# Recent Progress on Irradiation-Induced Defect Engineering of Two-Dimensional 2H-MoS2 Few Layers
## 5 Irradiation Mechanism and Theoretical Simulations  
Besides the experimental work reviewed in the previous sections, there are lots of theoretical approaches to investigate the irradiation mechanism of MoS\({}_{2}\) 2D nanosheets.  
[PERSON] et al. [78] calculated the displacement threshold energy and the minimum initial kinetic energy of the recoil atom to kick an atom from MoS\({}_{2}\) mono-layers, using the density-functional theory with the Perdew-Burke-Ernzerhof exchange-correlation function. The sulfur displacement threshold energy of MoS\({}_{2}\) was 6.9 eV, corresponding to incident-electron energies of about 90 keV. About 20 eV was required to displace one molybdenum atom from its site in MoS\({}_{2}\) mono-layer lattices, corresponding to an electron energy of 560 keV. Therefore, the sulfur sub-layers were easier destroyed while it was unlikely to generate molybdenum vacancies in molybdenum sub-layers under TEM observations (where 200 keV electron beams were employed). Figure 31 shows the calculated cross-section of sulfur atoms. Lattice vibrations were taken into account, assuming a Maxwell-Boltzmann velocity distribution. The cross denotes the experimentally determined cross-section for MoS\({}_{2}\). The inset shows the same data for a larger range of electron energies. The atom displacement cross-section was estimated from the electron threshold energy by using the McKinley-Feshbach formalism.  
The calculated displacement threshold energy was in agreements with experimental observations. Single sulfur vacancies (VS's) were frequently observed under transmission electron microscopes with an 200 kV acceleration voltage (the electron energy, 200 keV is higher than the displacement energy of sulfur atoms (90 keV) while lower than that of molybdenum atoms, 560 keV).  
Table 2 compares formation thresholds of five kinds of defect configurations for MoS\({}_{2}\) bulks and mono-layers. The thresholds for single S vacancies were very low, both in bulk and mono-layers. Single-line S-vacancy and double-line S-vacancy configurations are generated with increasing single S-vacancy concentration by prolonged electron irradiation. In addition, the formation thresholds for Mo-vacancy and DIV are not very high (18-29 eV).  
Figure 31: Cross-section for sputtering a sulfur atom from MoS\({}_{2}\) mono-layers as calculated through the McKinley-Feshbach formalism and the dynamical values of the displacement thresholds [78]. Reprinted with permission from Reference [78]. Copyright © 2012 by the American Physical Society.  
[PERSON] et al. [168] combined analytical potential molecular dynamics with Monte Carlo simulations to simulate helium and neon ion irradiation of MoS\({}_{2}\) nanosheets deposited on SiO\({}_{2}\) substrates. Their simulation indicated that substrates governed the defect production of irradiated MoS\({}_{2}\) layers. The irradiation-induced defect production was dominated by backscattered ions and sputtered substrate atoms, rather than by the direct helium and neon ion impacts.  
Molecular dynamics simulations were also employed to study the production of defects in MoS\({}_{2}\) mono-layers under noble gas ion irradiation, such as He, Ne, Ar, Kr and Xe [169]. Sulfur atoms were sputtered away predominantly from the top or bottom layers by the ion irradiation, depending on the incident angle, ion type, and ion energy.