One-dimensional Potential Profile Research Articles

A New Simple Method of Simulating One Dimensional Quantum Problem Based on Lattice Point Concepts

One-dimensional quantum problems have always been an important issue in various branches of quantum mechanics fields, and many quantum models can be idealized as one-dimensional potential profiles. Therefore, it is necessary to investigates the way to deal with and calculate the problems. This paper proposes a new and simple method for simulation and calculation of one-dimensional quantum problems. To be specific, by representing continuous X values by a series of discrete lattice points, the Hamiltonian matrix is constructed for the system in the way of dealing with monomer and many-body problems, so as to simply calculate the energy level distribution and draw the wave function image. In terms of simulating one-dimensional infinite deep potential well, one-dimensional finite deep potential well, one-dimensional multi-potential well and other one-dimensional quantum systems with this method, this paper shows that the method is accurate and practical. Compared with other methods for one-dimensional quantum problems, this paper also presents the superiority of this method. To deal with the problem based on such a method can save the computation cost and time cost, which is more convenient to study the one-dimensional quantum problem in the future. These results shed light on studying complex one-dimensional quantum problems conveniently.

Exciton states in GaAs [formula omitted] systems under magnetic fields and hydrostatic pressure

Excitons in GaAs n-type δ-doped quantum wells are studied taking into account the effects of externally applied magnetic fields as well as of hydrostatic pressure. The one-dimensional potential profile in both the conduction and valence bands is described including Hartree effects via a Thomas–Fermi-based local density approximation. The allowed uncorrelated energy levels are calculated within the effective mass and envelope function approximations by means of an expansion over an orthogonal set of infinite well eigenfunctions and a variational method is used to obtain the exciton states. The results are presented as functions of the two-dimensional doping concentration and the magnetic field strength for zero and finite values of the hydrostatic pressure. In general, it is found that the exciton binding energy is a decreasing function of the doping-density and an increasing function of the magnetic field intensity. A comparison with recent experiments on exciton-related photoluminescence in n-type δ-doped GaAs is made.

Binding energy of a donor impurity in GaAs [formula omitted] systems under electric and magnetic fields, and hydrostatic pressure

The problem of the impurity binding energy in GaAs n-type delta-doped systems is studied taking the field effect transistor as an archetypical structure. The theoretical investigation considers the effects of externally applied electric and magnetic fields as well as of hydrostatic pressure. The description of the one-dimensional potential profile is made including Hartree and exchange effects via a Thomas–Fermi-based local density approximation. The allowed energy levels are calculated within the effective mass and envelope function approximations by means of an expansion over an orthogonal set of infinite well eigenfunctions. The results for the impurity binding energy are presented also for different configurations of the impurity position within the system.

Nonlinear optical rectification and second and third harmonic generation in GaAs [formula omitted] systems under hydrostatic pressure

The GaAs n-type delta-doped field effect transistor is proposed as a source for nonlinear optical responses such as second order rectification and second and third harmonic generation. Particular attention is paid to the effect of hydrostatic pressure on these properties, related with the pressure-induced modifications of the energy level spectrum. The description of the one-dimensional potential profile is made including Hartree and exchange and correlation effects via a Thomas–Fermi-based local density approximation. The allowed energy levels are calculated within the effective mass and envelope function approximations by means of an expansion over an orthogonal set of infinite well eigenfunctions. The results for the coefficients of nonlinear optical rectification and second and third harmonic generation are reported for several values of the hydrostatic pressure.

Generalized phonon-assisted Zener tunneling in indirect semiconductors with non-uniform electric fields: A rigorous approach

A general framework to calculate the Zener current in an indirect semiconductor with an externally applied potential is provided. Assuming a parabolic valence and conduction band dispersion, the semiconductor is in equilibrium in the presence of the external field as long as the electron-phonon interaction is absent. The linear response to the electron-phonon interaction results in a non-equilibrium system. The Zener tunneling current is calculated from the number of electrons making the transition from valence to conduction band per unit time. A convenient expression based on the single particle spectral functions is provided, enabling the evaluation of the Zener tunneling current under any three-dimensional potential profile. For a one-dimensional potential profile an analytical expression is obtained for the current in a bulk semiconductor, a semiconductor under uniform field, and a semiconductor under a non-uniform field using the WKB (Wentzel–Kramers–Brillouin) approximation. The obtained results agree with the Kane result in the low field limit. A numerical example for abrupt p-n diodes with different doping concentrations is given, from which it can be seen that the uniform field model is a better approximation than the WKB model, but a direct numerical treatment is required for low bias conditions.

Measuring Electrostatic Potential Profiles across Amorphous Intergranular Films by Electron Diffraction

Amorphous 1-2-nm-wide intergranular films in ceramics dictate many of their properties. The detailed investigation of structure and chemistry of these films pushes the limits of today's transmission electron microscopy. We report on the reconstruction of the one-dimensional potential profile across the film from an experimentally acquired tilt series of energy-filtered electron diffraction patterns. Along with the potential profile, the specimen thickness, film orientation with respect to the grain lattice and specimen surface, and the absolute specimen orientation with respect to the laboratory frame of reference are retrieved.

Wave-packet analysis of electron-phonon interaction in the Wigner formalism

A theoretical and computational analysis is presented of the motion of a single one-dimensional electron, represented by a wave packet of given average momentum and position, in a fixed potential profile in the presence of electron-phonon interaction. The electron propagation can take place with or without an external bias. A perturbative approach is used in the theoretical framework of the Wigner function accounting for the continuous quantum dynamical evolution of the scattering process. The unperturbed Hamiltonian contains the one-dimensional potential profile and the external field, while the electron-phonon coupling potential is considered as the perturbation Hamiltonian. Computational results are presented for the case of an electron propagating (a) without applied forces, (b) through a region where a uniform electric field is applied, and (c) in a double-barrier potential in resonance conditions, due to the relevance of these physical cases for practical applications.

Effect of the nonparabolic mass on the electron confinement in arbitrarily shaped quantum wells.

A numerical technique for the calculation of electron eigenstates in one-dimensional potential profiles has been improved by including the nonparabolicity of electrons and the material dependence of effective mass in heterostructures. The method is demonstrated for GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells, showing its effectiveness and excellent agreement with experiment. It was found that the magnitude of the effective mass and the nonparabolicity have a significant influence on the confinement energy, especially for narrow wells.

Potential feedback in field-effect devices

One-dimensional potential profile inside the static induction transistors is analyzed. The potential profile rearranges itself due to negative feedback by a change in gate or drain voltage. The potential barrier shows a nonlinear variation with drain voltage and it tends toward nonexistence as the drain voltage increases, i.e., negative feedback reduces the barrier height. This negative feedback is an important factor in determining the barrier height, which in turn decides the static characteristics of the field-effect devices. Generalized curves of potential profile for field effect, static induction, and analog transistors are presented where secondary effects are neglected. This explains the vacuum-pentode- or vacuum-triode-type characteristics in the unipolar devices.