We investigate graphene and graphene layers on different substrates by monochromatic and white-light confocal Rayleigh scattering microscopy. The image contrast depends sensitively on the dielectric properties of the sample as well as the substrate geometry and can be described quantitatively using the complex refractive index of bulk graphite. For a few layers (<6), the monochromatic contrast increases linearly with thickness. The data can be adequately understood by considering the samples behaving as a superposition of single sheets that act as independent two-dimensional electron gases. Thus, Rayleigh imaging is a general, simple, and quick tool to identify graphene layers, which is readily combined with Raman scattering, that provides structural identification.

/pdf/rayleigh-imaging-of-graphene-and-graphene-layers-1er4ic4q6i.pdf

Rayleigh Imaging of Graphene and Graphene Layers

A universal method of extraction of the complex dielectric function ϵ(ω)=ϵ1(ω)+iϵ2(ω) from experimentally accessible optical quantities is developed. The central idea is that ϵ2(ω) is parameterized independently at each node of a properly chosen anchor frequency mesh, while ϵ1(ω) is dynamically coupled to ϵ2(ω) by the Kramers–Kronig (KK) transformation. This approach can be regarded as a limiting case of the multioscillator fitting of spectra, when the number of oscillators is on the order of the number of experimental points. In the case of the normal-incidence reflectivity from a semi-infinite isotropic sample the new method gives essentially the same result as the conventional KK transformation of reflectivity. In contrast to the conventional approaches, the proposed technique is applicable, without readaptation, to virtually all types of linear-response optical measurements, or arbitrary combinations of measurements, such as reflectivity, transmission, ellipsometry, etc., done on different types of sa...

Kramers–Kronig constrained variational analysis of optical spectra

Scattering and absorption of X-rays by interstellar dust is calculated for a model consisting of carbonaceous grains and amorphous silicate grains. The calculations employ realistic dielectric functions with structure near X-ray absorption edges, with resulting features in absorption, scattering, and extinction. Differential scattering cross sections are calculated for energies between 0.3 and 10 keV. The median scattering angle is given as a function of energy, and simple but accurate approximations are found for the X-ray scattering properties of the dust mixture, as well as for the angular distribution of the scattered X-ray halo for dust with simple spatial distributions. Observational estimates of the X-ray scattering optical depth are compared to model predictions. Observations of X-ray halos to test interstellar dust grain models are best carried out using extragalactic point sources.

https://iopscience.iop.org/article/10.1086/379123/pdf

Scattering by Interstellar Dust Grains. II. X-Rays

Intermixing the wells and barriers of quantum well structures generally results in an increase in the band gap and is accompanied by changes in the refractive index. A range of techniques, based on impurity diffusion, dielectric capping and laser annealing has been developed to enhance the quantum well intermixing (QWI) rate in selected areas of a wafer; such processes offer the prospect of a powerful and relatively simple fabrication route for integrating optoelectronic devices and for forming photonic integrated circuits (PICS). Recent progress in QWI techniques is reviewed, concentrating on processes which are compatible with PIC applications, in particular the achievement of low optical propagation losses.

https://iopscience.iop.org/article/10.1088/0268-1242/8/6/022/pdf

Quantum well intermixing

A simple optical method is presented for identifying and measuring the effective optical properties of nanometer-thick, graphene-based materials, based on the use of substrates consisting of a thin dielectric layer on silicon. High contrast between the graphene-based materials and the substrate is obtained by choosing appropriate optical properties and thickness of the dielectric layer. The effective refractive index and optical absorption coefficient of graphene oxide, thermally reduced graphene oxide, and graphene are obtained by comparing the predicted and measured contrasts.

Simple approach for high-contrast optical imaging and characterization of graphene-based sheets

Optical constants of graphite for ordinary and extraordinary waves are modeled with a modified Lorentz–Drude model with frequency-dependent damping. The model enables the shape of the spectral line to vary over a range of broadening functions with similar kernels and different wings, the broadening type being its adjustable parameter. The model parameters are determined by the acceptance-probability-controlled simulated annealing algorithm. Good agreement with the experimental data is obtained in the entire investigated spectral range (0.12–40 eV for ordinary wave and 2.1–40 eV for extraordinary wave). The significant discrepancies between the experimental data obtained by the reflectance measurements and the electron-energy-loss spectroscopy data are analyzed in details. Inconsistency in terms of unsatisfied Kramers–Kronig relations is discovered in the index of refraction data derived from reflectance measurements, and a method for correcting the data is proposed.

/pdf/optical-properties-of-graphite-37601zok1u.pdf

Optical properties of graphite

Optical functions of a specific semiconductor in a particular wavelength region are often needed in optics and optoelectronics research. Basic optical properties of some materials are available in handbooks, but recent advances in the experimental techniques for growth, sample preparation and determination of optical functions, as well as theoretical advances in modeling the optical functions, prompted demand for a review of the state of the art of the optical functions of some important semiconductor materials. This paper gives an overview of the experimental methods for the determination of optical functions in the 1–6 eV spectral range and the available models for calculating the optical functions. Also, the paper summarizes the progress in the study of optical functions of several important semiconductors such as GaP, InP, InAs, GaSb, InSb, AlSb, AlxGa1−xAs, HgxCd1−xTe, SixGe1−x, GaN, InN, AlN, 6H–SiC, and ZnO. Besides discussing the available data and expected positions of optical transitions, the paper focuses on the model of the dielectric function which allows reproducing accurately the experimental dielectric function values for all the materials considered here.

Progress in the room-temperature optical functions of semiconductors

Optical constants of hexagonal GaN (in the range 1.5–10 eV), InN (in the range 2–10 eV), and AlN (in the range 6–20 eV) for E⊥c are modeled using a modification of Adachi’s model of optical properties of semiconductors. Model parameters are determined using the acceptance-probability-controlled simulated annealing method. The employed model uses an adjustable broadening function instead of the conventional Lorentzian one. The broadening can vary over a range of functions with similar kernels but different wings. Therefore, excessive absorption inherent to Lorentzian broadening due to the large wings of a Lorentz function can be reduced, yielding better agreement with experimental data. As a result, excellent agreement with experimental data is obtained; the relative rms errors for the real part of the index of refraction are below 2% for all three materials, and, for the imaginary part, below 5% for GaN and below 3% for InN and AlN.

/pdf/modeling-the-optical-constants-of-hexagonal-gan-inn-and-aln-4v1p9aovst.pdf

Modeling the optical constants of hexagonal GaN, InN, and AlN

The disordering of In0.53Ga0.47As/InP single quantum wells has been studied using an error function distribution to model the compositional profile after interdiffusion. When considering interdiffusion on the group‐III sublattice only, a large strain buildup results during the early stages of disordering. Details are presented showing how this interdiffusion and the effects of strain lead to an interesting carrier confinement profile which differs from that of disordered AlGaAs/GaAs and InGaAs/GaAs quantum‐well structures. An abrupt confinement profile is maintained even after significant interdiffusion, with a well width equal to that of the as‐grown quantum well. The combined effects of strain with the unstrained band‐gap profile results in a potential buildup in the barrier near the interface, while it gives rise to two ‘‘miniwells’’ inside the potential wells. The sub‐band‐edge structure shows that the potential buildup can result in quasibound subband states, while the heavy‐hole well can support the ground state within the miniwells. In contrast, when identical interdiffusion on both group‐III and group‐V sublattices is considered, the structure remains lattice matched, the confinement profile changes to that of a graded profile, and the ground‐state transition energy shifts to shorter wavelengths.

Effects of interdiffusion on the sub‐band‐edge structure of In0.53Ga0.47As/InP single quantum wells

A modification of the Lorentz oscillator model for optical constants is proposed in an effort to achieve better agreement with experimental data while keeping the calculation simple. Improvement in agreement between theoretical and experimental data obtained with a variable line shape (frequency-dependent damping constant) over a wide spectral range is demonstrated through modeling the index of refraction of Si(3)N(4) (1-24 eV), SiO (0.15-25 eV) and amorphous and crystalline SiO(2) (0.15-25 eV). Model parameters are estimated by acceptance-probability-controlled simulated annealing. Excellent agreement between the modified model and the experimental data is obtained for both real and imaginary parts of the index of refraction.

E. Herbert Li

Papers

Optical properties of graphite

Progress in the room-temperature optical functions of semiconductors

Modeling the optical constants of hexagonal GaN, InN, and AlN

Effects of interdiffusion on the sub‐band‐edge structure of In0.53Ga0.47As/InP single quantum wells

Modeling the index of refraction of insulating solids with a modified lorentz oscillator model.