Resonant Zener tunneling in two-dimensional periodic photonic lattices

We study Zener tunneling in two-dimensional photonic lattices and derive, for the case of hexagonal symmetry, the generalized Landau-Zener-Majorana model describing resonant interaction between high-symmetry points of the photonic spectral bands. We demonstrate that this effect can be employed for the generation of Floquet-Bloch modes and verify the model by direct numerical simulations of the tunneling effect.     

Resonant tunneling,eigenvalue and energy band calculation for potential and periodic potential structures

Recursion formulae for the reflection and the transmission probability amplitudes and the eigenvalue equation for multistep potential structures are derived. Using the recursion relations, a dispersion equation for periodic potential structures is presented. Some numerical results for the transmission probability of a double barrier structure with scattering centers, the lifetime of the quasi-bound state in a single quantum well with an applied field, and the miniband of a periodic potential structure are presented.     

Resonant tunneling through double-barrier structures on graphene

Quantum resonant tunneling behaviors of double-barrier structures on graphene are investigated under the tightbinding approximation. The Klein tunneling and resonant tunneling are demonstrated for the quasiparticles with energy close to the Dirac points. The Klein tunneling vanishes by increasing the height of the potential barriers to more than 300 meV. The Dirac transport properties continuously change to the Schro¨dinger ones. It is found that the peaks of resonant tunneling approximate to the eigen-levels of graphene nanoribbons under appropriate boundary conditions. A comparison between the zigzag- and armchair-edge barriers is given.     

Resonant tunneling through double-barrier structures on grapheneResonant tunneling through double-barrier structures on grapheneResonant tunneling through double-barrier structures on grapheneResonant tunneling through double-barrier structures on graphene

Quantum resonant tunneling behaviors of double-barrier structures on graphene are investigated under the tight- binding approximation. The Klein tunneling and resonant tunneling are demonstrated for the quasiparticles with energy close to the Dirac points. The Klein tunneling vanishes by increasing the height of the potential barriers to more than 300 meV. The Dirac transport properties continuously change to the Schr6dinger ones. It is found that the peaks of resonant tunneling approximate to the eigen-levels of graphene nanoribbons under appropriate boundary conditions. A comparison between the zigzag- and armchair-edge barriers is given.     

Resonant electron tunneling in (111) GaAs/AlAs structures

Pseudopotential and scattering matrix methods are used to study the spectral details of the transmission of electrons as a function of the angle of incidence on a heterojunction in various structures based on (111) GaAs/AlAs. A simplified two-valley (Γ-L) model for describing the electronic states in such structures has been proposed and its parameters have been determined. The existence of quasilocalized “interfacial” states has been established. A formula has been found which well approximates the behavior of the scattering matrix elements near these resonances, and their decay times are estimated. Academician V. D. Kuznetsov Siberian Physicotechnical Institute at Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika No. 9, pp. 89–99, September, 1998.     

Resonant tunneling and confining phenomena in symmetrical rectangular triple-barrier structures with c-type deep wells

Theoretical study of resonant tunneling is carried out in rectangular triple-barrier structures with C-type deep wells. Analytical expressions for the transmission coefficient and the resonance conditions are derived. Transmission characteristics versus electron energy are investigated and it is shown analytically that the transmission spectrum is a Lorentzian in form near energies of resonance. It is confirmed that the resonance energy is almost equal to the eigenenergy of the double-well structure. Moreover, wave functions of an electron at the resonance level are examined and the confining phenomenon is studied.     

Resonant transmission in stop bands of acoustic waves in periodic structures

Acoustic resonant transmission (RT) phenomenon found in Bragg couplers made of alternatively high (H) and low (L) impedance materials is theoretically investigated. The existence of the RT within the Bragg stop bands is analytically demonstrated, along with the exact peak values expressed in closed form in terms of the coupler parameters. RT takes place either when the coupler is terminated with an L-layer and has its bottom surface free, or when it is terminated with an H-layer and the bottom clamped. Numerical results are given for the transmission and reflection rates in Bragg couplers made of tungsten and SiO(2) layers.     

Resonant tunneling in double barrier structures with GaAs and (InGa)As quantum wells

Resonant tunneling through an (AlGa)As/In_XGa_1−XAs/(AlGa)As double barrier structure has been observed. Three crystals with indium concentration x=0, x=0.08 and x=0.13 were grown. For x=0, GaAs wells, we investigated the variation in resonance voltage, i.e. voltage at peak current, between different diodes across a wafer. The resonance voltage exhibited a skew distribution which is interpreted as an effect of lateral alloy variation in the active layers and differences in contact resistance. For (InGa)Asv quantum wells we found a negative differential resistance at 77 K with a peak-to-valley ratio as large as 3:1. The resonance voltage decreased as the indium concentration x was increased. This is an effect of the position of the ground state which is lowered (due to smaller bandgap) compared to the Fermi level. At x=0.13 the ground state was found to be below the conduction band edge of the GaAs contact regions and therefore the ground state resonance was absent.     

Resonant tunneling GaAs/AlGaAs quantum well structures for p-i-n photovoltaic cells

This study is devoted to the development of resonant-tunneling structures of quantum wells implementing resonant matching of lower subbands of size quantization in an electric field of the p-i-n junction of photovoltaic elements. The method for controlling the lower subband position in quantum wells by introducing a series of the tunnel-transparent barriers into a quantum well is proposed. The possibility of varying the level position in deep quantum wells in a wide range up to the continuous spectrum is demonstrated on a grown model structure; in this case, agreement between calculated and experimental subband positions is achieved.     

Resonant tunneling field-effect transistors

We report an experimental project to incorporate double-barrier tunnel structures into three-terminal devices. These devices have the negative-differential-resistance (NDR) features of the double barrier, and the added flexibility of a third controlling electrode. One way to make such a device involves the series combination of a double-barrier tunnel structure with a field-effect transistor. We have realized this concept in two types of devices, using samples grown by metalorganic chemical vapor deposition. The devices consist of a GaAsAl_xGa_1−xAs double-barrier tunneling heterostructure, the current through which is controlled by either an integrated vertical field-effect transistor or a planar metal-semiconductor field effect transistor. The voltage location and peak-to-valley current ratio of the NDR present in the source-drain circuit can be modulated with gate voltage. Experimental results for four samples are presented.     

Resonant tunneling of electrons interacting with phonons

The effect of the electron-phonon interaction on resonant tunneling of electrons through a two-barrier nanostructure is investigated in the framework of a consistent quantum-mechanical model. The wave function is determined by solving the Schrödinger equation with correct boundary conditions in the semiclassical approximation in the electron-phonon interaction. The current calculated with the help of the wave function is averaged over the phonon subsystem with the help of the Bloch theorem. The analytic expressions derived for static and varying currents in a resonance tunnel diode taking into account the electron-phonon interaction formally coincide with the Mössbauer effect probability. In the adiabatic limit and for a strong electron-phonon interaction, the static current decreases in proportion to η, while the varying low-frequency current is proportional to η². The shape of the resonance curve becomes Gaussian with a width of τ _ph ^?1 . The fundamental result is that the properties inherent in coherent tunneling are preserved even in the limit η?1 (which is often regarded as incoherent). The most striking effect (analogous to the Mössbauer effect) is the conservation of a narrow Lorentzian resonance curve in the limit η?1, ω_ph?Γ. This means that even for η?1, the resonance current is due to coherent electrons (experiencing interference), but their fraction decreases in view of the electron-phonon interaction. It is concluded that the application of the rate equations and other approximate methods disregarding interference may lead to incorrect results. The expressions for the high-frequency and nonlinear responses are also derived. The quantum-mechanical regime is found to be less sensitive to the effect of phonons than the classical regime.     

Resonant tunneling properties of heterostructures

A general theory of resonance tunneling in planar structures, independent of the detailed form of the “well”, is developed. The transmission probability versus energy is Lorentzian, near each quasi-local level, with a width that is simply related to the lifetime for escape from the local state, the wave-packet transit time, and the dynamical response time. The charge-accumulation effect is estimated.     

Resonant tunneling through Andreev levels

We use a semiclassical approach for analyzing the tunneling transport through a normal conductor in contact with superconducting mirrors. Our analysis of the electron–hole propagation along semiclassical trajectories shows that resonant transmission through Andreev levels is possible resulting in an excess, low-energy quasiparticle contribution to the conductance. The excess conductance oscillates with the phase difference between the superconductors having maxima at odd multiples of π for temperatures much below the Thouless temperature.