Controlling light emission from semiconductor nanoplatelets using surface chemistry

Semiconductor nanoplatelets are ultrathin nanocrystals with thickness quantized at the monolayer level, enabling precise control of emission energy across a wide spectral range. Strong two-dimensional confinement and low dielectric screening yield large exciton binding energies, stable photoluminescence at room temperature, and short radiative lifetimes due to giant oscillator strength. However, measured emission linewidths remain unexpectedly broad—35–55 meV at room temperature and 10–20 meV at cryogenic temperatures—even for single nanoplatelets, indicating a temperature-independent broadening mechanism intrinsic to individual platelets. Lateral size/shape dispersion cannot account for these widths, and intrinsic lifetime broadening is too small. The central research question is to identify the intrinsic broadening mechanism and its impact on radiative recombination, and to determine whether controlling surface chemistry can sharpen emission lines and increase radiative rates.

Prior studies established the tunability, stability, and fast radiative recombination of nanoplatelets and identified giant oscillator strength in two-dimensional systems. Reported linewidths for CdSe nanoplatelets (35–55 meV at room temperature; 10–20 meV at cryogenic temperatures) exceed expectations from lifetime broadening and size dispersion, and single-particle measurements mirror ensemble linewidths, pointing to an intrinsic, platelet-level mechanism. Analogies to semiconductor alloys show that spatial compositional fluctuations create random band-gap landscapes that localize excitons and broaden optical lines. Prior theoretical work also links linewidth and radiative lifetime in weakly confined excitons. These insights motivate investigating surface ligand fluctuations in nanoplatelets as an alloy-like disorder source affecting exciton localization and optical properties.

The authors formulate a microscopic model in which spatial inhomogeneities in the surface ligand layer generate a random potential V(R) acting on the exciton center-of-mass (COM). The exciton wavefunction is separated into out-of-plane electron and hole envelope functions, a relative-motion 2D exciton function obtained variationally (Hanamura potential; optimized a_2D and binding energy), and a COM function Ψ(R) modified by disorder. The disorder is treated as a white-noise random potential characterized by three physical parameters: ligand mixing fraction x, areal density of ligand sites N, and band-gap sensitivity α = dEg/dx. These define a natural energy scale W ∝ x(1−x) α^2 M/(2π ħ^2 N) with M = m_e + m_h, enabling universal, dimensionless absorption lineshape A*(ε*) and recombination rate predictions via optimal fluctuation theory for 2D excitons. At low energies, optimal fluctuations localize excitons and yield an exponential absorption tail; at high energies, perturbation theory applies. The full A(ε) is constructed by smoothly connecting asymptotic forms and normalizing ∫A dε = S (platelet area). The density of states n(ε) is obtained from low-energy exponential asymptotics and high-energy coherent potential approximation, then smoothly connected. Radiative recombination rate at energy ε follows 1/τ(ε) ∝ A(ε)/n(ε), with the characteristic lifetime τ0 and overlap factors from the exciton relative wavefunction. Finite lateral sizes are included by modeling confined optimal fluctuations within rectangular platelets and numerically averaging over fluctuation centers; matching to high-energy forms yields size-dependent A(ε). For material-specific parameters, density-functional theory (VASP; PAW; 500 eV cutoff) computes band-gap shifts for CdSe nanoplatelets passivated by different ligands (acetate; Cl; I; S). Structures are relaxed with PBE+D3, then scaled and evaluated with HSE+D3 (mixing tuned to reproduce bulk CdSe gap 1.661 eV, lattice constant 0.608 nm). The ligand site density is N = 2/a^2 with a = 0.608 nm. The calculated ΔE_ll′(d) between ligands provides α(d) for the model. For lifetime predictions, bright and dark exciton manifolds are included with an exchange splitting ΔE_exch (short- and long-range components), and a Boltzmann population across bright states n(ε) and dark states n(ε+ΔE_exch) yields temperature-dependent average lifetimes. Comparisons to room-temperature linewidths account for thermal broadening by subtracting k_BT (~26 meV) as a heuristic correction.

• Ligand-induced random potential universally broadens excitonic absorption/emission. The dimensionless absorption lineshape A*(ε*) has FWHM 4.04, leading to a physical linewidth Δ = 4.04 x(1−x) α^2 M / (2π ħ^2 N). Broadening is maximal at x = 0.5 and scales with exciton mass and the square of the ligand-induced band-gap sensitivity, and inversely with ligand site density.
• The dimensionless recombination rate peaks at 1.36; the minimum radiative lifetime scales inversely with the linewidth (τ_min ∝ 1/Δ), a hallmark of weakly confined excitons. Disorder-induced localization both broadens lines and slows radiative recombination relative to the ideal delocalized case.
• In ideal platelets, giant oscillator strength predicts extremely short bright-state lifetimes (≈5–10 ps) and near-lifetime-limited linewidths (~1 meV), inconsistent with experiments. Including ligand fluctuations reproduces observed bright-state lifetimes (~15–20 ps) and room-temperature linewidths (35–55 meV) for CdSe, consistent with experimental reports, and explains cryogenic linewidths (10–20 meV) absent phonon broadening.
• Thickness dependence: linewidth varies with thickness via competing trends of increasing exciton mass M and decreasing α with increasing thickness. Predicted maximum linewidths (at x = 0.5) across thicknesses agree with cryogenic measurements and with room-temperature data after subtracting k_BT.
• Material-specific inputs: DFT-derived α for acetate vs sulfur passivation (representative ligand-type disorder) yields typical Δ in the tens of meV range. Estimated strain from short- vs long-chain carboxylate ligands (e.g., acetate vs oleate) gives α ≈ 0.14 eV, comparable to ligand-type α (≈0.237 eV), implying chain-length and ligand-type disorder can both generate similar broadening.
• Temperature dependence of lifetimes: Considering bright–dark exchange splitting, average exciton lifetimes are sub-nanosecond with non-monotonic T dependence—slower at low T due to dark-state occupation, faster as bright population increases, then slower again as higher-energy, weakly emitting localized states are thermally populated. Radiative lifetimes are always longer with fluctuations than in the ideal case.
• The model rationalizes strong dependence of measured linewidths on growth/processing as arising from differences in ligand layers and suggests that improving ligand uniformity will both narrow lines and increase emission rates.

The work directly addresses the unresolved origin of unexpectedly broad emission in semiconductor nanoplatelets by identifying spatial fluctuations in surface ligands as the intrinsic, platelet-level mechanism. The model maps ligand inhomogeneity onto a random COM potential that localizes excitons, thereby increasing scattering and linewidth while reducing radiative rates. Its universal predictions (linewidth scaling, lifetime–linewidth relation, temperature-dependent recombination) quantitatively match CdSe nanoplatelet data when material parameters are supplied via DFT, including agreement with cryogenic linewidths and with room-temperature linewidths after accounting for thermal broadening. This explains why efforts to reduce lateral size/shape dispersion have not yielded narrower lines: the dominant broadening is intrinsic to each platelet due to surface chemistry. The results highlight that controlling ligand uniformity—ligand type and chain length, as well as strain they induce—offers a viable path to sharpen emission and enhance brightness. The framework likely extends to other nanocrystal systems where surface chemistry modulates local band edges and exciton coherence areas.

The paper introduces a physically transparent, quantitative theory showing that spatial inhomogeneities in nanoplatelet surface ligands create a random potential that localizes excitons, broadens optical lines, and slows radiative recombination. A universal absorption lineshape and linewidth expression are derived, connecting measurable linewidths to ligand mixing, band-gap sensitivity, exciton mass, and ligand site density. Calibrated with DFT-derived ligand gap shifts for CdSe nanoplatelets, the model reproduces experimentally observed linewidths and explains lifetime trends versus temperature and thickness. Practically, it implies that optimizing surface chemistry—achieving more uniform, well-passivated ligand shells—can simultaneously narrow emission and increase radiative rates, whereas further reductions in size dispersion alone will not solve the linewidth problem. Future work should experimentally probe and control ligand disorder (type and chain length), directly correlate ligand distributions with optical properties, refine modeling of ligand-induced strain and curvature (e.g., via larger-scale or molecular dynamics simulations), and include phonon-induced decoherence to improve lifetime predictions at room temperature.

• The linewidth calculations neglect explicit phonon coupling; room-temperature comparisons use a heuristic subtraction of k_BT to remove thermal broadening.
• Radiative lifetimes are underestimated in part due to hard-wall boundary conditions in the z direction, which likely underestimate the exciton radius and overestimate |Φ(0)|.
• The random potential is modeled as white noise with parameters (x, N, α); real ligand landscapes may exhibit spatial correlations, anisotropy, curvature, and edge effects not fully captured.
• DFT-derived α values use small-cell models and do not fully include finite-temperature ligand motions, conformations, or large-scale curvature/strain fields; chain-length disorder is treated via a proxy rather than fully modeled.
• The universal results assume large lateral sizes; quantitative deviations arise for thicker and laterally finite platelets, requiring confined-fluctuation corrections.
• The model omits phonon-induced decoherence of localized excitons, which likely increases radiative decay times at room temperature.