MoTe₂ Under the Electron Beam

April 26, 2019 – New point and line defects have been revealed in single-layer MoTe₂ under the electron beam. With the C_c/C_s-corrected SALVE microscope at 40 kV, researchers from Ulm, Dresden and Aalto followed how tellurium vacancies cluster into tetravacancies and trefoils, line up into vacancy lines and finally form inversion domains and islands of the metallic 1T′ phase. First-principles calculations showed that some of the defects carry magnetic moments and that vacancy lines act as metallic quantum wires, which may make MoTe₂ a platform for quantum devices.

A perfect crystal is predictable, and for many future devices that is exactly its limitation. Missing atoms, rows of vacancies and boundaries between mirror-image domains can give a semiconductor sheet new electronic, magnetic and optical functions, provided that one knows how such defects form and what they do. Scientists from Ulm University, the Helmholtz-Zentrum Dresden-Rossendorf and Aalto University in Finland have now followed, atom by atom, how defects arise and evolve in single-layer molybdenum ditelluride (MoTe₂) under the electron beam. They imaged the material with the C_c/C_s-corrected SALVE microscope at 40 kV^[1]–[3], which both creates and resolves the defects, and used first-principles calculations to work out their electronic and magnetic properties. Several of the defects had never been observed before, and some of them carry a magnetic moment, which sets the stage for future quantum devices.

Defects as building blocks
Transition metal dichalcogenides (TMDs) such as MoTe₂ are layered materials that, depending on their elements, can be insulators, semiconductors, metals, superconductors or show charge density waves^[4]–[6]. Single sheets can be exfoliated^[4] or grown by chemical vapor deposition^[7], and they promise numerous practical applications^[8]. In a transmission electron microscope (TEM), they can be modified and imaged at the same time, with the electron beam serving both as an imaging tool and as a means to change the material^[9]–[13]. MoTe₂ is a particularly interesting case: its semiconducting 2H phase and its metallic 1T′ phase differ in energy by only about 31 meV per formula unit.

Defects and their agglomeration can drastically change the properties of these materials^[5],[8],[14], for example by creating catalytically active centers^[15]. Mirror twin boundaries (MTBs), the borders of inversion domains in which the lattice is turned by 180°^[16]–[18], can form one-dimensional metallic quantum objects inside a semiconducting matrix^[19]. Yet it was not clear what role point defects play in MTB formation or how mechanical strain affects it. The exact structure and direction of line defects can differ widely^[20],[21], and the reason remained elusive, partly because contrast and resolution are limited in conventional C_s-corrected TEMs.

Imaging at 40 kV
The researchers therefore used a microscope corrected for both spherical (C_s) and chromatic (C_c) aberration. The SALVE microscope reaches a resolution of 0.9 Å at 40 kV and records fully atomic-position-corrected images within about one second over a large field of view^[2]. In such images, a single missing tellurium atom can be told apart from two missing ones (Fig. 1): a Te column with one atom left is still slightly brighter than a neighboring Mo atom, while a column Te divacancy, in which both stacked Te atoms are gone, shows almost no signal. The DFT calculations gave formation energies of 4.87 eV for a single Te vacancy and 4.46 eV per Te atom for a column divacancy. Mo vacancies cost 10.45 eV, which agrees with the observation that only Te vacancies and related defects occurred.

Direct knock-on damage should not occur at 40 kV, because the Te and Mo atoms are heavy^[22]: the electrons can transfer at most 0.72 eV to a Te atom and 0.95 eV to a Mo atom, far below the formation energies, and actual displacement thresholds are even higher^[22]. Still, the vacancy concentration grew under the beam. The exact mechanism is not known, but beam-induced chemical etching by fragments of water and other molecules on the sample surface is a likely cause^[23]. How the samples were prepared and imaged is described in the box below (Fig. 2).

Vacancies that team up
The beam also produced more complex defects, in which several atoms are missing (Fig. 3). The team called them “extended point defects”, as they lie between true point defects, such as single vacancies, and extended structures, such as vacancy lines of arbitrary length. They start with two column Te divacancies. Two Te atoms migrate into the center and form a symmetric defect, tetravacancy I. This configuration is metastable: within 21 s it distorted into the more stable tetravacancy II (Fig. 3b). After further irradiation and the loss of another Te₂ column, a symmetric trefoil-like defect, trefoil I, appeared 271 s later (Fig. 3c). Tetravacancies I and II had never been observed before. Image simulations and further defect variants are shown in the box below (Figs. 4, 5 and 6).

Quantum dots with a magnetic moment
To learn what the defects do to the material, the researchers calculated the spin-polarized density of states (DOS), that is, how many electronic states with spin up and spin down exist at each energy (Fig. 7). The defects introduce many states inside the band gap. These are localized around the defects, which therefore scatter electrons and affect transport. In tetravacancies I and II, spin-up and spin-down states are shifted against each other, so the defects become magnetic. While pristine MoTe₂ is nonmagnetic^[24], the calculations gave a total magnetic moment of 4 μ_B for tetravacancy I and 2 μ_B for tetravacancy II, mainly localized on the three Mo atoms around the central Te atom. Embedded in a semiconducting matrix, such defects can be regarded as quantum dots. A single Te vacancy, by contrast, is hardly spin-polarized, and the trefoil defects are nonmagnetic.

“With the combination of first-principles calculations we are explaining the defect formation, migration, and their coalescence resulting ultimately in the formation of inversion domains,” said Ute Kaiser, head of the Electron Microscopy Group of Materials Science at Ulm University. “The controllable introduction of particular defects that introduce certain functionalities may be used application-related for devices with new optical, electronic, and magnetic properties.”

Vacancy lines as quantum wires
Continued imaging also produced line defects. Fig. 8 compares an experimental image of a single vacancy line with four missing Te atoms with an image calculated from the DFT structure; the best match was found for a sample tilt of 4°, and small differences likely stem from strain around the missing atoms. DFT calculations of various vacancy lines showed that vacancies prefer to line up along the zigzag direction of the lattice rather than the armchair direction (Fig. 9). Along zigzag, the energy released per Te atom is about 0.04 eV for a single vacancy line and 0.6 eV for a staggered divacancy line; along armchair, only the column divacancy line releases energy at all.

“We have a situation where subsequent TEM imaging also results in line defect formation,” said Ute Kaiser. “However, also for the extended defects, the comparison of the atom positions between experimental and simulated images today can provide understanding of the properties of the materials.”

For dense vacancy lines, the calculated DOS shows new states that act like a reduced band gap (Fig. 10). More importantly, the lines are metallic and confined within the semiconducting sheet, so they can be regarded as quantum wires. The spin-up and spin-down electron densities are localized in space, which suggests that some of these metallic structures, such as the column Te divacancy line, could be used in spintronics.

Lines or clusters: what the energies tell
The formation energies of all observed structures explain how the defects evolve under the beam (Fig. 11). Single Te vacancies gain energy by forming lines, which is why the experiments showed single vacancy lines along zigzag. For column Te divacancies, lines are only slightly favored, but clustering into extended point defects releases a substantial amount of energy. The system therefore forms tetravacancies, via the metastable tetravacancy I, rather than column vacancy lines. The trefoil, with 3.88 eV per Te atom, is strongly preferred over a divacancy line with the same number of missing atoms.

Inversion domains and metallic islands
At higher vacancy concentrations, inversion domains formed after a total dose of about 1.4 × 10⁹ electrons per nm², bordered by MTBs of the 4|4P and 4|4E types (Fig. 12a–c). 4|4P boundaries had been reported before after thermal annealing, which also removes Te, but the 4|4E boundary from Te deficiency had never been seen in MoTe₂. In another area, the strain of a single vacancy line with six missing Te atoms pushed neighboring Te atoms aside, and an island of the metallic 1T′ phase appeared within one second, while the vacancy line moved by two unit cells (Fig. 12d–f). Similar transformations had been observed under the electron beam in Re-doped MoS₂^[5]; they likely originate from strain induced by vacancies and possibly from charge transfer and vibrational effects^[25],[26].

“Finally, using the 40 kV electron beam, we were able to provide insights into the formation and evolution process of inversion domains with mirror twin boundaries of different types, along with the islands of the metallic phases that occur,” Kaiser said. The results are also relevant for other TMDs^{[20],[21],[27],[28]}, as they relate the atomic structure of the emerging MTBs^[16] to the experimental conditions^[21],[28]. The calculations behind them are summarized in the box.

What it opens up
The study showed a plethora of point and line defects in monolayer MoTe₂ and how they form, migrate and coalesce. Metallic islands of the T′ phase can act as quantum dots, while vacancy lines and mirror twin boundaries form one-dimensional metallic systems embedded in a semiconductor. “The latter structure is very interesting in the context of fundamental aspects of the physics of Tomonaga−Luttinger liquid and, as for practical aspects, plasmonics,” the authors write. Together with the defect-associated magnetism, this opens a route towards quantum devices made by defect engineering in single-layer MoTe₂.

“We showed that some of the observed defects have localized magnetic moments,” Kaiser said. “This may lead toward control of optical and electronic properties for quantum devices in 2D materials. Other systems that we observed are very interesting in the context of fundamental aspects of physics and for practical aspects in plasmonics.”

Resource:
Lehnert, T., Ghorbani-Asl, M., Köster, J., Lee, Z., Krasheninnikov, A. V., Kaiser, U. (2019).
Electron-Beam-Driven Structure Evolution of Single-Layer MoTe₂ for Quantum Devices.
ACS Appl. Nano Mater. 2(5), 3262–3270.
https://doi.org/10.1021/acsanm.9b00616

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