Asymmetric Double-barrier Structures Research Articles

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.

Electron transmission in symmetric and asymmetric double-barrier structures controlled by laser fields

The potential profiles of symmetric and asymmetric rectangular double-barrier structures made of (Ga, Al)As/GaAs and the transmission coefficient of an electron in these systems have been investigated under intense laser field. The results show that the field alters the potential profile, and the transmission coefficient can thus be controlled. The transmission at the first resonance energy for the symmetric structure is higher than that of the asymmetric structure. Therefore, the symmetric design is feasible. The properties exhibited in this work may establish guidance to device applications.

Splitting of the resonance levels of double-barrier structures in a high microwave electric field

The dependence of the width and shape of the resonance levels of asymmetric double-barrier resonance-tunneling structures with high narrow barriers on the amplitude of the resonance microwave field and specific features of the electron transport in the case of ballistic passage of electrons near the resonance levels has been investigated. It has been found that a resonance level can be first broadened significantly and be further split into two absolutely transparent levels with an increase in the microwave field amplitude. The conditions have been formulated under which nonresonance scattering channels near the resonance levels also become absolutely transparent.

Tunneling resonances in quantum dots: Coulomb interaction modifies the width

Single-electron tunneling through a zero-dimensional state in an asymmetric double-barrier resonant-tunneling structure is studied. The broadening of steps in the $I$--$V$ characteristics is found to strongly depend on the polarity of the applied bias voltage. Based on a qualitative picture for the finite-life-time broadening of the quantum dot states and a quantitative comparison of the experimental data with a non-equilibrium transport theory, we identify this polarity dependence as a clear signature of Coulomb interaction.

Resonant Tunneling Transmission Characteristics and Tunneling Time in Asymmetrical Double-Barrier Structures with Multiple Prewells

Resonant tunneling phenomenon in the asymmetrical double-barrier structures with multiple prewells is studied theoretically. First, analytical expressions for the tunneling transmission coefficient and the resonance condition are derived. Second, analytical expressions for the dwell time and for the shortest dwell time condition are obtained. It is found that the dwell time in the main well region decreases greatly with increasing number of prewells, and that there exists an optimum number of prewells which makes the dwell time in the whole region shortest.

Theoretical study on tunneling phenomena in asymmetrical rectangular double‐barrier structures with acceleration well

AbstractAs a promising resonant tunneling structure for reduction of tunneling time, the “asymmetric rectangular double‐barrier structure with an acceleration well” is proposed. Analytical expressions are derived for the tunneling transmission coefficient of the electrons and for the resonant condition. Also, the condition for the shortest tunneling time is analytically studied by using the dwell time as the tunneling time. From the resonant condition, the width of each layer can be determined for a given resonant energy. The resultant dwell time is calculated and discussed in terms of both theoretical and numerical analysis. Although the model proposed in this research is an idealized one, the proposed structure and the obtained results are considered useful in the design of tunneling devices in the sense that the tunneling time can be controlled. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 87(3): 1–11, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.10197

Lateral current density fronts in asymmetric double-barrier resonant-tunneling structures

We present a theoretical analysis and numerical simulations of lateral current density fronts in bistable resonant-tunneling diodes with Z-shaped current–voltage characteristics. The bistability is due to the charge accumulation in the quantum well of the double-barrier structure. We focus on asymmetric structures in the regime of sequential incoherent tunneling and study the dependence of the bistability range, the front velocity, and the front width on the structure parameters. We propose a sectional design of a structure that is suitable for experimental observation of front propagation and discuss potential problems of such measurements in view of our theoretical findings. We point out the possibility to use sectional resonant-tunneling structures as controllable three-terminal switches.

Role of interface optical phonons in magnetotunneling in asymmetric double-barrier structures

The role of interface-optical (IO) phonons in tunneling through an asymmetric double barrier structure in a magnetic field perpendicular to the barriers is studied. The phonon-assisted tunneling current densities are calculated and the numerical results for typical AlxGa1−xAs/GaAs/AlyGa1−yAs structures are given. The theoretical results show that the applied magnetic field sharpens and heightens the phonon-assisted tunneling peaks in agreement with experimental observations. In contrast to previous work, the calculated IO phonon-assisted tunneling current peak occurs at the energy the same as that of the bulk GaAs longitudinal-optical (LO) phonon energy. The IO phonon-assisted tunneling is much more important than the confined LO phonon-assisted tunneling. The phonon-assisted tunneling currents are sensitive to the thickness of the emitter barrier. Only one phonon-assisted tunneling peak can be easily observed for the wider well case.

TRANSFER MATRIX METHOD FOR ELECTRON-IO-PHONON INTERACTION IN ASYMMETRIC DOUBLE-BARRIER STRUCTURES

Within the framework of the dielectric continuum model, the interface-optical (IO) phonon modes and their interaction with electrons in an asymmetric double-barrier structure is studied by using a transfer matrix method. The dispersion equation of IO phonon modes and the electron-IO-phonon (e-IO-p) interaction Hamiltonian are derived. It is found that there are eight branches of IO-phonon modes coupling with electrons besides the confined LO-phonon modes. The numerical results are obtained for several GaAs/Al x Ga 1-x As systems. It is seen that the contributions of long-wavelength phonons to the e-IO-p coupling are important. The e-IO-p coupling related to the IO modes with the GaAs LO-frequency (phonon energy 36.25 meV) at the long-wavelength limit is strongest in the eight branches of IO-phonon modes.

Interface optical phonon-assisted tunneling in double-barrier structures

The phonon-assisted tunneling current in an asymmetric double-barrier structure is studied theoretically by considering the electron-interface optical-phonon interaction. The numerical results are obtained for the typical ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{y}{\mathrm{Ga}}_{1\ensuremath{-}y}\mathrm{As}$ structures and a new theoretical understanding about the experimental peaks of phonon-assisted tunneling current is proposed. It is found that only one phonon-assisted tunneling peak appears near the frequency of the well-longitudinal optical-phonon modes for the wider well case, and the contribution from the interface optical-phonon-assisted tunneling on the peak is dominant. The theory can explain the previous experimental results rationally.

Alternating space charge and ambiguity of quantum states in double-barrier structures

Summation of a series of perturbation theory was used to obtain a solution to the time-dependent self-consistent Schrodinger and Poisson equations describing the resonance interaction of electrons that tunnel through asymmetric double-barrier structures with a high-frequency electric field. In the case where electrons are uniformly distributed in energy within the width of the quasi-level, the solution is obtained analytically; if the beam is monoenergetic, solution of the equation is reduced to finding the roots of a fifth-degree algebraic polynomial. It is shown that, in a number of cases, the influence of alternating space charge gives rise to an effect that is quite new for the systems under consideration: several different wave functions may correspond to the same amplitude of the high-frequency voltage applied to the structure; consequently, the values obtained for the high-frequency conductivity and the coefficients of transmission and reflection can differ by several times. As a result, instability of the current flow and hysteresis of the current-voltage characteristics can be observed in these structures. Furthermore, the dependence of the coefficients of transmission and reflection of the electrons and high-frequency conductivity on the voltage amplitude are combinations of the N-and S-shaped characteristics for uniform distribution of electrons and are looplike in the case of a monoenergetic beam.

Spin-dependent resonant tunneling in semiconductor nanostructures

The spin-dependent quantum transport of electrons in non magnetic III-V semiconductor nanos-tructures is studied theoretically within the envelope function approximation and the Kane model for the bulk. It is shown that an unpolarized beam of conducting electrons can be strongly polarized in zero magnetic field by resonant tunneling across asymmetric double-barrier structures, as an effect of the spin-orbit interaction. The electron transmission probability is calculated as a function of energy and angle of incidence. Specific results for tunneling across lattice matched politype Ga0.47In0.53As / InP/Ga0.47In0.53As / GaAs0.5Sb0.5 / Ga0.47In0.53 As double barrier heterostructures show sharp spin split resonances, corresponding to resonant tunneling through spin-orbit split quasi-bound electron states. The polarization of the transmitted beam is also calculated and is shown to be over 50%.

Analytical treatment of wave packet tunneling through a resonant double barrier heterostructure

An analytical expression is found for the transmitted wave packet through a general, asymmetric double barrier structure, as well as for its width. This analytical expression is shown to be in agreement with previous treatments of wave packet tunneling and, as such, is in agreement with previous numerical calculations.

Resonant tunneling in step-barrier structures under an applied electric field

Resonant tunneling in step-barrier structures is investigated by using the transfer-matrix technique. The formulas for the transmission coefficient and the current density are derived when taking into account the coupling between components of the motion of an electron in directions parallel and perpendicular to the interfaces. By making a detailed comparison of resonant tunneling among single square-barrier structures, asymmetric double-barrier structures, and step-barrier structures, the tunneling properties in step-barrier structures are revealed. It is shown that the global behavior of step-barrier structures obtained resembles that of asymmetric double-barrier structures, and step-barrier structures are superior to both single- and double-barrier structures in many aspects. In comparison to asymmetric double-barrier structures, step-barrier structures have several features, such as a wider negative-differential resistance region, easier fabrication, high-speed response, and a relatively lower transmission coefficient and current peak-to-valley ratios. Moreover, higher resonant bias is required in order to obtain optimal transmission resonances in the step-barrier structure. The results shown in this work not only shed new light on the physics of resonant tunneling in electric-barrier structures but are also helpful in designing quantum devices based on step-barrier tunneling structures.

Resonant tunneling in asymmetrical double-barrier structures under an applied electric field

Resonant tunneling is studied theoretically for the asymmetrical rectangular double-barrier structures with deep well when a dc bias field is applied. Analytical expressions for the transmission coefficient and the resonance condition are derived by assuming that the effect of the space charge buildup in the well is neglected. It is found that the resonant tunneling with unity transmission (unity resonance) occurs when both the phase difference condition for resonance (PDCR) and the maximum condition for peak value hold simultaneously, while occurs the under-unity resonance that the peak value of transmission coefficient at resonance is below unity when only PDCR holds. The values of transmission peak and the resonance energy are investigated by two methods, Airy function analysis and multistep rectangular approximation. Wave-functions of an electron at the resonance level are calculated and the confining phenomenon is confirmed. Moreover, the effect of the right-hand side barrier height on the transmission coefficient characteristics is investigated.

Generalized-barrier parameters for single-barrier structures and resonance width in asymmetrical double-barrier structures

Generalized-barrier parameters are studied theoretically for rectangular and trapezoidal single-barriers as well as parallel-plane ones, which are basic units for double-barrier and multiple-barrier structures. Analytical expressions for these parameters are derived by taking into account the position-dependent effective-mass effect. Furthermore, the expressions for the generalized-barrier parameters of optical single-layer thin film structures are considered and permit direct application of previous results to thin film interference filters also. The heights of resonant peaks and the resonance widths in asymmetrical double-barrier structures are studied as functions of the generalized-barrier parameters.

Resonance Conditions in Asymmetrical Rectangular Double-Barrier Structures under DC Bias Field

Analytical expressions for the transmission coefficient and the resonance condition are derived for the first time for the asymmetrical rectangular double-barrier structures with deep well when a dc bias field is applied. It is found that the unity resonance of the resonant tunneling with unity transmission occurs when both the phase difference condition for resonance (PDCR) and the maximum condition for the peak value (MCPV) hold simultaneously, while the under-unity resonance occurs that the peak value of transmission coefficient at resonance is below unity if only PDCR holds. Wave functions of an electron at the resonance level are calculated and the confining phenomena are confirmed.

Resonance Conditions in Asymmetrical Rectangular Double-Barrier Structures under DC Bias Field

Resonance Conditions in Asymmetrical Rectangular Double-Barrier Structures under DC Bias Field

Resonant interaction of electrons with an rf electric field in asymmetric double-barrier structures

Analytical expressions for the electron wave functions, the low-signal, high-frequency conductance, and the widths of the energy levels (minibands) in a asymmetric double-barrier structure with thin barriers are obtained under conditions of coherent electron tunneling strictly along the centers of the energy levels and with the electron energies deviating from exact resonance. It is shown that an electron transmittance equal to 1 and a substantial increase in the integrated (taking into account the energy distribution of the electrons incident on the structure) rf conductance of the structure can be obtained by choosing the appropriate arrangement of the minibands of the structure relative to the conduction band bottom of the semiconductor materials to the left and right of the structure.

Dynamic Instabilities in Resonant Tunneling Induced by a Magnetic Field

We show that the addition of a magnetic field parallel to the current induces self-sustained intrinsic current oscillations in an asymmetric double barrier structure. The oscillations are attributed to the nonlinear dynamic coupling of the current to the charge trapped in the well, and the effect of the external field over the local density of states across the system. Our results show that the system bifurcates as the field is increased, and may transit to chaos at large enough fields.