Angular Emission Properties of Strained Transition-Metal Dichalcogenides

TL;DR

This study investigates how uniaxial strain affects angular emission and PL in monolayer WS2, focusing on practical low-strain operation for flexible devices. It combines spectrally resolved k-space imaging (SPRKI) with finite-difference time-domain (FDTD) simulations and an image-dipole framework to separate dipole orientation effects from curvature-induced intensity changes. The main findings are that the dipole remains in-plane under small strain, while PL intensity varies erratically due to substrate curvature modulating interference via the image dipole, with observed angular fringes tracking curvature through Fresnel-like effects. The results underscore substrate curvature as a dominant factor limiting quantitative PL yield in flexible TMD devices and demonstrate SPRKI as a sensitive diagnostic for strain-curvature effects on optical emission.

Abstract

Monolayers of transition-metal dichalcogenides have shown that uniaxial strain changes both the photoluminescence emission energy and intensity. The changes are attributed to the band-structure evolution under tensile strain where both the bandgap decreases and a direct-to-indirect transition occurs. This was shown for relatively high strains, whereas this is not the case at low strain values $<1\%$ in which in this work, we observe the erratic dependency of the photoluminescence intensity at low strain values as a function of strain. We find that the dominant physical property is the dependence of the optical-dipole emission on the curvature of the substrate. We validate the behavior of the photoluminescence intensity with experimental angular emission spectroscopy (k-space imaging). These findings are supported by Finite-Difference Time-Domain simulations, in agreement with the experimental data. Our findings present the importance of choosing the right substrate for flexible devices based on transition-metal dichalcogenides.

Figures (5)

• Figure 1: (a) Description of the experiment. Top - an unstrained sample emits light into the numerical aperture of a lens. Bottom - when strained, the emission redshifts and the light cone slightly changes, influencing the brightness of the emission. (b) A schematic illustration of the 3-point bending device. Note that the PET is strained directly and not the PDMS. The outer posts numbered 1,3 move up and down to strain the device while the middle post number 2 (where the sample is centered) does not move as it stays at the focus of the illuminating objective. (c) The experimental setup. BS - beam splitter. L1 - the k-space (Bertrand) lens that flips for PL acquisition. L2 - the imaging lens.
• Figure 2: The hysteresis of the energies of the excitons and the trions for both polarizations. The blue curves correspond to the forward direction (increasing strain) and the red to the backward direction (decreasing strain). The bottom x-axis (blue) corresponds to the classical calculated strain of the 3-point bending device and the top x-axis (red) corresponds to the inverse curvature. (a) TE exciton energy. (b) TM exciton energy. (c) TE trion energy. (d) TM trion energy.
• Figure 3: (a) The normalized PL as a function of strain. The excitonic peak red-shifts as a function of strain as previously reported Lloyd2016Conley2013Harats2020DynamicsWS2. (b) The non-normalized PL from (a) showing fluctuations in the PL intensity without a clear trend.
• Figure 4: Angular (k-space) emission spectrally resolved at $618nm$ for TE polarization. (a) The k-space at the lowest strain $\varepsilon=0\%$. (b) The k-space at the highest strain $\varepsilon=0.15\%$. (c) The angular emission at $k_y=0$ corresponding to the cases of no strain (dashed black line in (a)) and maximum strain (dashed red line in (b)). The calculations of IP dipole emission are presented as dotted curves and show that the emission consists of IP dipoles without any change due to strain. (d) Same as (a) and (b) for intermediate strain values. The colorbars and axis are omitted for clarity. (e) K-space emission normalized to the previous strain value. The fringes are changing along the $k_y$ direction. The colorbar at the bottom is common for all the normalized k-space.
• Figure 5: (a) FDTD far field pattern for an IP dipole in TE polarization. The variations between different strain values is visible. (b) Same as (a) for TM polarization. Note the lower intensity compared to TE polarization. (c) The normalized far-field intensities (FDTD and experimental). The similarity in the trend between the IP simulation results and the experimental values is striking. The OP dipole is negligible and indeed does not change under strain.