To investigate the effect of dislocation structures on the initial formation stage of helium bubbles, molecular dynamics (MD) simulations were used in this study. The retention rate and distribution of helium ions with 2 keV energy implanted into silicon with dislocation structures were studied via MD simulation. Results show that the dislocation structures and their positions in the sample affect the helium ion retention rate. The analysis on the three-dimensional distribution of helium ions show that the implanted helium ions tend to accumulate near the dislocation structures. Raman spectroscopy results show that the silicon substrate surface after helium ion implantation displayed tensile stress as indicated by the blue shift of Raman peaks.

  • Simulation results show that the retention rate of helium ions is related to the dislocation structure and its position.

  • The implanted helium ions tend to gather near the dislocation line.

  • The silicon substrate surface after helium ion implantation exists tensile stress.

Due to the wide use and promotion of nuclear energy, many studies involving reactor-related materials, especially silicon, have been carried out around the world to improve the safety and service life of reactors and build commercialized fusion reactors.1–3 The radiation damage of structural materials in reactors is mainly caused by atomic displacement damages due to high-energy neutrons and direct alpha particle bombardment or nuclear reaction product doping, especially helium doping and its evolution products produced by (n,α) reactions.4,5 These radiation damages cause defects that can result in the hardening/embrittlement of materials and seriously affect the service life of structural materials in the fusion reactors.6–11 Therefore, helium and its dopants have continuously attracted attention.

To further understand the nuclear reaction scene, ion implantation technology12 has been widely used, but it mainly focuses on the research of high-energy implantation.13,14 In recent years, low-energy helium ion implantation technology for generating helium bubbles has gradually attracted attention,15 but related research is limited. Stable helium–vacancy clusters and other vacancy-type defects can be formed by helium ion implantation.16,17 This phenomenon is basically independent of the host material, including metal,18–21 and covalent systems, such as silicon22–25 and silicon carbide, have been reported. To better understand the formation mechanism of helium bubbles, the dynamic mechanism of the initial stage of the bubble formation is highly demanded, and the molecular dynamics (MD) simulation is useful in this stage.26 

Compared with the perfect lattice model, semiconductor materials in an actual environment usually contain structural defects, such as vacancies and dislocations. Defect engineering in the semiconductor field has attracted increasing attention. Li et al.12 indicated that after a single-pixel point with a helium ion dose of 1.9 × 108 ions at a beam energy of 30 keV implanted into a single-crystal silicon, atomic structure defects were hard to detect, but a dislocation-like structure in the implanted area was found through the high-angle annular dark-field transmission electron microscopy (TEM) image, as shown in Fig. 1.12 Han et al.27 revealed that helium bubbles tended to preferentially form inside the defects of grain boundaries in He-irradiated polycrystalline α-SiC at 1000 °C. Therefore, the effect of the defect structures in the material on the initial stage of helium bubble formation is also crucial. In the initial stage of helium bubble formation, the distribution of helium ions in the material, as well as the retention, depth distribution, lateral distribution, and clustering, has an important influence on the formation of helium bubbles in the later evolution period.

Fig. 1.

Dark-field TEM image of a dislocation in silicon implanted by a single-pixel point with a helium ion dose of 1.9 × 108 ions at a beam energy of 30 keV.12 (Copyright permission @ AIP Publishing)

Fig. 1.

Dark-field TEM image of a dislocation in silicon implanted by a single-pixel point with a helium ion dose of 1.9 × 108 ions at a beam energy of 30 keV.12 (Copyright permission @ AIP Publishing)

Close modal

In this study, the MD simulation method was used to simulate the implantation of helium ions into silicon, which contains representative defects of dislocations, to investigate the effects of material defects on the retention and distribution of helium ions. Defect detection methods were used in the analysis process. Moreover, Stopping and Range of Ions in Matter (SRIM) simulation and Raman spectroscopy were used to study the helium ion implantation.

Large-scale Atomic/Molecular Massively Parallel Simulator code was used to simulate ion implantation.26 The MD method is based on Newton’s law of motion. It can model atomic systems using a variety of interatomic potentials (force fields) and boundary conditions and also 2D or 3D systems with only a few particles up to millions or billions.

2.1.1. Model setups

To better understand the influence of defects on the distribution of helium ions, two silicon models with different defect structure setups were established. For the comparative analysis, the model with a perfect silicon lattice structure, presented in Fig. 2(a), was also added to the experiment.

Fig. 2.

Schematic diagram of the three kinds of models with and without dislocation slip setup. Panel (a) represents not only a perfect crystalline silicon model but also the distribution of the three model structures. The two intersecting black lines inside the model in panels (b) and (c) are the specific locations of the dislocation line. The intersection of the former is the center of the plane in which it is located, whereas the latter is located at a quarter of the height along the negative Z-axis.

Fig. 2.

Schematic diagram of the three kinds of models with and without dislocation slip setup. Panel (a) represents not only a perfect crystalline silicon model but also the distribution of the three model structures. The two intersecting black lines inside the model in panels (b) and (c) are the specific locations of the dislocation line. The intersection of the former is the center of the plane in which it is located, whereas the latter is located at a quarter of the height along the negative Z-axis.

Close modal

Fig. 2 shows a schematic diagram of the three kinds of models. All the three models contain a fixed boundary layer, thermal layer, and Newton layer, which are represented from bottom to top. The helium ion implantation parameters of energy, position, and ion dose are the same for the three models. The only difference is the location of the defect structure contained within the individual model. The MD model for ion implantation has a dimension of 22a0 × 22a0 × 60a0 and includes 233,288 atoms. A total of 100 helium ions with 2 keV energy were implanted into the red square region with a size of 5 Å × 2 Å, corresponding to the implantation dose of 1.0 × 1017 ions/cm.2 The initial position of the helium ions implanted into the target material has a certain randomness, but the incidence rate is 100%. Moreover, the angles of the helium ions are all 7° from the negative direction of the Y axis. The specific simulation parameters are shown in Table 1.

Table 1.

Simulation parameters for ion implantation.

ConditionParameters
Model Si (100) 
Lattice Diamond 
Lattice constant a0 = 5.431 Å 
Size 22a0 × 22a0 × 60a0 
Temperature 300 K 
He ions 100 
Thermostat style Berendsen thermostat 
Potential style MEAM 
Incident angle 7° towards Y-axis 
ConditionParameters
Model Si (100) 
Lattice Diamond 
Lattice constant a0 = 5.431 Å 
Size 22a0 × 22a0 × 60a0 
Temperature 300 K 
He ions 100 
Thermostat style Berendsen thermostat 
Potential style MEAM 
Incident angle 7° towards Y-axis 

The defects of dislocations were built using the external software Atomsk.28 The two models in Fig. 2(b) and (c) each contain two dislocations with the (010) and (001) orientations, but the (010) orientation has a different location in the two models. The Burgers vectors of all the dislocations are all 2.80 Å in the models.

2.1.2. Potential function

The potential energy type of the modified embedded atom method (MEAM) potential was used, which is suitable for modeling metals and alloys with fcc, bcc, hcp, and diamond cubic structures and covalently bonded materials, such as silicon and carbon. The MEAM potential was validated on a few simple configurations, and the simulation parameters refer to the He:Si system established by Pizzagalli et al.29 The HCP lattice is composed of helium crystallizes in the HeHe system. Eq. (1) shows the Rose energy Er used in our work:

Er=EC(1+a+a3(a3)/(r/re))e(a),
(1)

where a = a(r/re − 1), ɑ is a pair potential between He and Si, which can be computed from the bulk modulus of the reference structure, re is the equilibrium distance between Si and He in the reference structure, r represents the distance between two interacting atoms, and Ec is the cohesive energy of the reference structure for the SiHe system. When a < 0, a3= repuls; when a >0, a3 = attrac. The “replus” and “attrac” respectively represent repulsive force and attractive force. The a3 has different values in different forces and different compounds. Refer to Table 2 for detailed parameters.

Table 2.

MEAM parameters used in this work.29 

CellStructureEcreαAβ(0)β(1)β(2)β(3)t(0)t(1)t(2)t(3)ρ0aa3(r > re)a3(r < re)
Si Diamond 4.63 5.431 4.87 1.0 4.4 5.5 5.5 5.5 1.0 3.13 4.47 −1.80 2.35 – – 
He Hcp 0.0073775 2.9113 10.5 −0.35 0.75 0.0 0.0 0.0 1.0 1.0 1.0 1.0 109.0 0.15 0.0 
SiHe Dimer 0.0077 2.912 9.0 – – – – – – – – – – 0.011 0.011 
CellStructureEcreαAβ(0)β(1)β(2)β(3)t(0)t(1)t(2)t(3)ρ0aa3(r > re)a3(r < re)
Si Diamond 4.63 5.431 4.87 1.0 4.4 5.5 5.5 5.5 1.0 3.13 4.47 −1.80 2.35 – – 
He Hcp 0.0073775 2.9113 10.5 −0.35 0.75 0.0 0.0 0.0 1.0 1.0 1.0 1.0 109.0 0.15 0.0 
SiHe Dimer 0.0077 2.912 9.0 – – – – – – – – – – 0.011 0.011 

2.2.1. Wigner–Seitz defect analysis modifier

The Wigner–Seitz defect analysis modifier identifies point defects in crystalline structures using the so-called Wigner–Seitz cell method.30 It can be used to count vacancies and interstitials and track their motion through the lattice. The Wigner–Seitz cell method works as follows (Fig. 3): Two configurations of the atomistic system are presumed to exist: the reference state, which is defect free (typically the perfect crystal lattice), and the displaced configuration, which represents the defective state of the crystal to be analyzed. In the latter, some atoms have been displaced or completely removed from their original sites.

Fig. 3.

Wigner–Seitz defect analysis modifier.

Fig. 3.

Wigner–Seitz defect analysis modifier.

Close modal

2.2.2. Cluster analysis method

This modifier decomposes a particle system into disconnected sets of particles (clusters) based on a local neighboring criterion. The neighboring criterion can either be based on the distance between particles (i.e., a cutoff) or on the bond topology. In this study, a 2.85 Å cutoff was used as the calculation criterion. If the distance between two particles is less than this value, then they are considered to be members of the same cluster; otherwise, they are grouped separately. This modifier assigns a cluster number to a single ion that does not meet the truncation radius condition, but the clusters of actual interest in this study are groups with more than one atom in the group. There are a total of 16,330 ions (Input) and 11,883 ion cluster (Output) in Fig. 4, the different colors represent the coloring of the ion beam numbers, but the visualization effect has no practical significance.

Fig. 4.

Principle diagram of the cluster analysis modifier.

Fig. 4.

Principle diagram of the cluster analysis modifier.

Close modal

2.2.3. Experimental setups

The single-crystalline Si (does not contain any pre-dislocation) was nitrogen-doped Czochralski-grown Si (111) wafer with a resistivity of 0.003–50 Ω cm.12 Helium ion microscope (Zeiss Orion NanoFab) was used to generate focused helium ion beam and make it irradiate on the Si surface along a single-pixel line. Helium ion implantation into Si was first achieved by using an energy of 30 keV and ion beam of 2 pA. Then, a focused ion beam system (FEI STRATA DB235) was utilized to prepare the standard TEM cross-section samples of irradiated regions through the lift-out technique for further analysis. Moreover, large-area helium ion implantation was conducted in a range of 6 μm × 6 μm with a dose of 110 ion/nm2 using a beam energy of 30 keV and ion beam of 3.27 pA for Raman spectroscopy. The single spectra and 2D Raman mapping of the large-area implantation region were examined using a laser Raman spectroscope XploRA PLUS from HORIBA Scientific. The Raman measurements were performed under a backscattered geometric configuration excited with a 532 nm laser at room temperature. The groove density of the spectrometer’s grating was 1200 g/mm, and the spectral resolution was better than 1 cm−1. Furthermore, 100× objective lens and a 500 μm hole were used.

Fig. 5(a) shows the SRIM simulation of helium ion implant Si. As the SRIM is based on Monte Carlo principles, the more helium ions (at least on the order of 100,000) implanted in the simulation, the more stable and the more scientific the simulation results. Thus, the parameters were set as 500,000 helium ions bombarding a monocrystal silicon, with a beam energy of 30 keV and incident angle of 7°. The existence of this simulation experiment can be compared with the actual experiment to verify the accuracy of the actual experiment through the SRIM simulation. As shown in Fig. 5(b), the maximum helium ion concentration appears at a depth of 320 nm, and the maximum damage concentration appears at a depth of 250 nm. The TEM microstructural features of the ion-implanted sample clearly showed the surface swelling results above the helium ion implantation area, as shown in Fig. 5(c). Helium bubbles appeared at the bottom of the ion implantation area. Due to the existence of defect structures, such as helium bubbles, the surface of the sample swells and the height of the swelling is 87 nm. Moreover, many large-sized helium bubbles were generated at 330 nm, which is consistent with the results of the maximum helium ion density appearing at a depth of 320 nm in Fig. 5(b). In the SRIM simulation, the local thermal annealing effect existed, the relative atomic mass of the incident helium ions and the target silicon atoms are very different, and SRIM is based on the Monte Carlo principle, considering only binary collisions. These reasons cause the depth range of helium ions in Fig. 5(b) to be greater than the depth range of the damage.

Fig. 5.

Results of the helium ion implantation into silicon. (a) Ion and recoiling atom trajectory of helium ion implant Si by SRIM simulation, (b) SRIM simulation of helium ion-induced damage distribution, (c) TEM cross-sectional results of swelling and ion-induced damages after helium ion implantation, (d) surface morphology after the implantation of 100 helium ions by MD simulation.

Fig. 5.

Results of the helium ion implantation into silicon. (a) Ion and recoiling atom trajectory of helium ion implant Si by SRIM simulation, (b) SRIM simulation of helium ion-induced damage distribution, (c) TEM cross-sectional results of swelling and ion-induced damages after helium ion implantation, (d) surface morphology after the implantation of 100 helium ions by MD simulation.

Close modal

Fig. 5(d) presents a simulation of the surface expansion caused by helium ion implantation in silicon. However, because the model size and implanted energy are much smaller than those in the experimental setups in Fig. 5(c), a sufficient number of helium bubbles were not formed, and only occasional bulging atoms underwent the surface bulging phenomenon.

Table 3 shows the number of retained helium ions after the implantation in the three models. The model in Fig. 2(a), (b), and (c) will be described later with Model 1, Model 2, and Model 3, respectively. Model 3 has the largest number of helium ions, whereas Model 2 has the least number of helium ions.

Table 3.

Number of retained helium ions after the implantation.

PatternHe ions
Model 1 56 
Model 2 48 
Model 3 57 
PatternHe ions
Model 1 56 
Model 2 48 
Model 3 57 

Fig. 6 shows the number of helium ions in the three models. The residual helium ions and dose shows a positive correlation. This positive correlation also exists between the damage and implanted ion dose,31 but a higher scope of damage does not mean that the number of vacancies also increases. Considering the energy, helium atoms combined with vacancies will be more stable, and in the initial stage of helium bubble formation, helium ions need to be combined with excess vacancies to form helium vacancy clusters.26 Models 2 and 3 have much more vacancies than Model 1 due to the dislocation structure.

Fig. 6.

Changes in the number of helium atoms residing in silicon and vacancy as the helium ion implantation dose increases.

Fig. 6.

Changes in the number of helium atoms residing in silicon and vacancy as the helium ion implantation dose increases.

Close modal

3.3.1. Depth distribution

Fig. 7 shows that Model 3 is mainly concentrated in a depth range of 20–120 Å, and it is continuously distributed in a depth range of 0–160 Å. Only a few parts are distributed in a depth range of 180–200 Å. The dislocation intersection in Model 3 is located near the depth slice of 60–80 Å. As shown in Fig. 7, the number of helium ions in the depth slice of Model 3 is more than that of the other two models. In Model 3, helium ions do not exist in the depth range of 160–180 Å. This is a random phenomenon caused by the program design and statistical selection, which does not affect the overall results of the experiment. Although Model 2 contains fewer helium ions than the other two models, it has the widest range (0–200+ Å) of helium ions and the clearest concentration region (20–80 Å). The dislocation structure changes the distribution of helium ions in silicon, so that helium ions tend to be concentrated in certain areas in depth.

Fig. 7.

Stacked bar chart of helium ion depth distribution.

Fig. 7.

Stacked bar chart of helium ion depth distribution.

Close modal

3.3.2. 3D distribution

Fig. 8 shows the distribution of helium ions in a specific model. The coloring is based on the cluster analysis function of Ovito. Intuitively, compared with Model 1, Models 2 and 3 have a better helium ion accumulation. Model 3 contains the largest number of helium ions, and its aggregation is significantly better than that of the other two models. Moreover, a cluster of three helium ions is formed, and the coordinates of this cluster are located at (−25.8451, 2.4411, 97.2323). An enlarged view of the cluster configuration is shown in the rightmost picture of Fig. 8. This configuration is near the intersection of two dislocation lines in Model 3. Compared with Model 2, because the dislocations contained in the former model are closer to the ion source, its helium ion retention and aggregation are better in Model 3.

Fig. 8.

Distribution of helium ions. Coloring is performed according to the helium ion cluster number. Helium ion cluster with more than one helium ion in the corresponding model are marked red in the figure. The right end picture is a partial enlarged view of red ions in Model 3.

Fig. 8.

Distribution of helium ions. Coloring is performed according to the helium ion cluster number. Helium ion cluster with more than one helium ion in the corresponding model are marked red in the figure. The right end picture is a partial enlarged view of red ions in Model 3.

Close modal

Figs. 9 and 10 show that after the implantation of 100 helium ions into silicon, the distribution of the damage caused by this process mainly occurred along the dislocation direction. The damage caused by the helium ion implantation in Model 2 is mainly distributed along the dislocation lines in the Z-axis direction, and the damage caused by the helium ion implantation in Model 3 is distributed along the two dislocation lines in the model. The damage distribution caused by the helium ion implantation is seriously affected by the dislocation structure. The dislocation structure causes the damaged structure to be distributed along the dislocation structure by adsorbing helium ions and damages atoms, such as vacancy.

Fig. 9.

Dislocation change corresponding to Model 2. (a) Initial model, (b) model after energy minimization, (c) model after implantation of 100 helium ions, and (d) 3D distribution of amorphous silicon in the model after implantation of 100 helium ions.

Fig. 9.

Dislocation change corresponding to Model 2. (a) Initial model, (b) model after energy minimization, (c) model after implantation of 100 helium ions, and (d) 3D distribution of amorphous silicon in the model after implantation of 100 helium ions.

Close modal
Fig. 10.

Dislocation change corresponding to Model 3. (a) Initial model, (b) model after energy minimization, (c) model after implantation of 100 helium ions, and (d) 3D distribution of amorphous silicon in the model after implantation of 100 helium ions.

Fig. 10.

Dislocation change corresponding to Model 3. (a) Initial model, (b) model after energy minimization, (c) model after implantation of 100 helium ions, and (d) 3D distribution of amorphous silicon in the model after implantation of 100 helium ions.

Close modal

The ion implantation area of the silicon sample in Fig. 11(a) and (b) is a square with a dimension of 6 μm × 6 μm, dose of 1.1 × 1016 ion/cm2, and beam size of 3.27 pA. The Raman characteristic peak of the raw silicon sample was 520.42 cm−1. 2D mapping was measured in a SWIFT working mode (ultra-fast Raman imaging) excited by 532 nm laser.

Fig. 11.

Raman scanning of the ion implantation area. (a) Distribution of the peak intensity morphology in the implantation area, (b) peak shift profile of the implantation area, and (c) stress distribution on the surface of Model 1 after the implantation of 100 helium ions.

Fig. 11.

Raman scanning of the ion implantation area. (a) Distribution of the peak intensity morphology in the implantation area, (b) peak shift profile of the implantation area, and (c) stress distribution on the surface of Model 1 after the implantation of 100 helium ions.

Close modal

The silicon peak intensity distribution is shown in Fig. 11(a), and the silicon peak shift distribution is shown in Fig. 11(b). After the helium ions were implanted into the sample, the silicon peak intensity of the implanted area decreases from red color to blue, with a transition surrounding the area colored with green, which was mainly induced by the ion-induced lateral damages. The Raman peak shift was linearly related with the residual stress of the sample.32 As shown in Fig. 11(b), the silicon Raman peak shifts in blue were approximately 1 cm−1 in the implantation area, although the blue shift is not so uniform like the peak intensity shown in Fig. 11(a). The blue shift of the silicon peak in the ion implantation region indicates a tensile residual stress, which might have a contribution to the evolution of damages induced by the helium ion implantation, such as the helium migration.33Fig. 11(c) shows that after the implantation of 100 helium ions into the target in the simulation experiment, a tensile stress was detected on the surface of the material, which is consistent with the actual Raman test experiment results shown in Fig. 11(a) and (b).

In this study, the retention rate and distribution of helium ions with an energy of 2 keV implanted into silicon with different dislocation structure setups were examined via MD simulation. The conclusions are as follows:

  1. The dislocation structure and its position in the silicon substrate can affect the helium ion implantation configuration.

  2. Depending on the position of the dislocation structure in the target, the retention rate of helium ions is also different.

  3. The implanted helium ions tend to accumulate around the dislocations.

  4. The ion implantation area showed tensile residual stress.

This work was supported by the National Natural Science Foundation of China (No. 51575389, 51761135106), the National Key Research and Development Program of China (2016YFB1102203), the State Key Laboratory of Precision Measurement Technology and Instruments (Plit1705), and the “111 Project” by the State Administration of Foreign Experts Affairs and the Ministry of China (Grant No. B07014). The authors would like to thank Dr. L Pizzagalli for the help on potential functions and Ms. Xiu Fu for her valuable discussions.

We do not have any conflict of interest.

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Li Ji, State Key Laboratory of Precision Measuring Technology and Instruments, School of Precision Instruments and Opto-Electronics Engineering, Tianjin University, China. Ms. Ji is studying for master degree. Her research interests include silicon material and helium bubbles.