Parametrización de la resistencia de a estructuras para la simulación en el modelo a escala. 87

First-principles calculations also allow studying the effect of additional charge on the energetics of the system. From previous investigations on the Li intercalation of MoS2, it is known that additional

Figure 4.3: Influence of strain on the phase stability of TMDCs. The total energy vs. strain curves are displayed for H- and T’-phase of MoS2 (left panel) and MoTe2 (right panel).

For MoTe2 which exhibits only a small energy difference (about 40 meV/f.u.) between the

semiconducting H-phase and metallic T’-phase, the transformation can be driven by strain and vacancy concentration. In MoS2, both quantities make the metallic phase more favorable in MoS2

but cannot explain the phase transformation for reasonable values of strain below the fracture strain (∼ 11% ref.166_{) because of the large energy difference of Δ𝐸= 550 meV/f.u. Biaxial}

strain tends to show a more pronounced effect on the phase energetics than uniaxial strain.

the metallic phase.33 _{Otherwise, it is unlikely that exposure to the electron beam in TEM will lead}

to negative charging. The other way around, it is well established that the sample may acquire positive charge under electron irradiation in wide-gap semiconductors with defects, due to the emission of secondary electrons.167, 168 _{However, it should be stressed that in the experiment under}

consideration, Re impurities were present in the MoS2 flakes. Due to their extra electron compared

with Mo, Re impurities act as perfect n-type dopants, introducing an occupied shallow state close to the conduction band minimum (CBM). As both the defects states in the vacancy lines and Fermi level of the metallic phase are lower than these impurity levels, partial charge redistribution into the metallic regions and their boundaries should be observed. In order to study this charge redistribution in detail, we chose a large supercell that allows embedding a triangle-shaped T’-phase region into the H-phase matrix, corresponding to the structure seen in the experiment.12 _{Because the triangular}

regions are sulfur deficient, a suitable reference with the same number of atoms needs to be chosen to compare with the energetics of the phase patterned system. The most stable configuration

65

for the reference system comprises a single vacancy line in the otherwise-pristine H-phase. All energetic considerations in the following are based on the comparison between the system with the triangular-shaped metallic region and the single vacancy line reference. Figure 4.4 summarizes the

Figure 4.4: Effect of n-type doping on the phases stability. Additional negative charge as introduced by extra electrons or Re impurities leads to the decrease of the energy difference between the phase patterned system and the single vacancy line reference. It emerges that Re is indeed an almost perfect n-type dopant, as the total energy difference only slightly deviates from the extra-electron model. The downshifted curves correspond to correcting the results for finite-size effects due to the edge energies. The charge redistribution illustrated in the inset can be identified as the origin of the energy difference decrease. The charge density difference plot for 0.0025 extra electrons per f.u. is shown, indicating the redistribution into the metallic triangle and its boundaries. Bader analysis reveals an increase in the number of valence electrons in this region of +22% compared to the situation with a uniformly distributed charge. Image adapted from publication [34].

results of this comparison. Two sets of calculations are carried out to study the charge redistribution and the total energy differences between the system and reference depending on the amount of additional charge. In one set of calculations, the number of electrons is directly modified by setting the number of valence electrons directly via the NELECT tag in VASP. Note that a compensating uniform background charge needs to be introduced in this case, assuring the neutrality required in the plane wave calculations. It must be stressed that the total energy obtained in these calculations depends on the amount of vacuum and other details of the calculation, such that it is meaningless –

as discussed previously169, 170 _{– although the energy difference between two configurations with the}

same amount of additional charge is a valid physical quantity. In the other set of calculations, the effect of a substantially increased Re impurity concentration on the energetics was studied. Both sets of calculations reveal a significant decrease in the energy difference while adding additional charge. The energy difference – which is only slightly larger for the Re doped systems – illustrates the almost perfect n-type behavior of the substitutional impurities. The results obtained for finite- sized triangles (seven missing sulfur atoms) can be extrapolated to infinitely large metallic regions by subtracting the edge energy differences. For larger but finite triangles, the energy difference lies in between the two limiting curves.

Furthermore, the charge redistribution was studied by analyzing the charge difference density be- tween the neutral system and the system with additional charge. The inset in Figure 4.4 shows the charge density difference image corresponding to one additional electron in the 20×20 supercell. This corresponds to a charge concentration of 0.0025 e/f.u. From the plot, it is apparent that most of the additional electrons concentrate in the metallic region and at its boundary. A detailed consideration using Bader analysis171, 172 _{revealed that an electron excess of +22% in this region}

was achieved as compared to the situation of a uniformly distributed charge. This electron excess in the triangular region supports the picture of charge transfer from the energetically higher lying defect states and impurity levels to the metallic phase. Accompanied by this charge redistribution is a decrease in the energy difference between metallic and semiconducting phase. Although addi- tional negative charge should give rise to a local transformation from H-phase with a vacancy line to T’-phase, the Re concentrations necessary to account for the transformation to the metallic phase proved to be unrealistically high, at about 15%. Given that these high impurity concentrations were not observed in the experiment and – as mentioned above – additional negative charge is not expected during the exposure of atomically thin samples to the high-energetic electron beam in TEM, the mechanism solely relying on the effect of additional negative charge cannot explain the experimental observations.