Weak Confinement Regime Research Articles

Exact and Efficient Sampling of Conditioned Walks

A computationally challenging and open problem is how to efficiently generate equilibrated samples of conditioned walks. We present here a general stochastic approach that allows one to produce these samples with their correct statistical weight and without rejections. The method is illustrated for a jump process conditioned to evolve within a cylindrical channel and forced to reach one of its ends. We obtain analytically the exact probability density function of the jumps and offer a direct method for gathering equilibrated samples of a random walk conditioned to stay in a channel with suitable boundary conditions. Unbiased walks of arbitrary length can thus be generated with linear computational complexity—even when the channel width is much smaller than the typical bond length of the unconditioned walk. By profiling the metric properties of the generated walks for various bond lengths we characterize the crossover between weak and strong confinement regimes with great detail.

Substrate effects on the exciton fine structure of black phosphorus quantum dots

We study the size-dependent exciton fine structure in monolayer black phosphorus quantum dots (BPQDs) deposited on different substrates (isolated, Si and SiO$_2$) using a combination of tight-binding method to calculate the single-particle states, and the configuration interaction formalism to determine the excitonic spectrum. We demonstrate that the substrate plays a dramatic role on the excitonic gaps and excitonic spectrum of the QDs. For reasonably high dielectric constants ($\varepsilon_{sub} \sim \varepsilon_{Si} = 11.7 \varepsilon_0$), the excitonic gap can be described by a single power law $E_X(R) = E_X^{(bulk)} + C/R^{\gamma}$. For low dielectric constants $\varepsilon_{sub} \leq \varepsilon_{SiO_2} = 3.9 \varepsilon_0$, the size dependence of the excitonic gaps requires the sum of two power laws $E_X(R) = E_g^{(bulk)} + A/ R^{n} - B/R^{m}$ to describe both strong and weak quantum confinement regimes, where $A$, $B$, $C$, $\gamma$, $n$, and $m$ are substrate-dependent parameters. We also predict that the exciton lifetimes exhibit a strong temperature dependence, ranging between 2-8 ns (Si substrate) and 3-11 ns (SiO$_2$ substrate) for QDs up 10 nm in size.

Wigner molecules and charged excitons in near-field magnetophotoluminescence spectra of self-organized InP/GaInP quantum dots

We used high-spatial-resolution, low-temperature near-field scanning optical microscopy (NSOM) operating at magnetic fields $B=0--10\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ to study the effects of Wigner localization (WL) on emission spectra of single self-organized InP/GaInP quantum dots (QDs) and investigate the stability of singly (trion) and doubly (tetron) charged exciton complexes in the weak quantum confinement regime. Using NSOM measurements together with configuration interaction calculations, we identify the dots having different electron population $\mathrm{N}(\mathrm{N}=1--12)$, quantum confinement $(\ensuremath{\hbar}{\ensuremath{\omega}}_{0}=0.6--8\phantom{\rule{0.16em}{0ex}}\mathrm{meV})$ and size $D(D=70--170\phantom{\rule{0.16em}{0ex}}\mathrm{nm})$. For $\mathrm{N}=2$, we observed a magnetic-field-induced molecular-droplet transition, accompanied by the decomposition of the tetron into a Wigner molecule complex (WMC), and the activation of rotovibronic structure. For $\mathrm{N}=1$, unusually strong vibronic structure resulting from a trion-type WMC was observed. We have shown that magnetic-field-induced shifts of this structure allow measurement of single particle Fock-Darwin levels and angular momentum transitions of the WMC. In addition, we demonstrated the use of NSOM imaging to probe the charge density distribution and observed anomalous dependence of the image size on the quantum confinement, implying a pairing of electrons or formation of whispering gallery modes in the QD. We demonstrated that InP/GaInP QDs, provide a Wigner-Seitz radius $({r}_{s})$ up to 13, and that the measurements of NSOM magneto-optical spectroscopy using these dots makes it possible to study effects arising from strong Coulomb interaction of a few confined electrons (holes).

Ground-State Electronic Structure of Quasi-One-Dimensional Wires in Semiconductor Heterostructures

We apply density functional theory, in the local density approximation, to a quasi-one-dimensional electron gas in order to quantify the effect of Coulomb and correlation effects in modulating, and therefore patterning, the charge density distribution. Our calculations are presented specifically for surface-gate-defined quasi-one-dimensional quantum wires in a GaAs-AlGaAs heterostructure but we expect our results to apply more generally for other low dimensional semiconductor systems. We show that at high densities with strong confinement, screening of electrons in the direction transverse to the wire is efficient and density modulations are not visible. In the low-density, weak-confinement regime, the exchange-correlation potential induces small density modulations as the electrons are depleted from the wire. At the weakest confinements and lowest densities, the electron density splits into two rows thereby forming a pair of quantum wires that lie beneath the surface gates. An additional double-well external potential forms at very low density which enhances this row splitting phenomenon. We produce phase diagrams that show a transition between the presence of a single quantum wire in a split-gate structure and two quantum wires. We suggest that this phenomenon can be used to pattern and modulate the electron density in low-dimensional structures with particular application to systems where a proximity effect from a surface gate would be valuable.

Efficient Biexciton Interaction in Perovskite Quantum Dots Under Weak and Strong Confinement.

Cesium lead halide perovskite quantum dots (PQDs) have emerged as a promising new platform for lighting applications. However, to date, light emitting diodes (LED) based on these materials exhibit limited efficiencies. One hypothesized limiting factor is fast nonradiative multiexciton Auger recombination. Using ultrafast spectroscopic techniques, we investigate multicarrier interaction and recombination mechanisms in cesium lead halide PQDs. By mapping the dependence of the biexciton Auger lifetime and the biexciton binding energy on nanomaterial size and composition, we find unusually strong Coulomb interactions among multiexcitons in PQDs. This results in weakly emissive biexcitons and trions, and accounts for low light emission efficiencies. We observe that, for strong confinement, the biexciton lifetime depends linearly on the PQD volume. This dependence becomes sublinear in the weak confinement regime as the PQD size increases beyond the Bohr radius. We demonstrate that Auger recombination is faster in PQDs compared to CdSe nanoparticles having the same volume, suggesting a stronger Coulombic interaction in the PQDs. We confirm this by demonstrating an increased biexciton binding energy, which reaches a maximum of about 100 meV, fully three times larger than in CdSe quantum dots. The biexciton shift can lead to low-threshold optical gain in these materials. These findings also suggest that materials engineering to reduce Coulombic interaction in cesium lead halide PQDs could improve prospects for high efficiency optoelectronic devices. Core-shell structures, in particular type-II nanostructures, which are known to reduce the bandedge Coulomb interaction in CdSe/CdS, could beneficially be applied to PQDs with the goal of increasing their potential in lighting applications.

Inverse parabolic quantum dot: The transition energy under magnetic field effect

We present here, the evolution of the transition energy with a static magnetic field, when the electron and the hole are confined in inverse parabolic quantum dot (IPQD). The unexpected behavior is found, at the weak confinement regime the conduction band minimum and the top of valance band change from s-state to p-state or d-state for confined electron and hole inside IPQD, respectively. The strength of the inverse parabolic potential (potential hump) inside a quantum dot has the upper hand in tuning the ground state momentum for both electron and hole, and consequently their interband transition energy is changed. Knowing that this is not the case for the other types of potentials. The quantum size, the magnetic field and inverse potential hump effects on electron and hole ground and excited states are discussed.

Investigation of Photoluminescence Mechanisms from SiO2/Si:SiO2/SiO2 Structures in Weak Quantum Confined Regime by Deconvolution of Photoluminescence Spectra.

Si nanocrystals embedded in SiO2 matrix were prepared by co-sputtering method followed by a post annealing process in N2 ambient. By fixing sputtering parameters, the effects of annealing time and annealing temperature on the optical properties of Si nanocrystals are investigated. Origin and evolution of the photoluminescence (PL) in weak quantum confinement regime are discussed in the light of X-ray diffraction, Fourier transform infrared, and temperature dependent photoluminescence measurements. For all samples, the PL peaks tend to decompose to four Gaussian peaks in which attributed to the radiative defects in SiO2 matrix, nc-Si/SiO2 interface related localized defects, localized states in the amorphous Si band gap and quantum confinement of excitons in smaller nanocrystals. Considering the observation of luminescence and its decomposition tendency in nanocrystals with average sizes larger than exciton's Bohr radius the necessity to distinguish between the role of smaller and larger nanocrystals in the PL mechanisms is discussed. Furthermore, possible origin of the interface related localized states in particular Si=O double bonds in the nc-Si/SiO2 interface and that of radiative defects in SiO2 matrix are discussed.

Excitation dependent multicolor emission and photoconductivity of Mn, Cu doped In2S3 monodisperse quantum dots

Indium sulphide (In2S3) quantum dots (QDs) of average size 6 ± 2 nm and hexagonal nanoplatelets of average size 37 ± 4 nm have been synthesized from indium myristate and indium diethyl dithiocarbamate precursors respectively. The absorbance and emission band was tuned with variation of nanocrytal size from very small in the strong confinement regime to very large in the weak confinement regime. The blue emission and its shifting with size has been explained with the donor–acceptor recombination process. The 3d element doping (Mn2+ and Cu2+) is found to be effective for formation of new emission bands at higher wavelengths. The characteristic peaks of Mn2+ and Cu2+ and the modification of In3+ peaks in the x-ray photoelectric spectrum (XPS) confirm the incorporation of Mn2+ and Cu2+ into the In2S3 matrix. The simulation of the electron paramagnetic resonance signal indicates the coexistence of isotropic and axial symmetry for In and S vacancies. Moreover, the majority of Mn2+ ions and sulphur vacancies (VS ) reside on the surface of nanocrystals. The quantum confinement effect leads to an enhancement of band gap up to 3.65 eV in QDs. The formation of Mn 3d levels between conduction band edge and shallow donor states is evidenced from a systematic variation of emission spectra with the excitation wavelength. In2S3 QDs have been established as efficient sensitizers to Mn and Cu emission centers. Fast and slow components of photoluminescence (PL) decay dynamics in Mn and Cu doped QDs are interpreted in terms of surface and bulk recombination processes. Fast and stable photodetctors with high photocurrent gain are fabricated with Mn and Cu doped QDs and are found to be faster than pure In2S3. The fastest response time in Cu doped QDs is an indication of the most suitable system for photodetector devices.

Baryon masses in the three-state Potts field theory in a weak magnetic field

The 3-state Potts field theory describes the scaling limit of the 3-state Potts model on the two-dimensional lattice near its continuous phase transition point. In the presence of thermal and magnetic field perturbations, the 3-state Potts field theory in the ordered phase exhibits confinement of kinks, which allows both mesons and baryons. We calculate the masses of light baryons in this model in the weak confinement regime in leading order of the small magnetic field. In leading order of perturbation theory, the light baryons can be viewed as bound states of three quantum particles—the kinks, which move on a line and interact via a linear potential. We determine the masses of the lightest baryons by numerical solution of the associated non-relativistic one-dimensional quantum three-body problem.

Screening effect on the exciton mediated nonlinear optical susceptibility of semiconductor quantum dots.

We study the exciton contribution to the third-order optical susceptibility of one-dimensional semiconductor quantum dots and show that the screening of the electron-hole interaction has a strong influence on the nonlinear optical properties in the weak confinement regime. Based on a density matrix formulation, we estimate the spectrum of the third-order optical susceptibility and its contribution to the refraction index and absorption coefficient. In particular, we show that the multipeaked spectrum of the nonlinear susceptibility, which results from the hydrogenoid character of the exciton eigenstates for a purely Coulombian electron-hole coupling, is reverted towards a single peaked structure as the interaction becomes strongly screened, thus leading to a substantial enhancement of the nonlinear optical properties of semiconductor quantum dots.

Toward weak confinement regime in epitaxial nanostructures: Interdependence of spatial character of quantum confinement and wave function extension in large and elongated quantum dots

In this paper we present a comprehensive and detailed analysis of carrier/exciton wave function extension in large low-strain ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}$As quantum dots (QDs). They exhibit rather shallow confinement potential with electron/hole localization energy below 30 meV and confinement strength substantially weakened in comparison to typical epitaxial quasi-zero-dimensional semiconductor nanostructures. The aim of this study is to investigate the influence of different factors on the wave function (probability density distribution) for carriers or excitons in this regime, i.e., object shape anisotropy as well as strain, piezoelectricity, and Coulomb interactions, and to identify the physical mechanisms determining the properties of optical emission. To probe the wave function symmetry, polarization-resolved photoluminescence has been performed, and the spatial extensions of the corresponding probability densities have been verified in magneto-optical measurements. The observed diamagnetic coefficients in the range of (15--31) $\ensuremath{\mu}\mathrm{eV}/{\mathrm{T}}^{2}$ reflect large in-plane QD size. These studies also enable us to investigate the importance of light hole states admixture to the valence band ground state in such nanostructures, which can be addressed via the degree of linear polarization of emission as well as the exciton ${g}_{X}$ factor. The linear-polarization-resolved measurements revealed an exceptionally low exciton fine structure splitting of $5 \ensuremath{\mu}\mathrm{eV}$ on average as well as a low emission polarization degree of \ensuremath{-}0.05, with the polarization perpendicular to the QD elongation direction dominating. The increased light hole contribution to the lowest energy hole level is reflected in the decreased exciton ${g}_{X}$ factor (in the range of 0--1) and is consistent with the results of the eight-band k\ifmmode\cdot\else\textperiodcentered\fi{}p modelling. Based on the temperature dependence of the diamagnetic coefficient, the problem of individual QD uniformity has additionally been discussed. To evaluate the impact of the confinment potential and the structure geometry on the optical properties of the QDs, a comparison between the investigated dots and InAs/InGaAlAs/InP quantum dashes exhibiting a much deeper confining potential is presented.

Influence of Ge content and annealing conditions on the PL properties of nc-Si1−xGex embedded in SiO2 matrix in weak quantum confined regime

Fabrication of Si (nc-Si), Ge (nc-Ge), and Si1−xGex (nc-Si1−xGex) nanocrystals embedded in SiO2 matrix is achieved by thermal annealing of magnetron-sputtered thin films. Effects of annealing conditions, namely duration and temperature, as well as Ge content on the photoluminescence properties are investigated. Origin and evolution of the photoluminescence signal in the weak quantum confinement regime are discussed. It is found that photoluminescence signals can be decomposed into four Gaussian peaks originating from Ge-related radiative defects located at the sub-oxide (GeOx), either inside the matrix or at the interface region (peak M), nc-Si1−xGex/SiO2 interface-related localized states (peak I), localized states in the amorphous Si1−xGex bandgap (peak A) and quantum confinement of excitons in small nanocrystals (peak Q). The role of small and large nanocrystals in the photoluminescence mechanism is investigated by varying the mean nanocrystal size from 3nm to 23nm (from strong to weak quantum confined regime). Our results demonstrate that the quantum confinement effect in Ge nanocrystals manifests though spectral blueshift due to increase in Ge content. We also propose that the decreasing photoluminescence signal intensity with an increase in Ge content may originate from Ge-related nonradiative Pb centers.

Design and simulation of perturbed onion‐like quantum‐dot‐quantum‐well (CdSe/ZnS/CdSe/ZnS) and its influence on fluorescence resonance energy transfer mechanism

In this study, the authors investigate one of the biological sensory applications (fluorescence resonance energy transfer (FRET)) that has astonishing influence on implementation of the bio-medical assays. For the first time, in this study, the new inorganic modified nanoparticle structure (quantum-dot quantum-well (QDQW) heteronanocrystal) is used as donor particle. By considering the mentioned structure, the authors can easily manipulate the donor emission spectrum and all parameters of FRET, such as overlapping between the donor emission and acceptor absorption. In this procedure, the Förster radius can be completely controlled. Moreover, the quantum confinement effects, including the strong-confinement and the weak-confinement regime, are investigated for FRET essential variables. As a main goal of this study, the authors will mathematically explore the influences of perturbation on the intrinsic parameters of nanoparticles (lifetime and bandwidth of emission spectrum) and on the sensitivity of FRET. It can be revealed that the presence of perturbation in nanoparticle has a devastating influence on biological assay characteristics, which will be probe in presented simulations. Furthermore, the physically analysing of QDQW heteronanocrystal structure is performed by the accurate eight-band K.P theory and finite-element method.

Exact solution of the compressed hydrogen atom

The exact solution to the problem of a hydrogen atom confined in a spherical well (CHA) is discussed; the standard results for the unconfined hydrogen atom (UHA) are recovered as the sphere size becomes large compared to the Bohr radius. The solutions are characterized by a set of three quantum numbers N (= 1, 2, 3,…), L (= 0, 1, 2,…), and M (= − L, − L + 1,…, L − 1, L), and the energy eigenvalues, in contrast to the situation in the UHA, depend on both N and L. All members of a given family n = N + L, however, evolve asymptotically toward the same energy level in the large-sphere limit, recovering the typical n2 degeneracy of the UHA. Besides numerically exact solutions for arbitrary sphere sizes, rigorous analytical approximations are provided for the physically relevant strong- and weak-confinement regimes. A conjecture concerning the ordering of the energy levels is rigorously confirmed. The validity of the virial theorem, Kato's cusp condition, and the role played by the density as an alternative basic variable for the case of the CHA are discussed.

Entanglement in S states of two-electron quantum dots with Coulomb impurities at the center

We study a system of two Coulombically interacting electrons in an external harmonic potential in the presence of an on-centre Coulomb impurity. Detailed results for the dependencies of the reduced von Neumann entropy on the control parameters of the system are provided for both the ground state and the triplet S states with the lowest energy. Among other features, it is found that in the weak confinement regime the entanglement is strongly affected by the presence of an acceptor impurity.

(Invited) Photoluminescence Efficiency of Germanium Dots Self-Assembled on Oxides

Self-assembled Ge quantum dots were formed by in-situ thermal annealing of a thin amorphous Ge layer deposited by molecular beam epitaxy either on a thin porous TiO2 layer grown on SiO2 on Si(001) or directly on the SiO2 layer itself. For samples with dot diameters ranging from 10 to 35 nm, the dot photoluminescence (PL) appeared primarily as a wide near-infrared band peaked near 800 meV. The peak energy of the PL band reflects the average dot size and its shape depends on the dot size distribution. Using tight binding and effective mass theoretical models, we have analyzed the PL spectrum in terms of the dot size distribution. The observed size distribution determined from transmission electron and atomic force microscopy allowed the determination of the nonlinear increase in the PL efficiency with decreasing dot diameter. Although the absolute intensities of the PL from the samples vary, the calculated efficiency curves are all well fitted by straight lines on a log-log plot, with essentially the same slope for all samples, thereby demonstrating that under the weak confinement regime investigated here there is a universal power-law increase in PL efficiency with decreasing dot size. Knowing this generic PL efficiency, we show that it is possible to evaluate the size distribution of Ge dots from their PL energy dependence.

On the missing links in quantum dot solar cells: a DFT study on fluorophore oxidation and reduction processes in sensitized solar cells

The possibility of achieving many electrons per absorbed photon of sufficient energy by quantum dots (QDs) drives the motivation to build high performance quantum dot solar cells (QDSCs). Although performance of dye-sensitized solar cells (DSCs), with similar device configuration as that of QDSCs, has significantly improved in the last two decades QDSCs are yet to demonstrate impressive device performances despite the remarkable features of QDs as light harvesters. We investigated the fundamental differences in the optical properties of QDs and dyes using DFT calculations to get insights on the inferior performance of QDSCs. The CdSe QDs and the ruthenium bipyridyl dicarboxylic acid dye (N3) were used as typical examples in this study. Based on a generalized equation of state correlating material properties and photoconversion efficiency, we calculated ground and excited state properties of these absorbers at the B3LYP/lanl2dz level of DFT and analyzed them on the basis of the device performance. Five missing links have been identified in the study which provides numerous insights into building high efficiency QDSCs. They are (i) fundamental differences in the emitting states of the QDs in the strong and weak confinement regimes were observed, which explained successfully the performance differences; (ii) the crucial role of bifunctional ligands that bind the QDs and the photo-electrode was identified; in most cases use of bifunctional ligands does not lead to a QD enabled widening of the absorption of the photo-electrode; (iii) wide QDs size distribution further hinders efficient electron injections; (iv) wide absorption cross-section of QDs favours photon harvesting; and (v) the role of redox potential of the electrolyte in the QD reduction process.

Hydrodynamic effects on confined polymers

We consider the statics and dynamics of a flexible polymer confined between parallel plates both in the presence and absence of hydrodynamic interactions. The hydrodynamic interactions are described at the level of the fluctuating, compressible Navier–Stokes equation. We consider two cases: (i) confinement for both the solvent and the polymer, and (ii) confinement for the polymer only (in a 3D solvent), which is experimentally feasible, for instance, by (optical) trapping. We find a continuous transition from 2D to 3D dynamic scaling as a function of decreasing degree of confinement within the de Gennes and the weak-confinement regimes. We demonstrate that, in the presence of hydrodynamics, the polymer's center-of-mass diffusion coefficient in the direction parallel to the walls scales differently as a function of the level of confinement in cases (i) and (ii). We also find that in the commonly used Langevin dynamics description, the polymer swells more parallel to the walls than in the presence of hydrodynamics, and the planar diffusion coefficient shows scaling behavior similar to case (ii) rather than case (i). In addition, we quantify the differences in the static structure factor of the polymer between cases (i) and (ii), and between case (i) and Langevin dynamics.

Pressure and temperature effects on the third-order nonlinear optical properties in GaAs quantum dots

Abstract This work is used in the density matrix formalism and the effective mass approximation to study the third harmonic generation coefficient in a GaAs disc-shaped quantum dot with parabolic confinement potential. It is discussed the strong and weak confinement regime. The results show that the third harmonic generation coefficient is strongly dependent on the excitonic pair localization. The study is extended to consider effects such as hydrostatic pressure and temperature to show that it is possible to induce a blue-shift and/or red-shift on the resonant peaks of the third harmonic generation coefficient.

The Entropic Cost of Polymer Confinement

The confinement of a polymer into a small space is thermodynamically unfavorable because of the reduction in the number of conformational states. The entropic penalty affects a variety of biological processes, and it plays an important role in polymer transport properties and in microfluidic devices. We determine the entropic penalty for the confinement of elastic polymer of persistence length P in the long-chain limit. We examine three geometries: (1) parallel planes separated by a distance d (a slit); (2) a circular tube of diameter d; and (3) a sphere of diameter d. We first consider infinitely thin (ideal) chains. As d/P drops from 100 to 0.01, TΔS rises from ∼5 × 10(-4) kT to ∼30 kT per persistence length for cases (1) and (2), with the entropic penalty for case (2) being consistently about twice that for case (1). TΔS is ∼5 kT per persistence length for confinement to a sphere when d = P, about twice the value predicted by mean field theory. For all three geometries, in the limit d/P ≫ 1, the asymptotic behavior of ΔS vs d is consistent with the d(-2) behavior predicted by theory. In the limit d/P ≪ 1, the scaling of ΔS for slits and tubes is also consistent with earlier predictions (d(-2/3)). Finally, we treat volume exclusion effects, examining chains of diameter D > 0. Confinement to a narrow slit or tube (d/P ≪ 1) has the same entropic penalty as that for an ideal chain in a slit or tube with d' = d - D; in the weak confinement regime (d/P ≫ 1), the entropic penalties are significantly larger than those for infinitely thin chains. When a chain of finite diameter is forced into a sphere or other closed cavity, the entropic confinement penalty rises without limit because there are no configurations available to the chain once its volume exceeds that of the cavity.