Electronic Structure of Biexcitons in Metal Halide Perovskite Nanoplatelets.

A theoretical description of biexcitons in metal halide perovskite nanoplatelets is presented. The description is based on a variational effective mass model, including polaronic effects by means of a Haken potential. The strong quantum and dielectric confinements are shown to squeeze the biexciton under the polaronic radius, which greatly enhances Coulomb attractions and (to a lesser extent) repulsions. This explains the need for effective dielectric constants approaching the high-frequency limit in previous simulations, and the binding energies exceeding 40 meV observed in single-monolayer nanoplatelets. Biexcitons are formed by a pair of weakly interacting excitons, with a roughly rectangular geometry. This translates into a constant ratio between biexciton and exciton binding energies (2D Haynes rule) well below the ideal value of ΔBX/ΔX = 0.228 proposed for squared biexcitons. The ratio is independent of the number of monolayers in the platelet, but it does depend on the lateral and dielectric confinement.

Correction: Excitons in metal halide perovskite nanoplatelets: an effective mass description of polaronic, dielectric and quantum confinement effects.

[This corrects the article DOI: 10.1039/D3NA00592E.].

Excitons in metal halide perovskite nanoplatelets: an effective mass description of polaronic, dielectric and quantum confinement effects.

A theoretical model for excitons confined in metal halide perovskite nanoplatelets is presented. The model accounts for quantum confinement, dielectric confinement, short and long range polaron interactions by means of effective mass theory, image charges and Haken potentials. We use it to describe the band edge exciton of MAPbI3 structures surrounded by organic ligands. It is shown that the quasi-2D quantum and dielectric confinement squeezes the exciton radius, and this in turn enhances short-range polaron effects as compared to 3D structures. Dielectric screening is then weaker than expected from the static dielectric constant. This boosts the binding energies and radiative recombination probabilities, which is a requisite to match experimental data in related systems. The thickness dependence of Coulomb polarization and self-energy potentials is in fair agreement with sophisticated atomistic models.

Two Biexciton Types Coexisting in Coupled Quantum Dot Molecules.

Coupled colloidal quantum dot molecules (CQDMs) are an emerging class of nanomaterials, manifesting two coupled emission centers and thus introducing additional degrees of freedom for designing quantum-dot-based technologies. The properties of multiply excited states in these CQDMs are crucial to their performance as quantum light emitters, but they cannot be fully resolved by existing spectroscopic techniques. Here we study the characteristics of biexcitonic species, which represent a rich landscape of different configurations essentially categorized as either segregated or localized biexciton states. To this end, we introduce an extension of Heralded Spectroscopy to resolve the different biexciton species in the prototypical CdSe/CdS CQDM system. By comparing CQDMs with single quantum dots and with nonfused quantum dot pairs, we uncover the coexistence and interplay of two distinct biexciton species: A fast-decaying, strongly interacting biexciton species, analogous to biexcitons in single quantum dots, and a long-lived, weakly interacting species corresponding to two nearly independent excitons. The two biexciton types are consistent with numerical simulations, assigning the strongly interacting species to two excitons localized at one side of the quantum dot molecule and the weakly interacting species to excitons segregated to the two quantum dot molecule sides. This deeper understanding of multiply excited states in coupled quantum dot molecules can support the rational design of tunable single- or multiple-photon quantum emitters.

Beyond Universal Volume Scaling: Tailoring Two-Photon Absorption in Nanomaterials by Heterostructure Design.

Colloidal semiconductor nanomaterials present broadband, with large cross-section, two-photon absorption (2PA) spectra, which turn them into an important platform for applications that benefit from a high nonlinear optical response. Despite that, to date, the only means to control the magnitude of the 2PA cross-section is by changing the nanoparticle volume, as it follows a universal volume scale, independent of the material composition. As the emission spectrum is connected utterly to the nanomaterial dimensions, for a given material, the magnitude of the nonlinear optical response is also coupled to the emission spectra. Here, we demonstrate a means to decouple both effects by exploring the 2PA response of different types of heterostructures, tailoring the volume dependence of the 2PA cross-section due to the different dependence of the density of final states on the nanoparticle volume. By heterostructure engineering, one can obtain 1 order of magnitude enhancement of the 2PA cross-section with minimum emission spectra shift.

Biexcitons in CdSe nanoplatelets: geometry, binding energy and radiative rate.

Biexciton properties in semiconductor nanostructures are highly sensitive to quantum confinement, relative electron-hole masses, dielectric environment and Coulomb correlations. Here we present a variational Quantum Monte Carlo model which, coupled to effective mass Hamiltonians, takes into account all of the above effects. The model is used to provide theoretical assessment on the biexciton ground state properties in colloidal CdSe nanoplatelets. A number of characteristic features is observed: (i) the finite thickness of these systems makes the biexciton geometry depart from the planar square expected in the two-dimensional (2D) limit, and form a distorted tetrahedron instead; (ii) the strong dielectric confinement enhances not only Coulomb attractions but also repulsions, which lowers the ratio of the biexciton-to-exciton binding energy down to EXXb/EXb = 0.07. (iii) EXXb is less sensitive than EXb to lateral confinement, and yet it can reach values above 30 meV, thus granting room temperature stability; (iv) the ratio of biexciton-to-exciton radiative rates, kradXX/kradX, decreases from 3.5 to ∼1 as the platelet area increases. These results pave the way for the rational design of biexciton properties in metal chalcogenide nanoplatelets.

Dielectric Confinement Enables Molecular Coupling in Stacked Colloidal Nanoplatelets.

We show theoretically that carriers confined in semiconductor colloidal nanoplatelets (NPLs) sense the presence of neighbor, cofacially stacked NPLs in their energy spectrum. When approaching identical NPLs, the otherwise degenerate energy levels red-shift and split, forming (for large stacks) minibands that are several millielectronvolts in width. Unlike in epitaxial structures, the molecular behavior does not result from quantum tunneling but from changes in the dielectric confinement. The associated excitonic absorption spectrum shows a rich structure of bright and dark states, whose optical activity and multiplicity can be understood from reflection symmetry and Coulomb tunneling. We predict spectroscopic signatures that should confirm the formation of molecular states, whose practical realization would pave the way for the development of nanocrystal chemistry based on NPLs.

CdSe/CdS/CdTe Core/Barrier/Crown Nanoplatelets: Synthesis, Optoelectronic Properties, and Multiphoton Fluorescence Upconversion.

Colloidal two-dimensional (2D) nanoplatelet heterostructures are particularly interesting as they combine strong confinement of excitons in 2D materials with a wide range of possible semiconductor junctions due to a template-free, solution-based growth. Here, we present the synthesis of a ternary 2D architecture consisting of a core of CdSe, laterally encapsulated by a type-I barrier of CdS, and finally a type-II outer layer of CdTe as so-called crown. The CdS acts as a tunneling barrier between CdSe- and CdTe-localized hole states, and through strain at the CdS/CdTe interface, it can induce a shallow electron barrier for CdTe-localized electrons as well. Consequently, next to an extended fluorescence lifetime, the barrier also yields emission from CdSe and CdTe direct transitions. The core/barrier/crown configuration further enables two-photon fluorescence upconversion and, due to a high nonlinear absorption cross section, even allows to upconvert three near-infrared photons into a single green photon. These results demonstrate the capability of 2D heterostructured nanoplatelets to combine weak and strong confinement regimes to engineer their optoelectronic properties.

Chloride-Induced Thickness Control in CdSe Nanoplatelets.

Current colloidal synthesis methods for CdSe nanoplatelets (NPLs) routinely yield samples that emit, in discrete steps, from 460 to 550 nm. A significant challenge lies with obtaining thicker NPLs, to further widen the emission range. This is at present typically achieved via colloidal atomic layer deposition onto CdSe cores, or by synthesizing NPL core/shell structures. Here, we demonstrate a novel reaction scheme, where we start from 4.5 monolayer (ML) NPLs and increase the thickness in a two-step reaction that switches from 2D to 3D growth. The key feature is the enhancement of the growth rate of basal facets by the addition of CdCl2, resulting in a series of nearly monodisperse CdSe NPLs with thicknesses between 5.5 and 8.5 ML. Optical characterization yielded emission peaks from 554 nm up to 625 nm with a line width (fwhm) of 9-13 nm, making them one of the narrowest colloidal nanocrystal emitters currently available in this spectral range. The NPLs maintained a short emission lifetime of 5-11 ns. Finally, due to the increased red shift of the NPL band edge photoluminescence excitation spectra revealed several high-energy peaks. Calculation of the NPL band structure allowed us to identify these excited-state transitions, and spectral shifts are consistent with a significant mixing of light and split-off hole states. Clearly, chloride ions can add a new degree of freedom to the growth of 2D colloidal nanocrystals, yielding new insights into both the NPL synthesis as well as their optoelectronic properties.

Piezoelectric Control of the Exciton Wave Function in Colloidal CdSe/CdS Nanocrystals.

Using multiband k·p calculations, we show that strain-engineered piezoelectricity is a powerful tool to modulate the electron-hole spatial separation in a wide class of wurtzite CdSe/CdS nanocrystals. The inherent anisotropy of the hexagonal crystal structure leads to anisotropic strain and, consequently, to a pronounced piezoelectric field along the c axis, which can be amplified or quenched through a proper design of the core-shell structure. The use of large cores and thick shells promotes a gradual departure from quantum confined nanocrystals to a regime dominated by piezoelectric confinement. This allows excitons to evolve from the usual type-I and quasi-type-II behavior to a type-II behavior in dot-in-dots, dot-in-rods, rod-in-rods, and dot-in-plates. Piezoelectric fields explain experimental observations for giant-shell nanocrystals, whose time-resolved photoluminescence reveals long exciton lifetimes for large cores, contrary to the expectations of standard quantum confinement models. They also explain the large differences in exciton lifetimes reported for different classes of CdSe/CdS nanocrystals.

Band structure engineering via piezoelectric fields in strained anisotropic CdSe/CdS nanocrystals.

Strain in colloidal heteronanocrystals with non-centrosymmetric lattices presents a unique opportunity for controlling optoelectronic properties and adds a new degree of freedom to existing wavefunction engineering and doping paradigms. We synthesized wurtzite CdSe nanorods embedded in a thick CdS shell, hereby exploiting the large lattice mismatch between the two domains to generate a compressive strain of the CdSe core and a strong piezoelectric potential along its c-axis. Efficient charge separation results in an indirect ground-state transition with a lifetime of several microseconds, almost one order of magnitude longer than any other CdSe/CdS nanocrystal. Higher excited states recombine radiatively in the nanosecond time range, due to increasingly overlapping excited-state orbitals. k˙p calculations confirm the importance of the anisotropic shape and crystal structure in the buildup of the piezoelectric potential. Strain engineering thus presents an efficient approach to highly tunable single- and multiexciton interactions, driven by a dedicated core/shell nanocrystal design.

Auger recombination suppression in nanocrystals with asymmetric electron-hole confinement.

Type II and quasi-type II nanocrystals with thick shells exhibit reduced blinking. However, after a number of monolayers, the influence of the shell thickness is found to vanish. Using a two-band Kane Hamiltonian, it is shown that this behavior is a consequence of interband coupling and asymmetric confinement of electrons and holes. Interface alloying provides an additional, order-of-magnitude contribution to the Auger suppression, in agreement with recent experiments. The existence is predicted of critical shell thicknesses that strongly quench Auger processes for any core size.