Generating large topologically protected surface currents using conventional III–V infrared materials such as InAsSb/InGaSbAs quantum wells (QWs) and superlattices (SLs) has been important. In such materials, topological states can be formed at the edge by hybridizing ordinary electronic band structures. However, achieving large surface currents out of these materials is still difficult due to low emission currents and high carrier defects. In this work, we present two hybridized topological structures: one for the 6.22 Å metamorphic QWs and the other for the 6.10 Å pseudomorphic SLs. Both structures are tailored for the same hybridization gap (Δ) of ∼60 meV and optimized for the minimum crystal defects. While the QW grown on metamorphic buffers generates a significant amount of mismatch-related crystal defects, the SL grown on lattice-matched buffers produces an excellent crystalline-quality. Quasiparticle interference mapping and calculations on a SL sample show good agreement of the band structure.

Monolayer transition-metal dichalcogenides (TMDC) have emerged as promising candidates for thermoelectric applications due to their large effective mass and low thermal conductivity. In this article, we study the thermoelectric performance of lateral TMDC heterostructures within a multiscale quantum transport framework. Both n-type and p-type lateral heterostructures are considered for all possible combinations of semiconducting TMDCs: MoS2, MoSe2, WS2, and WSe2. The band alignment between these materials is found to play a crucial role in enhancing the thermoelectric figure-of-merit (ZT) and power factor far beyond those of pristine TMDCs. In particular, we show that the room-temperature ZT value of n-type WS2 with WSe2 triangular inclusions is five times larger than that of the pristine WS2 monolayer. We also show that p-type MoSe2 with WSe2 inclusions has a room-temperature ZT value which is two times larger than that of the pristine MoSe2 monolayer. The peak power factor values, calculated here, are the highest reported amongst gapped monolayers at room temperature. Hence, monolayer lateral TMDC heterostructures open new avenues to develop ultra-efficient, planar thermoelectric devices.

The exploitation of band structure engineering as a means of designing optimized quantum structures with novel properties has led to a revolution in semiconductor electro-optics. This chapter reviews several specific device classes for which this remarkable degree of control over the interband and intersubband optical and electronic properties may be used to a particular advantage. Improved growth techniques yielding atomic-level control coupled with rapid advances in device-fabrication technologies have encouraged a trend toward increasingly complex structural configurations. The finite element method capability allows us to go beyond conventional bandgap or band-structure engineering, to a more general approach that may be designated wavefunction engineering. The primary obstacle blocking the progress of such important mid-wave infrared (IR) technologies as chemical sensing and IR countermeasures is the lack of inexpensive, convenient, and reliable sources capable of emitting high powers at non-cryogenic operating temperatures. The chapter illustrates the new opportunities for IR electrooptical devices based on antimonide quantum heterostructures.

Electron-phonon (e-ph) interaction in semiconductors is responsible for many phenomena such as electron mobility and hot electron thermalization, which are important to compute charge transport in semiconductors. In semiconductors, the application of hydrostatic pressure modifies the character of conduction band valleys, changing the effective mass of carriers, and, consequently, changing the carrier mobility. This, in turn, may limit electron transport in the semiconductor. Here, we present the effect of hydrostatic pressure on the e-ph interaction in GaAs, which goes from a direct to an indirect bandgap semiconductor at high pressures. A detailed study of e-ph self-energy and the resulting scattering rates is presented for hydrostatic pressure ranging between 0 and 9.2GPa. Individual contributions from phonon modes to the total scattering rates indicate that short wavelength LO phonon scattering is found to be the dominant mechanism at low pressures; and at higher pressures, acoustic as well as optic phonons contribute toward the overall e-ph scattering. Finally, relaxation times are evaluated and we find that at pressures above 2.9GPa, electron relaxation times are an order of magnitude lower than at equilibrium. These results will influence transport properties at higher pressures.

We perform first principles calculations to predict the electron–phonon (e–ph) scattering rates in AlAs and their dependence on phonon modes at energies close to the conduction band minima (CBM), as well as high into the conduction band. We then study the effect of hydrostatic pressure on the e–ph scattering in AlAs for pressures up to \(\sim\) 8.77 GPa. The effect of such pressures on the electronic structure and phonon dispersion is well documented. In AlAs, the bandgap becomes smaller, whereas the effect on phonon dispersion is to shift the optical phonon bands to higher frequencies and the acoustic branches to lower frequencies. In light of this, we explore the effect of hydrostatic pressure on the resulting scattering rates with increasing pressure along the high symmetry \(L\rightarrow \Gamma \rightarrow X\) path. The results suggest that hydrostatic pressure does not significantly affect electron–phonon scattering rate.

Based on the transfer matrix methodology, a new analysis is presented for the description of slopes of the ternary diffusion path for a solid-solid diffusion couple. Concentration profiles and diffusion paths for isothermal, ternary diffusion couples are examined in the context of eigenvalues and eigenvectors obtained from the diagonalisation of the[GRAPHICS]ternary interdiffusion coefficients employed for their representation. New relations are derived relating the decoupled interdiffusion fluxes to combinations of concentration gradients through the major and minor eigenvalues, and the diffusion path becomes parallel to the major eigenvector at each path end. General expressions for the slope of the ternary diffusion path at any section of the couple are also derived in terms of eigenvalue and eigenvector parameters. Expressions for the path slope at the Matano plane involve only concentrations, major and minor eigenvalues and eigenvector parameters. New constraints relating the eigenvalues and the concentration gradients of the individual components are also presented at selected sections, where the diffusion path is parallel to the straight line joining the terminal composition points on an isotherm. Applications of the various relations are illustrated with the aid of a hypothetical couple and an experimental Cu-Ni-Zn diffusion couple.

Maxwell's vector field equations and their numerical solution represent significant challenges for physical domains with complex geometries. There are several limitations in the presently prevalent approaches to the calculation of field distributions in physical domains, in particular, with the vector finite elements. In order to quantify and resolve issues, we consider the modeling of the field equations for the prototypical examples of waveguides. We employ the finite element method with a new set of Hermite interpolation polynomials derived recently by us using group theoretic considerations. We show that (i) the approach presented here yields better accuracy by several orders of magnitude, with a smoother representation of fields than the vector finite elements for waveguide calculations. (ii) This method does not generate any spurious solutions that plague Lagrange finite elements, even though the C1-continuous Hermite polynomials are also scalar in nature. (iii) We present solutions for propagating modes in inhomogeneous waveguides satisfying dispersion relations that can be derived directly, and investigate their behavior as the ratio of dielectric constants is varied both theoretically and numerically. Additional comparisons and advantages of the proposed method are detailed in this article. The Hermite interpolation polynomials are shown to provide a robust, accurate, and efficient means of solving Maxwell's equations in a variety of media, potentially offering a computationally inexpensive means of designing devices for optoelectronics and plasmonics of increasing complexity.

We report ab-initio results for electron-phonon (e-ph) coupling and display the existence of a large variation in the coupling parameter as a function of electron and phonon dispersion. This variation is observed for all phonon modes in Si and Ge, and we show this for representative cases where the initial electron states are at the band gap edges. Using these e-ph matrix elements, which include all possible phonon modes and electron bands within a relevant energy range, we evaluate the imaginary part of the electron self-energy in order to obtain the associated scattering rates. The temperature dependence is seen through calculations of the scattering rates at 0 K and 300 K. The results provide a basis for understanding the impacts of phonon scattering vs. orientation and geometry in the design of devices, and in analysis of transport phenomena. This provides an additional tool for engineering the transfer of energy from carriers to the lattice.

We calculate the variation of electron–phonon (e–ph) coupling as a function of phonon wavevector and the initial electron energy over the entire Brillouin zone (BZ) in diamond. We consider three cases of the initial electron energy, the first corresponds to an electron at the top of the valence band, the second where the electron is at the conduction band minimum at ∆, and the third is for electrons at the secondary conduction band minimum at Γ. The e–ph interaction exhibits a strong phonon wavevector dependence which indicates a need to go beyond the long-wavelength approximation typically used for treating electron–phonon scattering in transport simulations, especially for capturing high field effects. Within an ab initio electronic structure framework, we describe electron and phonon wavefunctions in terms of localized Wannier functions which allow the evaluation of e–ph coupling over a dense grid in the BZ with tractable computational effort. The full description of the e–ph coupling over the BZ is used to compute the electron linewidth which is applied to predict the associated total phonon scattering rates. Calculations at 0K and 300K are presented and show the corresponding linewidth increases with temperature and that the method is suitable for producing inputs to transport calculations.

The addition of nitrogen to III–V alloys has been widely studied as a method of modifying the band gap for mid-infrared (IR) applications. Lattice matching these alloys to convenient substrates such as GaSb, however, is challenging due to the significantly different lattice constants. One approach is to use InGaSbN/InAs grown on GaSb where the InGaSbN layer has a larger lattice constant than the substrate, and the InAs layer has a lower lattice constant, and thus the compressive and tensile stress of the superlattice layers can be balanced in a so called strained-layer superlattice. In this paper, we report InxGa1−xSb1−yNy/InAs strained-layer superlattices with type-II (staggered) energy offsets on GaSb substrates, where the design of the layer thickness is based on the lattice constants and the elastic moduli. Three different strain balance conditions are reported: fixed superlattice period thickness, fixed InAs well thickness, and fixed InxGa1−xSb1−yNy barrier thickness. Eight-band k·p simulations of these structures were used to analyze the superlattice miniband energies. For fully strain balanced InxGa1−xSb1−yNy/InAs superlattices lattice matched to the GaSb substrate, careful consideration of strain balance conditions was needed to achieve a lower effective miniband gap needed for longer cutoff wavelength detectors. For non-strained balanced InxGa1−xSb1−yNy/InAs superlattices, long-wavelength cutoff up to 8μm can be achieved as part of a trade-off between the deleterious effects of strain and the reduction of the barrier band gap through N incorporation.

With on going reduction in dimension of nano-devices it becomes imperative to include interface and structure boundaries accounting for complex, mixed boundary conditions. A Lagrangian approach to the physics provides the natural framework for such calculations, with computational work based on the finite element method. This variational approach has led to the design of mid-IR cascade lasers and the solution of the Schrödinger-Poisson self-consistency in arbitrary layered structures. Applications of this methodology lead to the solution for energy levels in a magnetic field in the Voigt geometry. The effect of surface proximity on binding energy for impurity states in nanowires and the beautiful physics of complex topological surfaces such as a Mobius ring are displayed as further examples of the issues addressable through multi-scale parallel computing within this variational framework.

We investigate the quantum mechanical energy levels of an electron constrained to motion on a nanoscale Mobius ring by solving the Schrodinger equation on the curved surface. The dimensions of the ring in terms of the lateral and transverse parameters {u, v} for the Mobius ring allow us to identify the quantum numbers for the levels by (n(u), n(v)). We show that the energy levels can still be labeled using the quantum numbers of the cylindrical ring of the same dimensions. While the Hamiltonian has invariance under parity in parameter space, the rotational symmetry about any axis in configuration space is lost, so that the double degeneracy of energy levels for azimuthal quantum number n(u) >= 1, that exists in cylindrical rings, is lifted by a small amount in the Mobius ring. The pattern of level splitting has been identified in terms of the number of twists sigma to be 2n(u) = s sigma where s is an integer. The scaling properties of the energy levels with respect to the dimensions of the ring are derived; using these properties, our numerical results which are given for a specific geometry can be extended to rings of other commensurate dimensions. The absence of rotational invariance for the Mobius ring manifests itself through the orbital angular momentum L-z not commuting with the Hamiltonian. Its expectation values are found to have nearly integral as well as half-integral values of (h) over bar, and its variances are small. The energy levels with half-integral azimuthal quantum numbers (n(u)) are also close to the approximate formula for the equivalent cylindrical ring, provided such half-integral quantum numbers are allowed for the cylindrical geometry. The Zeeman splitting of the energy levels in an external magnetic field is displayed, together with wave functions at a level anticrossing. The optical transitions between electronic states on the Mobius ring are obtained, and a table of oscillator strengths is provided. The results for energy levels for rings with multiple twists are presented. In view of recent technological advances in the production of graphene sheets, we may anticipate the making of such twisted rings with graphene strips of finite width. Graphene strips of finite width have an open band gap at the K points in the Brillouin zone, so that a nonrelativistic treatment with a small effective mass is appropriate. For Mobius rings of graphene, our results would be directly relevant, and we may anticipate their experimental verification in the near future.

We have developed a fundamental theory for electro-optical and nonlinear optical processes involving intersubband transitions in conduction valleys with arbitrary effective-mass anisotropy and orientation. New classes of amplitude and phase modulators, as well as frequency converters employing L-valley interactions in GaSb/AlSb-based quantum well systems are proposed. Key advantages of these devices include operation at normal incidence (enabled by the L-valley effective-mass anisotropy and tilted growth direction with respect to the L-valley constant energy ellipsoids) and adaptability to a wide range of infrared wavelengths (as short as 1.5 mu m, made possible by the large band offsets). The electro-optic coefficients and second-order nonlinear susceptibilities derived from our modeling are larger than any measured or predicted to date for conventional Gamma-valley processes.

Magnetic polarons are ferromagnetic spin clusters created by the exchange interaction of a carrier spin (electron or hole) with localized spins imbedded in a semiconductor lattice. They were first studied in magnetic semiconductors [1]; more recently, there have been extensive investigations [2] of polaron behavior in diluted magnetic semiconductors (DMS), such as Cd1−xMnxTe. DMS are favorable media for magnetic polaron studies because they have simple s-p bands and excellent optical properties. Two types of magnetic polarons have been identified in DMS - the bound magnetic polaron (BMP), whose carrier is localized by an impurity [3], and the free polaron (FP) consisting of a carrier trapped by its own, self-consistently-maintained, exchange potential [4].

The effect of the surrounding dielectric on the conductivity of GaN nanowires is measured experimentally. The two following configurations are considered: bare suspended and SiO2-coated nanowires. The measured conductivity is consistently fitted by two exponential terms with different activation energies, indicating multichannel conduction. The larger energy, attributed to activation of impurities into the conduction subband, shows essentially inverse dependence on nanowire radius, consistent with the dielectric confinement effect. This agrees with calculated values from finite element analysis. The smaller energy is independent of the nanowire radius, suggesting a surface conduction channel.

The finite element method (FEM) represents the numerical evaluation of the action integral for physical problems. In this sense, it is the numerical implementation of the fundamental principle of stationary action that is used throughout physics. The method overcomes issues of complex geometry, mixed boundary value issues, and any interface boundary conditions in composite systems. Being a variational approach, FEM can be used to systematically improve the accuracy of the results of the calculations to any degree of numerical precision. This method, which was first developed in connection with structural engineering and aeronautics problems, has been shown by Ram-Mohan to be an ideal method for the modeling of nanoscale physical systems obeying quantum mechanics. For typical eigenvalue problems, for nonseparable problems such as the hydrogen atom in an external magnetic field, and for the modeling of multi-physics problems such as the highly nonlinear Schrödinger-Poisson selfconsistent solution for energy band-bending in quantum nanoscale semiconductor structures of interest in devices, FEM provides convergent solutions with "spectroscopic" accuracy. Over the past 15 years we have seen a remarkable growth in the research outcomes using FEM in the published literature. It has led to the new paradigm of wavefunction engineering, the modeling of quantum systems with optimized design for particular applications. The book by Ram-Mohan * provides an introduction to the method and some of its applications in nanoscale systems. The present short course is designed to introduce the physical and mathematical concepts and the computational methodology that underlie the FEM, present examples in 1D and 2D with lectures, coursework, and experience in computer program development. It will initiate the participants into problems in 1-3D of interest to them. The example codes will make use of the C/C++ programming language, and the computational libraries developed at Quantum Semiconductor Algorithms, Inc. † These example codes and libraries will be available to the participants for use on computers using the UNIX operating system. In the last stage of the course, the parallelization needed for distributed computing over several CPUs for large scale problems will be introduced with work examples.