics table.

Table 6 .
Potential barriers for various types of point defects.

Table 6 .
Potential barriers for various types of point defects.