We model, in an elementary way, the excited electronic states of semiconductor crystallites sufficiently small (∼50 A diam) that the electronic properties differ from those of bulk materials. In this limit the excited states and ionization processes assume a molecular‐like character. However, diffraction of bonding electrons by the periodic lattice potential remains of paramount importance in the crystallite electronic structure. Schrodinger’s equation is solved at the same level of approximation as used in the analysis of bulk crystalline electron‐hole states (Wannier excitons). Kinetic energy is treated by the effective mass approximation, and the potential energy is due to high frequency dielectric solvation by atomic core electrons. An approximate formula is given for the lowest excited electronic state energy. This expression is dependent upon bulk electronic properties, and contains no adjustable parameters. The optical f number for absorption and emission is also considered. The same model is applied to the problem of two conduction band electrons in a small crystallite, in order to understand how the redox potential of excess electrons depends upon crystallite size.

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Electron–electron and electron‐hole interactions in small semiconductor crystallites: The size dependence of the lowest excited electronic state

The selection of nanoparticles for achieving efficient contrast for biological and cell imaging applications, as well as for photothermal therapeutic applications, is based on the optical properties of the nanoparticles. We use Mie theory and discrete dipole approximation method to calculate absorption and scattering efficiencies and optical resonance wavelengths for three commonly used classes of nanoparticles:  gold nanospheres, silica−gold nanoshells, and gold nanorods. The calculated spectra clearly reflect the well-known dependence of nanoparticle optical properties viz. the resonance wavelength, the extinction cross-section, and the ratio of scattering to absorption, on the nanoparticle dimensions. A systematic quantitative study of the various trends is presented. By increasing the size of gold nanospheres from 20 to 80 nm, the magnitude of extinction as well as the relative contribution of scattering to the extinction rapidly increases. Gold nanospheres in the size range commonly employed (∼40 nm)...

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Calculated Absorption and Scattering Properties of Gold Nanoparticles of Different Size, Shape, and Composition: Applications in Biological Imaging and Biomedicine

The use of optical measurements to monitor electrochemical changes on the surface of nanosized metal particles is discussed within the Drude model. The absorption spectrum of a metal sol in water is shown to be strongly affected by cathodic or anodic polarization, chemisorption, metal adatom deposition, and alloying. Anion adsorption leads to strong damping of the free electron absorption. Cathodic polarization leads to anion desorption. Underpotential deposition (upd) of electropositive metal layers results in dramatic blue-shifts of the surface plasmon band of the substrate. The deposition of just 0.1 monolayer can be readily detected by eye. In some cases alloying occurs spontaneously during upd. Alloy formation can be ascertained from the optical absorption spectrum in the case of gold deposition onto silver sols. The underpotential deposition of silver adatoms onto palladium leads to the formation of a homogeneous silver shell, but the mean free path is less than predicted, due to lattice strain in t...

Surface Plasmon Spectroscopy of Nanosized Metal Particles

The size and temperature dependence of the plasmon absorption is studied for 9, 15, 22, 48, and 99 nm gold nanoparticles in aqueous solution. The plasmon bandwidth is found to follow the predicted behavior as it increases with decreasing size in the intrinsic size region (mean diameter smaller than 25 nm), and also increases with increasing size in the extrinsic size region (mean diameter larger than 25 nm). Because of this pronounced size effect a homogeneous size distribution and therefore a homogeneous broadening of the plasmon band is concluded for all the prepared gold nanoparticle samples. By applying a simple two-level model the dephasing time of the coherent plasmon oscillation is calculated and found to be less than 5 fs. Furthermore, the temperature dependence of the plasmon absorption is examined. A small temperature effect is observed. This is consistent with the fact that the dominant electronic dephasing mechanism involves electron−electron interactions rather than electron−phonon coupling.

Size and temperature dependence of the plasmon absorption of colloidal gold nanoparticles

Gold nanorods: Synthesis, characterization and applications

Specimen size dependences of the dielectric constant and of its variations with temperature have been investigated by measuring the optical plasma resonance absorption of small silver particles embedded in glass. The following relations hold at the wavelength 405 nm: epsilon 2 (imaginary part at 300K)=0.23+2.64/R, and epsilon 2(300K)- epsilon 2(1.5K) approximately=0.07-0.08/R where R is the particle radius in nm. Agreement has been found with the free path effect but not with the quantum size effect theories of Kawabata and Kubo (1966) and of Glauberman and Adamyan (1969). The behaviour of the temperature dependence can partly be explained by thermal lattice contraction. The ratio of electron density to the optical effective mass shows no distinct changes as R varies from 10.5 nm to 1.1 nm. It may hence be concluded that normal metallic properties are present in silver particles embedded in glass which contain more than about 400 atoms.

https://iopscience.iop.org/article/10.1088/0305-4608/4/7/007/pdf

U Kreibig

Papers

Electronic properties of small silver particles: the optical constants and their temperature dependence