# Quantum-size effects of interacting electrons and holes in semiconductor microcrystals with spherical shape

TL;DR: In this article, an extensive numerical calculation for the eigenvalue problem is carried out by Ritz's variational technique, and the motional state of the lowest level is classified into three regimes: the regime of exciton confinement for R/${a}_{B}^{\mathrm{*}}$\ensuremath{\gtrsim}4, the regime for individual particle confinement forR/${b}^{*}+1.2.

Abstract: Quantum-size effects of an electron-hole system confined in microcrystals of semiconductors are studied theoretically with the spherical-dielectric continuum model. An extensive numerical calculation for the eigenvalue problem is carried out by Ritz's variational technique. The motional state of the lowest level is classified into three regimes: the regime of exciton confinement for R/${a}_{B}^{\mathrm{*}}$\ensuremath{\gtrsim}4, the regime of individual particle confinement for R/${a}_{B}^{\mathrm{*}}$\ensuremath{\lesssim}2, and the intermediate regime for 2\ensuremath{\lesssim}R/${a}_{B}^{\mathrm{*}}$\ensuremath{\lesssim}4, where R is the radius of the quantum well and ${a}_{B}^{\mathrm{*}}$ is the exciton Bohr radius. In the region R/${a}_{B}^{\mathrm{*}}$\ensuremath{\gtrsim}4, the high-energy shift of the lowest exciton state is described by the rigid-sphere model of the exciton quite well, which takes into account the spatial extension of the relative motion of the electron and the hole. The oscillator strength of the interband optical transition changes dramatically across the region 2\ensuremath{\lesssim}R/${a}_{B}^{\mathrm{*}}$\ensuremath{\lesssim}4. The metamorphosis of the absorption spectrum is shown as a function of R/${a}_{B}^{\mathrm{*}}$ and compared with the experimental data.

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TL;DR: Room-temperature ultraviolet lasing in semiconductor nanowire arrays has been demonstrated and self-organized, <0001> oriented zinc oxide nanowires grown on sapphire substrates were synthesized with a simple vapor transport and condensation process.

Abstract: Room-temperature ultraviolet lasing in semiconductor nanowire arrays has been demonstrated The self-organized, oriented zinc oxide nanowires grown on sapphire substrates were synthesized with a simple vapor transport and condensation process These wide band-gap semiconductor nanowires form natural laser cavities with diameters varying from 20 to 150 nanometers and lengths up to 10 micrometers Under optical excitation, surface-emitting lasing action was observed at 385 nanometers, with an emission linewidth less than 03 nanometer The chemical flexibility and the one-dimensionality of the nanowires make them ideal miniaturized laser light sources These short-wavelength nanolasers could have myriad applications, including optical computing, information storage, and microanalysis

8,592 citations

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TL;DR: In this article, the extinction coefficient per mole of nanocrystals at the first exitonic absorption peak, e.g., for high-quality CdTe, CdSe, and CdS, was found to be strongly dependent on the size of the nanocrystal, between a square and a cubic dependence.

Abstract: The extinction coefficient per mole of nanocrystals at the first exitonic absorption peak, e, for high-quality CdTe, CdSe, and CdS nanocrystals was found to be strongly dependent on the size of the nanocrystals, between a square and a cubic dependence. The measurements were carried out using either nanocrystals purified with monitored purification procedures or nanocrystals prepared through controlled etching methods. The nature of the surface ligands, the refractive index of the solvents, the PL quantum yield of the nanocrystals, the methods used for the synthesis of the nanocrystals, and the temperature for the measurements all did not show detectable influence on the extinction coefficient for a given sized nanocrystal within experimental error.

4,802 citations

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TL;DR: In this article, the authors introduce density functional theory and review recent progress in its application to transition metal chemistry, including local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and solids.

Abstract: We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.

1,449 citations

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TL;DR: In this article, the size quantization effect, synthesis and characterization of Q-particles, as well as with the spectroscopic, electrochemical, and electron-microscopic investigation of these particles are discussed.

Abstract: In semiconductor particles of nanometer size, a gradual transition from solid-state to molecular structure occurs as the particle size decreases. Consequently, a splitting of the energy bands into discrete, quantized levels occurs. Particles that exhibit these quantization effects are often called “Q-particles” or, generally, quantized material. The optical, electronic and catalytic properties of Q-particles drastically differ from those of the corresponding macrocrystalline substance. The band gap, a substance-specific quantity in macrocrystalline materials, increases by several electron volts in Q-particles with decreasing particle size. In Q-particles there are approximately as many molecules on the surface as in the interior of the particle. Therefore, the nature of the surface as well as the particle size is also largely responsible for the physico-chemical properties of the particle. Q-particles of many materials can be prepared in the form of colloidal solutions or embedded in porous matrices and are stable over a long period of time. In sandwich colloids, in which Q-particles of different materials are coupled, as well as in porous semiconductor electrodes containing Q-particles in the pores, very efficient primary charge separation is observed. As a result, sandwich colloids have greatly enhanced photocatalytic activity relative to the individual particles, while electrodes modified with Q-particles show high photocurrents. This article deals with the size quantization effect, the synthesis and characterization of Q-particles, as well as with the spectroscopic, electrochemical, and electron-microscopic investigation of these particles.

1,198 citations

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TL;DR: In this paper, a review is concerned with quantum confinement effects in low-dimensional semiconductor systems, focusing on the optical properties, including luminescence, of nanometre-sized microcrystals.

Abstract: This review is concerned with quantum confinement effects in low-dimensional semiconductor systems. The emphasis is on the optical properties, including luminescence, of nanometre-sized microcrysta...

1,030 citations