Airy Wave Functions Research Articles

Modeling of Spin-Polarized Currents in Zinc Blende-based Magnetic Tunnel Junctions Featuring the Dresselhaus Effect

In this study, the spin-polarized currents in a magnetic tunnel junction (MTJ) with a Fe/GaAs/Fe structure were calculated by considering the Dresselhaus effect. The spin-polarized current was calculated using the Airy wavefunction approach and then compared to the transfer matrix method (TMM) to check the accuracy. It was shown that the total spin-polarized current density evaluated via the Airy-wavefunction approach matches that obtained with the TMM. It was also shown that the current density increases as the barrier width decreases. In addition, the temperature and the incident angle of the electrons affect the current density, where the maximum current density is obtained when the electrons come in a direction perpendicular to the barrier. We herein determined analytically that a high device performance of the MTJ could be achieved by simply controlling the device parameters of barrier width, temperature and incident angle of the electron.

On the role of interactions in trans-sonically flowing atomic condensates (a) (a)Contribution to the Focus Issue Turbulent Regimes in Bose-Einstein Condensates edited by Alessandra Lanotte, Iacopo Carusotto and Alberto Bramati.

We provide a joint numerical-analytical study of the physics of a flowing atomic Bose-Einstein condensate in the combined presence of an external trap and a step potential which accelerates the atoms out of the condensate creating a pair of neighbouring black- and white-hole horizons. In particular, we focus on the rapidly growing density modulation pattern that appears in the supersonic region, an experimentally observed feature that was related to black-hole lasing phenomena. A direct assessment of the role of interactions in this process suggests an interpretation of the experimental data in terms of linear interference of atomic waves rather than collective effects. Our conclusions are further supported by an analytical solution of the Schrödinger equation in terms of Airy wave functions.

Modeling of electron transmittance in magnetic tunnel junctions

Abstract In this paper, we have calculated an electron transmittance through Fe/GaAs/Fe in a magnetic tunnel junction (MTJ). The transmittance was computed by using the Airy wavefunction approach by considering the Dresselhaus effect. The calculated result shows that the electron transmittance for each spin state is different. The incident angle affects electron transmittance and electron polarization. It was also shown that electron polarization is also affected by the energy of the electron and the barrier width. Besides, the electron transmittance is quasisymmetric to the incident angle.

A new approach to solve the one-dimensional Schrödinger equation using a wavefunction potential

A new approach to find exact solutions to one–dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions having vanishing and non–vanishing Bohm potentials. For most of the potentials, no solutions to the Schrödinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some quantum, such as accelerated Airy wavefunctions, are due to the presence of non–vanishing Bohm potentials. New examples of this kind are found and discussed.

Electron Spin-Dependent Tunneling Current through a Trapezoidal Potential Barrier under Airy Wavefunction Approach

In this paper, an analytical expression of the electron spin-dependent tunneling current through a potential barrier by applying a bias voltage was investigated. An Airy wavefunction was applied to derive the transmittance through the barrier by considering a zinc-blende material, which depends on the spin states indicated as ‘up’ and ‘down’. The obtained transmittance was employed to compute the polarization and spin-dependent tunneling current. The spin-dependent tunneling current was then observed at various bias voltages and temperatures. It was shown that the spin-polarized current increases as the bias voltage increases. It was also shown that the increase of temperature enhances the spin-dependent tunneling current.

Modeling of Electron Transmittance and Tunneling Current through a Trapezoidal Potential Barrier by Considering the Spin Polarization Effect

A modeling of the transmittance and tunneling current through a trapezoidal potential barrier was developed by taking into account the spin polarization of the electrons. The transmittance was calculated by using an Airy wavefunction approach and employing a zinc-blende material for the barrier in the heterostructure, which depends on the spin states indicated as ‘up’ and ‘down’. The obtained transmittance was then used to calculate the tunneling current by using the Gauss-Laguerre quadrature method. It was shown that the transmittance is not symmetric with the incident angle of the electron. It was also shown that the tunneling current increases with increasing the bias voltage and tends to be constant in a high voltage regime.

Transmittance and Tunneling Current through a Trapezoidal Barrier under Spin Polarization Consideration

The transmittance and tunneling current in heterostructures under spin polarization consideration were studied by employing a zinc-blended structure for the heterostructures. An electron tunnels through a potential barrier by applying a bias voltage to the barrier, which is called the trapezoidal potential barrier. In order to study the transmittance, an Airy wave function approach was employed to find the transmittance. The obtained transmittance was then utilized to compute the tunneling current by using a Gauss quadrature method. It was shown that the transmittances were asymmetric with the incident angle of the electron. It was also shown that the tunneling currents increased as the bias voltage increased.

Comparison of Electron Direct Transmittance and Tunneling Time of Si (100)/HfO2/Si (100) and Si (110)/HfO2/Si (110) Structures with Ultra-thin Trapezoidal Barrier

An analytical expression of electron direct transmittance and tunneling time through a nanometer-thick trapezoidal potential barrier have been derived by using a phase-time method with Airy wavefunction solution. The expression is applied to Si(100)/HfO2/Si(100) (isotropic) and Si(110)/HfO2/Si(110) (anisotropic) structures calculated under the consideration of barrier width, incident energy, incident angle, and bias voltage. The calculated results are discussed and comparisons between the isotropic and anisotropic heterostructures are discussed.

Airy-Tricomi-Gaussian compressed light bullets

Exact solution of the (3+1)D Schrodinger-type equation without external potential is obtained in cylindrical coordinates by using the method of separation of variables. Linear compressed light bullets are constructed with the help of a superposition of two counter-accelerating finite Airy wave functions and the Tricomi-Gaussian polynomials. We present some typical examples of the obtained solutions on the basis of four parameters: radial nodes, azimuthal nodes, the decay factor and the modulation depth. We find that the wave packets display different patterns and demonstrate that such linear light bullets can retain their shape over several Rayleigh lengths during propagation.

Dual accelerating Airy-Talbot recurrence effect.

We demonstrate the dual accelerating Airy-Talbot recurrence effect, i.e., the self-imaging of accelerating optical beams, by propagating a superposition of Airy beams with successively changing transverse displacements. The dual Airy-Talbot effect is a spontaneous recurring imaging of the input and of the input with alternating component signs. It results from the constructive interference of Airy wave functions, which is also responsible for other kinds of Airy beams, for example, Airy breathers. An input composed of finite-energy Airy beams also displays the dual Airy-Talbot effect, but it demands a large transverse displacement and diminishes fast along the propagation direction.

Three-dimensional localized Airy-Laguerre-Gaussian wave packets in free space.

We demonstrate three-dimensional (3D) Airy-Laguerre-Gaussian localized wave packets in free space. An exact solution of the (3 + 1)D potential-free Schrödinger equation is obtained by using the method of separation of variables. Linear compressed wave pulses are constructed with the help of a superposition of two counter-accelerating finite energy Airy wave functions and the generalized Laguerre-Gaussian polynomials in cylindrical coordinates. Such wave packets do not accelerate and can retain their structure over several Rayleigh lengths during propagation. The generation, control, and manipulation of the linear but localized wave packets described here is affected by four parameters: the decay factor, the radial mode number, the azimuthal mode number and the modulation depth.

Propagation Dynamics of Airy Water-Wave Pulses.

We observe the propagation dynamics of surface gravity water waves, having an Airy function envelope, in both the linear and the nonlinear regimes. In the linear regime, the shape of the envelope is preserved while propagating in an 18-m water tank, despite the inherent dispersion of the wave packet. The Airy wave function can propagate at a velocity that is slower (or faster if the Airy envelope is inverted) than the group velocity. Furthermore, the introduction of the Airy wave packet as surface water waves enables the observation of its position-dependent chirp and cubic-phase offset, predicted more than 35years ago, for the first time. When increasing the envelope of the input Airy pulse, nonlinear effects become dominant, and are manifested by the generation of water-wave solitons.

On the asymptotic evolution of finite energy Airy wave functions.

In general, there is an inverse relation between the degree of localization of a wave function of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is varied. One consequence of this is that the far-field diffraction rate of a finite energy Airy beam decreases as the beam localization at the launch plane increases. We analyze the asymptotic properties of finite energy Airy wave functions using the stationary phase method. We obtain one dominant contribution to the long-term evolution that admits a Gaussian-like approximation, which displays the expected reduction of its broadening rate as the input localization is increased.

Conductive-AFM topography and current maps simulator for the study of polycrystalline high-k dielectrics

In this work, a simulator of conductive atomic force microscopy (C-AFM) was developed to reproduce topography and current maps. In order to test the results, the authors used the simulator to investigate the influence of the C-AFM tip on topography measurements of polycrystalline high-k dielectrics, and compared the results with experimental data. The results show that this tool can produce topography images with the same morphological characteristics as the experimental samples under study. Additionally, the current at each location of the dielectric stack was calculated. The quantum mechanical transmission coefficient and tunneling current were obtained from the band diagram by applying the Airy wavefunction approach. Good agreement between experimental and simulation results indicates that the tool can be very useful for evaluating how the experimental parameters influence C-AFM measurements.

Effect of Thickness and Temperature of SiO2 Layer on Leakage Currents in MOS Capacitor Materials with High Dielectric Constant by Involving the Charge Trap

Modeling of the leakage current in a field-effect transistor metal-oxide-semiconductor (MOSFET) with high dielectric material has been developed by taking into account the effect of charge traps formed at the interface of high-k material/SiO2. Transmittance calculated using Airy wave function approach and involving the anisotropic electron mass and the effect of coupling between transverse and longitudinal energy represented by the speed of the electrons in the metal gate. Transmittance obtained is then used to calculate the leakage current in the structure of n+Poly-Si/HfSiOxN/trap/SiO2/p-Si for oxide voltage variations, temperature, and thickness of the SiO2. From the calculation that the leakage current decreases with decreasing of oxide voltage and increasing of the thickness of the oxide layer of SiO2. Also obtained that the temperature of the device does not give a great influence on the change of leakage current. Keywords: Leakage current, electron speed, charge traps

Comparison of electron transmittances and tunneling currents in an anisotropic TiNx/HfO2/SiO2/p-Si(100) metal—oxide—semiconductor (MOS) capacitor calculated using exponential- and Airy-wavefunction approaches and a transfer matrix method

Analytical expressions of electron transmittance and tunneling current in an anisotropic TiNx/HfO2/SiO2/p-Si(100) metal—oxide—semiconductor (MOS) capacitor were derived by considering the coupling of transverse and longitudinal energies of an electron. Exponential and Airy wavefunctions were utilized to obtain the electron transmittance and the electron tunneling current. A transfer matrix method, as a numerical approach, was used as a benchmark to assess the analytical approaches. It was found that there is a similarity in the transmittances calculated among exponential- and Airy-wavefunction approaches and the TMM at low electron energies. However, for high energies, only the transmittance calculated by using the Airy-wavefunction approach is the same as that evaluated by the TMM. It was also found that only the tunneling currents calculated by using the Airy-wavefunction approach are the same as those obtained under the TMM for all range of oxide voltages. Therefore, a better analytical description for the tunneling phenomenon in the MOS capacitor is given by the Airy-wavefunction approach. Moreover, the tunneling current density decreases as the titanium concentration of the TiNx metal gate increases because the electron effective mass of TiNx decreases with increasing nitrogen concentration. In addition, the mass anisotropy cannot be neglected because the tunneling currents obtained under the isotropic and anisotropic masses are very different.

Dual Airy beam

We derive a general form of Airy wave function which satisfies paraxial equation of diffraction. Based on this, we propose a new form of Airy beam, which is composed of two symmetrical Airy beams which accelerate mutually in the opposite directions. This 'dual' Airy beam shows several distinguishing features: it has a symmetric transverse intensity pattern and improved self-regeneration property. In addition, we can easily control the propagation direction. We also propose 'quad' Airy beam, which forms a rectangular shaped optical array of narrow beams that travel along a straight line. We can control its propagation direction without changing transverse intensity patterns. These kinds of superposed optical beams are expected to be useful for various applications with their unique properties.

Thermal Performance of a Functionally Graded Radial Fin

This paper investigates the steady-state thermal performance of a radial fin of rectangular profile made of a functionally graded material. The thermal conductivity of the fin varies continuously in the radial direction following a power law. The boundary conditions of a constant base temperature and an insulated tip are assumed. Analytical solutions for the temperature distribution, heat transfer rate, fin efficiency, and fin effectiveness are found in terms of Airy wave functions, modified Bessel functions, hyperbolic functions, or power functions depending on the exponent of the power law. Numerical results illustrating the effect of the radial dependence of the thermal conductivity on the performance of the fin are presented and discussed. It is found that the heat transfer rate, the fin efficiency, and the fin effectiveness are highest when the thermal conductivity of the fin varies inversely with the square of the radius. These quantities, however, decrease as the exponent of the power law increases. The results of the exact solutions are compared with a solution derived by using a spatially averaged thermal conductivity. Because large errors can occur in some cases, the use of a spatially averaged thermal-conductivity model is not recommended.

Noncommuting limits of oscillator wave functions

Quantum harmonic oscillators with spring constants k > 0 plus constant forces f exhibit rescaled and displaced Hermite—Gaussian wave functions, and discrete, lower bound spectra. We examine their limits when (k, f) → (0, 0) along two different paths. When f → 0 and then k → 0, the contraction is standard: the system becomes free with a double continuous, positive spectrum, and the wave functions limit to plane waves of definite parity. On the other hand, when k → 0 first, the contraction path passes through the free-fall system, with a continuous, nondegenerate, unbounded spectrum and displaced Airy wave functions, while parity is lost. The subsequent f → 0 limit of the nonstandard path shows the dc hysteresis phenomenon of noncommuting contractions: the lost parity reappears as an infinitely oscillating superposition of the two limiting solutions that are related by the symmetry.