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Semiconductor quantum dots (QDs) are one of the leading candidates for realizable qubits, as well as for many other advances in quantum computing and quantum communication. The spatial overlapping of wavefunctions describing each single electron in these nanoscale devices results in tunable spatial entanglement. In this article, we explore the case of two electrons in two-dimensional double quantum dot systems. We compute the two-particle wavefunction through a variational method combined with Hermite finite elements and study the spatial entanglement of electrons. We show that symmetry in the geometry of the double quantum dots plays a role in obtaining optimal entanglement, while a broken symmetry can lead to additional resonances in entanglement that are associated with the crossings of states. We also show that one can finely tune the level of spatial entanglement by altering the geometry of the quantum dots or by applying external fields, which corresponds to an "entanglement spectroscopy." Finally, we study how impurities in the potential profile of the QDs affect the level of entanglement. [ABSTRACT FROM AUTHOR]

Accurate analysis of the electromagnetic fields inside waveguides and cavities with re-entrant boundaries is crucial for many multi-scale device applications. In earlier approaches, the singularities that exist in electromagnetic field gradients inside such waveguides and cavities significantly reduce the accuracy of the calculations. In our scheme, these singular behaviors are treated using Hermite finite elements combined with analytical regularization of the action integral. We show that this approach provides considerably higher accuracy as compared with other methods employed in the literature. Specific calculations are presented for three typical regions: (a) an L-shaped waveguide, (b) an L-cavity, and (c) a cubic cavity with an octant removed to form a triple-junction corner. The method can be adapted to evaluate very high electromagnetic fields in any complex structures displaying "hot points." [ABSTRACT FROM AUTHOR]

In search of novel phononic crystals to effectively control the propagation of elastic waves, we propose a new single-material phononic crystal (PnC) with unit cells containing tapered resonators (TRs). The thickness of the circular taper radially decreases outward from the center. The device modulates dispersion of the wave by a local resonance mechanism and by slowly varying the group velocity of elastic waves. The TRs are layered on the top of a conventional PnC slab with a square arrangement of air holes. The band structure of the PnC is theoretically studied and a comparison is drawn between the avoided level crossings and the symmetry-protected ordinary degeneracies. In the absence of a bandgap, the zero group velocity at the band maximum restricts the waves from propagating. Moreover, the design shows anomalous dispersion phenomena such as self-collimation and bi-refringence, which are rare in conventional PnCs. We trace the origins of these phenomena by analyzing equifrequency contours associated with relevant frequencies. We show that the self-collimation effect persists even with a small variation in the angle of incidence and a perturbative hole at the center of each of the TRs. Within the classical limit, the scale invariance of the elastic wave equation makes the device useful in both the low frequency ultrasonic and the high frequency phononic regime. [ABSTRACT FROM AUTHOR]

The prospect of implementing quantum device architectures with technologically mature III–V semiconductors requires precisely controlled topologically protected edge states and bulk insulation. However, experimentally reaching this regime with III–V heterostructure epitaxy has been difficult due to charged bulk defects. Charged defects prevent bulk insulation and disturb the stability of edge states. Hence, we study carrier properties in a hybridized III–V InAs0.9Sb0.1/GaSb superlattice (SL) structure. We realize that an electron density (mobility) is limited to approximately 1012 cm−2 (104 cm2/V s). In order to understand these limits, the authors investigate the in-plane mobility of hybridized SLs as a function of current-carrying layer thickness, L, to determine scattering mechanisms that restrict carrier mobility. Although theory predicts the in-plane mobility is proportional to L6 dominated by interface roughness scattering (IRS) at low temperatures, we report that mobility follows the fourth power dependence, which is a weaker than expected from IRS theory. We attribute the discrepancy between experiment and the model to interface intermixing and wave function penetration into barrier regions. We use this understanding to develop a strategy for realizing high-performance topological materials. [ABSTRACT FROM AUTHOR]

Atomistic determination of carrier scattering properties is essential for designing nano-electronic devices in two-dimensional (2D) materials. Traditional quantum scattering theory is developed in an asymptotic limit, thus making it inapplicable for 2D materials and heterostructures. Here, we introduce a new paradigm of non-asymptotic quantum scattering theory to obtain the carrier scattering properties at finite distances from active scattering centers. We develop an atomistic multiscale formalism built on the k ⋅ p Hamiltonian, supplemented with parameters from first-principles electronic structure calculations. We apply this framework to investigate electron transport in lateral transition-metal dichalcogenide heterostructures and demonstrate enhanced high mobility of the order of 10 3 cm 2 V − 1 s − 1 at room temperature. The non-asymptotic quantum scattering formalism provides a new frontier to design high-performance mesoscopic devices in 2D materials. [ABSTRACT FROM AUTHOR]

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 9.2 GPa. 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 2.9 GPa, electron relaxation times are an order of magnitude lower than at equilibrium. These results will influence transport properties at higher pressures. [ABSTRACT FROM AUTHOR]

We show that in quantum waveguides, the Fano resonance profile associated with propagating modes has its analogs with evanescent modes as well. This is found to be an unusual and a universal effect for any attractive potential. Further, we show that quantum dots or attractive impurity potentials embedded in the interior of a quantum waveguide yield significantly large Seebeck coefficient (thermopower) and power factor. Hence, they are good candidates for enhancing the thermoelectric energy conversion efficiency. We study the effect of a waveguide tapering on transport properties for the first time and the effect of curvature on the transmission coefficients. We propose a nanoscale current rectification device in two dimensions using tapered quantum waveguides. [ABSTRACT FROM AUTHOR]

We develop a novel method based on sources and absorbers to examine quantum scattering in finite, nanoscale systems. We show that the Cauchy (mixed) boundary conditions (BCs) are required to put the scattering theory into an action integral formulation. These complex BCs are reduced to simpler Dirichlet BCs by introducing totally absorbing "stealth regions." Material properties of these enclosing regions are optimized to give decaying solutions so that the scattering amplitudes vanish at the finite boundaries. With the active scattering region now surrounded by absorbers, we construct an "electron antenna" to provide incident waves. The method retains all the physical aspects of the conventional theory while providing new insights into "near-field" scattering effects. The action integral is discretized and evaluated to derive the local wavefunction everywhere. In two-dimensional quantum waveguides, we obtain the scattered wavefunction for geometrically complex scattering centers, showing the flexibility of our method. The modal decomposition of reflected and transmitted waves allows us to obtain transmission coefficients for both propagating and evanescent modes. Using group theory, we develop selection rules for the scattered modes depending on the symmetry of the potential. Our method outperforms the limitations of traditional perturbative estimates, transfer-matrix, S-matrix discretizations, and other schemes to provide a complete nonasymptotic variational description for electron transport in quantum waveguides. [ABSTRACT FROM AUTHOR]

We show that the present approaches for the solution of Maxwell's equations in complex geometries have limitations that can be overcome through the use of C (1) -continuous Hermite interpolation polynomials. Our approach of calculating fields using the Hermite finite element method yields better accuracy by several orders of magnitude than comparable applications of the edge-based vector finite element method. We note that the vector finite element that is widely used yields pixelated solutions and ill-defined vector solutions at nodes. Our solutions have a smooth representation within and across the elements and well defined directions for the fields at the nodes. We reexamine the issue of removing spurious zero-frequency solutions. We investigate fields in an empty cubic metallic cavity and explain the level degeneracy that is larger than what is to be expected from the geometrical O h symmetry of the cube. This behavior is identified as an example of "accidental degeneracy" and is explained in detail. We show that the inclusion of a smaller dielectric cube of relative permittivity ϵ 2 within the cubic cavity leads to the removal of this accidental degeneracy so that the eigenfields have the symmetry O h. A further reduction of symmetry is obtained by allowing the dielectric function in the enclosed cube to have a linear dependence on z. The proposed method should be effective in obtaining results for scalar-vector coupled field problems such as in modeling quantum well cavity lasers and in plasmonics modeling, while allowing multi-scale physical calculations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Developing compact algorithms for accurate electrodynamic calculations with minimal computational cost is an active area of research given the increasing complexity in the design of electromagnetic composite structures such as photonic crystals, metamaterials, optical interconnects, and on-chip routing. We show that electric and magnetic (EM) fields can be calculated using scalar Hermite interpolation polynomials as the numerical basis functions without having to invoke edge-based vector finite elements to suppress spurious solutions or to satisfy boundary conditions. This approach offers several fundamental advantages as evidenced through band structure solutions for periodic systems and through waveguide analysis. Compared with reciprocal space (plane wave expansion) methods for periodic systems, advantages are shown in computational costs, the ability to capture spatial complexity in the dielectric distributions, the demonstration of numerical convergence with scaling, and variational eigenfunctions free of numerical artifacts that arise from mixed-order real space basis sets or the inherent aberrations from transforming reciprocal space solutions of finite expansions. The photonic band structure of a simple crystal is used as a benchmark comparison and the ability to capture the effects of spatially complex dielectric distributions is treated using a complex pattern with highly irregular features that would stress spatial transform limits. This general method is applicable to a broad class of physical systems, e.g., to semiconducting lasers which require simultaneous modeling of transitions in quantum wells or dots together with EM cavity calculations, to modeling plasmonic structures in the presence of EM field emissions, and to on-chip propagation within monolithic integrated circuits. [ABSTRACT FROM AUTHOR]

The extraordinary magnetoresistance (EMR) in metal-semiconductor hybrid structures was first demonstrated using a van der Pauw configuration for a circular semiconductor wafer with a concentric metallic inclusion in it. This effect depends on the orbital motion of carriers in an external magnetic field, and the remarkably high magnetoresistance response observed suggests that the geometry of the metallic inclusion can be optimized to further significantly enhance the EMR. Here, we consider the theory and simulations to achieve this goal by comparing both two-dimensional (2D) and three-dimensional (3D) structures in an external magnetic field to evaluate the EMR in them. New results for 3D structures are presented to show the feasibility of such modeling. Examples of structures that are compatible with present day technological capabilities are given together with their expected responses in terms of EMR. For a 10 μm 2D square structure with a square metallic inclusion, we find an MR up to 107 percent for an applied magnetic field of 1 T. In 3D, for a 10 μm cube with a 5 μm centered metallic inclusion, we obtain an MR of ∼104 percent, which is comparable with the 2D structure of equivalent dimensions. The results presented here for specific geometries are scalable to smaller dimensions down to the onset of ballistic effects in the transport. The present calculations open up the possibility of 3D magnetic field sensors capable of determining the magnitude and also direction of the magnetic field once a full characterization of the sensor response is performed. [ABSTRACT FROM AUTHOR]

In order to describe interdiffusion in layered structures in multicomponent systems, matrix Green’s functions may be employed in seeking solutions to multicomponent diffusion equations. A transfer matrix method employing a matrix notation is utilized for this analysis. For single-phase multilayered assemblies set up with thin alloy layers of different compositions between thick terminal alloy disks, expressions for the temporal and spatial evolution of the concentration profiles are developed on the basis of a set of constant interdiffusion coefficients. The theory is developed in general for multilayered diffusion assemblies containing any number of finite layers. It is applied to an experimental ternary diffusion assembly containing one layer sandwiched between two thick terminal alloys in the Cu–Ni–Zn system. The Cu–Ni–Zn layered diffusion assembly was assembled with three α (fcc) Cu–Ni–Zn alloys of different compositions and annealed at 775 °C for 4 days. The agreement between the experimentally observed concentration profiles and the predicted concentration profiles is found to be quite satisfactory. [ABSTRACT FROM AUTHOR]

For applications to extraordinary magnetoresistance (EMR) quantum well sensor design, the electron areal density n2D, the mobility μ, and the products n3D1/2μ2 and n3D1/2μ5/2 are key physical parameters to be optimized for enhanced device sensitivity and signal to noise ratio. We model the electron areal density and carrier mobility in a two-dimensional electron gas layer developed in a δ-doped AlInSb/InSb heterostructure. The nonparabolic band structure due to the nature of the small energy band gap of InSb is accounted for. The detailed description of the energy dispersion and the energy dependent effective mass are obtained by the k·P method of band structure calculation. The transport properties are calculated by including contributions of scattering from ionized impurities, the background neutral impurities, the deformation potential acoustic phonons, and the polar optical phonons. We calculate the dependencies of n2D, μ, n3D1/2μ2, and n3D1/2μ5/2 on temperature, spacer layer thickness, doping density, and the quantum well thickness. This has important implications for EMR sensor design. [ABSTRACT FROM AUTHOR]

We develop a self-consistent solution of the Schrödinger and Poisson equations in semiconductor heterostructures with arbitrary doping profiles and layer geometries. An algorithm for this non-linear problem is presented in a multiband k·P framework for the electronic band structure using the finite element method. The discretized functional integrals associated with the Schrödinger and Poisson equations are used in a variational approach. The finite element formulation allows us to evaluate functional derivatives needed to linearize Poisson’s equation in a natural manner. Illustrative examples are presented using a number of heterostructures including single quantum wells, an asymmetric double quantum well, p-i-n-i superlattices, and trilayer superlattices. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

It has been proposed earlier that the extraordinary magnetoresistance (EMR) observed at room temperature in nonmagnetic semiconducting materials containing metallic inhomogeneities can be used in suitably constructed read heads for magnetic storage devices. Here, we show that such read heads are much simpler in design, and allow for higher sensitivity than is observed using magnetic layered structures that employ the phenomenon of giant magnetoresistance. We calculate, with no adjustable material parameters, the room-temperature response of an EMR read-head design, using finite element analysis, as a function of the position of the magnetic bit relative to the read head. The scaling property of the EMR bodes well for increasing the storage density to 1 Tbit/in.[SUP2] in the near future. [ABSTRACT FROM AUTHOR]

We present a comprehensive, up-to-date compilation of band parameters for the technologically important III-V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other. © 2001 American Institute of Physics. We present! a comprehensive, up-to-date compilation of band parameters for the technologically important III-V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Details study of the electron phonon interaction in a triple quantum well structure which acts as the active region in an intersubband terahertz emitter. Calculation of phonon modes of the heterostructure using a transfer matrix method within the framework of the dielectric continuum model; Presence of specific interface and layer-confined phonon modes.

Presents information pertaining to the theoretical investigation regarding the internal losses in optically pumped type-II lasers. Moderation of losses; What the comparison of detailed numerical simulation showed; Information on the calculations of the temperature-dependent intervalence absorption cross section; Details on theoretical investigations.

Presents numerical calculations based on an elaborate microscopic model to confirm that normal incidence (TE) absorption of II-V quantum wells is usually negligible. Overview of previous studies on intersubband transitions in quantum wells; Factors which contributed to the origin of TE absorption; Conclusion.