Limits of funneling efficiency in non-uniformly strained 2D semiconductors

TL;DR

The paper analyzes the limits of exciton funneling in non-uniformly strained 2D TMDCs by modeling a bed-of-nails device that creates a non-uniform strain field and a bandgap funnel. It solves a cylindrical drift-diffusion equation for the exciton density $n(r)$ including drift, diffusion, finite lifetime $\tau$, Auger recombination $R_A$, and excitation sources $S(r)$ under two illumination profiles, across temperatures. The results show a room-temperature upper bound of about $eff^{max} \approx 0.5$ for typical strains and lifetimes, with actual monolayers often yielding $<5\%$ funneling; at cryogenic temperatures with long lifetimes the efficiency can surpass 50% and approach unity in diffusion-limited regimes. The findings highlight that Auger recombination and unknown low-temperature parameter trends limit high-intensity funneling, while long-lived excitons in heterobilayers can realize near-optimal funneling, providing guidance for efficient exciton collection and high-density exciton studies.

Abstract

Photoexcited electron-hole pairs (excitons) in transition metal dichalcogenides (TMDC) experience an effective force when these materials are non-uniformly strained. In the case of strain produced by a sharp tip pressing at the center of a suspended TMDC membrane, the excitons are transported to the point of the highest strain at the center of the membrane. This effect, exciton funneling, can be used to increase photoconversion efficiency in TMDC, to explore exciton transport, and to study correlated states of excitons arising at their high densities. Here, we analyze the limits of funneling efficiency in realistic device geometries. The funneling efficiency in realistic monolayer TMDCs is found to be low, $ <5 \;\%$ both at room and low temperatures. This results from dominant diffusion at room temperature and short exciton lifetimes at low temperatures. On the other hand, in TMDC heterostructures with long exciton lifetimes the funneling efficiency reaches $\sim 50\;\%$ at room temperature, as the exciton density reaches thermal equilibrium in the funnel. Finally, we show that Auger recombination limits funneling efficiency for intense illumination sources.

Figures (4)

• Figure 1: (a) A sketch of the funneling device. A TMDC monolayer is deposited onto sharp metallic electrodes inducing non-uniform strain in it. The monolayer is illuminated from the top. Photogenerated excitons are subjected to a drift force which transports them to the region of high strain at the apex of the tip. (b) The local strain, $tr(\varepsilon_{ij})(r)$, and bandgap, $u$, calculated as a function of distance from the membrane's center $r$ for different maximum strain ($\varepsilon_{max}$) values.
• Figure 2: Contour plots of the funneling efficiency as a function of the diffusion coefficient $D$ and the maximum strain value $\varepsilon_{max}$ at various temperatures. The panels (a)-(c) correspond to the laser illumination profile (Eq. \ref{['eq:laser_exc']}), while the panels (d)-(f) correspond to the solar illumination profile (Eq. \ref{['eq:solar_exc']}). The vertical black dashed line corresponds to the experimental room temperature diffusion coefficients $D=0.3\;cm^2/s$. The exciton lifetime is assumed to be constant $\tau=1\; ns$ in this plot.
• Figure 3: Funneling efficiency at cryogenic temperature $T=4\;K$. Funneling efficiency is shown as contour plots as a function of the diffusion coefficient $D$ and the maximum strain value $\varepsilon_{max}$ for various exciton lifetimes. The panels (a)-(c) correspond to the laser illumination profile (Eq. \ref{['eq:laser_exc']}), while the panels (d)-(f) correspond to the solar illumination profile (Eq. \ref{['eq:solar_exc']}). For all graphs the vertical black dashed line corresponds to the reported diffusion coefficient value at room temperature $D=0.3\;cm^2/s$Kulig2018.
• Figure 4: (a) The calculated efficiency for solar excitation profile at room temperature with $\tau=1\;\mu s$. (b) The maximum efficiency as a function of the maximum strain and the temperature, derived from the thermal equilibrium condition (Eq. \ref{['eq:max_eff']}). (c) Comparison of the efficiency calculated at thermal equilibrium for $T=300\;K$ from (b) (blue squares) and at $D=10^2\;cm^2/s$ from (a) (red circles).