Light-Converting Polymer/Si Nanocrystal Composites with Stable 60-70% Quantum Efficiency and Their Glass Laminates

Not all silicon quantum dots are equal: photostability of silicon quantum dots with and without a thick amorphous shell

Luminescent colloidal silicon quantum dots (SiQDs) are sustainable alternatives to metal-based QDs for various optical applications. While the materials are reliant on their photoluminescence efficiency, the relationship between the structure and photostability of SiQDs is yet to be well studied. An amorphous silicon (a-Si) shell was recently discovered in SiQDs prepared by thermally-processed silicon oxides. As a-Si is known as a source of defects upon UV irradiation, the disordered shell could potentially have an adverse effect on the optical properties of nanoparticles. Herein, the photostability of ∼5 nm diameter SiQDs with an amorphous shell was compared with that of over-etched SiQDs of equivalent dimensions that bore an a-Si shell of negligible thickness. An UV-induced degradation study was conducted by subjecting toluene solutions of SiQDs to 365 nm light-emitting diodes (LEDs) under an inert atmosphere for predetermined times up to 72 hours. The structure, composition, and optical responses of the exposed SiQDs were evaluated.

Enhanced Electroluminescence from a Silicon Nanocrystal/Silicon Carbide Multilayer Light-Emitting Diode

Developing high-performance Si-based light-emitting devices is the key step to realizing all-Si-based optical telecommunication. Usually, silica (SiO₂) as the host matrix is used to passivate silicon nanocrystals, and a strong quantum confinement effect can be observed due to the large band offset between Si and SiO₂ (~8.9 eV). Here, for further development of device properties, we fabricate Si nanocrystals (NCs)/SiC multilayers and study the changes in photoelectric properties of the LEDs induced by P dopants. PL peaks centered at 500 nm, 650 nm and 800 nm can be detected, which are attributed to surface states between SiC and Si NCs, amorphous SiC and Si NCs, respectively. PL intensities are first enhanced and then decreased after introducing P dopants. It is believed that the enhancement is due to passivation of the Si dangling bonds at the surface of Si NCs, while the suppression is ascribed to enhanced Auger recombination and new defects induced by excessive P dopants. Un-doped and P-doped LEDs based on Si NCs/SiC multilayers are fabricated and the performance is enhanced greatly after doping. As fitted, emission peaks near 500 nm and 750 nm can be detected. The current density-voltage properties indicate that the carrier transport process is dominated by FN tunneling mechanisms, while the linear relationship between the integrated EL intensity and injection current illustrates that the EL mechanism is attributed to recombination of electron-hole pairs at Si NCs induced by bipolar injection. After doping, the integrated EL intensities are enhanced by about an order of magnitude, indicating that EQE is greatly improved.

Boosting efficiency of luminescent solar concentrators using ultra-bright carbon dots with large Stokes shift

Luminescent solar concentrators (LSCs) are able to collect sunlight from a large-area to generate electric power with a low cost, showing great potential in building-integrated photovoltaics. However, the low efficiency of large-area LSCs caused by the reabsorption losses is a critical issue that hampers their practical applications. In this work, we synthesized novel yellow emissive carbon dots (CDs) with a large Stokes shift of 193 nm, which exhibit nearly zero reabsorption. The quantum yield (QY) of the yellow emitting CDs is up to 61%. The yellow emitting CDs can be employed to fabricate high-performance large-area LSCs due to successful suppression of the reabsorption losses. The as-prepared LSCs are able to absorb 14% of the sunlight as the absorption of the CDs matches well with the sun's spectrum. The large-area LSC (10 × 10 cm²) with a laminated structure based on the yellow emitting CDs achieves an optical conversion efficiency (η_opt) of 4.56% and power conversion efficiency (η_PCE) of 4.1% under natural sunlight (45 mW cm^-2), which are significantly higher than other previously reported works with similar sizes. Furthermore, the prepared high-performance LSCs show good stability. This method of synthesizing novel CDs for high-efficiency LSCs provides a useful platform for future study and practical application of LSCs.

Luminescence-guided and visibly transparent solar concentrators based on silicon quantum dots

In this work, we demonstrate a new tapered prism-shaped luminescent solar concentrator (LSC), which guides most of the luminescence toward one edge instead of four, for the solar window application. Only one Si photovoltaic (PV) strip attached to the light-emitting sidewall is needed to collect the luminescence, which further reduces PV material cost and avoids electrical mismatch. To achieve high visible transmission and mitigate reabsorption, colloidal silicon quantum dots (SiQDs) with ultraviolet-selective absorption and large Stokes shift are used as the fluorophores. With the SiQD concentration equal to 8 mg mL^-1, the SiQD-LSC as a solar window can attain a power conversion efficiency (PCE) equal to 0.27%, while ensuring high average visible transmission (AVT = 86%) and high color rendering index (CRI = 94 with AM1.5G as the incident spectrum). When adjusted to front-facing, the Si PV strip can harvest not only the direct sunlight but also the concentrated SiQD fluorescence guided from the LSC. As a result, the overall solar window PCE can be increased to 1.18%, and the PCE of the front-facing Si PV strip alone can be increased by 7% due to the luminescence guided from the SiQD-LSC.

Si-H Surface Groups Inhibit Methacrylic Polymerization: Thermal Hydrosilylation of Allyl Methacrylate with Silicon Nanoparticles

Hydrogen-terminated silicon nanoparticles (H-SiNPs) inhibit anerobic thermal autopolymerization of methacrylates. When heated to 100 °C under an inert atmosphere, allyl methacrylate (AMA) was stable for at least 95 h in the presence of 1.2 wt % H-SiNPs, exhibiting less than 0.15% conversion, whereas the neat monomer solidified within 24 h (over 10% conversion after 34 h). A mechanism is proposed that is based on H-transfer from SiNPs to the thermally activated methacrylic dimer biradical, quenching autopolymerization. An analysis of SiNPs isolated after heating in AMA reveals the grafting of ester groups. Thermal hydrosilylation offers a facile way to attach an allyl group to the surface of SiNPs.

Construction of highly efficient carbon dots-based polymer photonic luminescent solar concentrators with sandwich structure

The enhancement of photoluminescence (PL) emission and waveguide play a key role in improving the optical efficiency of luminescent solar concentrators (LSCs). In this work, to boosting PL emission and waveguide simultaneously, one photonic crystal (PC) structure (crystalline colloid arrays (CCAs)) was introduced into carbon dots (CDs)-based polymer LSCs. A sandwich-structured CDs-based polymer photonic LSC, comprising glass/CDs-based polymer PC film/glass, was created. First, CDs-based colloidal crystal suspensions were prepared by co-assembly of monodispersed p(MMA-NIPAm) colloids and multicolor-emitting CDs in HEMA monomer induced by the evaporation-driven assembly. The obtained suspensions not only had uniform PL and structural colors, but showed enhanced PL emission. Second, the above suspensions were sandwiched between two glass sheets and finally a photonic polymer LSC with sandwiched structure (25 × 25 × 1.8 mm³) were formed via one-step photopolymerization technique. Remarkably, the optimal CDs-based polymer photonic LSCs with sandwiched structure not only had high transparence at visible range (>60%), but exhibited PL emission enhancement (at least 2 times). Furthermore, the maximum external optical efficiency (η_opt) of 5.84% could be achieved based on yellow-emitting CDs-based polymer photonic LSC. The high external optical efficiency was mainly attributed to the PL emission enhancement and good PC waveguide.

Designing Efficient Si Quantum Dots and LEDs by Quantifying Ligand Effects

The impact of colloidal silicon quantum dots (SiQDs) on next-generation light sources is promising. However, factors determining the efficiency of SiQDs, such as the photoluminescence (PL) wavelength, PL quantum yield (PLQY), and the SiQD LED performance based on the type of ligand, ligand coverage, stress, and dangling bonds, have not been quantified. Characterizing these variables would accelerate the design and implementation of SiQDs. Herein, colloidal SiQDs were synthesized by pyrolyzing hydrogen silsesquioxane and their surfaces were terminated with 1-decene by either thermal hydrosilylation (HT-SiQDs) or room-temperature hydrosilylation using PCl₅ (RT-SiQD). As a result, PL, PL-excitation, and ultraviolet-visible absorption spectra were similar, but their PLQYs were significantly different: 54% (RT-SiQDs) vs 19% (HT-SiQDs). To understand their similarities and differences, surface coverages (dangling bonds, Si-H (≡Si-H₁, ═Si-H₂, and -Si-H₃), Si-O-Si, Si-C, Si-Cl) were determined. A core stress analysis established that a single ligand terminated to a SiQD bond site stretched the Si-Si bond length by 0.3%. From the two well-defined SiQDs, the PLQY and SiQD LED efficiency were attributed to four factors: low coverage of insulator ligands, the Cl ligand effect on radiative and nonradiative rates, negligible dangling bonds, and a SiQD core with low tensile stress. The PLQY of the RT-SiQDs in toluene was 80%. In addition, the 20× electroluminescence intensity difference of the LEDs originated from a 10× difference in current density and a 2× difference in Auger recombination. The concepts demonstrated here can be applied to further improve the PLQY and LED efficiencies of SiQDs with other ligands.

Low-Cost Synthesis of Silicon Quantum Dots with Near-Unity Internal Quantum Efficiency

As a cost-effective batch synthesis method, Si quantum dots (QDs) with near-infrared photoluminescence, high quantum yield (>50% in polymer nanocomposite), and near-unity internal quantum efficiency were fabricated from an inexpensive commercial precursor (triethoxysilane, TES), using optimized annealing and etching processes. The optical properties of such QDs are similar to those prepared from state-of-the-art precursors (hydrogen silsesquioxane, HSQ) yet featuring an order of magnitude lower cost. To understand the effect of synthesis parameters on QD optical properties, we conducted a thorough comparison study between common solid precursors: TES, HSQ, and silicon monoxide (SiO), including chemical, structural, and optical characterizations. We found that the structural nonuniformity and abundance of oxide inherent to SiO limited the resultant QD performance, while for TES-derived QDs this drawback can be avoided. The presented low-cost synthetic approach would significantly favor applications requiring high loading of good-quality Si QDs, such as light conversion for photovoltaics.

Thermal Disproportionation for the Synthesis of Silicon Nanocrystals and Their Photoluminescent Properties

In the past decades, silicon nanocrystals have received vast attention and have been widely studied owing to not only their advantages including nontoxicity, high availability, and abundance but also their unique luminescent properties distinct from bulk silicon. Among the various synthetic methods of silicon nanocrystals, thermal disproportionation of silicon suboxides (often with H as another major composing element) bears the superiorities of unsophisticated equipment requirements, feasible processing conditions, and precise control of nanocrystals size and structure, which guarantee a bright industrial application prospect. In this paper, we summarize the recent progress of thermal disproportionation chemistry for the synthesis of silicon nanocrystals, with the focus on the effects of temperature, Si/O ratio, and the surface groups on the resulting silicon nanocrystals’ structure and their corresponding photoluminescent properties. Moreover, the paradigmatic application scenarios of the photoluminescent silicon nanocrystals synthesized via this method are showcased or envisioned.

Silicon Quantum Dot-Polymer Fabry-Pérot Resonators with Narrowed and Tunable Emissions

Luminescent silicon nanoparticles have been widely recognized as an alternative for metal-based quantum dots (QDs) for optoelectronics partly because of the high abundance and biocompatibility of silicon. To date, the broad photoluminescence line width (often >100 nm) of silicon QDs has been a hurdle to achieving competitive spectral purity and incorporating them into light-emitting devices. Herein we report fabrication and testing of straightforward configuration of Fabry-Pérot resonators that incorporates a thin layer of SiQD-polymer hybrid/blend between two reflective silver mirrors; remarkably these devices exhibit up-to-14-fold narrowing of SiQD emission and achieve a spectral bandwidth as narrow as ca. 9 nm. Our polymer-based, SiQD-containing Fabry-Pérot resonators also provide convenient spectral tunability, can be prepared using a variety of polymer hosts and substrates, and enable rigid as well as flexible devices.

Wafer-scale fabrication of isolated luminescent silicon quantum dots using standard CMOS technology

A wafer-scale fabrication method for isolated silicon quantum dots (Si QDs) using standard CMOS technology is presented. Reactive ion etching was performed on the device layer of a silicon-on-insulator wafer, creating nano-sized silicon islands. Subsequently, the wafer was annealed at 1100 °C for 1 h in an atmosphere of 5% H₂ in Ar, forming a thin oxide passivating layer due to trace amounts of oxygen. Isolated Si QDs covering large areas (∼mm²) were revealed by photoluminescence (PL) measurements. The emission energies of such Si QDs can span over a broad range, from 1.3 to 2.0 eV and each dot is typically characterized by a single emission line at low temperatures. Most of the Si QDs exhibited a high degree of linear polarization along Si crystallographic directions [[Formula: see text]] and [[Formula: see text]]. In addition, system resolution-limited (250 μeV) PL linewidths (full width at half maximum) were measured for several Si QDs at 10 K, with no clear correlation between emission energy and polarization. The initial part of PL decays was measured at room temperature for such oxide-embedded Si QDs, approximately several microseconds long. By providing direct access to a broad size range of isolated Si QDs on a wafer, this technique paves the way for the future fabrication of photonic structures with Si QDs, which can potentially be used as single-photon sources with a long coherence length.

Geometry effects on luminescence solar concentrator efficiency: analytical treatment

Luminescence solar concentrators act as semitransparent photovoltaic cells of interest for modern urban environments. Here, their efficiencies were analytically derived for different regular unit shapes as simple, integral-free expressions. This allowed analysis of the shape and size effect on the device performance. All regular shapes appear to have a similar efficiency as revealed by optical path distribution formulas, despite differences in the perimeter length. Rectangles of the same area feature higher efficiency due to reduced average optical path. It comes with the cost of a longer perimeter, and the relation between these two is provided. An explicit formula for the critical size of an LSC unit, above which its inner part becomes inactive, has been obtained. For square geometry with matrix absorption coefficient α this critical size is ∼2.7/α, corresponding to 70-90 cm for common polymer materials. Obtained results can be used for treatment of individual units as well as for analysis of tiling for large areas.

Precise size separation of water-soluble red-to-near-infrared-luminescent silicon quantum dots by gel electrophoresis

Gel electrophoresis, which is a standard method for separation and analysis of macromolecules such as DNA, RNA and proteins, is applied for the first time to silicon (Si) quantum dots (QDs) for size separation. In the Si QDs studied, boron (B) and phosphorus (P) are simultaneously doped. Codoping induces a negative potential on the surface of a Si QD and makes it dispersible in water. Si QDs with different B and P concentrations and grown at different temperatures (950 °C-1200 °C) are studied. It is shown that native polyacrylamide gel electrophoresis can separate codoped Si QDs by size. The capability of gel electrophoresis to immobilize size-separated QDs in a solid matrix makes detailed analyses of size-purified Si QDs possible. For example, the photoluminescence (PL) studies of the dried gel of Si QDs grown at 1100 °C demonstrate that a PL spectrum of a Si QD solution with the PL maximum around 1.4 eV can be separated into more than 15 spectra with the PL maximum changing from 1.2 to 1.8 eV depending on the migration distance. It is found that the relationship between the PL peak energy and the migration distance depends on the growth temperature of Si QDs as well as the B and P concentration. For all the samples with different impurity concentrations and grown at different temperatures, a clear trend is observed in the relationship between the full width at half maximum (FWHM) and the peak energy of the PL spectra in a wide energy range. The FWHM increases with the increasing peak energy and it is nearly twice larger than those observed for undoped Si QDs. The large PL FWHM of codoped Si QDs suggests that excitons are further localized in codoped Si QDs due to the existence of charged impurities.

Bright Silicon Nanocrystals from a Liquid Precursor: Quasi-Direct Recombination with High Quantum Yield

Silicon nanocrystals (SiNCs) with bright bandgap photoluminescence (PL) are of current interest for a range of potential applications, from solar windows to biomedical contrast agents. Here, we use the liquid precursor cyclohexasilane (Si₆H₁₂) for the plasma synthesis of colloidal SiNCs with exemplary core emission. Through size separation executed in an oxygen-shielded environment, we achieve PL quantum yields (QYs) approaching 70% while exposing intrinsic constraints on efficient core emission from smaller SiNCs. Time-resolved PL spectra of these fractions in response to femtosecond pulsed excitation reveal a zero-phonon radiative channel that anticorrelates with QY, which we model using advanced computational methods applied to a 2 nm SiNC. Our results offer additional insight into the photophysical interplay of the nanocrystal surface, quasi-direct recombination, and efficient SiNC core PL.

Poly(methyl methacrylate) Films with High Concentrations of Silicon Quantum Dots for Visibly Transparent Luminescent Solar Concentrators

Silicon quantum dots (Si QDs) are attractive, nontoxic luminophores for luminescent solar concentrators (LSCs). Here, we produced Si QD/poly(methyl methacrylate) (PMMA) films on glass by doctor-blading polymer solutions and achieved films with low light scattering at an order of magnitude higher Si QD weight fraction than has been achieved previously in the bulk. We suggest that the fast solidification rate of films as compared to slow bulk polymerization is an enabling factor in avoiding large agglomerates within the nanocomposites. Scanning electron microscopy confirmed that ∼100 nm or larger QD agglomerates exist in light-scattering films, and photoluminescence intensity measurements show that light scattering, if present, significantly reduces waveguiding efficiencies for LSCs. Nonscattering films fabricated in this work exhibit high ultraviolet absorption (>80%) paired with high visible transmission (>87%) and minimal visible haze (∼1%), making them well suited for semitransparent coatings for LSCs realized as solar harvesting windows.

Introductory lecture: origins and applications of efficient visible photoluminescence from silicon-based nanostructures

This review highlights many spectroscopy-based studies and selected phenomenological studies of silicon-based nanostructures that provide insight into their likely PL mechanisms, and also covers six application areas.

Nearly perfect near-infrared luminescence efficiency of Si nanocrystals: A comprehensive quantum yield study employing the Purcell effect

Thin layers of silicon nanocrystals (SiNC) in oxide matrix with optimized parameters are fabricated by the plasma-enhanced chemical vapor deposition. These materials with SiNC sizes of about 4.5 nm and the SiO₂ barrier thickness of 3 nm reveal external quantum yield (QY) close to 50% which is near to the best chemically synthetized colloidal SiNC. Internal QY is determined using the Purcell effect, i.e. modifying radiative decay rate by the proximity of a high index medium in a special wedge-shape sample. For the first time we performed these experiments at variable temperatures. The complete optical characterization and knowledge of both internal and external QY allow to estimate the spectral distribution of the dark and bright NC populations within the SiNC ensemble. We show that SiNCs emitting at around 1.2-1.3 eV are mostly bright with internal QY reaching 80% at room temperature and being reduced by thermally activated non-radiative processes (below 100 K internal QY approaches 100%). The mechanisms of non-radiative decay are discussed based on their temperature dependence.

First synthesis of silicon nanocrystals in amorphous silicon nitride from a preceramic polymer

We report the first synthesis of silicon nanocrystals embedded in a silicon nitride matrix through a direct pyrolysis of a preceramic polymer (perhydropolysilazane). Structural analysis carried out by XRD, XPS, Raman and TEM reveals the formation of silicon quantum dots and correlates the microstructures with the annealing temperature. The photoluminescence of the nanocomposites was investigated by both linear and nonlinear measurements. Furthermore we demonstrate an enhanced chemical resistance of the nitride matrix, compared to the typical oxide one, in both strongly acidic and basic environments. The proposed synthesis via polymer pyrolysis is a striking innovation potentially allowing a mass-scale production nitride embedded Si nanocrystals.

Adjusting the Reduction Potential of Electrons by Quantum Confinement for Selective Photoreduction of CO2 to Methanol

The production of CH₃ OH from the photocatalytic CO₂ reduction reaction (PCRR) presents a promising route for the clean utilization of renewable resources, but charge recombination, an unsatisfying stability and a poor selectivity limit its practical application. In this paper, we present the design and fabrication of 0D/2D materials with polymeric C₃ N₄ nanosheets and CdSe quantum dots (QDs) to enhance the separation and reduce the diffusion length of charge carriers. The rapid outflow of carriers also restrains self-corrosion and consequently enhances the stability. Furthermore, based on quantum confinement effects of the QDs, the energy of the electrons could be adjusted to a level that inhibits the hydrogen evolution reaction (HER, the main competitive reaction to PCRR) and improves the selectivity and activity for CH₃ OH production from the PCRR. The band structures of photocatalysts with various CdSe particle sizes were also investigated quantitatively to establish the relationship between the band energy and the photocatalytic performance.

Multifunctional Platform Based on Electroactive Polymers and Silica Nanoparticles for Tissue Engineering Applications

Poly(vinylidene fluoride) nanocomposites processed with different morphologies, such as porous and non-porous films and fibres, have been prepared with silica nanoparticles (SiNPs) of varying diameter (17, 100, 160 and 300 nm), which in turn have encapsulated perylenediimide (PDI), a fluorescent molecule. The structural, morphological, optical, thermal, and mechanical properties of the nanocomposites, with SiNP filler concentration up to 16 wt %, were evaluated. Furthermore, cytotoxicity and cell proliferation studies were performed. All SiNPs are negatively charged independently of the pH and more stable from pH 5 upwards. The introduction of SiNPs within the polymer matrix increases the contact angle independently of the nanoparticle diameter. Moreover, the smallest ones (17 nm) also improve the PVDF Young's modulus. The filler diameter, physico-chemical, thermal and mechanical properties of the polymer matrix were not significantly affected. Finally, the SiNPs' inclusion does not induce cytotoxicity in murine myoblasts (C2C12) after 72 h of contact and proliferation studies reveal that the prepared composites represent a suitable platform for tissue engineering applications, as they allow us to combine the biocompatibility and piezoelectricity of the polymer with the possible functionalization and drug encapsulation and release of the SiNP.

Long-lived luminescence of colloidal silicon quantum dots for time-gated fluorescence imaging in the second near infrared window in biological tissue

Boron (B) and phosphorus (P) codoped silicon quantum dots (Si QDs) are dispersible in polar solvents without organic ligands and exhibit photoluminescence (PL) in the first (NIR-I) and second (NIR-II) near infrared (NIR) windows in biological tissues due to the optical transition from the donor to acceptor states. We studied the relationship between the PL wavelength, lifetime and quantum yield (QY) of the colloidal solution and the composition of the starting material for the preparation. We found that the PL lifetime and the QY are primarily determined by the composition, while the PL wavelength is mainly determined by the growth temperature. By optimizing the composition, we achieved QYs of 20.1% and 1.74% in the NIR-I and NIR-II regions, respectively, in methanol. We demonstrate the application for time-gated imaging in the NIR-II range.

Fabricating highly luminescent solid hybrids based on silicon nanoparticles: a simple, versatile and green method

In this work, we report a simple but novel method to transfer highly luminescent silicon nanoparticles (Si NPs) from solutions to solids without sacrificing their excellent photoluminescence (PL) properties. Hybrid Si NP/clay phosphors that glowed ultrabright and had colorful PL properties were first obtained. More importantly, large-area and flexible films with superior PL properties can be easily obtained via combining the Si NP/clay hybrids with different kinds of polymer. The Si NP-based phosphors and films from our method show high stabilities with no significant loss of PL performance after long-term storage (several months). In addition, bright yellow-emitting Si NPs were prepared and used as down-converters for white-light-emitting diodes (W-LEDs). Overall, this work presents a simple, versatile and green method to fabricate Si NP-based solid hybrids with superior PL properties, which has promise to be applied in the future in solid-state lighting fields.

Highly photoluminescent and stable silicon nanocrystals functionalized via microwave-assisted hydrosilylation

Herein, we report a microwave-assisted hydrosilylation (MWH) reaction for the surface passivation of silicon nanocrystals (Si-NCs) with linear alkenes. The MWH reaction requires only 20 minutes and allows us to produce Si-NCs with high photoluminescence quantum yields (PLQYs), reaching 39% with an emission maximum of 860 nm. Furthermore, we investigated the effect of ligand length on the photoluminescence properties of Si-NCs. We tested six alkenes with an even number of carbon atoms (from hexene-1 to hexadecene-1). The highest PLQY combined with a long stability (test period of 6 months) was observed when capping with the shortest ligand, hexene-1. The use of microwave heating turns the hydrosilylation step into a facile and sustainable process. In order to provide insight into the emissive properties of Si-NCs surface oxidation and luminescence decay were investigated using Fourier-transform infrared spectroscopy and time-resolved photoluminescence measurements.

Herein, we report a microwave-assisted hydrosilylation (MWH) reaction for the surface passivation of silicon nanocrystals (Si-NCs) with linear alkenes.

Silicon quantum dots with heavily boron and phosphorus codoped shell

Heavily boron and phosphorus codoped silicon quantum dots (QDs) are dispersible in water without organic ligands and exhibit near infrared luminescence. We summarize the fundamental properties and demonstrate the formation of a variety of nanocomposites.