Phase transformations in single-layer MoTe₂ stimulated by electron irradiation and annealing

MoTe₂ crystals were prepared by mechanical exfoliation using a Nitto wafer tape [52, 53]. After applying the flakes to a silicon/silicon dioxide wafer, covered first with Polyvinyl alcohol (PVA) and second with Polymethyl methacrylate (PMMA) (see figure 1(a)), suitable flakes were identified in the optical microscope. Subsequently, the chosen crystal and the PMMA layer were detached from the SiO₂-polymer wafer by scratching a circle into both polymers with the crystal located in the centre. Further, a drop of distilled water is dropped outside the circle toughing the scratch. After a few seconds, the underlying PVA layer is dissolved by the water drop, and thus, the PMMA layer is floating on the water drop. In the next step, the PMMA layer with the MoTe₂ crystal on top can be fished out by a metal stamp. Next, the PMMA layer was stamped onto a ThermoFisher micro-electro-mechanical system (MEMS)-chip [54], shown in figure 1(b) (note: isopropyl alcohol can help to bring the PMMA layer in contact with the chip surface). The accuracy of measurement for the temperature of the used chips is specified as 4%. To dissolve the PMMA layer, a drop of acetone was dropped on the chip while the metal stamp was still attached to the polymer membrane and the chip. After dissolving the polymer layer, the stamp was removed, and the chip was gently, but carefully washed first in acetone and then in distilled water to remove PMMA residuals. Graphene-encapsulated MoTe₂ was prepared by transferring three separate flakes to a TEM grid by iterative mechanical exfoliation [55]. For thermal annealing of graphene-encapsulated H-MoTe₂ on a Quantifoil grid, a side entry Double Tilt Heating Holder Model 652-Ta (Gatan Inc.) was used. The sample was heated at 850 °C for 20 min in a vacuum of the order of 10⁻⁴ mbar and analysed subsequently at room temperature.

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The high-resolution TEM images were acquired at the Cc/Cs-corrected Sub-Ångström low-voltage electron microscope (SALVE) operated at 80 kV [56]. Measured values for Cc and Cs were in the range of −5 to −15 μm. The vacuum in the column of the TEM was ∼2·10⁻⁷ mbar. Dose rates in the range of 10⁵ $\frac{{e}^{-}}{{\mathrm{nm}}^{2}\cdot {\rm{s}}}$ were used for the high-resolution images, and the images were recorded on a 4k × 4k CMOS camera with exposure times of 0.25–1 s. Spatially-resolved EELS with an energy resolution of 0.6 eV, as well as STEM HAADF and corresponding EDX elemental maps, were used to confirm the composition of NWs by Mo and Te with a ratio of 1:1 of Mo and Te (for a detailed analysis, see supporting information (SI)). All STEM HAADF and EDX experiments were conducted at the Talos F200X G2 STEM instrument at 80 kV.

The density functional theory calculations have been performed using the Perdew−Burke−Ernzerhof (PBE) generalized gradient approximation (GGA) exchange–correlation functional as implemented in VASP code [57, 58]. Formation enthalpies have been calculated using an energy cutoff of 400 eV, typically 12 k-points in each periodic direction (one k-point in all other directions), and a force convergence criterion of <0.01 eV Å⁻¹. van-der-Waals interactions are considered by the DFT-D3 method by Grimme with Becke–Johnson damping function [59].

For the automatic identification of isolated Te defects in HRTEM images of single-layer H-MoTe₂, an adapted version of a convolutional neural network (CNN) was used, as presented in [60]. Further, the implementation is based on the deep-learning API Keras [61]. CNNs are trained to label the different atomic species and positions (i.e. Mo and Te columns) as well as to detect vacancies (i.e. single and double Te vacancies). For each atomic species and vacancy type, an individual network was trained. The training input data were simulated HRTEM images. In addition, for each HRTEM training image, the target output data was a separate label for each vacancy type and atomic species, which resembles a heat map with peaks around the target positions (i.e. positions of the target atomic species or vacancies). The target positions (i.e. atom positions and vacancies) were extracted and counted from the output label of each trained network for the simulated and experimental images. To account for drifts during the acquisition of image series, a phase correlation algorithm [62] was used to align the individual images. Areas in the images containing surface contamination were identified via FFT filtering and masked so that data from only 'clean' areas were considered for the determination of the damage cross-sections. The applied dose rates were determined from the experimentally acquired images by the combination of the known acquisition times, the average counted electrons in the images, and the known conversion rate of the utilized CMOS camera. Further details on the CNN application paradigm and the histograms of the experimentally determined damage cross-sections are presented in the SI.

The colouring of the raw HRTEM image of the graphene-encapsulated MoTe₂ shown in figure 5(c) was carried out with the free software ImageJ using lookup tables (LUTs).

Figure 2(a) shows a colour coated 60 kV Cc/Cs-corrected HRTEM image of single-layer H-MoTe₂. As for MoS₂ [55] and MoSe₂ [47], continuous electron irradiation leads to the formation of defects in single-layer H-MoTe₂ [40]. Similar to the previous study carried out at 40 kV [39], electron-beam-driven structure evolution in single-layer MoTe₂ starts at 60 kV and 80 kV with the formation of isolated single (V_Te) and double tellurium vacancies (V_2Te). To automatically detect V_Te and V_2Te, we applied a dedicated trained convolution neural network (CNN) based on U-net architecture, enabling a quantitative description of V_Te and V_2Te distributions in single-layer MoTe₂. By automatic determination of the atom positions, atomic species, and isolated defects, a high number of images were evaluated and thus, our study gives a statistically significant statement about the growth rate of vacancies. Further, by observing the rate at which vacancy concentration increases, one can directly evaluate the intrinsic Te vacancy damage cross-section $\sigma .$ From a HRTEM image series σ can be calculated following the paradigm presented in [55], and the formula for the damage cross-section reads as follows:

$$\begin{eqnarray*}&&\sigma =({V}_{\mathrm{end}}-{V}_{\mathrm{initial}})/({N}_{\mathrm{tot}}{\rm{\cdot }}{{\rm{\varnothing }}}_{\mathrm{total}}).\end{eqnarray*}$$

Here, $\unicode{x02206}V={V}_{\mathrm{end}}-{V}_{\mathrm{initial}}$ is the number of vacancies produced during observation, $\unicode{x02206}t$ the observation time, ${N}_{{\rm{tot}}}$the number of chalcogen atoms in the evaluated area, and ${\varnothing }_{\mathrm{total}}={\varnothing }_{\mathrm{rate}}\times \unicode{x02206}t$ the total accumulated dose. Images acquired for the determination of $\sigma$ were screened, so that no extended defects were included. Moreover, care was taken to ensure that only clean sample regions were used for evaluation. Further, the vacancy formation was analysed in the linear regime, which means that the increase in the number of vacancies in an image series follows a nearly linear relation with respect to the applied dose (see figure 2(b)).

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The experimentally determined damage cross-sections for single-layer H-MoTe₂ at 40 kV, 60 kV, and 80 kV are presented in table 1 and in the inset of figure 2(c). The results for all three voltages are in the same order of magnitude and significantly lower, in the order of several barn, compared to values for single-layer H-MoS₂ and H-MoSe₂ as reported in the literature [47, 55, 63]. Therefore, single-layer H-MoTe₂ shows intrinsically reduced irradiation damage compared to the other Mo-based TMDs counterparts in the studied voltage range.

Table 1. Quantitative results of damage cross-sections σ (Median/Mean) for single-layer H-MoTe₂ at different acceleration voltages U with the corresponding standard deviation of the values in a TEM. N is the total number of Te atoms in the analyzed area, and Ø_rate is the applied dose rate for the conducted experiments. Further, ΔV is the total number of vacancies created during imaging.

U [kV]	$\sigma$ (Median/Mean) [b]	Standard deviation [b]	N (103)	Ørate [e/nm2s]	ΔV
80	0.29 / 0.44	0.53	250	(0.80–1.79)106	863
60	0.35 / 0.41	0.23	161	(0.62–2.25)106	594
40	0.32 / 0,47	0.5	404	(0.55–1.63)106	3408

Further, to understand the damage mechanism in single-layer H-MoTe_2, the elastic damage cross-sections were predicted using the McKinley–Feshbach formalism (described in detail in the SI), summarized in figure 2(c). Our calculations predict knock-on threshold (T_thr) of about 225 kV at room temperature (see figure 2(c), dashed blue curve), that is significantly higher compared to single-layer H-MoS₂ (T_d = 6.9 eV; T_thr ∼ 75 kV) and H-MoSe₂ (T_d = 6.4 eV; T_thr ∼160 kV) [64], and well above the voltage range of 40–80 kV studied in this work.

To sum up, our results show that elastic damage including lattice vibrations is not sufficient to describe damage in this material, because, the formation of vacancies in a single sheet of MoTe₂ is possible at electron voltages (40 kV, 60 kV, and 80 kV) well below the knock-on threshold (225 kV at 20 °C), see inset figure 2(c). Here, for instance, the model gives a cross-section which is zero at 80 keV, however, the experimentally determined cross-section gives a median value of 0.29 barn. Therefore, the amount of elastic damage can be assumed to be zero and, thus, in the utilized voltage range the primary contribution to the damage in MoTe₂ should be inelastic interactions like radiolysis and chemical etching. Here, a cross-section value of 0.001 barn was taken as the limit to determine the threshold voltages.

However, the observed standard deviations of the presented values for the individual voltages are in the same range as the median/mean of the conducted experiments proofing a significant spread of the observed damage cross-sections between different sample positions. Due to the high sensitivity of MoTe₂ to oxygen, the analysed single-layers were not heated up to remove any surface contaminations before being inserted into the TEM chamber. This should significantly impact $\sigma$ and, thus, could partially explain the experimentally observed spread. It is worth noting that the material decomposes differently in sample areas contaminated by amorphous hydrocarbons on the surface. It is not clear if this can be attributed to damage caused by inelastic interactions within the hydrocarbons or due to a protecting effect of the material layer caused by the underlying hydrocarbon contamination.

A high number of vacancies can lead to the formation of various extended and line defects, up to 4|4P mirror twin boundaries, depending on the used TMD. Figure 3(a) exemplifies the evolution of various defect types via an image sequence of experimentally acquired 80 kV HRTEM images, from left to right with increasing total electron dose. The listed defect structures are also exemplary for the defects found at 60 kV and have already been published for 40 kV [39]. Thus, we conclude that the defect evolution within the analysed voltage range of 40–80 kV can be assumed to be of the same nature and evolves from single defects via extended defects to the formation of nanowires. Note that the analysis of the electron resistance of double-layers of H-MoTe₂ showed that they withstand a multiple of the total electron dose compared to the single-layer. Detailed presentation of the results can be found in the SI.

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First-principles calculations are employed to analyse the stability of the structures observed in the experiment. For that, the formation enthalpy is calculated. The structures with the lowest formation enthalpy for a given composition are considered thermodynamically stable if the curve connecting these points is convex. This is a well-established construction, referred to as the convex hull, see for example [65]. If structures have negative formation enthalpy but are above the convex hull they are deemed to be thermally unstable (or metastable), and likely decompose into stable phases.

The convex hull of different Mo–Te compounds is shown in figure 3(b). Our calculations predict that Mo₆Te₆ nanowires and the H-MoTe₂ phase are stable. The energy penalty for the formation of a 4|4P MTB in MoTe₂ is very low, in agreement with the previous calculations [66], and the MTB is energetically preferable over single Te vacancies (for 4|4P MTB triangular structure, the formation energy difference $E\left({V}_{{\rm{Te}}}\right)-E\left(4|4{\rm{P}}\,{\rm{MTB}}\right)=-0.8\,{\rm{eV}}$ per vacancy) meaning that vacancies tend to cluster to form MTBs. However, the proposed MTB network by Junqiu Zhang et al [67] is found to be metastable, as evident from figure 3(b).

After the agglomeration of defects in the hexagonal lattice structure of MoTe₂, crystalline nanowires with the formula Mo₆Te₆ can form (see figure 3(c)). In figure 4(a), the structure model of the found nanowires is displayed. To verify the structure, orientation, and composition of the experimentally acquired nanowires, image simulations based on the structure models are performed using the abTEM API (see figure 4(b)). The details of image simulation with abTEM are given in SI. Line scans taken between the red and blue arrows of the experimental and simulated images are plotted and overlaid in figure 4(c). It is evident from the intensity plot that the experimental image agrees well with the simulated image.

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In addition, our experiments have shown that emerging nanowires are extremely radiation resistant and insensitive to oxidation. Figure 2(c) summarizes the calculated cross section for sputtering a Te atom from Mo₆Te₆ in the red curves (bold; static case, dashed; Maxwell–Boltzmann (T_20°C)). Our DFT calculation estimates T_d = 4.90 eV required for displacing a Te atom from a pristine Mo₆Te₆ nanowire. By taking lattice vibrations into account, the corresponding knock-on threshold is 170 kV. Consequently, no elastic damage is expected in the acceleration voltage range of 40–80 kV. In a second set of simulations, we assessed the required energy to oxidize pristine Mo₆Te₆ resulting in

$$\begin{eqnarray*}&&{{\rm{Mo}}}_{6}{{\rm{Te}}}_{6}+1/2{{\rm{O}}}_{2}\to {{\rm{Mo}}}_{6}{{\rm{Te}}}_{5}{\rm{O}}+{\rm{Te}}\end{eqnarray*}$$

$$\begin{eqnarray*}&&{E}_{\mathrm{ox}}\left(\mathrm{Te}\right)=2.08\,\mathrm{eV}.\end{eqnarray*}$$

The value of 2.08 eV proves that the pristine nanowire is predicted to be oxidation insensitive, as observed in the experiments. On the contrary, the required energy to oxidize an existing single Te vacancy site is predicted to be

$$\begin{eqnarray*}&&{\mathrm{Mo}}_{6}{\mathrm{Te}}_{5}+1/2{{{\rm{O}}}_{2}\to \mathrm{Mo}}_{6}{\mathrm{Te}}_{5}{\rm{O}}\end{eqnarray*}$$

$$\begin{eqnarray*}&&{E}_{\mathrm{ox}}\left(\mathrm{Te}\right)=-3.21\,\mathrm{eV},\end{eqnarray*}$$

indicating that spontaneous oxidation of a V_Te is energetically favorable. Since the properties of a one-dimensional structure should be extremely sensitive to defects, due to the confinement in two-dimensions, and defects can easily appear in low-dimensional materials due to effects of the environment, it appears interesting to access the electronic structure of the nanowires with vacancies. Therefore, the total density of states (DOS) was calculated for the pristine and the defective structure. Figure 4(d) shows the total DOS of pristine (blue) and defect-associated (red) Mo₆Te₆ nanowires. While pristine MoTe₂ with the 4d² configuration of Mo atoms is a semiconducting material, our calculations predict a metallic character for Mo₆Te₆. Furthermore, the depicted DOS for the defect-associated case in figure 4(d) shows that the metallic character should be preserved.

Although defect creation is a promising way to tailor the properties of a single-layer, we want to demonstrate a route to prevent radiation damage in H-MoTe₂, allowing structural analysis even under high electron doses. Figure 5(a) shows a structure model of a vertical heterostructure of G/MoTe₂/G in which a single-layer MoTe₂ is enclosed between two graphene (G) sheets. Samples were prepared via subsequent transfer of the mechanically exfoliated layers onto a Quantifoil grid, shown in (b). From the experiments we conducted with the G/MoTe₂/G structures, it became clear that this type of protection for MoTe₂ is an almost indestructible structure for analysis at 40–80 kV voltages. The G/MoTe₂/G sample, however, showed dramatically different behaviours, and the vacancy concentration remained unchanged after the electron dose, which completely destroyed the freestanding target. In this context, estimated damage cross-sections of ∼0.006 b and ∼0.005b were determined for a G/MoTe₂/G sample at 80 kV and 60 kV, respectively, see inset in figure 2(c).

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However, a sufficiently high dose rate can lead to defects in one (or both) graphene layers of the sample, such that the protective effect of the graphene sandwich is locally abolished. Thus, tellurium and molybdenum atoms can escape the graphene encapsulation [68]. This enables the Mo and Te atoms to leave the graphene pocket so that, subsequently, the formation of NWs encapsulated in between (bi-) graphene is feasible, see figure 5(c). To demonstrate the validity of the protective ability of intact graphene-encapsulation, graphene-encapsulated single-layer H-MoTe₂ was annealed to 850 °C in a vacuum. No significant changes in the freestanding H-MoTe₂ layer were observed (heating holder, Model 652-Ta) in contrast to emerging changes in the annealing experiments in freestanding H-MoTe₂ of lower temperature, which is elaborated in the following.

Various crystals were transferred onto a micro-electro-mechanical system to investigate the temperature-induced structure evolution of H-MoTe₂. We begin our discussion by briefly reviewing the results obtained on crystals with the number of layers (L) between 5 and 20. Despite the use of the dedicated MEMS chips, in which the freestanding flakes are annealed locally, two edge effects occurred. (i) Structural changes mainly formed in areas contacted by the silicon nitride Si₃N₄ of the heating coil. (ii) Structural changes occur initially at freestanding flake edges. The latter indicates a temperature gradient originating from Si₃N₄ and a high sensitivity of the flake edges to temperature-driven changes. With the help of EDX and HRTEM at 80 kV, the observed structural changes were analysed in detail, see SI. While the 2D structure H-MoTe₂ naturally has twice as much Te as Mo, a 1:1 ratio was detected in EDX after the pristine crystals were annealed. Especially by conducting HRTEM experiments, the changes in the stoichiometry of the material composition could be investigated at the atomic scale and specified as Mo₆Te₆ nanowires. These have the same structure as previously obtained by electron irradiation. Here, the critical temperature for the phase transformation in few-layer MoTe₂ in the range of 550 °C–600 °C was measured. A more detailed study on the structural changes in few-layer H-MoTe₂ crystals is provided in the Supporting Information.

As the number of layers decreased, a reduction in the phase transformation temperature was also observed. For the extreme case of a single-layer, phase transitions have occurred already at 550 °C. Figure 6(a) shows a single-layer H-MoTe₂ image just before the abrupt transformation into nanowires. The area used for detail transformation evolution is marked in red, and several atoms are highlighted in solid orange (Te₂) and solid turquoise (Mo) to specify the different atomic columns. The area was determined to be 29.6 nm², corresponding to 548 Te and 274 Mo atoms in a pristine hexagonal single-layer. The number of atoms in the red-framed area was manually counted and resulting in 520 Te and 282 Mo atoms, which corresponds to a Te deficiency of 8.5%.

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This single-layer also exhibits a high concentration of triangular-shaped 4/4P MTBs (green dotted lines), connected by symmetric centres marked by red dashed rings. These symmetric centres have one Te₂ atomic column located in the middle of a Mo triangle. Showing a high agreement with the published new polymorph v1H-Mo₅Te₈ structure [67]. In our example, however, the superior structure is not symmetric over a larger distance since the triangular MTB structures are of different sizes. From (a) to (b), the single-layer partially collapses and forms Mo₆Te₆ nanowires, marked by red arrows $({\varnothing }_{{\rm{rate}}}=1.4\times {10}^{5}\,\frac{{{\rm{e}}}^{-}}{{{\rm{nm}}}^{2}{\rm{s}}}).$ To ensure general validity, the Te deficiency was determined on a second sample by the aforementioned paradigm resulting in a Te deficiency of 9.5%. Only short nanowires were observed in all samples analysed in the single-layer case. We assume that the formation of short nanowires can be attributed to the fast transformation process. It is possibly stimulated by the interplay of the electron beam with the annealed single-layer exhibiting the high Te deficiency, enabling it to overcome the energy barrier to form the energetically stable nanowires (see convex hull in figure 3(b)).

Having shown that the phase transformation in single-layer H-MoTe₂ takes place at about 550 °C ± 22 °C, we move on to study whether the Mo₆Te₆ nanowires are stable at higher temperatures and how the discrepancy between our transition temperature (550 °C) and that reported by Hui Zhu et al 2017 (500 °C) can be explained. Therefore, we analysed the stability of the in figure 6(b) shown nanowire structure. Here, we want to point out that polymorphic carbon can be appreciated, covering the Mo₆Te₆ network after phase transition at 550 °C, as shown in figure 6(c). As explained in the previous sections, the stability of a single-layer of H-MoTe₂ can be significantly enhanced against electron irradiation by encapsulating it with graphene. We therefore assume that carbon contamination on the surface of the single-layer can act as a protecting layer. Thus, this protection effect can explain the differences in the transition temperatures for the solid-to-solid transformation in our experiments, which is 550 °C for the single-layer case, compared to the reported temperature in literature, which is 500 °C reported by Hui Zhu et al 2017.

It is obvious that if more Te atoms are removed from the sample, the Mo concentration will continue to increase until Mo crystals are formed. Even at temperatures as low as 550 °C, we were able to image crystal seeds with a cubic crystal structure, see the turquoise marked region in figure 6(c). It cannot be ruled out that residual Te atoms are still present in the structure, but structural analyses have shown that these seeds can be attributed to Mo crystals. Additional analyses of the crystals shown are attached in the SI. The theory that Mo crystals form was further supported by the fact that we annealed the sample to a higher temperature and performed EDX on the crystals that formed. Therefore, the structure was annealed to 1000 °C for 15 min. Subsequently, pure Mo clusters formed, which no longer have any Te residues, as shown in figure 6(d). The EDX analysis of the Mo clusters is presented in SI. In addition, previously performed annealing experiments with amorphous carbon showed that graphene can be formed under such conditions [69, 70]. In particular, in our experiments we recognized that hydrocarbon contamination on the sample surface, illustrated in figure 6(c), could form polymorphic carbon films, shown in figure 6(d). In addition, this could have been favored by the catalytic effect of the Mo-metal crystals [70]. An exact phase transformation temperature for the transformation of Mo₆Te₆ to pure Mo crystals could not be worked out. However, with our annealing study in combination with HRTEM, we were able to show that pure ultrathin Mo crystals form from Mo₆Te₆ nanowires as soon as further Te atoms are released from the structure, at temperatures higher than 550 °C, while graphene is grown.

Eventually, we would like to mention that annealing at 250 °C ± 10 °C of 2H-MoTe₂ in an ambient atmosphere leads to oxidation of the material (see Supporting Information), emphasizing again the necessity of vacuum conditions for annealing experiments of two-dimensional materials.