Bulk Optical Constants Research Articles

Size-Dependent Band-Gap and Molar Absorption Coefficients of Colloidal CuInS2 Quantum Dots.

The knowledge of the quantum dot (QD) concentration in a colloidal suspension and the quantitative understanding of the size-dependence of the band gap of QDs are of crucial importance from both applied and fundamental viewpoints. In this work, we investigate the size-dependence of the optical properties of nearly spherical wurtzite (wz) CuInS2 (CIS) QDs in the 2.7 to 6.1 nm diameter range (polydispersity ≤10%). The QDs are synthesized by partial Cu+ for In3+ cation exchange in template Cu2–xS nanocrystals, which yields CIS QDs with very small composition variations (In/Cu = 0.91 ± 0.11), regardless of their sizes. These well-defined QDs are used to investigate the size-dependence of the band gap of wz CIS QDs. A sizing curve is also constructed for chalcopyrite CIS QDs by collecting and reanalyzing literature data. We observe that both sizing curves follow primarily a 1/d dependence. Moreover, the molar absorption coefficients and the absorption cross-section per CIS formula unit, both at 3.1 eV and at the band gap, are analyzed. The results demonstrate that the molar absorption coefficients of CIS QDs follow a power law at the first exciton transition energy (εE1 = 5208d2.45) and scale with the QD volume at 3.1 eV. This latter observation implies that the absorption cross-section per unit cell at 3.1 eV is size-independent and therefore can be estimated from bulk optical constants. These results also demonstrate that the molar absorption coefficients at 3.1 eV are more reliable for analytical purposes, since they are less sensitive to size and shape dispersion.

Optically thin hybrid cavity for terahertz photo-conductive detectors

The efficiency of photoconductive (PC) devices, including terahertz detectors, is constrained by the bulk optical constants of PC materials. Here, we show that optical absorption in a PC layer can be modified substantially within a hybrid cavity containing nanoantennas and a Distributed Bragg Reflector. We find that a hybrid cavity, consisting of a GaAs PC layer of just 50 nm, can be used to absorb >75% of incident photons by trapping the light within the cavity. We provide an intuitive model, which describes the dependence of the optimum operation wavelength on the cavity thickness. We also find that the nanoantenna size is a critical parameter, small variations of which lead to both wavelength shifting and reduced absorption in the cavity, suggesting that impedance matching is key for achieving efficient absorption in the optically thin hybrid cavities.

Quantum-Confined and Enhanced Optical Absorption of Colloidal PbS Quantum Dots at Wavelengths with Expected Bulk Behavior.

Nowadays it is well-accepted to attribute bulk-like optical absorption properties to colloidal PbS quantum dots (QDs) at wavelengths above 400 nm. This assumption permits to describe PbS QD light absorption by using bulk optical constants and to determine QD concentration in colloidal solutions from simple spectrophotometric measurements. Here we demonstrate that PbS QDs experience the quantum confinement regime across the entire near UV-vis-NIR spectral range, therefore also between 350 and 400 nm already proposed to be sufficiently far above the band gap to suppress quantum confinement. This effect is particularly relevant for small PbS QDs (with diameter of ≤4 nm) leading to absorption coefficients that largely differ from bulk values (up to ∼40% less). As a result of the broadband quantum confinement and of the high surface-to-volume ratio peculiar of nanocrystals, suitable surface chemical modification of PbS QDs is exploited to achieve a marked, size-dependent enhancement of the absorption coefficients compared to bulk values (up to ∼250%). We provide empirical relations to determine the absorption coefficients at 400 nm of as-synthesized and ligand-exchanged PbS QDs, accounting for the broadband quantum confinement and suggesting a heuristic approach to qualitatively predict the ligand effects on the optical absorption properties of PbS QDs. Our findings go beyond formalisms derived from Maxwell Garnett effective medium theory to describe QD optical properties and permit to spectrophotometrically calculate the concentration of PbS QD solutions avoiding underestimation due to deviations from the bulk. In perspective, we envisage the use of extended π-conjugated ligands bearing electronically active substituents to enhance light-harvesting in QD solids and suggest the inadequacy of the representation of ligands at the QD surface as mere electric dipoles.

Modeling TiO2׳s refractive index function from bulk to nanoparticles

In recent decades, the use of nanomaterials has become very common. Different nanomaterials are being used in over 1600 consumer products. Nanomaterials have been defined as having at least one dimension in the range of 1−100nm. Such materials often have unique properties. Despite some warnings of applying bulk optical constants for nano size materials, stated already in 1980s, bulk constants are still commonly used in the light scattering measurements of nano size particles. Titanium dioxide is one of the materials that is manufactured and used as an engineered nanomaterial in increasing quantities. Due to the aforementioned facts, it is quite crucial for successful research and production of nanoparticles to find out the dependence of the refractive index function (RIF) of the material on its crystal size. We have earlier performed several ab initio computations for obtaining the dependence of the RIF of TiO2 on the crystal or on the cluster size, for particles of size up to ca. 2nm. Extending the calculations to greater sizes has turned out to be infeasible due to the unbearable increase in computational time. However, in this study we show how the crystal-size-dependent-RIF (CS-RIF), for both rutile and anatase can be modeled from measured extinction or turbidity spectra of samples with varying crystal and particle sizes. For computing the turbidity spectrum, we constructed a model including primary crystals whose distributions were parameterized by mean and standard deviation, and also including aggregates consisting of mean sized primary particles, parameterized just by mean aggregate size. Mainly because of the long computing times Mie calculation was used in the computation of extinction spectra. However, in practical process applications, the obtained RIF will be used together with the T-matrix method. We constructed the RIFs used in the model using generalized oscillator model (GOM) as expanded to crystal size dependence. The unknown parameters of the model were solved using nonlinear least squares estimation. When the crystal size becomes smaller than the bulk size the shape of the estimated CS-RIFs reveal two distinct regions for both rutile and anatase. In the first region, starting apparently already from ca. 200nm, the height of both the real part and the imaginary part of CS-RIF decreases on crystal diameter. However, the band gap remains constant. In the second region, starting when the crystal diameter is decreased to ca. 3nm, a blue shift starts to increase the band gap. The band gap dependence on crystal size is quite consistent with the existing experimental values. Consequently, it is of great importance to use CS-RIF in light scattering measurements for nanoparticle size determination. Neglecting this, the smaller particles in the size distribution will have too small values, already for sub-micrometer particles, naturally distorting also the mean value. To our knowledge, this is the first time ever that a CS-RIF from bulk to 1nm size is determined for any material.

Thickness dispersion of surface plasmon of Ag nano-thin films: determination by ellipsometry iterated with transmittance method.

Effective optical constants of Ag thin films are precisely determined with effective thickness simultaneously by using an ellipsometry iterated with transmittance method. Unlike the bulk optical constants in Palik's database the effective optical constants of ultrathin Ag films are found to strongly depend on the thickness. According to the optical data two branches of thickness dispersion of surface plasmon energy are derived and agreed with theoretical predication. The thickness dispersion of bulk plasmon is also observed. The influence of substrate on surface plasmon is verified for the first time by using ellipsometry. The thickness dependent effective energy loss function is thus obtained based on this optical method for Ag ultrathin films. This method is also applicable to other ultrathin films and can be used to establish an effective optical database for ultrathin films.

Evaluation of thickness and strain of thin planar layers of InAs on GaAs(001) using spectroscopic ellipsometry

We develop a technique for accurately measuring thickness of planar InAs films grown on (001) GaAs by spectroscopic ellipsometry, using bulk optical constants. We observe that the critical point structure for the E1 and E1 + Δ1 transitions extracted from the measured dielectric properties varies with strain in the layer. Transmission electron microscopy confirms the extracted thickness and measures the residual strain based on the dislocation spacing in the film. At small thickness, the E1 critical point is seen to markedly deviate from the dependence predicted by deformation potential theory and appears to be consistent with additional quantum confinement effects.

Optical properties of free sub-10-nm diameter Fe2O3 nanoparticles studied by broad-band cavity enhanced absorption spectroscopy (BB-CEAS)

We present direct optical extinction measurements on free size filtered iron oxide nanoparticles in the size range between 3 nm and 10 nm diameter. The high number density of nanoparticles required for the cavity enhanced absorption spectroscopy (CEAS) measurements was achieved by combining a high intensity plasma synthesis source of iron oxide particles with an aerodynamic lens inlet into the vacuum system and radiofrequency particle guiding and storage devices. The extinction cross sections can be quantitatively explained using the bulk optical constants of hematite, which may exist in the form of nanoparticles in the mesosphere.

Single-layer terahertz metamaterials with bulk optical constants

We investigate the conditions under which single layer metamaterials may be described by bulk optical constants. Terahertz time domain spectroscopy is utilized to investigate two types of geometries, both with two different sizes of embedding dielectric---cubic and tetragonal unit cells. The tetragonal metamaterials are shown to yield layer dependent optical constants, whereas the cubic metamaterials yielded layer independent optical constants. We establish guidelines for when $\ensuremath{\epsilon}$ and $\ensuremath{\mu}$ can be used as material parameters for single layer metamaterials. Experimental results at terahertz frequencies are presented and supported by full wave three-dimensional electromagnetic simulations.

Orbital-separation approach for consideration of finite electric bias within density-functional total-energy formalism

We present a simple approach for the consideration of bias voltage within the Kohn-Sham formalism of density-functional theory. To be specific, the electronic charging of a metal-insulator-metal capacitor under bias voltage is considered explicitly. This is achieved by separating the Kohn-Sham orbitals around the Fermi level into anode or cathode parts and applying different Fermi levels in the determination of occupation numbers. The formal basis of the present approach is discussed in detail. We test this method against Au-vacuum-Au and Au-MgO-Au capacitors with various dielectric thicknesses. It is shown that the bulk optical and static dielectric constants can be obtained accurately. We also demonstrate that interface effects on capacitance can be investigated straightforwardly. Furthermore, we apply this method to the graphene capacitor and identify the quantum effects in the capacitance, which is well explained by the contribution of the kinetic energy of electrons to the capacitance. The present method can be readily implemented in conventional first-principles codes and provides a unified approach to evaluate capacitance of nanodevices.

Midinfrared spectra and optical constants of bulk hematite: Comparison with particulate hematite spectra

Hematite is an iron oxide that is very important for the study of climatic evolution of Mars. It can occur in three forms: nanophase (dark purple), fine-grained (red) and coarse-grained (gray). In a previous work, we studied the influence of particle size and shape on the infrared spectra (in the wavelength range 6.25–50 μm) of submicron red hematite particles and found that bulk optical constants did not fit the spectra of very fine particles with several classes of models. In the present paper, we derive bulk optical constants of a sample of the same parent material of hematite already used in a previous work in order to determine the particulate optical constants. As a first result we find that, also in this case, bulk and particulate optical constants are different from each other. Furthermore, we show that these bulk optical constants, although derived starting from the same parent material of hematite and used with a model adopting the laboratory measured grain size distribution of the sample, cannot be used to reproduce the spectra of submicron particles. Our results can help the scientific community to appropriately model the contribution of hematite submicron grains to the martian dust for a better understanding of the geologic evolution of the planet.

An alternative approach to understand the photoluminescence and the photoluminescence peak shift with excitation in porous silicon

There have been many different models proposed for the luminescence in porous silicon (PS), yet it is believed that the quantum confinement effect persists at the absorption. However, from our investigation on both constant and pulsed electrochemically etched silicon (PS), the absence of quantum confinement effect at the absorption has been identified from the close correspondence of photoluminescence excitation (PLE) spectra of PS to the simulated absorption spectrum of an ultrathin silicon film with the bulk optical constants. In the simulation of absorption spectrum, the spectral dependence of reflectivity of the solid, which had been omitted in the traditional analysis of PLE, is considered. Further, although nanocrystallites of silicon are present in the PS matrix, the absence of quantum confinement is explained on the basis of structural characteristics of PS. Following that, many common observations in the luminescence of PS are attributed to the surface states. The blueshift of the PL peak with the increase in excitation energy is explained with the idea of quasithermal equilibrium and the probability of occupation of the carriers at the surface states.

Plasmon Line Widths of Single Silver Nanoprisms as a Function of Particle Size and Plasmon Peak Position

We study the homogeneous line width of the plasmon resonance scattering peaks of anisotropic silver nanoparticles using single particle darkfield scattering spectroscopy. We correlate the scattering spectra with scanning electron microscopy images of the particles to investigate the effects of nanoparticle size on the plasmon line width. We observe that the scattering line widths of silver nanoprisms increase both as the particle volume increases and as the plasmon resonance energy increases. We attribute the size dependence to radiation damping and compare our data both to simple dipole-limit approximations for the radiative and nonradiative decay rates and with finite-difference time-domain (FDTD) calculations of the scattering line width. We find the data and calculations in good agreement for an appropriate choice of the bulk optical constants of silver and find that the dipole-limit approximations capture the observed size and energy-dependence of the plasmon line widths.

Infrared reflection spectra of forsterite crystal

Polarized infrared reflectance of large single crystals of forsterite was measured for each crystal axis at frequencies between 5000 cm-1 and 100 cm-1 with a resolution of 1 cm-1. The reflectance spectra were analyzed based on classical dispersion theory. A set of oscillator parameters for crystalline axes of forsterite was obtained. Those parameters are used to derive optical constants of forsterite, which are important for analyses of observed spectra of astronomical objects and laboratory spectra of particle samples. Calculations of absorption for small particles using the bulk optical constants are compared with mid-infrared and far-infrared absorption spectra measured in the laboratory.

Simulated measurement of small metal clusters by frequency-modulation non-contactatomic force microscopy

The apparent height and lateral extent of very small metallic clusters and particles adsorbedon flat substrates have been calculated for frequency-modulation non-contact atomic forcemicroscopy (ncAFM). The ncAFM scanning tip was modelled as a Si sphere covered by 1 nm ofSiO2. This tip sphere of either 5 or 20 nm total radius (including anSiO2 layer) is attached to a cantilever of spring constantk = 40 N m−1 and oscillated with a 10 nm amplitude. The tip was rastered across the centre of a singlecluster of Pd atoms or a single Pd particle located on a flat continuum substrateof alumina or Pd. The clusters were one-atom-thick close-packed arrangementsof 19 or 91 atoms (1.4 or 3.0 nm wide); the particles were continuum spheres ofdiameter 2.0 or 4.0 nm. The tip–substrate and tip–particle interactions were modelledwith 6–12 Lennard-Jones potentials. The attractive interaction was takento be the London–van der Waals dispersion interaction whose magnitude wasestimated from Hamaker constants calculated from bulk optical constants of Si,SiO2, Pd, and alumina. The repulsive interaction was determined from estimates of the atomicradii using densities of the bulk materials. These simulations show that the apparentheights of particles imaged by ncAFM range from just 12% of the actual height for thesmallest Pd cluster on a Pd substrate to 95% of the actual height for the largest Pd particleon an alumina substrate. The apparent widths of the clusters were similar to those incontact AFM. These results show the most accurate height measurements occurwhen the lateral extent of the cluster or particle is comparable to or larger thanthe radius of the tip and when the Hamaker constant for the interaction of thetip with a cluster or particle is larger than that for the tip with the substrate.

Correct application of Fresnel’s equations for intensity analysis of angle-resolved photoemission data

The electromagnetic field relevant for the excitation process in angle-resolved photoemission is studied. We show that Fresnel’s equations together with the known bulk dielectric constants can be used to calculate the complex vector potential at the metal surface. A model is developed which accounts correctly for the special experimental geometry with focused light. It is used to calculate the variation of photoemission intensity with changing light incidence angle and polarization. Experimental data for the photoemission intensity as a function of light incidence angle are presented for direct transitions out of bulk, surface and adsorbate states at a Cu(1 1 0) surface. The comparison to our model shows that the application of copper bulk optical constants is justified even when electronic states are localized to the topmost atomic layer.

The square columnar model in enhancement of an electromagnetic field

Experimental infrared absorbance in the normal configuration of vacuum-evaporated silver films on a transparent wafer is inconsistent with the calculated electromagnetic field based on bulk optical constants, the effective-medium approximation, and classical electromagnetic theory. We propose a model of a non-resonant-type enhancement mechanism based on the square columnar structure model. The calculated infrared absorption intensity is then in better quantitative agreement with the experimental observations of enhanced infrared absorption of adsorbed species.

Semiconductor nanoparticles (CdS, ZnS and ZnxCdS1_x) in reverse micellar media

Nanoparticles CdS, ZnS and mined crystals of Zn x Cd 1 - x S can be generated in situ in AOT-heptane-water and CTAB-chloroform-water microemulsions using an ultrasonic processor. The nanoparticles exhibit the quantum size effect. The average diameter of nanoparticles, as manifested in the photoabsorbtion threshold of colloidal semiconductors, increases as the water content of reverse micelles and the concentration of φ-state particles increases. The composition of mixed sulfides and water content (pool size) of inverted micelles can be varied systematically and the band gap energies of the semiconductor particles can be determined from photoabsorption threshold (edges). A method is proposed for determining the bulk optical dielectric constants of solid solutions of two semiconductor employing the Brus equations.

The Optical Properties of Copper Phthalocyanine Ultrathin Films Deposited on Silver: An ATR Study

Ultrathin copper phthalocyanine adsorbate layers have been deposited onto silver films, and their optical properties in the visible spectral range have been investigated by angle-dependent attenuated total reflection measurements in Kretschmann-Raether prism coupler geometry. Down to an adsorbate mass coverage of 2 nm, the optical behaviour of the adsorbate is in accordance with the bulk optical constants of copper phthalocyanine. For thinner layers, the optical behaviour indicates an increase in the average absorption cross section of the copper phthalocyanine molecules at the silver surface. The effect may be explained as resulting from “hot spots” at the silver surface, originating from surface irregularities.

The prospects of reflectometry and ellipsometry with Colorado State University tabletop XUV laser

The capillary discharge ArIX laser (wavelength 46.9nm) is a new device attractive for various applications due to its unique for XUV lasers properties: high average power and compactness. Reflectometry and ellipsometry are among them. The first is capable to provide fundamental data on optical constants of solids, which are still rather limited. Reflection coefficient in this spectral range is highly sensitive to the presence of an overlayer at the surface of a sample. This hinders bulk optical constants determination, but offers the possibility to study chemical contamination by ambience. The theory of reflection from a surface with a thin overlayer is developed. It enables to rigorously include overlayer into reflectometry data processing and derive separately the parameters of bulk and overlayer. Ellipsometry in general is more powerful than reflectometry method to measure optical constants. In addition it offers the accurate methods to measure film thickness and properties of magnetic materials. Unfortunately high quality analyzers and polarizers are not available in this spectral range, which requires specific approach to ellipsometric measurements. We discuss and use for this purpose Sc/Si multilayer structures.

Influence of surface plasmons on the Faraday effect in bismuth-substituted yttrium iron garnet films

The Kerr rotation and ellipticity of Bi1.8Y1.2Fe5O12 films (Bi:YIG) with the easy axis of magnetization perpendicular to the film plane was investigated in a Kretschmann setup at the wavelength 1.31 μm. The sample was coated by a thin Au film in order to excite plasmons at the free Au surface. An ellipsometric setup, supplemented with a magnetic field oriented perpendicularly to the film plane was used to measure the reflected p and s components of an incoming p polarized wave. The phase difference between the outgoing p and s waves was found by an indirect procedure. A minimum in Kerr rotation and a maximum in Kerr ellipticity could be observed at the surface plasmon resonance angle. Using the Berreman formalism, the experimental curves for the prism/Bi:YIG/Au system could be reproduced by bulk optical constants of the constituents. The asymmetry of the ellipticity curve is demonstrated to arise from a sudden variation in the phase. The effects of the field distribution and the surface roughness are discussed.