Radiative lifetime of localized excitons in transition-metal dichalcogenides

Abstract

Disorder derived from defects or strain in monolayer TMDs can lead to a dramatic change in the physical behavior of the interband excitations, producing inhomogeneous spectral broadening and localization; leading to radiative lifetime increase. In this study, we have modeled the disorder in the surface of the sample through a randomized potential in monolayer WSe2. We show that this model allows us to simulate the spectra of localized exciton states as well as their radiative lifetime. In this context, we give an in depth study of the influence of the disorder potential parameters on the optical properties of these defects through energies, density of states, oscillator strengths, photoluminescence (PL) spectroscopy and radiative lifetime at low temperature (4K).We demonstrate that localized excitons have a longer emission time than free excitons, in the range of tens of picoseconds or more, and we show that it depends strongly on the disorder parameter and dielectric environment. Finally, in order to prove the validity of our model we compare it to available experimental results of the literature.

Dynamics of Free and Localized Excitons in Two‐Dimensional Transition Metal Dichalcogenides

“…In fact according to ref. and our previous work, there are two pronounced peaks which are attributed to localized exciton states at T = 4 K: the state XL 1 located at 1678 meV with long radiative lifetime about 76 ps and the state XL 2 located at 1700 meV with a shorter radiative lifetime about 26 ps. We note that the scope of this work is the studying of the dynamics of these two states (see Section 3) as well as the different parameters that influence their behavior.…”

“…By using the oscillator strength and the excitonic energy obtained by numerically diagonalizing the Hamiltonian of the free exciton [see refs. and Appendix A), we can determine the radiative lifetime of free exciton using the relation .…”

“…In fact, at low temperature and under low‐density excitation, when the exciton center of mass motion is localized in random disorder potential derived from defects or local strain, the decay mechanism is different. Here, the radiative decay rate of localized exciton is calculated using Fermi's Golden Rule from the dipole interaction , where A ( r , t ) is the vector potential of light in the sample in second quantized form, p is the electron momentum operator and m 0 is the free‐electron mass . The initial state consists of the localized exciton state with no photons, while the final state consists of the crystal ground state plus one photon.…”

“…Many experimental and theoretical results demonstrated that typical spectra of WSe 2 monolayer at T = 4 K and for low excitation density is characterized by: i) a peak centered at 1752 meV corresponds to the recombination of the A‐exciton; ii) a peak appearing at 30 meV bellow the A exciton peak (1720 meV) attributed to the recombination of the negatively charged exciton (trion); and iii) at lower energies a series of anharmonic peaks (comb‐like lines) corresponding to localized exciton states located about 74 meV below the PL peak of the free neutral exciton. In fact according to ref.…”

“…Following our earlier work, in which we studied the effect of structure imperfections on the optical properties of localized exciton states (energy, oscillator strength, radiative lifetime), in this work, we developed a model comprising of a complete set of Boltzmann rate equations to study the dynamics of excitonic complexes for two different cases (high and low quality sample), referring to two distinct experimental conditions: i) in the case of high quality sample, we aim to simulate the experimental data of Robert et al and to investigate the effect of the alignment of bright and dark (spin and momentum forbidden) exciton states on the dynamics of darkish materials; ii) for low quality sample, disorder derived from defects or local strain in monolayer TMDCs can lead to a dramatic change in the physical behavior of the excitons kinetics, hence motivated by the work of Wang et al, we will develop our model in order to investigate the dynamics of localized exciton in WSe 2 materials. We note that our results are developed for low temperature and weak excitation power, in order to exclude biexciton channel, Auger‐type exciton–exciton annihilation, and strong exciton–phonon interaction from our models .…”