Fig. 2. Size-dependent emission line-broadening in perovskite QDs and its origin.

a Two representative PL spectra of single QDs with different sizes. Solid lines are best fits of a Lorentzian function to the experimental data (colored open circles). b Statistics of emission line-broadening for various QDs: red and blue circles denote the emission broadening of QDs from two different batches. The circles filled in dark red and dark blue denote the emission linewidth values of the PL spectra in a. c The reorganization energy $S_{\omega }\cdot \hslash \omega$ as a function of the phonon energy $\hslash \omega$ ($S_{\omega }$ is the Huang–Rhys parameter for the lowest energy band-to-band transition). The different phonon modes are highlighted by shaded rectangles and dashed lines. The low-to-intermediate energy modes (2 and 7 meV) dominate the broadening. d Computationally explored QD size range from 1.8 to 4.2 nm (top plot). Computed size-dependent Huang–Rhys factor $S_{<\omega >}$ (left plot) for the three phonon modes, where $<\omega >$ indicates an effective coupling assuming a single mode in each of the three regions shown in c indicated by the dashed lines (see Supplementary Eq. (6)): while the high-energy mode (17 meV, blue triangles) has no dependence vs. QD size, strong variation is observed for the low-to-intermediate energy modes (red squares and green circles, respectively). Colored dashed lines are guide for the eye. The calculated emission broadening ${\Gamma }_{\mathrm{PL}}$ (blue circles) vs. QD diameter is reported in the plot on the right. e Calculated electron and hole wavefunctions in a CsPbBr₃/CsCaBr₃ heterostructure, showing a clear type-I alignment. f Comparison of calculated line-broadening for core-only and core/shell QDs: for QDs with an edge length of 3.6 nm, the emission in a core/shell QD (90 meV) is narrower than in a core-only QD (126 meV). The shell-induced PL narrowing is even more significant when compared to a core-only QD emitting at the same energy, i.e. a QD with an edge length of 2.4 nm exhibiting a PL broadening of 164 meV.