E. Herbert Li

Optical properties of graphite

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.

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

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.

REFRACTIVE INDEX OF INGAN/GAN QUANTUM WELL

In this article, the optical properties of the InxGa1−xN/GaN quantum well (QW) are investigated. The refractive index spectrum of a QW is essential to the design and implementation of optoelectronic devices. Yet, the refractive index of the InGaN/GaN QW system over a wide spectral range has been unavailable so far. This article presents a comprehensive model, which includes the exciton effect and most of the major critical points, to calculate the complex index of refraction of the InGaN/GaN QW at room temperature. The calculations have been performed for QW’s with various alloy compositions and well widths in the spectral range from 1 to 9 eV. The model presented here fully considers transitions near the band edge and above barrier gap contributions.

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

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.

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

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.

Quantum‐confined Stark effect in interdiffused AlGaAs/GaAs quantum well

The quantum‐confined Stark effect is analyzed in an interdiffused Al0.3Ga0.7As/GaAs single quantum well (QW) with an as‐grown well width of 100 A, where the confinement profile is modeled by an error function. Results indicate a twofold enhancement of the Stark shift for the interdiffused quantum well over that of the square quantum well for a 50 kV/cm applied field. The fundamental exciton absorption peak also shows a much larger reduction with increasing applied field in the more extensively interdiffused QW. These characteristics may be used to realize optical modulators with higher on/off ratios and lower drive voltages.

Polarization dependent refractive index of an interdiffusion induced AlGaAs/GaAs quantum well

The polarization dependent refractive index, nR, at room temperature is calculated for interdiffusion‐induced Al0.3Ga0.7As/GaAs single quantum well (QW) structures for the wavelength range 0.75–2 μm. The confinement profile is modeled by an error function and nR is determined using the real and imaginary parts of the dielectric function, including contributions from the Γ, X, and L Brillouin zones. Results show that at longer wavelengths nR decreases with increasing interdiffusion, which normally provides a positive index step with respect to a less interdiffused QW. For shorter wavelengths (around the QW band edge), the wavelength range for a positive refractive index step increases as the extent of disordering between two interdiffused QWs is increasing.

Effect of interdiffusion of quantum well infrared photodetector

The intersubband infrared photodetector performance is theoretically analyzed for various stages of interdiffusion in AlGaAs/GaAs quantum well. The absorption strength and responsivity are enhanced for certain extents of interdiffusion and the peak detection wavelength red shifts continuously with a large tunable range from 7 to 38.4 μm. The dark current is at an acceptable value for small diffusion extent.

Effects of Different Cation and Anion Interdiffusion Rates in Disordered In0.53Ga0.47As/InP Single Quantum Wells

The effects of different cation and anion interdiffusion rates when disordering In0.53Ga0.47As/InP single quantum wells are investigated using an error function distribution to model the compositional profile after interdiffusion. The early stages of disordering result in a spatially dependent strain buildup, which can be either compressive or tensile. The effects of this strain profile and the compositional distribution give rise to interesting carrier confinement profiles after disordering. A significantly faster cation interdiffusion rate produces a red shift of the ground-state transition energy, which with prolonged interdiffusion saturates and then decreases. A significantly higher anion interdiffusion rate causes a blue shift in the ground state transition energy, and shifts the light hole ground state above the heavy hole ground state. The results from the model are compared with reported experimental results which have been interpreted in terms of different interdiffusion rates on the two sublattices.

Dielectric function models for describing the optical properties of hexagonal GaN

Several different models have been employed for modeling the dielectric function of hexagonal GaN in the range from 1 to 10 eV. Models are compared in terms of number of parameters required, intricacy of model equations, and possibility of accurate estimation of important physical parameters, such as energies of critical points and exciton binding energies. Shortcomings and advantages of each model are discussed in detail. Excellent agreement with the experimental data for GaN has been achieved with three of the investigated models. It has also been shown that an assumption of adjustable broadening instead of a purely Lorentzian one improves the agreement with the experimental data and enables elimination of excessive absorption below the gap which is inherent to the models with Lorentzian broadening.