Conduction Band Fine Structure in Colloidal HgTe Quantum Dots.

HgTe colloidal quantum dots (QDs) are of interest because quantum confinement of semimetallic bulk HgTe allows one to synthetically control the bandgap throughout the infrared. Here, we synthesize highly monodisperse HgTe QDs and tune their doping both chemically and electrochemically. The monodispersity of the QDs was evaluated using small-angle X-ray scattering (SAXS) and suggests a diameter distribution of ∼10% across multiple batches of different sizes. Electron-doped HgTe QDs display an intraband absorbance and bleaching of the first two excitonic features. We see splitting of the intraband peaks corresponding to electronic transitions from the occupied 1Se state to a series of nondegenerate 1Pe states. Spectroelectrochemical studies reveal that the degree of splitting and relative intensity of the intraband features remain constant across doping levels up to two electrons per QD. Theoretical modeling suggests that the splitting of the 1Pe level arises from spin-orbit coupling and reduced QD symmetry. The fine structure of the intraband transitions is observed in the ensemble studies due to the size uniformity of the as-synthesized QDs and strong spin-orbit coupling inherent to HgTe.

Continuous-wave infrared optical gain and amplified spontaneous emission at ultralow threshold by colloidal HgTe quantum dots.

Colloidal quantum dots (QDs) raise more and more interest as solution-processable and tunable optical gain materials. However, especially for infrared active QDs, optical gain remains inefficient. Since stimulated emission involves multifold degenerate band-edge states, population inversion can be attained only at high pump power and must compete with efficient multi-exciton recombination. Here, we show that mercury telluride (HgTe) QDs exhibit size-tunable stimulated emission throughout the near-infrared telecom window at thresholds unmatched by any QD studied before. We attribute this unique behaviour to surface-localized states in the bandgap that turn HgTe QDs into 4-level systems. The resulting long-lived population inversion induces amplified spontaneous emission under continuous-wave optical pumping at power levels compatible with solar irradiation and direct current electrical pumping. These results introduce an alternative approach for low-threshold QD-based gain media based on intentional trap states that paves the way for solution-processed infrared QD lasers and amplifiers.

A phonon scattering bottleneck for carrier cooling in lead chalcogenide nanocrystals.

The cooling dynamics of hot charge carriers in colloidal lead chalcogenide nanocrystals is studied by hyperspectral transient absorption spectroscopy. We demonstrate a transient accumulation of charge carriers at a high energy critical point in the Brillouin zone. Using a theoretical study of the cooling rate in lead chalcogenides, we attribute this slowing down of charge carrier cooling to a phonon scattering bottleneck around this critical point. The relevance of this observation for the possible harvesting of the excess energy of hot carriers by schemes such as multiexciton generation is discussed.

Mercury telluride colloidal quantum dots: electronic structure, size-dependent spectra, and photocurrent detection up to 12 µm.

HgTe colloidal quantum dots are synthesized with high monodispersivity with sizes up to ∼15 nm corresponding to a room temperature absorption edge at ∼5 µm. The shape is tetrahedral for larger sizes and up to five peaks are seen in the absorption spectra with a clear size dependence. The size range of the HgTe quantum dots is extended to ∼20 nm using regrowth. The corresponding room temperature photoluminescence and absorption edge reach into the long-wave infrared, past 8 µm. Upon cooling to liquid nitrogen temperature, a photoconductive response is obtained in the long-wave infrared region up to 12 µm. Configuration-interaction tight-binding calculations successfully explain the spectra and the size dependence. The five optical features can be assigned to sets of single hole to single electron transitions whose strengths are strongly influenced by the multiband/multiorbital character of the quantum-dot electronic states.

Multiple exciton generation and ultrafast exciton dynamics in HgTe colloidal quantum dots.

The investigation of sub-nanosecond exciton dynamics in HgTe colloidal quantum dots using ultrafast transient absorption spectroscopy is reported. The transmittance change spectrum acquired immediately after pumping is dominated by a bleach blue-shifted by ~200-300 nm from the photoluminescent emission band. Comparison with a tight-binding model of the electronic structure allows this feature to be attributed to the filling of band edge states. The form of the pump-induced transmittance transients is dependent on the excitation rate and the rate of sample stirring. For moderate pumping of stirred samples, the transmittance transients are well-described by a mono-exponential decay associated with biexciton recombination, with a lifetime of 49 ± 2 ps. For samples that are strongly-pumped or unstirred, the decay becomes bi-exponential in form, indicating that trap-related recombination has become significant. We also present a new analysis that enables fractional transmittance changes to be related to band edge occupation for samples with arbitrary optical density at the pump wavelength. This allows us to identify the occurrence of multiple exciton generation, which results in a quantum yield of 1.36 ± 0.04 for a photon energy equivalent to 3.1 times the band gap, in good agreement with the results of the model.

Ultrafast exciton dynamics in InAs/ZnSe nanocrystal quantum dots.

Colloidal nanocrystal quantum dots with a band gap in the near infra-red have potential application as the emitters for telecommunications or in vivo imaging, or as the photo-absorbing species in next generation solar cells or photodetectors. However, electro- and photoluminescence yields and the efficiency with which photo-generated charges can be extracted from quantum dots depend on the total rate of recombination, which can be dominated by surface-mediated processes. In this study, we use ultrafast transient absorption spectroscopy to characterise the recombination dynamics of photo-generated charges in InAs/ZnSe nanocrystal quantum dots. We find that recombination is dominated by rapid, sub-nanosecond transfer of conduction band electrons to surface states. For the size of dots studied, we also find no evidence of significant multiple exciton generation for photon energies up to 3.2 times the band gap, in agreement with our theoretical modelling.

Loosening quantum confinement: observation of real conductivity caused by hole polarons in semiconductor nanocrystals smaller than the Bohr radius.

We report on the gradual evolution of the conductivity of spherical CdTe nanocrystals of increasing size from the regime of strong quantum confinement with truly discrete energy levels to the regime of weak confinement with closely spaced hole states. We use the high-frequency (terahertz) real and imaginary conductivities of optically injected carriers in the nanocrystals to report on the degree of quantum confinement. For the smaller CdTe nanocrystals (3 nm < radius < 5 nm), the complex terahertz conductivity is purely imaginary. For nanocrystals with radii exceeding 5 nm, we observe the onset of real conductivity, which is attributed to the increasingly smaller separation between the hole states. Remarkably, this onset occurs for a nanocrystal radius significantly smaller than the bulk exciton Bohr radius a(B) ∼ 7 nm and cannot be explained by purely electronic transitions between hole states, as evidenced by tight-binding calculations. The real-valued conductivity observed in the larger nanocrystals can be explained by the emergence of mixed carrier-phonon, that is, polaron, states due to hole transitions that become resonant with, and couple strongly to, optical phonon modes for larger QDs. These polaron states possess larger oscillator strengths and broader absorption, and thereby give rise to enhanced real conductivity within the nanocrystals despite the confinement.

Optimization of carrier multiplication for more effcient solar cells: the case of Sn quantum dots.

We present calculations of impact ionization rates, carrier multiplication yields, and solar-power conversion efficiencies in solar cells based on quantum dots (QDs) of a semimetal, α-Sn. Using these results and previous ones on PbSe and PbS QDs, we discuss a strategy to select QDs with the highest carrier multiplication rate for more efficient solar cells. We suggest using QDs of materials with a close to zero band gap and a high multiplicity of the bands in order to favor the relaxation of photoexcited carriers by impact ionization. Even in that case, the improvement of the maximum solar-power conversion efficiency appears to be a challenging task.

Size-dependent optical properties of colloidal PbS quantum dots.

We quantitatively investigate the size-dependent optical properties of colloidal PbS nanocrystals or quantum dots (Qdots), by combining the Qdot absorbance spectra with detailed elemental analysis of the Qdot suspensions. At high energies, the molar extinction coefficient epsilon increases with the Qdot volume d(3) and agrees with theoretical calculations using the Maxwell-Garnett effective medium theory and bulk values for the Qdot dielectric function. This demonstrates that quantum confinement has no influence on epsilon in this spectral range, and it provides an accurate method to calculate the Qdot concentration. Around the band gap, epsilon only increases with d(1.3), and values are comparable to the epsilon of PbSe Qdots. The data are related to the oscillator strength f(if) of the band gap transition and results agree well with theoretical tight-binding calculations, predicting a linear dependence of f(if) on d. For both PbS and PbSe Qdots, the exciton lifetime tau is calculated from f(if). We find values ranging between 1 and 3 mus, in agreement with experimental literature data from time-resolved luminescence spectroscopy. Our results provide a thorough general framework to calculate and understand the optical properties of suspended colloidal quantum dots. Most importantly, it highlights the significance of the local field factor in these systems.

Optical investigation of quantum confinement in PbSe nanocrystals at different points in the Brillouin zone.

We present detailed investigations on the optical properties of PbSe nanocrystals. The absorption spectra of monodisperse, quasispherical nanocrystals exhibit sharp features as a result of distinct optical transitions. To study the size dependence, absorption spectra of nanocrystals ranging from 3.4 to 10.9 nm in diameter are analysed and a total of 11 distinct optical transitions are identified. The assignment of the various optical transitions is discussed and compared to theoretically calculated transition energies. By plotting all transitions as a function of nanocrystal size (D) we find that the energy (E) changes with the following relationship [Formula: see text] for the lowest energy transitions. The transition energy extrapolates to approximately 0.3 eV for infinite crystal size, in agreement with the bandgap of bulk PbSe at the L-point in the Brillouin zone. In addition, high-energy transitions are observed, which extrapolate to 1.6 eV for infinite crystal size, which is in good agreement with the bulk bandgap of PbSe at the Sigma-point in the Brillouin zone. Tight-binding calculations confirm that the high-energy transitions originate from the Sigma-point in the Brillouin zone. The Sigma-character of the high-energy transitions may be of importance to explain the mechanism behind multiple exciton generation in PbSe nanocrystals.

Uncovering forbidden optical transitions in PbSe nanocrystals.

The 1S(h,e)-1P(e,h) exciton transition energy of PbSe nanocrystals was determined via two-photon photoluminescence excitation spectroscopy and was found to be in good agreement with predictions from a tight-binding calculation. The two-photon excitation peak occurs at energies very close to a strong feature in the one-photon absorption spectrum and suggests that it should be assigned as a formally forbidden S-P transition. Leading explanations for the unusual strength of the forbidden transition are discussed.

Density of states measured by scanning-tunneling spectroscopy sheds new light on the optical transitions in PbSe nanocrystals.

The density-of-states function of individual colloidal PbSe nanocrystals varying in diameter between 3 and 7 nm is measured by resonant tunneling spectroscopy. It is in semiquantitative agreement with tight-binding calculations, but the energy separation between electron (hole) levels of S and P symmetry is systematically smaller than predicted by the theory. These results provide an explanation for the second and third excitonic optical transitions, which have been debated for a long time.

Long-range transport in an assembly of ZnO quantum dots: the effects of quantum confinement, Coulomb repulsion and structural disorder.

We have studied the storage and long-range transport of electrons in a porous assembly of weakly coupled ZnO quantum dots permeated with an aqueous and a propylene carbonate electrolyte solution. The number of electrons per ZnO quantum dot is controlled by the electrochemical potential of the assembly; the charge of the electrons is compensated by ions present in the pores. We show with optical and electrical measurements that the injected electrons occupy the S, P, and D type conduction electron levels of the quantum dots; electron storage in surface states is not important. With this method of three-dimensional charge compensation, up to ten electrons per quantum-dot can be stored if the assembly is permeated with an aqueous electrolyte. The screening of the electron charge is less effective in the case of an assembly permeated with a propylene carbonate electrolyte solution. Long-range electron transport is studied with a transistor set-up. In the case of ZnO assemblies permeated with an aqueous electrolyte, two quantum regimes are observed corresponding to multiple tunnelling between the S orbitals (at a low occupation) and P orbitals (at a higher occupation). In a ZnO quantum-dot assembly permeated with a propylene carbonate electrolyte solution, there is a strong overlap between these two regimes.

Confinement effects and tunnelling through quantum dots.

Several recent theoretical advances concerning semiconductor quantum dots are reviewed. First of all, the effect of the quantum confinement on the energy gap is revisited on the basis of GW and Bethe-Salpeter calculations, showing that the excitonic gap is practically equal to the ordinary eigenvalue gap of single-particle approximations. The second part demonstrates that it is now possible to calculate the conductance peaks for the tunnelling current through a nanostructure. Finally, we discuss in some detail the concept of a macroscopic dielectric constant for nanostructures, showing that, except for a thin surface layer, the local dielectric constant still keeps its bulk value down to pretty small nanostructures.