Strong Exciton Binding Research Articles

Heterostructures via a Solution-Based Anion Exchange in Microcrystalline 2D Layered Metal-Halide Perovskites.

Layered perovskites consist of stacks of inorganic semiconducting metal-halide octahedra lattices sandwiched between organic layers with typically dielectric behavior. The in-plane confinement of electrical carriers in such two-dimensional metal halide perovskites drives a large range of appealing electronic properties, such as strong exciton binding, anisotropic charge diffusion, and polarization-directionality. Heterostructures provide additional control on carrier diffusion and localization, and in-plane heterojunctions are interesting because of the associated high charge mobility. Here, this work demonstrates a versatile solution-based approach to fabricate in-plane heterostructures with different halide composition in two-dimensional lead-halide perovskite microcrystals. This leads to spatially separated halide phases with different band gap and light emission. Interestingly, the composition of the exchanged phase and the morphology of the phase boundary depends on the exchange route, which can be related to the preferred localization of the halides at the equatorial or axial octahedra positions that either leads to dissolution and recrystallization of the octahedra lattice (for bromide to iodide), or allows for ion diffusion within the lattice (for iodide to bromide). These detailed insights on the ion exchange processes in layered perovskites will stimulate the development of heterostructures that can be tailored for different applications such as photocatalysis, energy storage, and light emission.

Spectrally Tunable Lead-Free Perovskite Rb2ZrCl6:Te for Information Encryption and X-ray Imaging.

A series of lead-free Rb2ZrCl6:xTe4+ (x = 0%, 0.1%, 0.5%, 1.0%, 2.0%, 3.0%, 5.0%, 10.0%) perovskite materials were synthesized through a hydrothermal method in this work. The substitution of Te4+ for Zr in Rb2ZrCl6 was investigated to examine the effect of Te4+ doping on the spectral properties of Rb2ZrCl6 and its potential applications. The incorporation of Te4+ induced yellow emission of triplet self-trapped emission (STE). Different luminescence wavelengths were regulated by Te4+ concentration and excitation wavelength, and under a low concentration of Te4+ doping (x ≤ 0.1%), different types of host STE emission and Te4+ triplet state emission could be achieved through various excitation energies. These luminescent properties made it suitable for applications in information encryption. When Te4+ was doped at high concentrations (x ≥ 1%), yellow triplet state emission of Te4+ predominated, resulting in intense yellow emission, which stemmed from strong exciton binding energy and intense electron-phonon coupling. In addition, a Rb2ZrCl6:2%Te4+@RTV scintillating film was fabricated and a spatial resolution of 3.7 lp/mm was achieved, demonstrating the potential applications of Rb2ZrCl6:xTe4+ in nondestructive detection and bioimaging.

Theoretical study of the electronic and optical properties of ZnO/MgO rock salt superlattices

An analysis of some electronic and optical properties of rock salt (RS) ZnO/MgO superlattices related to potential applications in optoelectronics and electronics is carried out.In order to find possible light emission mechanisms, the electronic band structure, projected and k-resolved projected density of states and optical parameters such as the refractive index, reflection and absorption coefficients are calculated.We show that the bandgap of the RS ZnO/MgO superlattice is indirect for all considered thicknesses of quantum wells and barriers. Despite the indirect character of the bandgap, other features of the studied superlattice, such as the flat character of the top of the valence band and the bottom of the conduction band, combined with strong electron-phonon coupling and high exciton binding energy, may indicate the possibility of light emission similar to that in hexagonal BN.

Thermodynamic Limit for Excitonic Light-Emitting Diodes.

We derive the thermodynamic limit for organic light-emitting diodes (OLEDs), and show that strong exciton binding in these devices requires a higher voltage to achieve the same luminance as a comparable inorganic LED. The OLED overpotential, which does not reduce the power conversion efficiency, is minimized by having a small exciton binding energy, a long exciton lifetime, and a large Langevin coefficient for electron-hole recombination. Based on these results, it seems likely that the best phosphorescent and thermally activated delayed fluorescence OLEDs reported to date approach their thermodynamic limit. The framework developed here is broadly applicable to other excitonic materials, and should therefore help guide the development of low voltage LEDs for display and solid-state lighting applications.

Giant excitonic effects in vacancy-ordered double perovskites

Using first-principles GW plus Bethe-Salpeter equation calculations, we identify anomalously strong excitonic effects in several vacancy-ordered double perovskites Cs2MX6 (M = Ti, Zr; X = I, Br). Giant exciton binding energies about 1 eV are found in these moderate-gap, inorganic bulk semiconductors, pushing the limit of our understanding of electron-hole (e-h) interaction and exciton formation in solids. Not only are the exciton binding energies extremely large compared with any other moderate-gap bulk semiconductors, but they are also larger than typical 2D semiconductors with comparable quasiparticle gaps. Our calculated lowest bright exciton energy agrees well with the experimental optical band gap. The low-energy excitons closely resemble the Frenkel excitons in molecular crystals, as they are highly localized in a single [MX6]2- octahedron and extended in the reciprocal space. The weak dielectric screening effects and the nearly flat frontier electronic bands, which are derived from the weakly bonded [MX6]2- units, together explain the significant excitonic effects. Spin-orbit coupling effects play a crucial role in red-shifting the lowest bright exciton by mixing up spin-singlet and spin-triplet excitons, while exciton-phonon coupling effects have minor impacts on the strong exciton binding energies.

First-principles investigation on the structural, vibrational, mechanical, electronic, and optical properties of MSi2Z4 ( M : Pd and Pt, Z : N and P) monolayers

The recent synthesis of two-dimensional (2D) layered crystals of ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ and ${\mathrm{WSi}}_{2}{\mathrm{N}}_{4}$ has received significant attention due to their novel properties and potential applications. The inclusion of silicon during chemical vapor deposition growth enhances the ambient stability of transition metal nitrides and enables large-scale growth in monolayer limit. The transition metal and nitrogen elements can potentially be replaced with other metal and pnictogen atoms, which can constitute a new and large 2D family. In this respect, based on first-principles calculations, we design $M{\mathrm{Si}}_{2}{Z}_{4}$ ($M$: Pd and Pt, $Z$: N and P) monolayers and investigate their structural, vibrational, mechanical, electronic, and optical properties. The dynamical, thermal, and mechanical stabilities of the proposed systems are confirmed through phonon band dispersion calculations, ab initio molecular dynamics simulations, and elastic tensor analyses, respectively. The computed Raman and infrared spectra of the nanosheets reveal that the frequency and the intensity of the most prominent peaks are specified by the type of pnictogen atom in the structures. The mechanical response of the considered systems in the elastic regime is investigated in terms of in-plane stiffness (${Y}_{\text{2D}}$) and the Poisson's ratio ($\ensuremath{\nu}$). The obtained values of ${Y}_{\text{2D}}$ indicate that $M{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$ monolayers are stiffer than $M{\mathrm{Si}}_{2}{\mathrm{P}}_{4}$ nanosheets and the $\ensuremath{\nu}$ values are found to be within the same range and close to the ductile-brittle transition limit. The electronic structure investigation shows that while $M{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$ monolayers are quasidirect wide-band-gap semiconductors, the $M{\mathrm{Si}}_{2}{\mathrm{P}}_{4}$ monolayers are semiconductors with an indirect narrow band gap. Additionally, these monolayers have isotropic optical spectra and, depending on the type of pnictogen atom, significant optical absorption peaks within the infrared, visible, and ultraviolet regions can be attained. Additionally, it is found that $M{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$ monolayers possess multiple bound excitons with strong exciton binding when electron-hole interactions are taken into account. Our results not only expand the class of 2D $M{\mathrm{Si}}_{2}{Z}_{4}$ crystals but also offer valuable insights on the physical properties of the designed systems and suggest them as promising materials in diverse optoelectronic applications.

Electron structure and exciton energy level of HgI2, CH3NH3HgI3 and (CH3NH3)2HgI4

The electronic structures and exciton properties of HgI2, CH3NH3HgI3 and (CH3NH3)2HgI4 are reported. Compared with HgI2, organic-inorganic hybrids CH3NH3HgI3 and (CH3NH3)2HgI4 have lower dimension and higher band gap, which show significant excitonic properties. The effective masses of electrons and holes of these three materials were predicted by their energy band structures. Their exciton binding energy at room temperature therein was calculated to be 13.77, 166.81, and 256.00 meV, respectively. HgI2 has low exciton binding energy that cannot exist stably, while CH3NH3HgI3 and (CH3NH3)2HgI4 have strong charge localization and high exciton binding energy. In addition, the UV–vis diffuse reflectance spectra reveal the presence of exciton absorption in CH3NH3HgI3 and (CH3NH3)2HgI4, and the exciton energy levels is confirmed by combining the diffuse reflectance spectra with its exciton binding energy. Importantly, the exciton luminescence peaks of CH3NH3HgI3 and (CH3NH3)2HgI4 were observed at 468 nm and 419 nm in their photoluminescence spectra at room temperature, respectively. This indicates that CH3NH3HgI3 and (CH3NH3)2HgI4 have strong exciton properties and are potential candidates for high-light-yield scintillators and light-emitter applications.

A ligand strategy retarding monovalent copper oxidation toward achieving Cs3Cu2I5 perovskite emitters with enhanced stability for lighting.

0D copper-based perovskites (Cs3Cu2I5) have fascinating optical properties, such as strong exciton binding energy, high photoluminescence quantum yield (PLQY) and large Stokes shifts from self-trapped excitons (STEs), which make them highly considerable candidates in the field of lighting. However, the stability of Cs3Cu2I5 is compromised by the oxidation of Cu+ to Cu2+ during the storage or operation process. Here, we proposed a ligand engineering strategy to improve the stability of Cs3Cu2I5via an organic molecule (ethylenediaminetetraacetic acid, EDTA) with multiple functional groups. The strong interaction between carboxyl groups and Cu+ was evidenced through FTIR and XPS, and it could retard monovalent copper oxidation. After storing for 90 days, the EDTA-engineered Cs3Cu2I5 (EDTA-Cs3Cu2I5) maintained its original crystalline structure, while the control Cs3Cu2I5 exhibited an impurity phase. Through quantitative analysis, the content of Cu2+ in EDTA-Cs3Cu2I5 was found to be 83.9% lower than that in control Cs3Cu2I5. Benefiting from the inhibition of Cu+ oxidation, EDTA-Cs3Cu2I5 exhibited improved light emission stability. For example, the optimized EDTA-Cs3Cu2I5 retained 74.7% of the initial photoluminescence (PL) intensity after 90-day storage under ambient conditions, while the pure Cs3Cu2I5 retained only 41.7%. Furthermore, EDTA could passivate defects and enhance the PL properties of the optimized Cs3Cu2I5, which showed a PLQY of 94.7%, much higher than that of 71.4% for pure Cs3Cu2I5. We further constructed a WLED based on the EDTA-engineered Cs3Cu2I5, which showed CIE at (0.3238, 0.3354), a CRI of 91.7, and a T50 of 361 h. The proposed EDTA ligand strategy provides a new way to regulate the light-emitting properties and stabilities of Cs3Cu2I5 for future industrialization.

Electronic and optical properties of the buckled and puckered phases of phosphorene and arsenene

Using first-principles calculations, we have investigated the structural, electronic, and optical properties of phosphorene and arsenene, group V two-dimensional materials. They have attracted the scientific community’s interest due to their possible applications in electronics and optoelectronics. Since phosphorene and arsenene are not planar monolayers, two types of structures were considered for each system: puckered and buckled arrangements. Computations of band gap were performed within the GW approach to overcome the underestimation given by standard DFT and predict trustable band gap values in good agreement with experimental measurements. Our calculated electronic band gaps lie in the range from near-infrared to visible light, suggesting potential applications in optoelectronics devices. The computed electronic band gaps are 2.95 eV and 1.83 eV for blue and black phosphorene systems. On the other hand, the values for buckled and puckered arsenene are 2.56 eV and 1.51 eV, respectively. Moreover, the study of the optical properties has been dealt by computing the dielectric function imaginary part, which was obtained using the Bethe–Salpeter approach. The use of this technique allows the consideration of excitonic effects. Results indicate strong exciton binding energies of 830 meV for blue phosphorene, 540 meV for black phosphorene, 690 meV for buckled arsenene, and 484 meV for puckered arsenene. The results of our study suggest the possibility of using these materials in electronic and optoelectronic devices.

Effects of Growth Temperature on Morphological and Structural Properties of ZnO Films

Zinc oxide (ZnO) is one of the most promising oxide possibilities for use in a number of industries due to its unique properties. Because of its broad direct bandgap (3.37 eV) and strong exciton binding energy (60 meV) at ambient temperature, ZnO not only conducts electricity well but also transmits visible light and emits UV light. Here, we investigated the effect of growth temperature on ZnO thin films by changing the growth temperatures from 400 oC to 450 oC. Radio-frequency (RF) magnetron sputtering was used to create ZnO thin films on Si(100) substrates. The atomic force microscopy (AFM) results show that the root-mean-square (RMS) roughness decreases from 6.1 ± 1.0 nm to 4.8 ± 0.6 nm as the growth temperatures increase. XRD patterns display the enhancement of ZnO’s structure when increasing the growth temperature. Our findings indicate that controlling growth temperature is the critical factor in producing high quality ZnO thin films.

Direct observation of photoinduced carrier blocking in mixed-dimensional 2D/3D perovskites and the origin

Mixed-dimensional 2D/3D halide perovskite solar cells promise high stability but practically deliver poor power conversion efficiency, and the 2D HP component has been held as the culprit because its intrinsic downsides (ill charge conductivity, wider bandgap, and strong exciton binding) were intuitively deemed to hinder carrier transport. Herein, we show that the 2D HP fragments, in fact, allow free migration of carriers in darkness but only block the carrier transport under illumination. While surely limiting the photovoltaic performance, such photoinduced carrier blocking effect is unexplainable by the traditional understanding above but is found to stem from the trap-filling-enhanced built-in potential of the 2D/3D HP interface. By parsing the depth-profile nanoscopic phase arrangement of the mixed-dimensional 2D/3D HP film for solar cells and revealing a photoinduced potential barrier up to several hundred meV, we further elucidate how the photoinduced carrier blocking mechanism jeopardizes the short-circuit current and fill factor.

Sumanene Monolayer of Pure Carbon: A Two-Dimensional Kagome-Analogy Lattice with Desirable Band Gap, Ultrahigh Carrier Mobility, and Strong Exciton Binding Energy.

The design and synthesis of novel two-dimensional (2D) materials that possess robust structural stability and unusual physical properties may open up enormous opportunities for device and engineering applications. Herein, a 2D sumanene lattice that can be regarded as a derivative of the conventional Kagome lattice is proposed. The tight-binding analysis demonstrates sumanene lattice contains two sets of Dirac cones and two sets of flat bands near the Fermi surface, distinctively different from the Kagome lattice. Using first-principles calculations, two possible routines for the realization of stable 2D sumanene monolayers (named α phase and β phase) are theoretically suggested, and an α-sumanene monolayer can be experimentally synthesized with chemical vapor deposition using C21 H12 as a precursor. Small binding energies on Au(111) surface (e.g., -37.86eVÅ-2 for α phase) signify the possibility of their peel-off after growing on the noble metal substrate. Importantly, the GW plus Bethe-Salpeter equation calculations demonstrate both monolayers have moderate band gaps (1.94eV for α) and ultrahigh carrier mobilities (3.4 × 104 cm2 V-1 s-1 for α). In particular, the α-sumanene monolayer possesses a strong exciton binding energy of 0.73eV, suggesting potential applications in optics.

A Review on Materials and Methods for the Fabrication of Microcavity Laser

Optical microcavities are resonators that have at least one dimension on the order of a single optical wavelength. These structures enable one to control the optical emission properties of materials placed inside them. One of their most dramatic potential features is threshold-less lasing,unlike the conventional lasers. This is possible due to 2D monolayers, Heterostructures, Hybrid materials which are used as active layers for polariton-exciton strong coupling. In this review paper, a different method of Microcavity laser fabrication is reviewed, where a different type of active materials is utilized to improve the laser efficiency. Materials such as WS2, MoS2, WSe2 and MoSe2are used due to their strong exciton binding energy. These use high reflecting DBR mirrors fabricated using oxides of a higher refractive index such as SiO2, NbO2, HfO2/Al2O3, SiO2/Ta2O5 and SiO2/TiO2. In this way, the controlled spontaneous emission is expected to play a vital role in a new generation of optical devices and can have a wide range of applications in Optics, Quantum computing, high-speed signal transmission, etc.

Bose enhancement of excitation-energy transfer with molecular-exciton-polariton condensates.

Room-temperature Bose-Einstein condensates (BECs) of exciton polaritons have been realized in organic molecular systems owing to strong light-matter interaction, strong exciton binding energy, and low effective mass of a polaritonic particle. These molecular-exciton-polariton BECs have demonstrated their potential in nonlinear optics and optoelectronic applications. In this study, we first demonstrate that molecular-polariton BECs can be utilized for Bose enhancement of excitation-energy transfer (EET) in a molecular system with an exciton donor coupled to a group of exciton acceptors that are further strongly coupled to a single mode of an optical cavity. Similar to the stimulated emission of light in which photons are bosonic particles, a greater rate of EET is observed if the group of acceptors is prepared in the exciton-polariton BEC state than if the acceptors are initially either in their electronic ground states or in a normal excited state with an equal average number of molecular excitations. The Bose enhancement also manifests itself as the growth of the EET rate with an increasing number of exciton polaritons in the BEC. Finally, a generalization to the EET in many-donor-many-acceptor molecular systems is considered, and a permutation-symmetry-based approach to suppress the EET to the huge manifold of dark states in the acceptor group is proposed to facilitate the Bose-enhanced EET to the polariton BEC.

First principles study of the structural stability, lattice dynamics, optical and thermoelectric properties of NaSrX(X = As, Sb and Bi)

First principles methods are utilized in exploring the structural stability, electronic, optical, phonon, thermal properties and electronic transport coefficients of NaSrX materials. Based on the calculated cohesive and formation energies, NaSrX compounds are found to be energetically stable. NaSrX materials are also shown to be direct band gap semiconductors with strong exciton binding energies between ∼0.13 and 0.20 eV. The dynamical and mechanical stabilities of NaSrX materials are further confirmed from their phonon dispersion curves and elastic constants. The calculated lattice thermal conductivities, κL, for NaSrX compounds exhibit anisotropic behaviour with the lowest value of κL found in the a-direction. Moreover, NaSrBi is shown to possess the lowest average value of κL (1.29 Wm−1K−1) as compared to NaSrAs and NaSrSb at 300 K. p-doped NaSrX compounds are shown to record large values of thermoelectric figure of merits. For instance, the highest calculated figure of merit (ZT) for p-doped NaSrAs is estimated to be 1.66 at 1200 K when p = 1020 cm−3 whereas those of NaSrSb and NaSrBi are 2.78 (at 1000 K) and 3.16 (at 900 K) respectively when p = 1019 cm−3. The large ZT values obtained in these calculations indicate that NaSrX compounds are promising candidates for thermoelectric applications.

Molding 2D Exciton Flux toward Room Temperature Excitonic Devices

AbstractDevices operating with excitons have promising prospects for overcoming the dilemma of response time and integration in current generation of electron‐ or/and photon‐based elements and devices. In combination with the advantages of emerging twistronics and valleytronics, the atomically thin transition metal dichalcogenide semiconductors open up new opportunities for pursuing practical excitonic devices, where the strong exciton binding energy enables operating exciton at room temperature. The essential and foremost step toward exciton devices is the control of spatiotemporal exciton flux, which is density‐dependent and affected by the complex many‐body interactions. It can be effectively controlled by the strain, electric field, electron‐doping, and local dielectric environment. Intriguingly, exotic phenomena such as exciton condensation, electron‐hole liquid, exciton Hall effects, and exciton halo effects can be occurred in 2D exciton system, providing new possibilities for excitonic devices. Up to now, the proof‐of‐principle of room temperature exciton devices, including excitonic switching and transistor, exciton guides, and excitonic nanolaser, have been realized. Here the authors review the recent advances in molding 2D exciton flux from basic principle, manipulation, exotic phenomena to promising applications and discuss the opportunities and challenges in pushing the frontiers of room temperature excitonic devices.

Ternary pentagonal BNSi monolayer: Two-dimensional structure with potentially high carrier mobility and strong excitonic effects for photocatalytic applications

In recent years many attempts have been made to discover new types of two-dimensional (2D) nanostructures with novel properties beyond the hexagonal crystals. The prediction of pentagraphene has sparked a great deal of research interest to investigate 2D pentagonal systems. In line with these efforts, in this paper, we propose a 2D ternary pentagonal monolayer of BNSi (penta-BNSi) and systematically investigate its structural, vibrational, mechanical, piezoelectric, electronic, photocatalytic, and optical properties by performing first-principles methods. We verify the stability of the penta-BNSi monolayer from the dynamical, thermal, and mechanical aspects based on phonon dispersion, ab initio molecular dynamics, and elastic tensor analysis, respectively. The mechanical properties are examined by calculating in-plane stiffness $({Y}_{2\mathrm{D}})$, Poisson's ratio $(\ensuremath{\nu})$, and ultimate tensile strength and penta-BNSi is found to be soft and ductile. The electronic structure and electronic transport calculations indicate that the penta-BNSi monolayer possesses a quasidirect band gap and anisotropic, potentially high carrier mobility. Due to the noncentral symmetric character and semiconducting feature, an intrinsic piezoelectric response emerges in the structure. In addition, penta-BNSi has a suitable band gap as well as proper band edge positions for photocatalytic water splitting within practical pH levels. The analysis of optical properties, including many-body effects, points out strong exciton binding and high light absorption in the visible and near-UV parts of the spectrum. Our findings not only expand the family of 2D pentagonal materials but also uncover an ideal ultrathin material for photocatalytic applications.

Quasiparticle energies and optical response of RbTiOPO4 and KTiOAsO4

Many-body perturbation theory based on density-functional theory calculations is used to determine the quasiparticle band structures and the dielectric functions of the isomorphic ferroelectrics rubidium titanyl phosphate (RbTiOPO4) and potassium titanyl arsenide (KTiOAsO4). Self-energy corrections of more than 2 eV are found to widen the transport band gaps of both materials considerably to 5.3 and 5.2 eV, respectively. At the same time, both materials are characterized by strong exciton binding energies of 1.4 and 1.5 eV, respectively. The solution of the Bethe–Salpeter equation based on the quasiparticle energies results in onsets of the optical absorption within the range of the measured data.

Expanded Phase Distribution in Low Average Layer‐Number 2D Perovskite Films: Toward Efficient Semitransparent Solar Cells

AbstractThe application of low average layer‐number (〈n〉 ≤ 2) 2D perovskites in semitransparent photovoltaics (ST‐PVs) has been hindered by their strong exciton binding energy and high electrical anisotropy. Here, the phase distribution is expanded fully and orderly to enable efficient charge transport in 2D (NMA)2(MA)Pb2I7 (NMA: 1‐naphthylmethylammonium, MA: CH3NH3+) perovskite films by regulating the sedimentation dynamics of organic cation‐based colloids. Ammonium chloride is synergistically introduced to enhance the phase separation further and construct a favorable out‐of‐plane orientation. The wide and graded phase distribution well aligns the energy level to facilitate charge transfer. As a result, the first application of an average 〈n〉 = 2 2D perovskite is implemented in ST‐PVs with visible power conversion efficiency (PCE) of 7.52% and high average visible transmittance (AVT) of 40.5%. This study offers a new candidate and an effective strategy for efficient and stable ST‐PVs and is relevant to other perovskite optoelectronic devices.

Metallic phase transition metal dichalcogenide quantum dots showing different optical charge excitation and decay pathways

The charge excitation and decay pathways of two-dimensional heteroatomic quantum dots (QDs) are affected by the quantum confinement effect, bandgap structure and strong exciton binding energy. Recently, semiconducting transition metal dichalcogenides (TMDs) have been intensively studied; however, the charge dynamics of metallic phase QDs (mQDs) of TMDs remain relatively unknown. Herein, we investigate the photophysical properties of TMD-mQDs of two sizes, where the TMD-mQDs show different charge excitation and decay pathways that are mainly ascribed to the defect states and valence band splitting, resulting in a large Stokes shift and two excitation bands for maximum photoluminescence (PL). Interestingly, the dominant excitation band redshifts as the size increases, and the time-resolved PL peak redshifts at an excitation wavelength of 266 nm in the smaller QDs. Additionally, the lifetime is shortened in the larger QDs. From the structural and theoretical analysis, we discuss that the charge decay pathway in the smaller QDs is predominantly affected by edge oxidation, whereas the vacancies play an important role in the larger QDs.