Optical properties of nanocrystal films: blue shifted transitions as signature of strong coupling

We present a theoretical study at the atomistic level of the optical properties of semiconductor nanocrystal films. We investigate the dependence of the absorption coefficient on size, inter-dot separation, surface stoichiometry and morphology, temperature, position of the Fermi level and light polarization. Our results show that, counter-intuitively, huge blue shifts are expected in some intra-band transitions for strongly coupled arrays, in contrast with the predicted and observed red shift of the band gap absorption in such systems. Furthermore, we find that the energies of such transitions can be tuned within a range of several hundreds of meV, just by engineering the inter-dot separation in the film through the choice of appropriately sized capping ligands. Finally we discuss the application of this effect to nanocrystal-based intermediate-band solar cells

Liquid-Liquid Phase Transition for an Attractive Isotropic Potential with Wide Repulsive Range

Recent experimental and theoretical results have shown the existence of a liquid-liquid phase transition in isotropic systems, such as biological solutions and colloids, whose interaction can be represented via an effective potential with a repulsive soft-core and an attractive part. We investigate how the phase diagram of a schematic general isotropic system, interacting via a soft-core squared attractive potential, changes by varying the parameters of the potential. It has been shown that this potential has a phase diagram with a liquid-liquid phase transition in addition to the standard gas-liquid phase transition and that, for a short-range soft-core, the phase diagram resulting from molecular dynamics simulations can be interpreted through a modified van der Waals equation. Here we consider the case of soft-core ranges comparable with or larger than the hard-core diameter. Because an analysis using molecular dynamics simulations of such systems or potentials is too time-demanding, we adopt an integral equation approach in the hypernetted-chain approximation. Thus we can estimate how the temperature and density of both critical points depend on the potential's parameters for large soft-core ranges. The present results confirm and extend our previous analysis, showing that this potential has two fluid-fluid critical points that are well separated in temperature and in density only if there is a balance between the attractive and repulsive part of the potential. We find that for large soft-core ranges our results satisfy a simple relation between the potential's parameters

Efficient, non-stochastic, Monte-Carlo-like-accurate method for the calculation of the temperature-dependent mobility in nanocrystal films

We present a new non-stochastic framework for the calculation of the temperature dependence of the mobility in nanocrystal films, that enables speed-ups of several orders of magnitude compared to conventional Monte Carlo approaches, while maintaining a similar accuracy. Our model identifies a new contribution to the reduction of the mobility with increasing temperature in these systems (conventionally attributed to interactions with phonons), that alone is sufficient to explain the observed experimental trend up to room temperature. Comparison of our results with the theoretical predictions of the hopping model and the observed temperature dependence of recent field-effect mobility measurements in nanocrystal films, provides the means to discriminate between band-like and hopping transport and a definitive answer to whether the former has been achieved in quantum dot films

Liquid-Liquid Phase Transitions for Soft-Core Attractive Potentials

Using event driven molecular dynamics simulations, we study a three dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of a narrow attractive well, it has been shown that this potential has two metastable gas-liquid critical points. Here we systematically investigate how the changes of the parameters of this potential affect the phase diagram of the system. We find a broad range of potential parameters for which the system has both a gas-liquid critical point and a liquid-liquid critical point. For the liquid-gas critical point we find that the derivatives of the critical temperature and pressure, with respect to the parameters of the potential, have the same signs: they are positive for increasing width of the attractive well and negative for increasing width and repulsive energy of the soft core. This result resembles the behavior of the liquid-gas critical point for standard liquids. In contrast, for the liquid-liquid critical point the critical pressure decreases as the critical temperature increases. As a consequence, the liquid-liquid critical point exists at positive pressures only in a finite range of parameters. We present a modified van der Waals equation which qualitatively reproduces the behavior of both critical points within some range of parameters, and give us insight on the mechanisms ruling the dependence of the two critical points on the potential's parameters. The soft core potential studied here resembles model potentials used for colloids, proteins, and potentials that have been related to liquid metals, raising an interesting possibility that a liquid-liquid phase transition may be present in some systems where it has not yet been observed.Comment: 29 pages, 15 figure

Generic mechanism for generating a liquid-liquid phase transition

Recent experimental results indicate that phosphorus, a single-component system, can have two liquid phases: a high-density liquid (HDL) and a low-density liquid (LDL) phase. A first-order transition between two liquids of different densities is consistent with experimental data for a variety of materials, including single-component systems such as water, silica and carbon. Molecular dynamics simulations of very specific models for supercooled water, liquid carbon and supercooled silica, predict a LDL-HDL critical point, but a coherent and general interpretation of the LDL-HDL transition is lacking. Here we show that the presence of a LDL and a HDL can be directly related to an interaction potential with an attractive part and two characteristic short-range repulsive distances. This kind of interaction is common to other single-component materials in the liquid state (in particular liquid metals), and such potentials are often used to decribe systems that exhibit a density anomaly. However, our results show that the LDL and HDL phases can occur in systems with no density anomaly. Our results therefore present an experimental challenge to uncover a liquid-liquid transition in systems like liquid metals, regardless of the presence of the density anomaly.Comment: 5 pages, 3 ps Fig

New strategies for colloidal-quantum-dot-based intermediate-band solar cells

The intermediate-band solar cell (IBSC) concept promises to increase the efficiency limit in a single-junction solar cell through the absorption of below-bandgap-energy photons. Despite their operating principle having been proposed over 20 years ago, IBSCs have not delivered on this promise yet, and the devices fabricated so far, mainly based on embedded epitaxial quantum dots, have instead operated with lower efficiency than conventional solar cells. A new paradigm, based on the exploitation as the intermediate band of the intragap states naturally occurring in the density functional theory description of colloidal (i.e., chemically synthesized) quantum dots, was suggested recently. Here, we revisit this intriguing concept unveiling its shortcomings and propose two alternative schemes: in the first, the localized electron surface trap states, ubiquitously found in commonly synthesized colloidal quantum dots, are used as intermediate bands in strongly coupled films made of small InAs nanocrystals and, in the second scheme, the intermediate band is provided by the conduction-band-minimum-derived miniband in films of larger InAs nanocrystals. Both schemes yield estimated limiting IBSC efficiencies exceeding Shockley-Queisser’s limit for a single absorber

Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly

We investigate the phase behavior of a single-component system in 3 dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an intermediate distance, and a hard-core repulsion at a short distance, similar to potentials used to describe liquid systems such as colloids, protein solutions, or liquid metals. We showed [Nature {\bf 409}, 692 (2001)] that, even with no evidences of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gas--low-density liquid (LDL) critical point, and the other in a gas--high-density liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the 3-parameter space of the soft-core potential and we perform molecular dynamics simulations in the interesting region of parameters. For the equilibrium phase diagram we analyze the structure of the crystal phase and find that, within the considered range of densities, the structure is independent of the density. Then, we analyze in detail the fluid metastable phases and, by explicit thermodynamic calculation in the supercooled phase, we show the absence of the density anomaly. We suggest that this absence is related to the presence of only one stable crystal structure.Comment: 15 pages, 21 figure

On the Relationship between the Conditional and Unconditional Distribution of a Random Variable

This paper studies the relationship between the unconditional and conditional distribution of the same random variable, say Y, when the distribution of the conditioning random variable X is of a known form. The problem is tackled in the general case where the distribution of Y and Y given X are mixed. Attention is focused to two particular cases. In the first X is assumed to follow a Poisson distribution; in the second X is allowed to have a mixed Poisson form. Potential applications are also discusse

Band-like electron transport in 2D quantum dot periodic lattices: the effect of realistic size distributions

Electron mobility in nanocrystal films has been a controversial topic in the last few years. Theoretical and experimental studies evidencing carrier transport by hopping or showing band-like features have been reported in the past. A relevant factor to analyze transport results is the progressive improvement in quantum dot superlattice fabrication, leading to better regimented structures for which band-like transport would be more relevant. This work presents an efficient model to compute temperature-dependent band-like electronic mobilities in 2D quantum dot arrays when a realistic quantum dot size distribution is considered. Comparisons with experimental results are used to estimate these size distributions, in good agreement with data of the samples

Reference Bayesian methods for recapture models with heterogeneity

Capture–recapture models, Heterogeneity, Bayesian inference, Population size, Default prior, Model choice, 62F15, 62G05,