The balance of excitation transfer and recombination processes in MoS 2 nanotubes and flakes Olga Smirnova 1,2 , Anna V. Rodina 2 , Tatiana V. Shubina 2 1 ITMO University, St. Petersburg 197101, Russia; 2 Ioffe Institute, St. Petersburg 194021, Russia Modeling 1 Theory Introduction Modeling 2 Conclusion Micro-photoluminescence of MoS 2 multiwalled nanotubes and flakes, synthesized by chemical transport reaction method, were measured at the Ioffe In the monolayer limit Institute [1]. They have exhibited specific properties unexpected for multiwalled MoS 2 becomes a direct- samples which have indirect band structure: gap semiconductor The radiation of indirect exciton, which is energetically the lowest in • multilayered structures, is absent at temperatures up to 80-100 K With increasing temperature, the simultaneous emission of direct and • indirect excitons is observed In nanotubes, the direct exciton emission can dominate over the indirect • exciton one in the entire temperature range In the 1-2 monolayer-thick flakes, the indirect emission increases in the low- temperature region and, as for the photoluminescence from direct states, drops with the increasing temperature. Our goal is to propose a theoretical model that allows us to describe the experimental data for various samples and to estimate the relationship between the internal parameters for qualitatively different structures. References [1] Shubina T. V. et al, Annalen der Physik, 531,1800415 (2019)
The balance of excitation transfer and recombination processes in MoS 2 nanotubes and flakes Lab symbolics Olga Smirnova, Anna V. Rodina, Tatiana V. Shubina Modeling 1 Theory Introduction Modeling 2 Conclusion Theoretical model Mathematical description The balance of the processes of transfer of excitation and System of rate equations: N 2 = Γ 12 We study the recombination is considered for both direct and indirect ⟶ ∂ N 1 steady state: N 1 Γ 2 ∂ t = − ( Γ 1 + Γ 12 ) N 1 + G 1 ( t ) excitonic systems, including bright (A) and dark (F) states of different nature (forbidden in spin and momentum). ∂ N 2 N iA 1) Sub-ensemble radiative ∂ t = Γ 12 N 1 − Γ 2 N 2 We assume the lowest state of the direct exciton to be bright Γ rad = Γ iA , recombination rate i and vice versa for the indirect one. N iA + N iF 2) For the equilibrium populations (fast inner relaxation) N 1 F N 2 F Δ E 1 Δ E 2 = e − kBT , = e kBT N 1 A N 2 A 3) In addition to the main dark state, there is an 4) We assume the temperature ejection from the light cone dependent relaxation between sub- E upper ensembles N 1 Γ 12 = γ e − ˜ kBT + f ∫ Δ E 1 Δ E e − E = 1 + e − kBT dE k B T N 1 A E lower ˜ - relaxation activation energy Δ E Finally, we derive the fitting formula: , c = Γ 1 A d = Γ 2 A where γ , Δ E 1 E lower e − E E upper Γ nr 1 + e − kBT + f ∫ ξ = de − ˜ Δ E kBT dE 2 k B T I 1 ( T ) = Γ rad - energy splittings in Δ E 1 , Δ E 2 The temperature dependence ξ ( T ) = I 2 ( T ) 2 N 2 sub-ensembles is given by the ratio: Δ E 2 c Γ rad 1 N 1 - prefactor f d + 1 + e kBT
The balance of excitation transfer and recombination processes in MoS 2 nanotubes and flakes Olga Smirnova, Anna V. Rodina, Tatiana V. Shubina Modeling 1 Modeling 2 Conclusion Introduction Theory As-grown and treated samples Bulk flake on a SiN 4 substrate We studied a flake and a tube grown via Thick flake on the SiN 4 substrate showed the chemical transport reaction method, qualitatively the same dependencies which then underwent the intercalation, ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ supposedly leading to the layer 1.0 separation. Fitting of the experimental 0.8 dependencies measured in the as-grown ■ ■ ξ 0.6 I 1 and treated samples is presented in 0.4 I 2 figures. ●● ● ● ● ● ● ● ● ● ● ● 0.2 ◆◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ To reduce the number of parameters 0.0 we make some assumptions: 0 50 100 150 200 250 300 𝑡 (tube) = 0.2 Δ 𝐹 # = 3 meV • • T, K Fitting parameters • 𝑡 (flake) = 0.02 𝐹 $%&'( = 0.01 • 𝐹 )**+( = Δ - • 𝐹 s = Γ 2 A Fitting parameters Γ 1 A Values of Δ𝐹 . in all samples are of the order of 10 meV • Energy value of E 2 is of the same order as in In treated structures the relaxation and non-radiative • the previous samples. rates become stronger. We suppose that this is caused Relaxation in this sample is on the order by the growth of the number of defects formed during weaker. intercalation
The balance of excitation transfer and recombination processes in MoS 2 nanotubes and flakes Olga Smirnova, Anna V. Rodina, Tatiana V. Shubina Modeling 1 Modeling 2 Conclusion Introduction Theory Different behavior of photoluminescence in thin flakes In thin flakes of 1-2 monolayer thickness, another photoluminescence behavior was observed: At low temperatures the emission of indirect • Monolayer Bilay states exceeds that of the direct ones er Both intensities drop with the increasing • temperature Therefore we assume the change of the level order in the subsystem of the indirect excitonic states: the lower one is bright, the upper is dark. This obliges to Fitting parameters take into account the dark states out of the light cone in the indirect exciton subsystem. Δ E 1 kBT + f 1 ∫ dEe − E 1 + e − In this case the ξ = d kBT c e − ˜ Δ E kBT formula is modified: Comparison of the obtained parameters with those of multiwalled structures indicates Δ E 2 kBT + f 2 ∫ dEe − E d + 1 + e kBT increase in relative radiative rate of the indirect bright state and relaxation between sub-ensembles. Also we set what makes relaxation temperature-independent; ˜ Δ E = 0 is still 3 meV Δ E 1
The balance of excitation transfer and recombination processes in MoS 2 nanotubes and flakes Olga Smirnova 1,2 , Anna V. Rodina 2 , Tatiana V. Shubina 2 1 ITMO University, St. Petersburg 197101, Russia; 2 Ioffe Institute, St. Petersburg 194021, Russia Introduction Theory Modeling 1 Modeling 2 Conclusion 1. We propose a theoretical model of a complex structure of the excitonic states for explaining the temperature dependences of photoluminescence of MoS 2 flakes and tubes. The model includes bright and dark states of different nature. 2. We assume that qualitative changes in this model are possible when the thickness is going down to the monolayer limit. 3. By fitting of the experimental data with the obtained formulas for intensities, we obtain possible sets of internal parameters of the system under consideration. In the future, we plan to increase the number of the model implementation to the experimental data and find the more or less stable ranges for the parameters. We also intend to determine the values of the parameters from other experimental data as a photoluminescense kinetic and theoretical calculations for the studied MoS 2 structures. Smirnova.olga248@gmail.com
Recommend
More recommend
