External Photoelectric Effect Research Articles

Modeling the Photoelectric Effect on Photocells Using Python

To simulate the laboratory work «Study of the Photoelectric Effect with External Photoelectric Effect» in Python, a program was developed that models the interaction of light with the surface of the metal and measures the kinetic energy of emitted electrons depending on the frequency of light. The program uses the matplotlib library to visualize the results and includes various blocks, such as library imports, definition of constants, functions for calculating kinetic energy and plotting graphs, as well as interactive widgets for changing parameters and observing results in real time.

Transduction of UV-light energy into alternating-current electricity via a neglected internal photoelectric effect of metal foil-based nanogenerator

Massive free electrons in metals could escape from the metal surface to generate a convection current when colliding with high-energy photons (e.g. UV light). Namely, metals with specific work functions could transduce light energy into direct-current (DC) electricity via the famous external photoelectric effect. However, obtaining alternating-current (AC) electricity via a non-Faraday’s law of electromagnetic induction directly using metal foil is challenging. Inspired by our recent work, we herein for the first time report a subtle method to directly transduce UV light energy into AC electricity by metal foil nanogenerators and propose a new mechanism regarding the transduction of UV light into AC electricity entitled the neglected internal photoelectric effect (NIPE). According to the NIPE, a zinc foil-based NIPE nanogenerator (NIPEG) can output an optimal open-circuit voltage (Voc) and a short-circuit current (Isc) of 108 V and 320 μA, respectively. The maximum output power and the photoelectric conversion efficiency of the fabricated nanogenerator approach 23.9 W m−2 and 77.02%, respectively. Meantime, the electrical energy stored in the capacitor connected to the Zn foil-based nanogenerator after rectification is several orders of magnitude higher than that of the conventional Cu/PTFE/PET/Cu-based triboelectric nanogenerator and Cu/PTFE/Al-based water droplet nanogenerator. The herein approach potentially offers a novel energy harvesting and conversion avenue to develop self-powered and wearable electronic devices.

Photomechaelectric nanogenerator

<h2>Summary</h2> Metal and inorganic or organic conjugate semiconductors can convert solar energy into electricity through the well-known external photoelectric effect and internal photovoltaic effect, respectively. The photoelectric effect cannot be detected in electron-insulated polymers due to a lack of free electrons or the redistribution of holes and electrons under illumination. Here, we report a subtle method to efficiently convert UV-light energy into electricity for electron-insulated co-polymers via a photomechaelectric (PME) effect, in which a PME effect means that photo induces isomerization of photosensitive segments and further results in generating dynamic dipoles and equal amounts, but opposite signs, of induced charges at electrodes. To this aim, functional azobenzene (AZO) and imidazole ionic liquid (ILO) oligomers have been used as photoisomer and dipole units, respectively. The produced electron-insulated AZO-<i>co</i>-ILO co-polymer-based nanogenerator can directly output an alternating current (up to 5.8 V and 247 μA) under UV illumination, implying extensive potential applications in self-powered electronic devices.

History of Development of the Methods and Interference Devices for Measuring a Small Optical Phase Difference (Review)

Interferometry methods, which are applied for measuring quite small phase differences in fundamental and applied problems, are considered. It is shown that first improvements of the interferometric methods for measuring small phase differences to detect various physical phenomena in the second half of the 19th century and in the early 20th century were made by H. Fizeau, A.A. Michelson, E.W. Morley, Lord Rayleigh, D.C. Miller, and G. Sagnac. It is also shown that the most sensitive method of modulation interferometry was developed in 1949–1952 by Soviet radiophysicists A.A. Andronov, I.L. Bershtein, and G.S. Gorelik. Note that the method of modulation interferometry could be implemented even in 1914 using a photocell with external photoelectric effect or in 1923 using a photocell with internal photoelectric effect (photodiode). However, professional opticians used conventional methods of measuring a small phase difference at that time, and radiophysics only began to develop as science. It is shown that the methods of electric and photoelectric harmonic analysis developed in the late 19th century and in the beginning of the 20th century could be successfully applied in interferometry; however, they have been almost completely forgotten by the time of their possible practical application.

External photoelectric effect of CsPb&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; perovskite in X-ray region

As a novel low-cost semiconductor with extraordinary photoelectric property, the inorganic CsPb&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; perovskites have become emerging materials for the next generation of X-ray detectors in the past decade. However, most of recent studies of CsPb&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; perovskite X-ray detectors are based on their internal photoelectric effect. Though it is also important and widely used in vacuum X-ray detectors, the external photoelectric effect of CsPb&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; perovskite has been rarely studied by now. Thus, the response sensitivity of the CsPb&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; perovskite’s external photoelectric effect in the X-ray region is studied in the present paper. First, a 230-nm-thick CsPbI&lt;sub&gt;2&lt;/sub&gt;Br membrane is prepared on a metal substrate by a conventional one-step deposition method, with a precursor solution used. Then the external photoelectric responsivity and quantum efficiency of the CsPbI&lt;sub&gt;2&lt;/sub&gt;Br membrane are calibrated in a range from 2000 to 5500 eV at Beijing Synchrotron Radiation Facility. The responsivity is over 5.1 × 10&lt;sup&gt;–5&lt;/sup&gt; A/W in the range and the quantum efficiency is over 23%. These calibration data are close to those of a traditional X-ray photoelectric material CsI. The Monte-Carlo method is utilized to simulate the external photoelectric effect of CsPbI&lt;sub&gt;2&lt;/sub&gt;Br perovskite, and the external photoelectric responsivity is calculated. The calculated data match well with the calibration, proving the Monte-Carlo method feasible for the external photoelectric effect simulation of CsPb&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; perovskite. Then the external photoelectric responsivities and quantum efficiencies of CsPb&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; perovskites are calculated via the Monte-Carlo method in the X-ray range from 2000 to 10000 eV. The calculated responsivities of different CsPb&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; perovskites are all close to the responsivity of CsI, and an order of magnitude higher than that of Au, and the CsPb&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; quantum efficiencies also follow a similar scenario. This indicates that CsPb&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; perovskites have good external photoelectric properties and potential applications in X-ray vacuum detectors such as photocathode and photomultiplier. The influence of thickness on CsPb&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; photoelectric response is also studied in this paper via Monte-Carlo simulation. The results show that the responsivity increases with the material thickness increasing, which is due to the increased X-ray absorption. The responsivities all reach their upper limits at a material thickness of about 150 nm, which means that the electrons generated at 150 nm can hardly escape from the material surface. It is indicated that the thickness of CsPb&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; should be no less than 150 nm to obtain the optimal photoelectric response.

История развития методов и интерференционных приборов для измерения малой разности оптических фаз (обзор)

Methods of interferometry, which are used to measure very small phase differences, are considered. in fundamental and applied problems. It is shown that the first improvements in interferometric methods for measuring small phase differences for recording various physical phenomena in the second half of the XIX - early XX centuries. carried out by I.A. Fizeau, A.A. Michelson, E. Morley, Lord Rayleigh, D.C. Miller and J.M. Sagnac. It was also shown that the most sensitive method of modulation interferometry was created in the period 1949-1952. Soviet radiophysicists A.A. Andronov, I.L. Berstein and G.S. Gorelik. It is noted that the modulation interferometry method could be implemented even in 1914 with a photocell on an external photoelectric effect, or in 1923 with a photocell on internal photoelectric effect (photodiode). However, then professional opticians used traditional methods for measuring small phase differences, and radiophysics as a science was just beginning its formation. It is shown that the methods of electrical and photoelectric harmonic analysis developed in late XIX - early XX centuries could find successful application in interferometry, but by that time, when they could find practical use, they were almost completely forgotten.

Femtosecond PLD-grown YF3 nanoparticle thin films as improved filterless VUV photoconductive detectors

A photoconductive detector (PCD) responding only to vacuum ultraviolet (VUV) radiations below 180 nm without any filter was fabricated using an yttrium fluoride (YF3) thin film grown by femtosecond (fs) laser pulsed laser deposition (PLD). The structural morphology (particle size and surface roughness) of the thin film was improved using a low laser fluence and a high substrate temperature during the fabrication. The smallest average particle size achieved was 159 nm with a roughness of 37 nm at a laser fluence of 13.5 J cm−2 and a substrate temperature of 400 °C. The resistances for the dark current of the PCD increased from 10 TΩ to 680 TΩ using YF3 thin films with a smaller average nanoparticle diameter of 159 nm rather than 330 nm. The time response of the PCD to a VUV flash lamp emitting at 170 nm showed that a small average nanoparticle diameter results to a fast response time. By covering the Al electrode pairs with another fs PLD-grown YF3 film, the influence of external photoelectric effect was suppressed and the response wavelength edge decreased from 280 nm to 180 nm without any filter. The filterless PCD is expected to enhance the use of fluoride thin films in conjunction with VUV light sources for various scientific and industrial applications.

Enhancement of photoemission capability and electron collection efficiency of field-assisted GaN nanowire array photocathode

GaN has interesting prospects in applications for spectrum-tunable solid-state devices with photoelectric conversion function. Similarly, single nanowires or nanowire arrays (NWAs) proceed to exhibit good photon absorbance and photoemission characteristics as vacuum devices based on the external photoelectric effect. However, the collection of photoelectrons emitted from a nanowire surface has become the greatest impediment to the progress of GaN NWAs photocathodes. In this study, a field-assisted GaN NWA photocathode is proposed. The photoemission efficiency and electron collection efficiency of the field-assisted GaN NWA photocathode are derived. The results suggest that the external field can effectively enhance the photoemission capacity and electron collection efficiency of the photocathode. Based on the theoretical model, the structural parameters of NWAs and the field intensity are optimized. When the field intensity is 1 V μm−1, the collected photocurrent of the GaN NWA photocathode reaches a maximum. For NWAs with an aspect ratio of 1:1, the optimal incident angle of light is 70°. This study provides a theoretical guide for the incorporation of an external field in a GaN NWA photocathode with the purpose of enhancing photoemission and electron collection capacity.

Ultraviolet Light-Induced Persistent and Degenerated Doping in MoS2 for Potential Photocontrollable Electronics Applications.

Efficient modulation of carrier concentration is fundamentally important for tailoring the electronic and photoelectronic properties of semiconducting materials. Photoinduced doping is potentially a promising way to realize such a goal for atomically thin nanomaterials in a rapid and defect-free manner. However, the wide applications of photoinduced doping in nanomaterials are severely constrained by the low doping concentration and poor stability that can be reached. Here, we propose a novel photoinduced doping mechanism based on the external photoelectric effect of metal coating on nanomaterials to significantly enhance the achievable doping concentration and stability. This approach is preliminarily demonstrated by an MX2 (M is Mo or Re; X is S or Se) nanoflake modified through a simple process of sequentially depositing and annealing an Au layer on the surface of the flake. Under ultraviolet (UV) light illumination, the modified MX2 achieves degenerated n-type doping density of 1014 cm-2 rapidly according to the experimentally observed >104 times increment in the channel current. The doping level persists after the removal of UV illumination with a nonobservable decrease over 1 day in vacuum (less than 23% over 7 days under an ambient environment). This photoinduced doping approach may contribute a major leap to the development of photocontrollable nanoelectronics.

Mechanistic Analysis of Plasmon-Induced Charge Separation by the Use of Chemically Synthesized Gold Nanorods

Chemically synthesized Au nanorods (AuNRs) with different aspect ratios were used for plasmon-induced charge separation (PICS) at a Au–TiO2 interface to elucidate the dependence of its efficiency on photon energy. To produce good electrical contact between the AuNRs and TiO2, the AuNR–TiO2 electrode was washed with hot ethanol and annealed under reduced pressure to remove the cetyltrimethylammonium bromide that protected the AuNR surface. Each photocurrent action spectrum of the electrode showed two discrete peaks due to transverse and longitudinal modes as did the corresponding absorption spectrum, indicating that the photoresponse was derived from the plasmonic light absorption of the AuNRs. It was found that the internal quantum efficiency of the longitudinal mode was lower than that of the transverse mode. The photocurrent action spectra were reproduced from the absorption spectra on the basis of a model for an external photoelectric effect (hot electron injection) and an interference effect from the ...

The Conclusions from TOE (Theory of Everything)

In 1887, Heinrich Hertz observed the external photoelectric effect and the production and reception of electromagnetic waves.1 In 1888-1890, the photoelectric system was studied by the physicist lexander Stoletov.2–7 In 1900, Planck proposed a formula with a constant (subsequently called the Planck constant).8 The photoelectric effect was explained in 1905 by Albert Einstein.9 In TOE10 is given description about 33 standard gravitational constants. If the Planck constant defines the boundary between the macrocosm, where the laws of Newton’s mechanics operate, and the micro world, where the laws of quantum mechanics operate. Then it shall be also 33 boundaries between the macrocosm and the micro world and therefore 33 Planck constants.

Photo-stimulated discharge current in polyimide films

Photo-stimulated discharge (PSD) method is one of the ways to measure the trap level of space charge in the dielectric materials. Compared with the thermally stimulated discharge (TSD) method, it has no observable destroy to the sample's microstructure during the procedure of the light scanning and can therefore be considered to be a more accurate measuring method. However, the light scanning procedure may possibly lead to the occurrence of the external photoelectric effect between the electrode-dielectric interfaces or the internal photoelectric effect in the sample bulk, where the extra current due to the two photoelectric effects can seriously distort the PSD current. In this paper, the total current excited by the scanning light on the polarized or being polarized polyimide films are studied. The influence of the applied field intensity, the electrode structures, the evaporated electrode thickness and the isothermal decaying current of the polarized films on the stimulated current is evaluated, which is comprehensively analyzed to extract the space charge dependent PSD current from the distorted current. The charge trap level based on the PSD method is finally obtained.

In Russian

The paper describes the physical principles of X-ray photoelectron and ultraviolet spectroscopy and Auger electron spectroscopy. We consider the distribution of the kinetic energy of the electrons formed as a result of the external photoelectric effect, and electrons leaves the atom with the relaxation of the initial state of its core-shell. We discuss the phenomena that determine the shape, the fine structure and the intensity of the spectral lines. Analyzed in detail the possibility of qualitative and quantitative analysis of the atomic composition, "false line", the chemical shifts of the lines of the core levels of atoms in different chemical environments. Analysis of these lines allows the chemical composition of the solid surface and near-surface region. Proper attention is paid to quantum-chemical methods of finding the energy levels of core states and density of states of the valence-electron levels and approaches developed to compare the experimentally obtained spectra of X-ray photoelectron and ultraviolet spectroscopy and Auger electron spectroscopy and theoretical calculations.

Site-Selective Plasmonic Etching of Silver Nanocubes.

Plasmon-induced charge separation (PICS) at the interface between a plasmonic nanoparticle and semiconductor is now widely used for photovoltaics and photocatalysis. Here we take advantage of PICS for site-selective nanoetching of silver nanocubes on TiO2 beyond the diffraction limit. A silver nanocube exhibits two resonance modes localized at the top and bottom of the nanocube (distal and proximal modes, respectively) when it is placed on TiO2. We achieved selective etching at the top and the bottom of the nanocubes by PICS based on the distal and proximal modes, respectively. The site-selective nanophotonic etching reveals that the anodic reaction involved in PICS is induced by the plasmonic near field, which causes an external photoelectric effect. In particular, the distal mode etching at the top edges is explained in terms of ejection of energetic electrons (or hot electrons) from the distal site to TiO2 across the nanocube.

(Invited) Plasmon-Induced Charge Separation: Mechanisms and Applications

Plasmonic nanoparticles, which are characterized by strong light absorption, scattering, and their controllability, attract much attention as new photofunctional materials. Plasmonic metal nanoparticles in contact with semiconductor exhibit charge separation under visible and near infrared light, i.e. plasmon-induced charge separation (PICS, Fig. 1).1 PICS involves carrier transfer from plasmonic nanoparticles (e.g. gold or silver nanoparticles) to semiconductor (e.g. TiO2)1-3 due to external photoelectric effect, hot carrier injection, or interfacial electron transition. In addition, PICS and/or accompanying redox reactions are accelerated by localized electric field (i.e. optical near field).4,5 PICS attracts increasing attention, because it can be applied to wet1 or solid-state6 photovoltaics under visible and near infrared light. It is also applied to photocatalysis1 and LSPR sensors,7 in which stable gold nanoparticles are used. In the case where less stable silver nanoparticles are used, PICS gives rise to oxidative dissolution of silver to silver ions. This process can be applied to multicolor photochromism,8 near infrared photochromism,9 single nanoparticle multicolor changes,5 and photomorphing hydrogels.10 1. Y. Tian and T. Tatsuma, J. Am. Chem. Soc., 127, 7632 (2005). 2. T. Tatsuma, Bull. Chem. Soc. Jpn., 86, 1 (2013). 3. E. Kazuma and T. Tatsuma, Adv. Mater. Interfaces, 1, 1400066 (2014). 4. E. Kazuma, N. Sakai, and T. Tatsuma, Chem. Commun., 47, 5777 (2011). 5. I. Tanabe and T. Tatsuma, Nano Lett., 12, 5418 (2012). 6. Y. Takahashi and T. Tatsuma, Appl. Phys. Lett., 99, 182110 (2011). 7. T. Tatsuma, Y. Katagi, S. Watanabe, K. Akiyoshi, T. Kawawaki, H. Nishi, and E. Kazuma, Chem. Commun., 51, 6100 (2015). 8. Y. Ohko, T. Tatsuma, T. Fujii, K. Naoi, C. Niwa, Y. Kubota, and A. Fujishima, Nat. Mater., 2, 29 (2003). 9. E. Kazuma, and T. Tatsuma, Chem. Commun., 48, 1733 (2012). 10. T. Tatsuma, K. Takada, and T. Miyazaki, Adv. Mater., 19, 1249 (2007). Figure 1

An analysis of solar energy conversion systems based on photon and thermal processes

Solar spectral irradiance covers a fairly broad wavelength range. Solar radiation is part of the electromagnetic spectrum which is described by the concept of wave-particle duality. The corpuscular theory of electromagnetic radiation states that energy is transmitted by photons. Photons carry specific amounts of energy which can be used to convert solar energy into other types of energy, in particular electricity. The internal photoelectric effect is important for the conversion of solar energy to electricity because the efficiency of the external photoelectric effect is too low. Every quantum of solar energy also carries a certain amount of energy which can be converted into heat energy. The objective of the paper is to analyze and compare the efficiency of solar energy conversion in photon and thermal processes, to review the technological advances made in this field, and to indicate potential directions for the development of systems converting solar energy to electricity.

Plasmon-Induced Charge Separation (PICS) and Plasmonic Nanoantenna Effects: Similarities and Differences

Metal nanoparticles including gold, silver, and copper nanoparticles absorb visible and near infrared light due to localized surface plasmon resonance (LSPR). We found plasmon-induced charge separation (PICS)1,2 at the interface between plasmonic metal nanoparticles and semiconductor such as TiO2 and applied it to photocatalysis,2 photovoltaic cells,2,3 multicolor photochromism,1,4 infrared photochromism,5 single particle multicolor changes,6 and photomorphing gells.7 PICS is also applied by other groups in particular to photocatalysis8,9 and photovoltaic cells.10,11 However, PICS is often confused with plasmonic nanoantenna effects. Au or Ag nanoparticles assist semiconductors and dye molecules in light absorption by trapping photons based on LSPR. As a result, nanoparticles enhance photocurrents, photocatalytic reactions, and other photochemical reactions. The enhancement based on the plasmonic nanoantenna effects occurs at wavelengths at which both of the semiconductor/dye molecule and the metal nanoparticles absorb light. In addition, the maximum enhancement is reached when the distance between the metal nanoparticle and the semiconductor/dye is about 10 nm.1 2-1 4 The enhancement is suppressed in the case of direct contact.On the other hand, PICS occurs at LSPR wavelengths even if those are longer than the absorption edge wavelength of the semiconductor.1- 11 PICS is based on direct electron transfer from the resonant metal nanoparticles to semiconductor2,15due to external photoelectric effect or hot electron injection. Therefore, it occurs when the metal nanoparticle is in direct contact with the semiconductor, if electron tunneling or hopping is not possible between them. In the paper, recent developments related to PICS would also be described. This work was supported in part by “R&D on Innovative PV Power Generation Technology” which The University of Tokyo contracted with New Energy and Industrial Technology Development Organization (NEDO) and a Grant-in-Aid for Scientific Research (No. 25288063, No. 25107511).ReferencesY. Ohko, T. Tatsuma, T. Fujii, K. Naoi, C. Niwa, Y. Kubota, and A. Fujishima, Nature Mater., 2, 29 (2003).Y. Tian and T. Tatsuma, J. Am. Chem. Soc., 127, 7632 (2005).Y. Takahashi and T. Tatsuma, Appl. Phys. Lett., 99, 182110 (2011).K. Naoi, Y. Ohko, and T. Tatsuma, J. Am. Chem. Soc., 126, 3664 (2004).E. Kazuma, and T. Tatsuma, Chem. Commun., 48, 1733 (2012).I. Tanabe and T. Tatsuma, Nano Lett., 12, 5418 (2012).T. Tatsuma, K. Takada, and T. Miyazaki, Adv. Mater., 19, 1249 (2007).E. Kowalska, R. Abe, and B. Ohtani, Chem. Commun., 2009, 241.C. G. Silva, R. Juárez, T. Marino, R. Molinari, and H. Garcìa, J. Am. Chem. Soc., 133 , 595 (2011). M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, Science, 332, 702 (2011).P. Reineck, G. P. Lee, D. Brick, M. Karg, P. Mulvaney, and U. Bach, Adv. Mater., 24, 4750 (2012).T. Kawawaki, Y. Takahashi, and T. Tatsuma, Nanoscale, 3, 2865 (2011).T. Torimoto, H. Horibe, T. Kameyama, K. Okazaki, S. Ikeda, M. Matsumura, A. Ishikawa, and H. Ishihara, J. Phys. Chem. Lett., 2, 2057 (2011).T. Kawawaki and T. Tatsuma, Phys. Chem. Chem. Phys., 15, 20247 (2013).N. Sakai, Y. Fujiwara, Y. Takahashi, and T. Tatsuma, ChemPhysChem, 10, 766 (2009).E. Kazuma, N. Sakai, and T. Tatsuma, Chem. Commun., 47, 5777 (2011).

Nonperturbing observation of optical near field

The spatial distribution of light intensity in the near field is studied by observing the photoelectron projection images of a subwavelength nanoaperture. The imaging electrons are obtained as a result of a two-photon external photoelectric effect induced in the aperture formed at the end of an optical fiber by femtosecond pulses of the second-harmonic radiation (410 nm) of a Ti:sapphire laser. The light-field distribution in the aperture is not distorted by any near-by object (such as a medium containing fluorescent molecules), which allows nonperturbing measurement of such a distribution.

Two-photon processes in faint biphoton fields

The goal of this research is to determine and study a physical system that will enable a fast and intrinsically two-photon detector, which would be of interest for quantum information and metrology applications. We consider two types of two-photon processes that can be observed using a very faint, but quantum-correlated biphoton field. These are optical up-conversion and an external photoelectric effect. We estimate the correlation enhancement factor for the biphoton light compared to coherent light, report and discuss the preliminary experimental results.

Femtosecond Two-Photon Laser Photoelectron Microscopy

It is shown that high-resolution photoelectron images (with a resolution of up to 3 nm for ultrasharp silicon tips) can be obtained for practically all materials when irradiating tips made of these materials by pulses of the second harmonic of a femtosecond Ti:sapphire laser. In addition to the images, absolute values of the two-photon external photoelectric effect for these tips also can be measured using this method. The first experimental realization of this two-photon femtosecond laser projection photoelectron microscope is presented, and corresponding data for silicon, diamond, and calcium fluoride tips are analyzed.