Symmetric Double Barrier Research Articles

Double barrier structure of Mo/AlN/Mo/AlN/Mo multilayer and its resonant tunneling effect

We prepare a symmetrical double barrier structure of Mo/AlN/Mo/AlN/Mo by using the reactive magnetron sputtering on a sapphire substrate and examine its resonant tunneling effect. Characterizations of multilayers demonstrate that the AlN (0002) aligns well along the Mo (110). Direct current-voltage (DC I–V) test finds significant negative differential resistance at room temperature around 0.7 and 0.9 V carrier energy and with peak-to-valley current ratios of about 1.1 and 1.2. The simulation using conventional transfer matrix method suggests good consistence between the designed structure, the quantized energy level and the switching voltage. The large signal DC model also fits the experimental I–V properties. Our work provides a new type of resonant tunneling device in room temperature.

The discussion of the transmission coefficient of one-dimensional double barrier

Quantum theory plays a significant part in the modern physics and makes modern technology rapidly developed. Quantum tunnel effect is one of the most important discoveries. The exact expression of potential barrier is tough to derive, even for the double barrier. Many researchers have analysed the applications of quantum tunnel effect in real electronic devices. However, the exact expression of double barriers transmission coefficient was discussed rarely. In this article, the exact expression of the transmission coefficient will be given and the effect of parameters of barrier such as the width and the height will be discussed. In addition, the difference between symmetric and asymmetric double barrier will be given. This paper has the discussion of the transmission coefficient in order to not only give a clear understanding of the effect of parameters of double barrier to tyro and researchers, but also give a simpler way to consider the periodic barrier.

Resonant tunneling of electrons in biased symmetric triangular double barrier nanostructure triodes

The present work investigates the resonant tunneling of electrons in symmetric triangular double barrier triodes composed of GaAs-Ga1-yAlyAs nanostructures under a step bias voltage. This work employs the complex energy method to compute the resonant tunneling energy and the associated lifetimes. In the mathematical analysis of this work, the matching conditions are taken at specific points on both lateral sides of the triangular barrier. Results showed decreasing the resonant tunneling energies for both the lowest and excited states by applying step bias voltage and disappearing the lowest energy states at a specific applied bias voltage. The resonant tunneling lifetimes of the present structure exhibited nearly constant behavior at constant values of both well half-width and barrier half-thickness although the enhancement of the bias voltage. Moreover, the lifetimes of both the lowest and the first excited states increased nearly non-linearly by increasing the aluminum concentration, with the enhancement of the lowest resonant lifetimes over those values associated with the first excited states. The results showed considerable agreement with the data published in the literature for both magnitude and tendency. The present work highlights the importance of employing the mass-mismatch condition in studying heterostructures. It is found from the present study that resonant tunneling energies and their related lifetimes are more affected by the variations of the aluminum concentration in the barrier region, barrier thickness, and well width, which can be adjusted to improve the performance of the resonant tunneling triangular triodes and other nanostructure devices.

The resonant condition of transmission in the graphene-based double-barrier structures

The Klein tunneling of Dirac fermions through a symmetric double potential barrier of a rectangular shape in graphene has been investigated. A new analytical formula for a dependence of the transmission coefficient of electrons on the angle of incidence on the barrier was obtained, on the basis of which the conditions for the angles of incidence with 100% transmission were found. In the case of a double potential barrier we have three conditions for resonance tunneling, two of which are similar to those conditions for one barrier, and the third one reflects the presence of the second barrier.

Klein Tunneling through Double Barrier in ABC‐Trilayer Graphene

AbstractKlein tunneling and conductance for Dirac fermions in ABC‐stacked trilayer graphene through symmetric and asymmetric double potential barrier are investigated. This was done by using the continuum model of two and six‐bands. The numerical results show that the transport is sensitive to the height, the width, and the distance between the two barriers. It is found that the Klein paradox at normal incidence () and resonant features at in the transmission result from resonant electron states in the wells or hole states in the barriers. It is shown that such features strongly influence the ballistic conductance of the structures.

Wormhole potentials and throats from quasi-normal modes

Exotic compact objects refer to a wide class of black hole alternatives or effective models to describe phenomenologically quantum gravitational effects on the horizon scale. In this work we show how the knowledge of the quasi-normal mode spectrum of non-rotating wormhole models can be used to reconstruct the effective potential that appears in perturbation equations. From this it is further possible to obtain the parameters that characterize the specific wormhole model, which in this paper was chosen to be the one by Damour and Solodukhin. We also address the question whether one can distinguish such type of wormholes from ultra compact stars, if only the quasi-normal mode spectrum is known. We have proven that this is not possible by using the trapped modes only, but requires additional information.The inverse method presented here is an extension of work that has previously been developed and applied to the oscillation spectra of ultra compact stars and gravastars. However, it is not limited to the study of exotic compact objects, but applicable to symmetric double barrier potentials that appear in one-dimensional wave equations. Therefore we think it can be of interest for other fields too.

Transmitting Coefficient and Quasi-Stationary States of Electron in Symmetric Double-Barrier Nanostructure with Position-Dependent Potential and Effective Mass

Transmitting Coefficient and Quasi-Stationary States of Electron in Symmetric Double-Barrier Nanostructure with Position-Dependent Potential and Effective Mass

Transmission singularities in resonant electron tunneling through double complex potential barrier

Tunneling of electrons through a barrier with complex potential is investigated. We focus on two cases, symmetric double rectangular barrier and double delta potential barrier, and give expressions for resonant transmission probability for both cases. Expressions for reflection amplitude and absorption are also obtained in the case of delta potential. It will be shown that for given incident particle energy, parameters of the potential structure can be obtained so that the resonant transmission probability approaches infinity. The phenomenon of infinite transmission occurs only for potentials which have positive imaginary part.

Dark soliton scattering in symmetric and asymmetric double potential barriers

Motivated by the recent theoretical study of (bright) soliton diode effects in systems with multiple scatterers, as well as by experimental investigations of soliton-impurity interactions, we consider some prototypical case examples of interactions of dark solitons with a pair of scatterers. In a way fundamentally opposite to the case of bright solitons (but consonant to their “anti-particle character”), we find that dark solitons accelerate as they pass the first barrier and hence cannot be trapped by a second equal-height barrier. A pair of unequal barriers may lead to reflection from the second one, however trapping in the inter-barrier region cannot occur. We also give some examples of dynamical adjusting of the barriers to trap the dark soliton in the inter-barrier region, yet we show that this can only occur over finite time horizons, with the dark soliton always escaping eventually, contrary again to what is potentially the case with bright solitons.

Band tunneling through double barrier in biased graphene bilayer

We calculate the transport properties of charge carriers in graphene bilayers across symmetric and asymmetric double potential barrier considering energies exceeding the inter-layer coupling where two transport modes exist. Evaluating the transmission and reflection probabilities and corresponding conductances, we show that the transport is sensitive to the distance between the two barriers. Moreover, we explain the characteristic features observed in the numerical calculations, such as resonance tunneling at normal incidence, based on the Febry–Pèrot oscillations and ballistic transmission carried out by the evanescent waves. Finally, we compute the conductance of each mode separately and investigate contributions from inter-mode scattering and show that some geometric potential parameters can be used to control the total conductance of the system.

Dark soliton scattering in symmetric and asymmetric double potential barriers

Dark soliton scattering in symmetric and asymmetric double potential barriers

Tunable dwell time in gated silicene nanostructures

Residing on the gate-tunable electronic properties of silicene, we have systematically examined the dwell time for quantum tunneling through the single and multiple-gated silicene nanostructures. It is shown that unlike the graphene, superluminal tunneling is observable even at the normal incidence due to the sizeable spin–orbit gap of silicene. Together with its field-tunable bandgap, we show that this superluminal tunneling can be further flexibly switched on and off via electric mean. By simulating the dwell time through the symmetric and asymmetric double barrier structures, it is also shown here that the dwell time displays the distinct dependence on the former and latter barrier profiles. Those observations provide some favorable strategies to experimentally examine and fundamentally understand the time-dependent aspect of tunneling in solid state nanosystems.

Phonon tunneling through a double barrier system

The tunneling of optical and acoustic phonons at normal incidence on a double-barrier is studied in this paper. Transmission coefficients and resonance conditions are derived theoretically under the assumption that the long-wavelength approximation is valid. It is shown that the behavior of the transmission coefficients for the symmetric double barrier has a Lorentzian form close to resonant frequencies and that Breit–Wigner's formula have a general validity in one-dimensional phonon tunneling. Authors also study the so-called generalized Hartman effect in the tunneling of long-wavelength phonons and show that this effect is a numerical artifact resulting from taking the opaque limit before exploring the variation with a finite barrier width. This study could be useful for the design of acoustic devices.

Effect of Dimension & Material Composition on Transmission Coefficient and Tunneling Current of Double Quantum Barrier Structure with Band Nonparabolicity

Transmission coefficient, eigen states and tunneling current density of a potentially symmetric quantum double barrier structure has been numerically computed using transfer matrix technique for qualitative analysis of resonant tunneling probability when realistic band structure of higher band gap material is taken into account. GaAs/AlxGa1-xAs material composition is taken as an example for calculation, and thickness of the barrier and well regions are varied along with material compositions of AlxGa1-xAs to study the effect on electrical parameters; and also to observe the existence of quasi-bound states. Effective mass mismatch at junctions is considered following envelope function approximation, and conduction band discontinuity is taken into account for computational purpose. Under low biasing condition, negative differential regions (NDR) can be obtained which speaks in favor of tunneling current.

Line-type resonance peaks and their suppression through graphene-based symmetric and asymmetric double barriers

Resonant tunneling through symmetric and asymmetric double barriers based on monolayer graphene at non-normal incidence is investigated. Due to the evanescent modes inside the barrier, the transmission, as a function of the incident energy, has a gap which can be tuned by the height of the barrier and the incident angle of the electrons. In terms of the coupling between the barriers and the well in the symmetric double barriers, several line-type resonance peaks with a unity value appear in the transmission gap, and the number of the resonance peaks is closely related to the incident angle, the height, and the width of the barrier. The resonant conditions in the transmission gap are derived and discussed. However, the line-type resonance peaks are greatly suppressed through the asymmetric double barriers. The authors demonstrate that line-type peaks possess potential applications in resonant tunneling devices and energy filters.

Salecker-Wigner-Peres clock and double-barrier tunneling

In this work we revisit the Salecker-Wigner-Peres clock formalism and show that it can be directly applied to the phenomenon of tunneling. Then we apply this formalism to the determination of the tunneling time of a non relativistic wavepacket, sharply concentrated around a tunneling energy, incident on a symmetric double barrier potential. In order to deepen the discussion about the generalized Hartmann effect, we consider the case in which the clock runs only when the particle can be found inside the region \emph{between} the barriers and show that, whenever the probability to find the particle in this region is non negligible, the corresponding time (which in this case turns out to be a dwell time) increases with the barrier spacing.

Quasi-bound states induced by one-dimensional potentials in graphene

We suggest a simple approach for studying the quasi-bound fermion states induced by one-dimensional potentials in graphene. Detailed calculations have been performed for symmetric double barrier structures and $n\text{\ensuremath{-}}p\text{\ensuremath{-}}n$ junctions. Besides the crucial role of the transverse motion of carriers, we systematically examine the influence of different structure parameters such as the barrier width in double barrier structures or the potential slope in $n\text{\ensuremath{-}}p\text{\ensuremath{-}}n$ junctions on the energy spectrum and, especially, on the resonant-level width and, therefore, the localization of quasi-bound states.

Spin orientation and spin-Hall effect induced by tunneling electrons

It is shown that a flux of unpolarized electrons across a symmetric double barrier quantum well induces a spin polarization inside the well. Besides, the transmitted current acquires a spin polarized component and the spin-Hall current flows in the planar direction. These phenomena are due to a combined effect of Dresselhaus interaction and the spin-orbit interaction induced by gradients of heterostructure material parameters. In contrast to previous studies of the spin filtering effect, we predict that it can be observed in the case of an isotropic distribution of incident electrons.

The effect of transverse wave vector and magnetic fields on resonant tunneling times in double-barrier structures

The effect of transverse wave vector and magnetic fields on resonant tunneling times in double-barrier structures, which is significant but has been frequently omitted in previous theoretical methods, has been reported in this paper. The analytical expressions of the longitudinal energies of quasibound levels (LEQBL) and the lifetimes of quasibound levels (LQBL) in symmetrical double-barrier (SDB) structures have been derived as a function of transverse wave vector and longitudinal magnetic fields perpendicular to interfaces. Based on our derived analytical expressions, the LEQBL and LQBL dependence upon transverse wave vector and longitudinal magnetic fields has been explored numerically for a SDB structure. Model calculations show that the LEQBL decrease monotonically and the LQBL shorten with increasing transverse wave vector, and each original LEQBL splits to a series of sub-LEQBL which shift nearly linearly toward the well bottom and the lifetimes of quasibound level series (LQBLS) shorten with increasing Landau-level indices and magnetic fields.

Time-resolved spin filtering in semiconductor symmetric resonant barrier structures

Spin-dependent tunneling in semiconductor symmetric double barrier structures is studied theoretically. Our calculation is based on the effective one-band Hamiltonian and Dresselhaus spin-orbit coupling. We demonstrate that the ratio of the tunneling times of electrons with opposite spin orientations can vary over a few orders in magnitude. The large and tunable ratio of the tunneling times can serve as the basis in the development of all-semiconductor dynamic spin filters.