Large-supercell tight-binding calculations are presented for GaBi$_{x}$As$_{1-x}$/GaAs single quantum wells (QWs) with Bi fractions $x$ of 3.125% and 12.5%. Our results highlight significant distortion of the valence band states due to the alloy disorder. A large full-width-half-maximum (FWHM) is estimated in the ground state interband transition energy ($approx$ 33 meV) at 3.125% Bi, consistent with recent photovoltage measurements for similar Bi compositions. Additionally, the alloy disorder effects are predicted to become more pronounced as the QW width is increased. However, they are less strong at the higher Bi composition (12.5%) required for the design of temperature-stable lasers, with a calculated FWHM of $approx$ 23.5 meV at $x$=12.5%.
Using an $sp^{3}s^{*}$ tight-binding model we demonstrate how the observed strong bowing of the band gap and spin-orbit-splitting with increasing Bi composition in the dilute bismide alloy GaBi$_{x}$As$_{1-x}$ can be described in terms of a band-anticrossing interaction between the extended states of the GaAs valence band edge and highly localised Bi-related resonant states lying below the GaAs valence band edge. We derive a 12-band $textbf{k}cdottextbf{p}$ Hamiltonian to describe the band structure of GaBi$_{x}$As$_{1-x}$ and show that this model is in excellent agreement with full tight-binding calculations of the band structure in the vicinity of the band edges, as well as with experimental measurements of the band gap and spin-orbit-splitting across a large composition range. Based on a tight-binding model of GaBi$_{x}$N$_{y}$As$_{1-x-y}$ we show that to a good approximation N and Bi act independently of one another in disordered GaBi$_{x}$N$_{y}$As$_{1-x-y}$ alloys, indicating that a simple description of the band structure is possible. We present a 14-band $textbf{k}cdottextbf{p}$ Hamiltonian for ordered GaBi$_{x}$N$_{y}$As$_{1-x-y}$ crystals which reproduces accurately the essential features of full tight-binding calculations of the band structure in the vicinity of the band edges. The $textbf{k}cdottextbf{p}$ models we present here are therefore ideally suited to the simulation of the optoelectronic properties of these novel III-V semiconductor alloys.
Incorporation of bismuth (Bi) in dilute quantities in (In)GaAs has been shown to lead to unique electronic properties that can in principle be exploited for the design of high efficiency telecomm lasers. This motivates the development of simple models of the electronic structure of these dilute bismide alloys, which can be used to evaluate their potential as a candidate material system for optical applications. Here, we begin by using detailed calculations based on an $sp^{3}s^{*}$ tight-binding model of (In)GaBi$_{x}$As$_{1-x}$ to verify the presence of a valence band-anticrossing interaction in these alloys. Based on the tight-binding model the derivation of a 12-band $textbf{k}cdottextbf{p}$ Hamiltonian for dilute bismide alloys is outlined. We show that the band structure obtained from the 12-band model is in excellent agreement with full tight-binding supercell calculations. Finally, we apply the 12-band model to In$_{0.53}$Ga$_{0.47}$Bi$_{x}$As$_{1-x}$ and compare the calculated variation of the band gap and spin-orbit-splitting to a variety of spectroscopic measurements performed on a series of MBE-grown In$_{0.53}$Ga$_{0.47}$Bi$_{x}$As$_{1-x}$/InP layers.
A model for realistic InAs quantum dot composition profile is proposed and analyzed, consisting of a double region scheme with an In-rich internal core and an In-poor external shell, in order to mimic the atomic scale phenomena such as In-Ga intermixing and In segregation during the growth and overgrowth with GaAs. The parameters of the proposed model are derived by reproducing the experimentally measured polarization data. Further understanding is developed by analyzing the strain fields which suggests that the two-composition model indeed results in lower strain energies than the commonly applied uniform composition model.
The incorporation of bismuth (Bi) in GaAs results in a large reduction of the band gap energy (E$_g$) accompanied with a large increase in the spin-orbit splitting energy ($bigtriangleup_{SO}$), leading to the condition that $bigtriangleup_{SO} > E_g$ which is anticipated to reduce so-called CHSH Auger recombination losses whereby the energy and momentum of a recombining electron-hole pair is given to a second hole which is excited into the spin-orbit band. We theoretically investigate the electronic structure of experimentally grown GaBi$_x$As$_{1-x}$ samples on (100) GaAs substrates by directly comparing our data with room temperature photo-modulated reflectance (PR) measurements. Our atomistic theoretical calculations, in agreement with the PR measurements, confirm that E$_g$ is equal to $bigtriangleup_{SO}$ for $textit{x} approx$ 9$%$. We then theoretically probe the inhomogeneous broadening of the interband transition energies as a function of the alloy disorder. The broadening associated with spin-split-off transitions arises from conventional alloy effects, while the behaviour of the heavy-hole transitions can be well described using a valence band-anticrossing model. We show that for the samples containing 8.5% and 10.4% Bi the difficulty in identifying a clear light-hole-related transition energy from the measured PR data is due to the significant broadening of the host matrix light-hole states as a result of the presence of a large number of Bi resonant states in the same energy range and disorder in the alloy. We further provide quantitative estimates of the impact of supercell size and the assumed random distribution of Bi atoms on the interband transition energies in GaBi$_{x}$As$_{1-x}$. Our calculations support a type-I band alignment at the GaBi$_x$As$_{1-x}$/GaAs interface, consistent with recent experimental findings.
III-V growth and surface conditions strongly influence the physical structure and resulting optical properties of self-assembled quantum dots (QDs). Beyond the design of a desired active optical wavelength, the polarization response of QDs is of particular interest for optical communications and quantum information science. Previous theoretical studies based on a pure InAs QD model failed to reproduce experimentally observed polarization properties. In this work, multi-million atom simulations are performed to understand the correlation between chemical composition and polarization properties of QDs. A systematic analysis of QD structural parameters leads us to propose a two layer composition model, mimicking In segregation and In-Ga intermixing effects. This model, consistent with mostly accepted compositional findings, allows to accurately fit the experimental PL spectra. The detailed study of QD morphology parameters presented here serves as a tool for using growth dynamics to engineer the strain field inside and around the QD structures, allowing tuning of the polarization response.
Low-loss optical communication requires light sources at 1.5um wavelengths. Experiments showed without much theoretical guidance that InAs/GaAs quantum dots (QDs) may be tuned to such wavelengths by adjusting the In fraction in an InxGa1-xAs strain-reducing capping layer (SRCL). In this work systematic multimillion atom electronic structure calculations qualitatively and quantitatively explain for the first time available experimental data. The NEMO 3-D simulations treat strain in a 15 million atom system and electronic structure in a subset of ~9 million atoms using the experimentally given nominal geometries and without any further parameter adjustments the simulations match the nonlinear behavior of experimental data very closely. With the match to experimental data and the availability of internal model quantities significant insight can be gained through mapping to reduced order models and their relative importance. We can also demonstrate that starting from simple models has in the past led to the wrong conclusions. The critical new insight presented here is that the QD changes its shape. The quantitative simulation agreement with experiment without any material or geometry parameter adjustment in a general atomistic tool leads us to believe that the era of nano Technology Computer Aided Design (nano-TCAD) is approaching. NEMO 3-D will be released on nanoHUB.org where the community can duplicate and expand on the results presented here through interactive simulations.
Based on the dAlembert-Lagrange-Poincar{e} variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We write these equations in a canonical form called the Poincar{e}-Hamilton equations, and study a version of corresponding Poincar{e}-Cartan integral invariant which are derived by means of a type of asynchronous variation of the Poincar{e} variables of the problem that involve the variation of the time. As a consequence, it is shown that the invariance of a certain line integral under the motion of a mechanical system of the type considered characterizes the Poincar{e}-Hamilton equations as underlying equations of the motion. As a special case, an invariant analogous to Poincar{e} linear integral invariant is obtained.
