Scientists calculate displacement threshold for two-dimensional atomic crystals

the atomic setup
Figure 1. The atomic setup.

July 17, 2012 - After the first accurate measurement and computation of the scattering cross section of graphene [1, this newsarticle] researchers now calculated the displacement and substitution energies for the more complex class of two-dimensional transition metal di-chalcogenide (TMD) materials, some of which have recently been synthesized. The results were validated by observing the generation and replacement of defects under the electron beam, which also proves the possibilities to modify the properties of TMDs in the electron microscope.

In the study conducted by scientists from the Universities of Helsinki and Aalto in Finland and the University of Ulm in Germany, density functional theory (DFT) [2-4] is used to study the response of a large amount of layered TMDs: MoX2, WX2, NbX2, TaX2, PtX2, TiX2 and VX2 (with X = S, Se or Te) to electron irradiation. Besides graphene [5] and h-BN [6-10], TMDs are recently discovered two-dimensional materials that can exist under normal conditions. Some of them have recently been synthesized by mechanical [11, 12] and chemical [6, 13] exfoliation of their layered massive counterparts and have shown great potential in nanoelectronic [12, 14] and photonic [13, 15] applications.

While high-resolution transmission electron microscopy (HR-TEM) has already been used to characterize TMDs [16], the effect of electron irradiation on TMDs has not yet been studied in detail. In addition to the results obtained earlier for h-BN monolayers, [17, 18], the new results now give insights in the generation of impurities in TMDs. This may allow designing experimental conditions necessary to minimize radiation damage and may help to develop beam-mediated post-synthesis doping techniques. The fundamental understanding of the interaction of high-energy particles with solids can also benefit from the study [19].

"We study the behavior of a representative number of TMDs under electron beam irradiation and calculate the threshold energies for atomic exchange processes in each system and make predictions for the radiation-mediated doping of TMD materials for the first time." says Arkady Krasheninnikov, who led the theoretical studies.

To increase the accuracy of the results, the scientists also calculated the vacancy energies Ef in addition to the minimum initial kinetic energy of the recoil atom Td. This allowed including relaxation within the material in in the study, which was published this month in the prestigious journal Physical Review Letters. It was funded by the Deutsche Forschungsgemeinschaft (DFG) and the MWK as part of the SALVE project, as well as the University of Helsinki Funds and the Academy of Finland.

graph of T<sub>d</sub> and Ef for various TMD
Figure 2. Displacement threshold.
graph of knock-on cross section vs. E_electron
Figure 3. Displacement threshold.

Theoretical simulation with DFT

In the unrelaxed case, the energies are very similar for all TMDs, and the match between Td and Ef is high. The energies for the calculations, in which the relaxation of the system is taken into account, show a different dynamic. There is a considerable decrease in Ef over Td in some systems. This drop is due to the degree of structural relaxation around the void. It is low for MoS2 and all other semiconducting materials (MoX2, WX2 and PtX2), see Fig. 1 (b). For metallic and semi-metallic TMDs, the simulation gives greater relaxation and lower energy of formation (see Fig. 2).

The electron removal threshold energy (knock-on threshold) (the energy that is necessary to remove an atom from the lattice [20]) is higher for Se and Te compounds than in S compounds, since the higher atomic mass leads to significantly lower energy transfer from the electron beam to the atoms. Scientists from Ulm University had shown that an accurate estimate of the knock-on threshold requires the inclusion of the effects of lattice vibrations of the atoms [1]. The scientists now calculated the cross-sections for vacancy production as a function of the electron energy for MoS2, WS2, and TiS2, as shown in Figure 3. The threshold energy for the production of S vacancies for virtually all TMDs is within the energies used for LV-TEM studies. The threshold energy for Se or Te vacancies due to electron irradiation is significantly higher (200-300 kV). For other compounds that were not part of the study, the required electron energies should be similar, based on the narrow values of Td in Fig. 2.

The study demonstrates that there is no significant effect on the generation of further defects in the case of an existing single defect. However, at the edges of the nanostructures, the threshold energy is significantly reduced [21, 22]. For example, the calculations for a WS2 band indicate that the chalcogen atoms at the edge may have a shift threshold of 4.2 eV, as compared to 7.0 eV away from the edge. In that case, the knock-on threshold is reduced below 60 keV.

HRTEM image of MoS2
Figure 4. HRTEM image.

Experimental validation in the TEM

Experimental observation of the development of a MoS2 monolayer under the 80 kV electron beam revealed, in accordance with the simulation, that vacancies production only occurs on the S sub lattice, accompanied by shrinkage of the membrane [see Fig. 4 (a)]. The cross section for the atomic distance was determined to be 1.8 barn, which is in reasonable agreement with the calculated cross section of 0.8 barn, considering that the theoretical results at energies below the static threshold, are very sensitive to inaccuracies in, for example, the velocity distribution of the atoms.

substitution energies for various species
Figure 5. HRTEM image.

Targeted doping under the electron beam is possible

The study revealed large differences in the energies and local state densities (LDOS) for different substitution atoms and molecules. Due to the DFT calculations, targeted doping is also possible for diatomic molecules or molecules containing hydrogen (Figure 5).

The filling of the vacancies was also observed in the TEM images (Figs. 4, 5 (c, e)). Although the type of substitution atom could not be identified, the TEM images also prove experimentally that electron beam mediated doping is possible. Consequently, by controlling atomic species in the TEM chamber and choosing the electron energy, it should be possible to achieve a modification of the physical properties of TMDs by electron irradiation.

"Electron microscopists will now be able to make decisions on the optimum accelerating voltage for damage-free observation of a TMD material based on more certain threshold simulations, and also for purposeful doping," Ute Kaiser, lead scientist for the TEM study, said.

Resource: Komsa, H. P., Kotakoski, J., Kurasch, S., Lehtinen, O., Kaiser, U., & Krasheninnikov, A. V. (2012). Two-dimensional transition metal dichalcogenides under electron irradiation: defect production and doping. Physical review letters, 109, 035503, doi: 10.1103/PhysRevLett.109.035503, [PDF]

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