Antonio Capretti

Surface integral method for second harmonic generation in metal nanoparticles including both local-surface and nonlocal-bulk sources

Second harmonic (SH) radiation in metal nanoparticles is generated by both nonlocal-bulk and local-surface SH sources, induced by the electromagnetic field at the fundamental frequency. We propose a surface integral equation (SIE) method for evaluating the SH radiation generated by metal nanoparticles with arbitrary shapes, considering all SH sources. We demonstrate that the contribution of the nonlocal-bulk SH sources to the SH electromagnetic field can be taken into account through equivalent surface electric and magnetic currents. We numerically solve the SIE problem by using the Galerkin method and the Rao-Wilton-Glisson basis functions in the framework of the distribution theory. The accuracy of the proposed method is verified by comparison with the SH-Mie analytical solution. As an example of a complex-shaped particle, we investigate the SH scattering by a triangular nano-prism. This method paves the way for a better understanding of the SH generation process in arbitrarily shaped nanoparticles and can also have a high impact in the design of novel nanoplasmonic devices with enhanced SH emission.We propose a numerical method, based on surface integral equations (SIE), for evaluating the second harmonic (SH) scattering by metal nanoparticles (NPs) of arbitrary shape, considering both nonlocal-bulk and local-surface SH sources, induced by the electromagnetic field at the fundamental frequency. We demonstrate that the contribution of the nonlocal-bulk sources can be taken into account through equivalent surface electric and magnetic currents. We numerically solve the SIE problem by using the Galerkin method and the Rao–Wilton–Glisson basis functions in the framework of the distribution theory. The accuracy of the proposed method is verified by comparing with the SH-Mie analytical solution. As an example of a complex-shaped particle, we investigate the SH scattering by a triangular nanoprism. This method paves the way for a better understanding of the SH generation process in arbitrarily shaped NPs and can also have a high impact on the design of novel nanoplasmonic devices with enhanced SH emission.

Generation of second harmonic radiation from sub-stoichiometric silicon nitride thin films

Enhancing second-order optical processes in Si-compatible materials is important for the demonstration of innovative functionalities and nonlinear optical devices integrated on a chip. Here, we demonstrate significantly enhanced Second-Harmonic Generation (SHG) by silicon-rich silicon nitride materials over a broad spectral range, and show a maximum conversion efficiency of 4.5 × 10−6 for sub-stoichiometric samples with 46 at. % silicon. The SHG process in silicon nitride thin films is systematically investigated over a range of material stoichiometry and thermal annealing conditions. These findings can enable the engineering of innovative Si-based devices for nonlinear signal processing and sensing applications on a Si platform.

Substantial enhancement of red emission intensity by embedding Eu-doped GaN into a microcavity

We investigate resonantly excited photoluminescence from a Eu,O-codoped GaN layer embedded into a microcavity, consisting of an AlGaN/GaN distributed Bragg reflector and a Ag reflecting mirror. The microcavity is responsible for a 18.6-fold increase of the Eu emission intensity at ∼10K, and a 21-fold increase at room temperature. We systematically investigate the origin of this enhancement, and we conclude that it is due to the combination of several effects including, the lifetime shortening of the Eu emission, the strain-induced piezoelectric effect, and the increased extraction and excitation field efficiencies. This study paves the way for an alternative method to enhance the photoluminescence intensity in rare-earth doped semiconductor structures.

Integrating Quantum Dots and Dielectric Mie Resonators: A Hierarchical Metamaterial Inheriting the Best of Both

Nanoscale dielectric resonators and quantum-confined semiconductors have enabled unprecedented control over light absorption and excited charges, respectively. In this work, we embed luminescent silicon nanocrystals (Si-NCs) into a 2D array of SiO2 nanocylinders and experimentally prove a powerful concept: the resulting metamaterial preserves the radiative properties of the Si-NCs and inherits the spectrally selective absorption properties of the nanocylinders. This hierarchical approach provides increased photoluminescence (PL) intensity obtained without utilizing any lossy plasmonic components. We perform rigorous calculations and predict that a freestanding metamaterial enables tunable absorption peaks up to 50% in the visible spectrum, in correspondence with the nanocylinder Mie resonances and of the grating condition in the array. We experimentally detect extinction spectral peaks in the metamaterial, which drive enhanced absorption in the Si-NCs. Consequently, the metamaterial features increased PL intensity, obtained without affecting the PL lifetime, angular pattern, and extraction efficiency. Remarkably, our best-performing metamaterial shows +30% PL intensity achieved with a lower amount of Si-NCs, compared to an equivalent planar film without nanocylinders, resulting in a 3-fold average PL enhancement per Si-NC. The principle demonstrated here is general, and the Si-NCs can be replaced with other semiconductor quantum dots, rare-earth ions, or organic molecules. Similarly, the dielectric medium can be adjusted on purpose. This spectral selectivity of absorption paves the way for an effective light down-conversion scheme to increase the efficiency of solar cells. We envision the use of this hierarchical design for other efficient photovoltaic, photocatalytic, and artificial photosynthetic devices with spectrally selective absorption and enhanced efficiency.

Block-copolymer-based plasmonic metamaterials

Block-copolymer (BCP) self-assembling provides a unique tool for realizing large-area ordered metamaterials, with desired optical properties. The benefits of using BCPs as templates for metamaterials come from two main aspects: first, BCPs show a rich range of available nano-morphologies, whose domains can be conveniently tuned in size, shape and periodicity, by changing molecular parameters; second, the chemical properties of the block polymers can lead to the selective inclusion of functionalized nanoparticles (NPs) of different materials in specific nanodomains, generating periodic arrays of NPs according to the geometry of the BCP acting as template. This approach allows finely modulating the optical properties of NPs and can be used as an intriguing and versatile tool to build useful devices for Optics & Photonics applications, with significant benefits for both fundamental and applied investigations. In this work, we investigate nanostructured thin films of polystyrene-block-poly(methyl methacrylate) BCP (PS-PMMA), characterized by an hexagonal array of PS cylinders in the PMMA matrix. The PS cylindrical domain are selectively filled by functionalized metallic (Au, Ag) NPs. The optical properties of such nano-structures are strongly affected by localized surface plasmons (LSPs) in the NPs, arising from the collective resonances of conduction electrons in the metal at a characteristic spectral range, usually in the visible range. LSPs induce high field enhancement (FE), with respect to an incident light, in proximity of the NP surface, and in particular in the gap between two close NPs (hot-spot). Moreover, LSPs increase the intensity of absorption and scattering of light by the NPs in their range of resonance.

Reply to 'Absence of redshift in the direct bandgap of silicon nanocrystals with reduced size'

De Boer et al. reply — We appreciate the interest from Jun-Wei Luo et al. and are certainly glad to see that our past work1 keeps providing motivation for theoretical modelling. In contrast to their main claim and the title of their comment, we find that the presented results are in reasonably good agreement with our original report. However, the simulations concern small nanocrystals, with diameters ≤3 nm, and this limits the direct comparison with the experimental findings of our study. Also, the extrapolation procedure used in their Fig. 1a is unjustified, and several citations of the literature are incomplete or misleading. The microscopic mechanisms suggested by Luo et al. as alternative explanations for the redshifting ultrafast emission band identified in our original report have already been considered by us and rejected as being at variance with the experiment. Here, we address these points in some detail. Luo et al. use the modern theory of nanocrystals developed in the group of Zunger2 based on semi-empirical pseudopotentials. The method is stateof-the-art and represents an advance in comparison to the effective mass modelling3 recalled in our paper for a possible explanation of the redshifting photoluminescence band. It can be compared with the later work4 by one of us using a tight-binding approach. Luo et al. model the electronic structure of Si nanocrystals: they calculate the absorption cross-section and model the conductionband states for Si nanocrystals of diameters between 1 and 3 nm. To validate the methodology, Luo et al. cite their recently published work5. Based on the results of their calculations, the authors argue that for nanocrystals smaller than 3 nm, the Γ-valley moves to higher energies showing a blueshift — hence the title of their piece. In their Fig. 1a, Luo et al. plot the experimentally measured positions of the fast and slow emission bands1 and then extrapolate them towards still smaller nanocrystal diameters. Here, several comments are necessary. First, on the formal side, we note that the experimental accuracy needs to be taken into account. On the energy scale, this is given by the full-width at half-maximum (FWHM) of the (ensemble) photoluminescence spectra and is rather broad (see Fig. 2 in ref. 1). For the nanocrystal size, the log-normal size distribution should be considered. Second, the linear extrapolation of our data, introduced by the dashed lines in their Fig. 1a, implies an unphysical linear relation between the nanocrystal size and its bandgap(s). Third, the possibility of further redshift of the fast photoluminescence band, as given by the extrapolation, is explicitly excluded in our original report1, where we state that the redshift of the efficient channel of radiative recombination induced by the admixture of Γ-character (‘direct bandgap’) is a transient effect that takes place “only... for a certain range of [nanocrystal] sizes”. We feel that this should have been taken into account by Luo and co-authors when they extrapolated the data. In their Fig. 1c, the percentage of the Γ-valley component they calculated is given as a function of the state energy for Si nanocrystals with diameters of 3, 2, 1.4 and 1 nm. The red-shaded trace corresponds to the predicted development of the Γ-valley defined, in an arbitrary way, by states with ≥50% of the Γ-character, and does indeed show a blueshift. Here we point out that this very nice result was actually predicted in our original paper. We cite: “...it can be expected that with a (further) decrease in nanocrystal size, the energy and the relative efficiency of the no phonon radiative recombination channel might increase.” We note that the Γ-valley identified by Luo et al. appears for 3-nm nanocrystals at an energy of around 3 eV; that is, it is clearly redshifted with respect to bulk Si. In that way, the modelling that they present confirms the appearance of direct-bandgap-like states, with a considerable percentage of the Γ-valley component below the direct bandgap of Si, so the ‘redshift’ is induced by quantum confinement at the nanoscale. Moreover, a closer inspection of the lowest panel of their Fig. 1c reveals good agreement with the experiment: the calculations predict a state with considerable (about 20%) Γ-character at the energy of ~2.3 eV, which, within the experimental accuracy, agrees very well with our experimental point from ref. 1. Further, assuming the radiative recombination rate of a pure Γ-state to be of the order of 107 to 108 s–1 (similar to GaAs) and taking into account the experimentally determined1 decay time of hot photoluminescence of 10–100 ps, we arrive at a quantum efficiency of 20% × (107–108 s–1)/(1010–1011 s–1) ≈ 10–3–10–4 for the hot photoluminescence band, which is in the same range as the experimental value of 10–4 (ref. 1). For an easy comparison of theory and experiment, we include them in a schematic figure (Fig. 1); a very reasonable agreement between the data of ref. 1 and the modelling by Luo et al. is evident. For completeness, we briefly comment on the two alternative explanations proposed by Luo et al. for the efficient and redshifting hot photoluminescence band reported in ref. 1. In fact, we explored those at the time of the study and dismissed them as incorrect. Luo et al. propose “state filling ... with subsequent fast recombination of multi-excitons may be responsible for the measured emission, as has been demonstrated for Si nanocrystals17. The redshift would then correspond to the multiexciton depopulation due to an enhanced recombination rate at the fundamental bandgap of smaller nanocrystals.” State filling, however, can lead to only a marginal shift of photoluminescence, of a few tens of meV, much smaller than observed in our study (see, for example, ref. 6). Moreover, citation of the work of Sykora et al.7 (ref. 17 of Luo et al.) for an observation and discussion of a similar effect is incorrect: a brief inspection of this work reveals that these authors have observed a fast photoluminescence band but at a lower energy, and that they assigned it to interband recombination. The concept of ‘multiexcitons’ is not at all mentioned in ref. 7. Luo et al. also mention “surfacedefect related transitions” (in their Supplementary Information). Surface defect states in Si nanocrystals in SiO2 are well investigated and, in fact, a defect-related photoluminescence band is also observed and discussed in our work. The general consensus is, however, that these transitions exhibit a fairly stable emission wavelength, independent of the nanocrystal size6. We also note that the citation of works by Wolkin et al.8 and Biteen et al.9 in the context of the ‘redshift’ reported in ref. 1 is erroneous: both consider reduction of the effective fundamental bandgap of Si nanocrystals by oxygen-related defects; this stabilizes the enhancement of the exciton recombination energy for smaller nanocrystal sizes, but never leads to its effective decrease, as observed in our study. In summary, we conclude that JunWei Luo et al. neither “question the main points” of our original report nor have they “deciphered the mystery of the redshifting band”. Rather, as explained, the results of their state-of-the-art modelling support our original microscopic assignment of the Reply to ‘Absence of redshift in the direct bandgap of silicon nanocrystals with reduced size’

Efficient carrier multiplication in CsPbI 3 perovskite nanocrystals

The all-inorganic perovskite nanocrystals are currently in the research spotlight owing to their physical stability and superior optical properties—these features make them interesting for optoelectronic and photovoltaic applications. Here, we report on the observation of highly efficient carrier multiplication in colloidal CsPbI3 nanocrystals prepared by a hot-injection method. The carrier multiplication process counteracts thermalization of hot carriers and as such provides the potential to increase the conversion efficiency of solar cells. We demonstrate that carrier multiplication commences at the threshold excitation energy near the energy conservation limit of twice the band gap, and has step-like characteristics with an extremely high quantum yield of up to 98%. Using ultrahigh temporal resolution, we show that carrier multiplication induces a longer build-up of the free carrier concentration, thus providing important insights into the physical mechanism responsible for this phenomenon. The evidence is obtained using three independent experimental approaches, and is conclusive.In semiconductor nanocrystals, efficient carrier multiplication counteracts hot carrier thermalization, increasing the overall carrier generation yield. Here, de Weerd et al. observe a quantum yield of up to 98% in CsPbI3 nanocrystals as a result of efficient carrier multiplication.

Thermally stimulated exciton emission in Si nanocrystals

Increasing temperature is known to quench the excitonic emission of bulk silicon, which is due to thermally induced dissociation of excitons. Here, we demonstrate that the effect of temperature on the excitonic emission is reversed for quantum-confined silicon nanocrystals. Using laser-induced heating of silicon nanocrystals embedded in SiO2, we achieved a more than threefold (>300%) increase in the radiative (photon) emission rate. We theoretically modeled the observed enhancement in terms of the thermally stimulated effect, taking into account the massive phonon production under intense illumination. These results elucidate one more important advantage of silicon nanostructures, illustrating that their optical properties can be influenced by temperature. They also provide an important insight into the mechanisms of energy conversion and dissipation in ensembles of silicon nanocrystals in solid matrices. In practice, the radiative rate enhancement under strong continuous wave optical pumping is relevant for the possible application of silicon nanocrystals for spectral conversion layers in concentrator photovoltaics.