Phonon-enhanced strain sensitivity of quantum dots in two-dimensional semiconductors

Abstract

Two-dimensional semiconductors have attracted considerable interest for integration into emerging quantum photonic networks. Strain engineering of monolayer transition-metal dichalcogenides (ML-TMDs) enables the tuning of light-matter interactions and associated optoelectronic properties, and generates new functionalities, including the formation of quantum dots (QDs). Here, we combine spatially resolved micro-photoluminescence ($μ$-PL) spectroscopy from cryogenic (4$\text{-}$94 K) to room temperature with micro-Raman spectroscopy at room temperature to investigate the strain-dependent emission energies of thousands of individual QDs in ML-WS$_2$ and ML-WSe$_2$, integrated across multiple heterostructures and a piezoelectric device. Compared with delocalized excitons, QDs in both materials exhibit enhanced strain sensitivities of their emission energies $-$ approximately fourfold in WS$_2$ and twofold in WSe$_2$ $-$ leading to pronounced broadening of the ensemble emission linewidth. Temperature-dependent $μ$-PL spectroscopy combined with dynamic strain tuning experiments further reveal that the enhanced strain sensitivity of individual QDs originates from strengthened interactions with low-energy phonons induced by quantum confinement. Our results demonstrate a versatile strain-engineering approach with potential for spectral matching across solid-state, atomic, and hybrid quantum photonic networks, and provide new insights into phonon-QD interactions in two-dimensional semiconductors.

Figures (5)

• Figure 1: Redshifted quantum dots (QDs) and ensemble broadening in ML-WS$_2$. Representative $\mu$-PL spectrum of QDs at (a) a spherical nanoparticle (SNP) location in sample S1 and (b) a shape-engineered nanoparticle (ENP) location in sample C1. Vertical dotted lines indicate the highest and lowest QD emission energies observed across the PL spectra in (a) and (b), corresponding to an energy span of approximately 292 meV. Inset in (a): Optical micrographs of samples S1 (top) and C1 (bottom), with ML-WS$_2$ flakes outlined by dotted lines. (c-e) Spatial maps of $\mu$-PL peak intensity of QDs in ML-WS$_2$ at low temperature ($T\,=\,4\,$K) from samples (c) S1 in the 600– 655 nm range, (d) C1 in the 660– 720 nm range, and (e) S1 in the 660– 720 nm range, revealing that highly redshifted QDs are observed only at ENP locations. (f) Schematics of four different sample structures containing SNPs or ENPs as nanostressors. (g) Histograms of QD emission energies from the four samples shown in (f), illustrating ensemble emission spanning the 1.81– 2.08 eV range (bin size: 20 meV). Solid curves are the Gaussian fits, vertical dotted lines mark the ensemble peak energies, and arrows indicate the ensemble full width at half maximum linewidths.
• Figure 2: Thermoelastic strain relaxation at the NP location upon cooling from room temperature (RT) to 4 K. (a) Bar plot of the average local in-plane strain $\left(\epsilon_\parallel\right)$ in ML-WS$_2$ at the NP location for six samples, showing a biaxial strain range of 0.30– 0.90% at RT. (b) 4 K $\mu$-PL spectra of ML-WS$_2$ taken at the NP (thin curve) and flat (thick curve) locations in sample S1. The vertical dotted (solid) line marks the X$^0$ emission energy. (c) Bar plot of average X$^0$ energy shifts at NP (wide bars) and flat (narrow bars) locations for samples S1 and S4 upon cooling to 4 K, compared with the expected energy shift (open bar) according to Varshni equation. (d) Bar plot comparing $\epsilon_\parallel$ at RT and 4 K at the NP location for samples S1 and S4. Inset: Thermoelastic strain relaxation upon cooling from RT to 4 K for these samples. Error bars in (a), (c), and (d) are described in the Methods section.
• Figure 3: Correlations of emission energy and linewidth of QD ensemble with localized strain at 4 K. Strain-dependent emission energies of QD ensembles in (a) ML-WS$_2$ from six different samples, and (b) ML-WSe$_2$ from four different samples. Different symbols represent measurements from each sample; the solid line is a linear fit. (c) Comparison of gauge factors (strain sensitivity of emission energy) across multiple QD platforms; symbol shapes represent the tuning techniques. Strain-dependent linewidth of QD ensemble in (d) ML-WS$_2$ across six samples, and (e) ML-WSe$_2$ across four samples, showing significant strain-induced QD ensemble broadening in both materials. Closed symbols represent measured data; solid lines are linear fits.
• Figure 4: Statistical investigation of dynamic strain tuning of individual QDs and X$^0$ emission in ML-WS$_2$ at 4 K. (a) Schematic of ML-TMD flakes integrated onto a piezoelectric device D; layers are labeled. Strain in the ML-TMDs is induced by applying an electric field $\left(F_{\text{P}}\right)$ between the top and bottom surfaces of a piezoelectric PMN-PT substrate. (b) Optical micrograph of WS$_2$ and WSe$_2$ flakes transferred onto device D. ML regions of both materials are outlined by dotted lines. (c) SEM image of the SiO$_x$ surface of a piezo device, showing engineered SiO$_x$ nanodroplets (NDs) that locally strain the ML-TMDs. (d) $F_{\text{P}}$– dependent emission energies of X$^0$(squares), QD1 (triangles), and QD2 (circles) from ML-WS$_2$ at ND locations. These are representative examples: the average tuning rate of X$^0$, and large positive and negative tuning rates of individual QDs, respectively. (e) Histogram of energy tuning at $F_{\text{P}}=15$ kV cm$^{-1}$ for X$^0$ (textured bars) and QDs (closed bars) in ML-WS$_2$ at ND locations, highlighting the broad range of tuning observed for individual QDs (bin size: 0.4 meV). Error bars in (d) are defined in the Methods section.
• Figure 5: Interactions of phonons with QDs and X$^0$ in ML-WSe$_2$. Temperature-dependent $\mu$-PL spectra of (a) QD3 and (b) QD5 in ML-WSe$_2$ from sample S6, illustrating the gradual redshift of their emission peaks as the temperature increases above 5 K. (c) Temperature-dependent emission energies of X$^0$ and (d) corresponding changes in emission energies $\left(\Delta E(T)\right)$ of QD3 (circle), QD4 (star), QD5 (triangle), QD6 (diamond), and X$^0$ (square) in ML-WSe$_2$, demonstrating that QDs possess higher temperature sensitivity than X$^0$. The dotted lines in (a)– (b) and solid lines in (c) – (d) represent O'Donnell equation fits to $\Delta E(T)$. (e) $\Delta E(T)$ at $T$ = 40 K and (f) Huang– Rhys factors ($S$) of QDs as a function of their zero-temperature emission energies, together demonstrating enhanced electron-phonon interactions in QDs induced by quantum confinement. A dotted line in (e) represents $\Delta E(T)$ at $T$ = 40 K for X$^0$.