Symmetric Double Barrier Research Articles

Spin-selected resonant tunneling through a magnetic-controlled diode

The spin resonant tunneling through a semiconductor double-barrier structure are investigated by solving static Schrödinger equations. In the case of symmetric double barriers, both spin-up and spin-down electrons show resonant tunneling, but the peaks appear at different magnetic field. This can be used to realize magnetic-controlled spin filter. We perform calculation of conductance and conclude that the conductance decreases by increasing the temperature. The results may shed light on the possibility of designing resonant-tunneling devices and spin selecting systems.

Frequency Dependence of Shot Noise in Resonant Diodes under Coherent Tunneling

The current spectral density and the Fano factor of a resonant diode are investigated as a function of frequency up to values just below the inverse of the transit time. We consider the case of coherent tunneling for a symmetric double barrier structure at voltages up to the first current peak at 77 K. At high frequencies the Fano factor is found to become suppressed systematically at a value of 0.25 independently of frequency. This suppression below 0.5 is an indication of coherent against sequential tunneling transport.

‘Tunable spin‐injection and magnetoconductance in a novel 2DEG‐ferromagnet structure’” [phys. stat. sol. (b) 241, No. 1, 222 (2004)

AbstractIn this reply, we agree with the comments from Papp et al. that a symmetric (S) double barrier induces only a weak spin‐polarization (P). But the main objective of us was to propose a practical arrangement to achieve a symmetric double barrier because P vanishes for any antisymmetric configuration. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Transit and Reflection Times for a Non-Symmetric Barrier and a Symmetric Double Barrier

Many calculations of transit and reflection times focus on symmetric barriers in which the dwell time equals the Larmor precession time. We show for a non-symmetric barrier that this is not generally true and that all the characteristic transmission and reflection times (except the phase time) are finite for all ranges of the incident momentum. We also verify these observations for a symmetric double barrier (except for the finiteness of the reflection time).

Current and spin torque in double tunnel barrier ferromagnet-superconductor- ferromagnet systems

We calculate the current and the spin-torque in small symmetric double tunnel barrier ferromagnet - superconductor - ferromagnet (F-S-F) systems. Spin-accumulation on the superconductor governs the transport properties when the spin-flip relaxation time is longer than the transport dwell time. In the elastic transport regime, it is demonstrated that the relative change in the current (spin-torque) for F-S-F systems equals the relative change in the current (spin-torque) for F-N-F systems upon changing the relative magnetization direction of the two ferromagnets. This differs from the results in the inelastic transport regime where spin-accumulation suppresses the superconducting gap and dramatically changes the magnetoresistance [S. Takahashi, H. Imamura, and S. Maekawa, Phys. Rev. Lett. 82, 3911 (1999)]. The experimental relevance of the elastic and inelastic transport regimes, respectively, as well as the reasons for the change in the transport properties are discussed.

Resonant Delay in Tunnelling through Smooth Double and Triple Barriers

The energy dependence of the delay time associated with tunnelling through smooth (symmetric) double and triple barriers is investigated. Sharp resonances in the delay are found to mirror resonances in the transmission rate. In the strong-localization limit, particles with off-resonant energies do not perceive the inner potential relief and tunnel through the given double, or triple, barrier in much the same way as they would tunnel through a simple, unstructured barrier. Verification of the derived relations through a high-precision numerical solution of the Schrodinger equation confirms the quality of the obtained expressions in wide energy ranges up to the barrier top.

Transmission through the Symmetrical Double Delta Barrier with a Rectangular Well in between

The solution of the Schrodinger equation is examined for the one-dimensional potential that is formed of a symmetrical double delta barrier with a rectangular well in between. The eigenfunctions and the eigenvalue conditions are obtained for the bound-state solutions. There is a possibility for a particle with infinitesimally small negative energy to be localized in the well. The transmission coefficient and the resonant tunnelling condition are derived from the unbound-state solutions. The well is shown to influence the transmission through the double delta barrier substantially. The conditions are determined under which a particle with infinitesimally small positive energy will tunnel resonantly through the double delta barrier. Moreover, the connection between the resonant tunnelling states and the bound states is discussed.

Influence of the barrier thickness on the noise performance of AlAs/GaAs/AlAs double barrier resonant tunneling diodes

The noise characteristics of symmetrical double barrier resonant tunneling structures were measured in two samples with a fixed well width of 50 Å and barrier thicknesses of LB=8 monolayer and 10 ML, respectively. The measurement was done in the frequency range of 1 Hz–100 kHz and temperature range of 77–300 K. The noise due to the excess current in the valley region, observed in both devices, was associated with defect assisted tunneling which is a two-step process: generation-recombination noise due to the trapping and detrapping mechanism, and 1/f noise due to the scattering by phonons. The current dependence of 1/f noise contribution was investigated in the resonant tunneling and valley regions. The frequency exponent of the 1/f noise component was found to vary between 0.9–1.1 for double barrier resonant tunneling diode (DBRTD) with LB=8 ML and 1.1–1.2 for DBRTD with LB=10 ML. This noise investigation implies that there is a difference in the physics governing the transport between DBRTD with LB=8 ML and DBRTD with LB=10 ML.

Resonance and reaction

We examine two thermal reaction rates which can be defined for a one-dimensional model of a reaction dominated by a transient resonance. One of the rates corresponds to thermally equilibrated reactants in the region preceding the symmetrical double barrier potential supporting the intermediate complex. The other rate corresponds to pre-reaction thermal equilibration extending over the intermediate species. One rate is found to be twice the other. Numerical and analytical arguments are given to reach this conclusion. This discussion leads to a restrictive condition in the application of a formula given previously (R. Lefebvre and N. Moiseyev, J. Chem. Phys., 93 (1990) 7173) to relate the rate in the tunnelling regime to the set of artificial resonances produced by box quantization.

Realizing a completed‐resonant level by using an asymmetrical triple‐barrier structure

AbstractBecause of the rapid development of quantum effect devices, it is necessary to obtain a synthesis method which can give the expected quantum effect symptoms. Using a triple‐barrier structure, quantum effects which cannot be obtained with a double‐bather structure can be realized. However, only a few studies have been made on the triple‐bather structure, in particular, on the asymmetric triple‐bather structure.In this paper, based on the circuit theoiy, the syn thesis method of an asymmetrical triple‐barrier structure where a single perfect resonant level is formed in its quantum well is proposed. It is assumed that an original symmetrical double‐barrier structure has a first resonant level E1 and a second resonant level E2 whose resonant energy is four times higher than that of E1. One of the single barriers is replaced by another symmetrical double barrier with the first resonant level equal to the second resonant level E2 of the original one.In the nonsymmetrical triple‐barrier structure formed by the forementioned method, the transmission probability at E1 is 1 and that at higher‐energy levels is sufficiently low. This synthesis can be achieved by using the power reflection coefficient and the Smith chart of a complex equivalent circuit. the validity of this method can be established by means of the Smith chart. By carrying out a numerical calculation on the electron transmission characteristic of the synthesized nensymmetrical triple barrier, it was confirmed that the transmission probability at the energy level that is four times higher than E1 can be around 0.1.

Type II narrow double barrier quantum well structures : Γ-X coupling and interface effects

Photoluminescence (PL), PL excitation and time resolved PL experiments have been performed on Al 0.42 Ga 0.58 As/AlAs/GaAs symmetric double barrier quantum wells (DBQW) with only one or two AlAs monolayers constituting the intermediate barriers. In agreement with the envelope function predictions we show that such DBQW's undergo a type I-type II transition when the GaAs thickness is reduced below 7 and 5 monolayers for 2 and 1 AlAs molecular planes respectively. In type II configuration the PL decay time is found to be strongly dependent on the energy difference between AlAs X z - and gaAs Γ-electron confined states and the coupling parameter of the Γ and X z valleys can be reduced (4.2 meV on average). Similar experiments on DBQW's grown on 2 o off (001) vicinal surfaces show that the excition lifetime remains close to that of nominal samples. It is concluded that the Γ-X mixing potential in quantum structures is intrinsically linked to the ALAs/GaAs interface

Characteristic times for resonant tunneling through double barrier heterostructures

Time dependent resonant tunneling of electron wave packets scattered through symmetric and asymmetric double barrier heterostructures under an external electric field is studied by systematically varying the barrier lengths. The different times involved, the charging time, the dwell time, the life time and passage time by transmission, are examined and grouped according to their qualitative behaviour against the barrier widths. It is found that the life time and dwell time are not always proportional.

Effect of Γ–X mixing on electron tunneling times in GaAs/AlAs double barrier heterostructures

The effect of Γ–X mixing on electron tunneling time in GaAs/AlAs symmetric double barrier heterostructures is studied theoretically using an empirical tight-binding band structure model. It is found that the Γ quasibound state tunneling times can be shortened or lengthened by Γ–X mixing, depending on whether the AlAs barriers consist of an even or odd number of monolayers. This is attributed to the interference between the Γ and X conduction channels in the AlAs barriers.

Zero dimensional resonant tunneling through single donor states

We have observed remarkable new structure in the source-drain I(V) characteristics of a symmetric double barrier resonant tunneling device in which the cross sectional area may be varied from ≅ 1μm 2 to ≅0.1 μm 2 by applying a voltage to a gate. In the source-drain voltage range close to, but slightly below, the threshold for current flow, peaks are observed with a peak value of ≅ 20 pA, and peak/valley ratio up to 10 1 . The structure in I(V) is independent of temperature between 35 mK and 10 K, and of gate voltage between 0 and −2 V. The first peak in I(V) in each polarity is unaffected by a magnetic field applied parallel to the current flow for fields up to 6 T. This structure cannot be explained by lateral quantisation or Coulomb blockade arising from the confinement. We propose that it is due to resonant tunneling between zero-dimensional states formed in the active region by the Coulombic potential of a single ionised donor, combined with the barrier potential.

The quantum traversal times of Nassar and of Jonson

The completely different approaches of Nassar and of Jonson lead to identical expressions for the quantum traversal time. Their result is applied to resonant tunneling through a symmetric double rectangular barrier exactly on resonance, a special case for which the correct result is known, and found to seriously underestimate the average time that the particle is trapped in the quantum well.

Tunneling through highly transparent symmetric double barriers

We consider the tunneling through double barriers with different heights for the outer and inner edges. This difference affects the transmission coefficient, which under some conditions has non-Lorentzian behavior (absence of resonant tunneling), showing monotonic changes and a very weak dependence on energy.

Sequential versus coherent tunneling through double barrier diodes investigated by calibrated measurement of charge accumulation

We use differential absorption spectroscopy to get absolute values for the accumulated charge Q and transit time τ in symmetric and asymmetric double barrier diodes. We show that Q and τ are nearly constant between 10K to 300K. We also measure the dependence of τ on the bias voltage in an asymmetric structure and find a monotonic decrease as the voltage increases. We discuss these observations in the context of coherent and sequential models of tunneling.

The (InGa)As-(InAl)As resonant tunnelling double barrier structure subjected to a transverse magnetic field

Magneto-tunnelling ( B· J) is investigated in a symmetric double barrier resonant tunnelling device based on (InGa)As-(InAl)As. The effects of the Γ conduction band non-parabolicity are observed through the appearance of terms proportional to B 3 and B 4 in the dependence of Vp, the voltage at the current peak position of the I–V characteristics, on the magnetic field. A theoretical analysis considering pertubation theory and a simplified form of the formalism developed by Ekenberg [Phys. Rev. B40 , 7714(1989)] is done which is in qualitative agreement with the experimental results.

Quasi-ballistic resonant tunneling of minority electrons into the excited states of a quantum well

Observation of energy-dependent transmission of nonequilibrium minority electrons through a symmetric double-barrier (DB) quantum well heterostructure is reported. The DB is placed in the base of a GaInAs/AlInAs bipolar transistor. The electrons are launched into the DB with variable kinetic energies using a tunnel barrier in the emitter and varying the emitter-base voltage. The resulting peak in the collector current provides for the first time evidence of quasi-ballistic resonant tunneling of minority carriers into the eigenstates of a quantum well. The small peak-to-valley ratio and the broad peak also demonstrate the importance of scattering and of the anisotropy in momentum space of the incident distribution function in the region between the ballistic electron launcher and the DB.

Tunneling times for wave packets narrow in wave-number space

The tunneling times for wave packets narrow in k-space are considered for an arbitrary, localized potential barrier in one dimension. To zeroth order the classic phase times are rederived. Corrections are briefly discussed. An identity between the dwell time and the phase times is presented. Finally, we give an exact expression for the transmission time at resonance for a symmetric double barrier.