Effective Mass Schrodinger Equation Research Articles

Numerical Simulation of Thermal Conductivity of SiNW–SiGe0.3 Composite for Thermoelectric Applications

The electron band structure and phonon energy dispersion of the silicon nanowires (SiNWs) embedded in SiGe0.3 (SiNW–SiGe0.3 composite) are simulated by using the effective mass Schrodinger equation and the elastodynamic wave equation, respectively. Then, the TE properties of the SiNW–SiGe0.3 composite are investigated by the Landauer approach. The simulation shows the contribution from electrons/holes on both electrical conductance and thermal conductance increases few times by introducing SiNWs, but on the other hand, lattice thermal conductance reduces around two orders. These results are consistent with the experimental measurement and indicates that much lower lattice thermal conductance dominates the TE performance of the SiNW–SiGe0.3 composite.

Analytical modeling for nanostructure quantum wells with equispaced energy levels in semiconductor ternary alloys (Ax B1-x C)

The purpose of this study is to formulate an Analytical model of equispaced energy levels quantum wells (QWs) in semiconductor ternary alloys (A x B 1 -x C). The procedure is by mapping the envelop function Schrodinger equation for realistic QW, with the local conduction band edge as the potential experienced by an electron in the QW into an effective mass Schrodinger equation with a linear harmonic oscillator potential by the method of coordinate transformation. The electron effective mass and potential are then obtained as the signature for the equispaced energy level for QWs in semiconductor ternary alloys. Keywords: Semiconductor nanostructures, Ternary alloys, Quantum wells, Equispaced energy levels, Effective mass

Modeling of pyramidal shape quantum dot infrared photodetector: the effects of temperature and quantum dot size

Quantum dot base infrared detectors have many advantages such as lower dark current, higher operating temperature, higher photoconductive gain, and broader infrared response. For this reason, we have studied a pyramidal shape quantum-dot infrared photodetector (QDIP) in which the different mechanisms of noise and dark current, the effects of QD size variation, the temperature, and applied electric field are considered. Self-assembled In0.3Ga0.7As / GaAs pyramidal shape quantum dots have been considered and optical properties in the conduction band using effective mass Schrodinger equation by the finite-difference time-domain (FDTD) method have been analyzed. Finally, the detectivity calculated as functions of the applied electrical field and temperature. For example, at the T = 77 ° K and E = 2 kV / cm, the detectivity is 3 × 1013 cmHz − 1/2 / W.

Tailoring the optical properties of InAs/GaAs quantum dots by means of GaAsSb, InGaAs and InGaAsSb strain reducing layers

Self-organized InAs QDs have been grown by Molecular Beam Epitaxy with different strain reducing layers (SRL) having nearly similar lattice mismatches to GaAs. The used SRLs are GaAsSb, InGaAs and InGaAsSb. Atomic Force Microscopy (AFM), transmission electron microscopy (TEM), high resolution X-ray diffraction (HRXRD), power dependent photoluminescence (PL) from low to room temperature have been employed for the characterization of the grown samples. Our results revealed that the emission wavelength reaches 1.32 μm when the InAs QD are either covered by InGaAs or GaAsSb with a PL spectrum broadening when using GaAsSb. However, the incorporation of only 1% of Sb in the InGaAs SRL extends further the wavelength to 1.37 μm without altering the PL spectrum. For more quantitative analysis of the observed results, the QDs size dependence on the SRL type has been estimated by tuning the theoretical transition energies, obtained by solving the single band effective mass Schrodinger equation for an ellipsoidal QD through changing the dot size to fit the experimental transition energies. Indeed, in addition to the QDs strain reduction, the type of alloy capping layer is found to seriously alter the QD size and aspect ratio and consequently the energy separation between the first and second excited state. However, from the temperature dependence of the PL, the thermionic emission activation energies were found to be close to separation between the ground and first excited state independently of the SRL type.

Nonlinear terahertz response associated to electronic intersubband transitions in a V-groove quantum wire

The electron states as well as the nonlinear optical rectification and second and third harmonic generations are investigated in a GaAs-based V-groove quantum wire. The single band effective mass Schrodinger equation is solved using the finite element method. The nonlinear optical coefficients were calculated from expressions derived within the compact density matrix method. It is found that this kind of nanostructures can exhibit noticeable nonlinear responses in the domain of the terahertz when the V-groove is in the open-wide geometrical configuration.

In-situheight engineering of InGaAs / GaAs quantum dots by chemical beam epitaxy

This work reports on a chemical beam epitaxy growth study of InGaAs/GaAs quantum dots (QDs) engineered using an in-situ indium-flush technique. The emission energy of these structures has been selectively tuned over 225 meV by varying the dot height from 7 to 2 nm. A blueshift of the photoluminescence (PL) emission peak and a decrease of the intersublevel spacing energy are observed when the dot height is reduced. Numerical investigations of the influence of dot structural parameters on their electronic structure have been carried out by solving the single-particle one-band effective mass Schrodinger equation in cylindrical coordinates, for lens-shaped QDs. The correlation between numerical calculations and PL results is used to better describe the influence of the In-flush technique on both the dot height and the dot composition.

Effect of quantum force discontinuity on electron transmission across abrupt heterojunctions

Matching conditions for the envelope function in the effective mass approximation are determined based on the feasibility of exactly solving the effective mass Schrodinger equation. The transmission and reflection probabilities for these conditions at an abrupt heterojunction are determined for a step mass and step potential and an alternative description of transport across the heterojunction based on the interplay between discontinuities of the quantum force and the effective mass is discussed.

Effect of position-dependent effective mass on optical properties of spherical nanostructures

The effects of position-dependent effective mass on the absorption coefficients (ACs) of spherical quantum dot (QD) and quantum antidot (QAD) have been investigated. We show that the radial position-dependent effective mass Schrodinger equation can be reduced into ordinary one-dimensional Schrodinger equation with some suitable transformations. Our numerical calculations are performed using both a constant effective mass and the position-dependent effective mass. The comparative approach is used for presenting the results of both QD and QAD models. It is found that not only for the effective constant mass but also for the position-dependent effective mass, the ACs curves corresponding to QD and QAD are considerably different in shapes and behaviors. Our obtained results show that the spatial variation of the electron effective mass can not be neglected in the optical ACs of both QD and QAD nanostructures.

COOS: a wave-function based Schrödinger–Poisson solver for ballistic nanotube transistors

This paper gives an in depth overview on a wave-function based simulation framework (called coos) for modeling ballistic nanotube transistors by solving the effective-mass Schrodinger equation. The framework considers non-parabolic electronic band structure effects, band-to-band tunneling as well as a heterojunction-like model for extended contacts to describe the injection and reception of charge carriers into and from the channel. Special emphasis is put on an efficient and reliable numerical implementation. The applicability of the simulation framework and the necessity to include the aforementioned phenomena are shown by comparing simulation results with experimental data of a $$50\hbox { nm}$$ 50 nm long carbon nanotube transistor (cntfet). The intrinsic transit frequencies and the output characteristics for higher drain-source voltages are predicted and analyzed.

Strain-Modulated L-Valley Ballistic-Transport in (111) GaAs Ultrathin-Body nMOSFETs

Electron transport through the quantized L valley of (111) surface orientation is a possible solution to density-of-states bottleneck of GaAs. Quantization splits the L valley into L[111] valley pair and remote L valley pairs, L[111], L[111], and L[111]. The L[111] valley pair projects to the 2-D Brillouin zone center above the Γ valley and its population enhances the drive current. However, for a typical 5-nm thin body, the Γ-L[111] energy separation is still ≈0.17 eV and the Γ valley primarily governs the electron transport. We analyze the compressive biaxial strain effects on the energy levels and effective masses of Γ, L[111], and remote L valleys of a 5-nm (111) GaAs ultrathin body using a sp <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s*d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> orbital basis tight binding model. We then evaluate the ballistic performance of a 10-nm double-gate device using an effective mass Schrodinger's equation with the extracted masses and band energies from sp <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s*d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> model. Compressive strain promotes the L[111] and remote L valleys transport by reducing the Γ-L[111] and Γ-remote L valleys energy offsets. This results in a significant improvement in charge density and drive current. A compressive stress larger than 2.5 GPa brings the remote L valleys even below the L[111] valley. Under this stress condition, the remote L[1̅11] and L[11̅1] valleys govern the ON-state transport. The different wavefunction symmetries of L[111] and remote L valleys are the physics behind the stress modulated enhanced L valley transport.

High-Frequency Ballistic Transport Phenomena in Schottky Barrier CNTFETs

The effective-mass Schrodinger equation is solved directly for the wave functions to explore the steady state and the time-dependent quantum-ballistic transport in Schottky barrier carbon nanotube (CNT) field-effect transistors (FETs). The employed contact parameters allow for discontinuities of the effective mass at the metal-CNT interface, and carefully chosen boundary conditions minimize spurious reflections at the simulation domain boundaries. Two-port Y-parameters of a selected device structure are computed and qualitatively explained with the time dependence of coherent quantum-ballistic charge injection. The finite escape times of the charge carriers in an open quantum system are identified for determining the inertial response to high-frequency terminal signals. Since the escape times depend on the shape of the Schottky barriers, the latter contribute to the dynamic behavior of ballistic CNTFETs.

Equispaced level conduction band design in the Cd Zn Se/Cd Se quantum well

A derivation for equispaced conduction band in the CdxZn1-xSe quantum well is presented using the coordinate transform (CT) based procedure. The procedure starts with the effective mass Schrodinger equation, with potential tailored along the one dimensional harmonic oscillator (IDHO). The electron effective mass in the well is space dependent and varies proportionally with the potential, taking as the local conduction band edge. A value of 720 meV the conduction band edge according to Dingle’s proposal of 85.15 of conduction-valence band partition (Basu, 1997) is adopted in this article. Two Hamiltonians were derived, one exhibits a confining potential (for ) that may be realized by appropriate grading of . The second Hamiltonian has a non-confining potential (for) with the electron effective mass . This is not realizable. Equaispaced level quantum well are scare in the interest of pursuing this work. Key words: Quantum well, effective mass, Schodinger equation, confinement.

Accuracy of Transfer Matrix Approaches for Solving the Effective Mass SchrÖdinger Equation

The accuracy of different transfer matrix approaches, widely used to solve the stationary effective mass Schrodinger equation for arbitrary one-dimensional potentials, is investigated analytically and numerically. Both the case of a constant and a position-dependent effective mass are considered. Comparisons with a finite difference method are also performed. Based on analytical model potentials as well as self-consistent Schrodinger-Poisson simulations of a heterostructure device, it is shown that a symmetrized transfer matrix approach yields a similar accuracy as the Airy function method at a significantly reduced numerical cost, moreover avoiding the numerical problems associated with Airy functions.

Exact Solution of Effective Mass Schrödinger Equation for the Hulthen Potential

A general form of the effective mass Schrodinger equation is solved exactly for Hulthen potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function.

Characteristics of quadratic electro-optic effects and electro-absorption process in CdSe parabolic quantum dots

The nonlinear susceptibilities have been calculated theoretically for CdSe disk-like parabolic quantum dots by using a two-energy-level model in the strong-confinement regime. The confined wave functions and eigenenergies of excitons in parabolic quantum dots have been studied by solving the electron–hole effective-mass Schrodinger equation. The third-order susceptibilities of the quantum dots for quadratic electro-optic effects (QEOE) and electro-absorption (EA) process as a function of quantum dot size, relaxation time, parabolic confinement frequency, and pump photon energy have been also analyzed.

A many-particle quantum-trajectory approach for modeling electron transport and its correlations in nanoscale devices

Electron transport in mesoscopic systems is analyzed in terms of quantum (Bohm) trajectories associated to wave-function solutions of a many-particle (effective-mass) Schrodinger equation. Many-particle Bohm trajectories can be computed from single-particle Schrodinger equations. As an example, electron correlations for a triple-barrier tunneling system with electron-electron interactions are computed. Simulated noise results for interacting electrons that tunnels through triple barriers are presented. The approach opens a new path for studying electron transport and quantum noise in nanoscale systems, beyond the “Fermi liquid” paradigm.

A study of envelope functions in FD-SOI devices for non-parabolic bands

In this study we analyzed the envelope functions obtained by solving the effective-mass Schrodinger equation including the non-parabolicity of the valence band in p-type FD-SOI devices. In order to carry out this task, we used two different algorithms to solve the effective-mass Schrodinger equation in barriers, and calculated the envelope functions and eigenenergies yielded by these methods for several states along the subbands. This study enabled us to propose a method for selecting the most appropriate envelope functions for each subband. Finally, we quantified the differences in phonon and interface-roughness scattering rates resulting from using the envelope function proposed rather than that obtained by simpler approaches in barriers.

Shubnikov-de Haas oscillations in Digital Magnetic Heterostructures

In this paper we theoretically investigate the magnetic-field and temperature dependence of the Shubnikov-de Haas oscillations in group II-VI modulation-doped Digital Magnetic Heterostructures. We self-consistently solve the effective-mass Schrodinger equation within the Hartree approximation and calculate the electronic structure and the magneto-transport properties. Our results show i) a shift of the Shubnikov-de Haas minima to lower magnetic fields with increasing temperature, and ii) an anomalous oscillation which develops when two opposite Landau levels cross near the Fermi energy. Both of these are consistent with recent magneto-transport measurements in such heterostructures.

The position-dependent effective mass Schrodinger equation: a quasi-exact solution

The energy spectra and eigenfunctions of the one-dimensional position-dependent effective mass Schrodinger equation can be obtained by using the standard methods of quasi-exactly solvable quantum mechanical models. Some special examples of position-dependent mass m( x) leading to real energy spectra and bounded wave functions for the Schrödinger equation, are also discussed in detail.

Dynamics of a two-dimensional electron-hole system in a coupled quantum well

In this work, we have numerically integrated in space and time the effective-mass Schrödinger equation for a two-dimensional electron-hole system in a coupled quantum well system. Considering a time-dependent Hartree potential and an external electric field, we derive the nonlinear dynamical evolution of the carrier wave function. It is found that charge dynamically trapped in both wells produces a reaction field that modifies the system resonant condition. At different electron-hole sheet densities we show the possibility of multiple resonant tunneling peaks in a bilayer system.