Thoeretical modelling of opto-electronic properties of monolayer TMDC materials
Smaller, more flexibel, more efficient! This trend is clearly visible in the development of electronic devices. Transition metal dichalcogenides are considered promising candidates to push this goal to the extreme as samples as thin as a few atoms can be prepared from these materials. Nevertheless,...
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|Summary:||Smaller, more flexibel, more efficient! This trend is clearly visible in the development of electronic devices. Transition metal dichalcogenides are considered promising candidates to push this goal to the extreme as samples as thin as a few atoms can be prepared from these materials. Nevertheless, they exhibit strong coupling to electromagnetic field which, due to the small thickness, are highly sensitive to environmental conditions.
In this dissertation, selected aspects of the opto-electronic properties of semiconducting TMDC monolayers were investigated in several studies.
The materials were studied using a hybrid approach that combines density functional theory methods with density matrix theory methods to produce an effective and accurate tool for a parameter-free description of the investigated systems. Results of DFT calculations were taken as a starting point to develop a model description of the non-interacting ground state of the system, on the basis of which the optical and dynamical properties could be analysed using a Dirac/semiconductor Bloch equation approach. Here, in particular, the modelling to describe the Coulomb interaction formed a fundamental link between the two approaches.
The focus of a first study was consequently the extension and analysis of a model of this interaction, as well as further investigations of the modification of the interaction by excited charge carriers and the dielectric environment, and finally its implication for the electronic and optical energy spectra. Based on the Coulomb potential of a layer system and the wave functions resulting from DFT calculations, an isotropic model was found for the Coulomb matrix elements in the vicinity of the direct band gap. Direct experimental observation of the interaction is not possible, but the good agreement of the results for the charge carrier- and environment-induced reduction of the band gap and exciton binding energies with experimental values and established theoretical models indicates that the elaborated model is a reasonable and efficient approximation to describe the interaction. In all subsequent investigations, this model was adapted material-specifically and used for the interaction description in the area of the main valleys (K/K′) and the side valleys.
In a second study, thmagnetic field dependence of the excitonic spectrum was investigated. The predicted diamagnetic shift of the s-like states with a g-factor of g_ns > 2 was found to be equivalent to experimental studies. In addition, the p-like exciton series, which is not directly optically addressable – i.e. cannot be excited via one-photon processes –, was investigated. Due to its angular momentum quantum number, this series exhibits an additional linearr magnetic dependence, which leads to a Zeeman splitting of the states. An indirect optical investigation of these p-like states is possible under suitable excitation conditions, since transitions between s- and p-like excitonic states can be optically induced. Due to the energetic order of the excitons, the case of an initial occupation of the 2s state is particularly interesting, since here the transition to the energetically lower 2p states implies an amplification of the signal in the terahertz (THz) range. Due to the different magnetic field dependence, this amplification, which is partly superimposed by absorptive features of 2s-3p-transitions, is tunable by a magnetic field. Furthermore, the position of the gain maximum can be shifted by the choice of the dielectric environment.
While excitonic properties dominate the optical response of the material in the regime of low excitation densities, strong excitation leads to a strong renormalisation of the band gap, reducing the band gap by several 100meV, to a bleaching of the excitonic resonances, and finally to an amplification of the optical probe-signal in the region below the lowest exciton resonance. Our analysis of the charge carrier dynamics using the example of MoTe2 has shown that in this material system the charge carriers relax into hot Fermi-like distributions after optical excitation due to the strong Coulomb interaction
already on time scales of a few femtoseconds. In a first study, the focus was placed on the dynamics in the immediate vicinity of the direct band gap (K/ K′), whereby an estimation of the contribution of the side valleys showed that this causes an increase in optical amplification. A second study, in which the analysis was extended to the entire Brillouin zone (BZ), showed that scattering times into the side minima (side valleys) depend sensitively on the excitation conditions. However, for none of the investigated molybdenum-based materials could be shown that the scattering of optically induced charge carriers into the side valley the side valley to push energetically under the main valley – for all constellations studied, the band gap of the monolayer remained direct.
Finally, it was investigated how the 1s exciton resonance in the linear optical spectrum changes when an electron-hole plasma has formed in the material. A linear broadening of the resonance was observed, which can be measured in a faster decay of the integrated four-wave mixed signal, separated from contributions of a possible inhomogeneous broadening. Furthermore, it was shown that both relaxation processes, i.e. both the cooling of the charge distribution and the regrouping of the charge carriers in the different valleys, lead to a narrowing of the resonance.|