Resonant tunneling and enhanced Goos–Hänchen shift in a graphene double velocity barrier structure

Resonant transmission and Goos–Hänchen (GH) shift for Dirac fermion beams tunneling through graphene double velocity barrier structures (DVBs) are investigated theoretically. Analytical and numerical results demonstrate that strong resonant tunneling effect occurs in this structure and is highly dependent on the incident angle and the structure of velocity barriers. The resonant tunneling in graphene DVBs belongs to the Fabry–Pérot resonance and leads to oscillated conduction at wide energy range. It is also found that GH shifts in this structure can be enhanced by the resonant tunneling and multi-GH shift peaks with giant magnitudes can occur at these resonant energy positions. These special properties of GH shifts in graphene DVBs may have good application in lateral manipulation of electron beams and valley or spin beam splitter.     

电子横向运动对共振隧穿的影响

讨论了电子横纵方向运动耦合时的隧穿现象,对CdSe/Zn1-xCdxSe方形双势垒结构和抛物形双势垒结构的数值计算表明,在零偏压和非零偏压情况下,电子横向运动对共振隧穿的影响是不容忽略的。     

Effects of structural disorders on sequential tunneling in multiple quantum wells

Based on an isotropic random distribution model, the effects of structural disorders embedded in the barriers on the sequential electron tunneling in multiple quantum wells were studied at low temperatures. By using a sequential tunneling model [Stievenard et al., Appl. Phys. Lett. 61 (1992) 1582], the transmission coefficient through a single barrier was calculated using a finite-difference method and averaged over random configurations of disorders. To compute the tunneling current, a self-consistent calculation for the electronic states was performed, including the Hartree and exchange interactions and non-parabolic energy dispersion. Both disorder-assisted and disorder-impeded electron tunneling phenomena were found as a function of the activation energy. The effects of electric field, barrier width, and temperature were also studied. The predicted resonant disorder-assisted electron tunneling should be large enough to be observable at low temperatures in an experiment.     

Tunneling in double-barrier ZnSe/ZnTe structures — time-dependent analysis

Wave-packet time-dependent quantum mechanics is used to calculate the tunneling probability through a double-barrier ZnSe/ZnTe structure. The time-dependent transmission characteristics are obtained for several structures, and detailed electron dynamics is presented. The resonant peaks due to the presence of the discrete energy levels in the quantum well as well as in the barrier region are observed.     

Resonant tunneling properties of inverted Morse double quantum barrier

We study resonant tunneling characteristics of inverted Morse double quantum barrier structures. The effect of electric bias and structure parameters is calculated by using non-equilibrium Green's function method. Results for the transmission coefficients are compared with the structure parameters. Our results show that the widths of the wells and heights of barriers have a significant effect on the transmission properties. We found that the resonant peak of the transmission coefficient decreases with increasing electric field bias. Moreover, resonant energy level increases with increasing barrier height and increasing width parameters.     

InAs/InP柱型量子线中隧穿时间和逃逸问题的研究

在有效质量近似和绝热近似下,利用转移矩阵法研究了电子通过In As/In P/In As/In P/In As柱形量子线共振隧穿二极管的输运问题,分析和讨论了电子居留时间以及电子的逃逸过程.详细研究了外加电场、结构尺寸效应对居留时间和电子逃逸的影响.居留时间随电子纵向能量的演化呈现出共振现象;同时,结构的非对称性对电子居留时间有很大的影响,随着结构非对称性的增加,居留时间表现出不同的变化.利用有限差分方法研究了非对称耦合量子盘中电子的相干隧穿逃逸过程.     

Growth and characterization of delta type Si---SiOx-heterostructures

We present a procedure whereby 2–3nm thick layers of SiO_x are incorporated in (100) Si during molecular beam epitaxial growth. Analysis by Auger electron spectroscopy and transmission electron microscopy shows, that the delta function SiO_x layers with a width of only a few lattice planes are embedded in a monocrystalline Si matrix. Capacitance — voltage measurements and resonant tunneling spectroscopy give evidence that the layers act as sharp potential barriers.     

Quantum scattering in one-dimensional systems satisfying the minimal length uncertainty relation

In quantum gravity theories, when the scattering energy is comparable to the Planck energy the Heisenberg uncertainty principle breaks down and is replaced by the minimal length uncertainty relation. In this paper, the consequences of the minimal length uncertainty relation on one-dimensional quantum scattering are studied using an approach involving a recently proposed second-order differential equation. An exact analytical expression for the tunneling probability through a locally-periodic rectangular potential barrier system is obtained. Results show that the existence of a non-zero minimal length uncertainty tends to shift the resonant tunneling energies to the positive direction. Scattering through a locally-periodic potential composed of double-rectangular potential barriers shows that the first band of resonant tunneling energies widens for minimal length cases when the double-rectangular potential barrier is symmetric but narrows down when the double-rectangular potential barrier is asymmetric. A numerical solution which exploits the use of Wronskians is used to calculate the transmission probabilities through the Pöschl–Teller well, Gaussian barrier, and double-Gaussian barrier. Results show that the probability of passage through the Pöschl–Teller well and Gaussian barrier is smaller in the minimal length cases compared to the non-minimal length case. For the double-Gaussian barrier, the probability of passage for energies that are more positive than the resonant tunneling energy is larger in the minimal length cases compared to the non-minimal length case. The approach is exact and applicable to many types of scattering potential.     

Velocity fluctuations of a column of water streaming down a wire: the possibility of one-dimensional turbulence

In this paper we study the influence of the magneto-coupling effect between the longitudinal motion component and the transverse Landau orbits of an electron on transmission features in single barrier structures. Within the parabolic conduction-band approach, a modified one-dimensional effective-mass Schr?dinger equation, including the magneto-coupling effect generated from the position-dependent effective mass of the electron, is strictly derived. Numerical calculations for single barrier structures show that the magneto-coupling effect brings about a series of the important changes for the transmission probability, the above-barrier quasi-bound states, and the tunneling time. Through examining the variation of the above-barrier resonant-transmission spectrum with the barrier width and observing the well-defined Lorentzian line-shape of the above-barrier resonant peaks, we convincingly show that the above-barrier resonant transmission in single barrier structures is delivered by the above-barrier quasibound states in the barrier region, just as the below-barrier resonant tunneling in double barrier structures is mediated by the below-barrier quasi-bound states in the well. Furthermore, we come to the conclusion that the magneto-coupling effect brings about not only the splitting of the above-barrier quasi-bound levels but also the striking reduction of the level-width of the quasi-bound states, correspondingly, the substantial increase of the density of the quasi-bound states. We suggest that magneto-coupling effects may be observed by the measurements of the optical absorption spectrum associated with the above-barrier quasi-bound states in the single barrier structures. Received: 26 September 1997 / Revised: 26 November 1997 / Accepted: 15 December 1997     

Theoretical study of resonant-tunneling and confining phenomena with mass variation in unsymmetrical rectangular double-barrier structures

Analytical expressions for the transmission coefficient and the resonance condition in unsymmetrical rectangular double-barrier structures are derived theoretically by taking into account the mass difference between well and barrier layers. It is found that resonant tunneling with a transmission peak equal to 1 (unity resonance) and resonant tunneling with a transmission peak less than 1 (below unity resonance) may occur in the unsymmetrical double-barrier structures. Two independent conditions are required for unity-resonant transmission: One is the Phase-Difference Condition for Resonance (PDCR) and the other is the Maximum Condition for the Peak Value (MCPV). The below-unity resonant transmission occurs when only condition PDCR holds. It is believed that the two conditions are useful for calculating values of the transmission coefficient and the resonance energy for the unsymmetrical double-barrier structures. They may be useful for resonant tunneling-device fabrication. Furthermore, wave functions of an electron at resonance level are calculated and the confining phenomenon is confirmed.     

Synthesis of aligned gallium nitride nanowire quasi-arrays

Self-aligned GaN nanowire quasi-arrays were synthesized on MgO crystal through a simple gas reaction method. They were characterized by powder X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), energy-dispersive X-ray (EDX) spectroscopy and high-resolution transmission electron microscopy (HRTEM). FE-SEMimages showed that the product consisted of quasi-arrays of nanowires. XRD, EDX and HRTEM indicated that the nanowires were wurtzite GaN single crystals. Received: 19 June 2000 / Accepted: 21 June 2000 / Published online: 9 August 2000     

Modified gap states in Fe/MgO/SrTiO3 interfaces studied with scanning tunneling microscopy

The geometric and electronic structures of Fe islands on MgO film layers were studied with scanning tunneling microscopy and spectroscopy. The MgO layers were grown on a Nb-doped single crystal SrTiO₃ (100) surface. Deposited Fe atoms aggregate into islands, the height and diameter of which are about 2.5 and 9.4 nm respectively. Fe islands modify the electronic structure of MgO surface; a ring type depression in the scanning tunneling microscope topography appears by lowered local electron density of states around Fe islands. We find that adsorbed Fe atoms reduce the gap states of MgO layers around Fe islands, which is attributed to the reason for the depletion of the electronic density of states.     

Magnetotransport in a graphene monolayer with two tunable magnetic barriers

The magnetotransport property for a monolayer graphene with two turnable magnetic barriers has been investigated by the transfer-matrix method. We show that the parameters of barrier height, width, and interval between two barriers affect the electron wave decaying length, which determine the conductance with parallel or antiparallel magnetization configuration, and consequently the tunneling magnetoresistance (TMR) for the system. Interestingly, a graphene attached by two barriers with different heights can produce a resonant TMR peak at low energy region one order of magnitude larger than that for the system with two same height barriers because that the asymmetry of magnetic barriers block the electron transmission in the case of antiparallel magnetization configuration. The results obtained here may be useful in understanding of electron tunneling in graphene and in designing of graphene-based nanodevices.     

A comparison of the transport properties of bilayer graphene,monolayer graphene,and two-dimensional electron gas

We studied and compared the transport properties of charge carriers in bilayer graphene, monolayer graphene, and the conventional semiconductors (the two-dimensional electron gas (2DEG)). It is elucidated that the normal incidence transmission in the bilayer graphene is identical to that in the 2DEG but totally different from that in the monolayer graphene. However, resonant peaks appear in the non-normal incidence transmission profile for a high barrier in the bilayer graphene, which do not occur in the 2DEG. Furthermore, there are tunneling and forbidden regions in the transmission spectrum for each material, and the division of the two regions has been given in the work. The tunneling region covers a wide range of the incident energy for the two graphene systems, but only exists under specific conditions for the 2DEG. The counterparts of the transmission in the conductance profile are also given for the three materials, which may be used as high-performance devices based on the bilayer graphene.     

Crystallization characteristics of a middle CoFeB layer in a double MgO barrier magnetic tunnel junction

The crystallization characteristics of a middle CoFeB free layer in a magnetic tunnel junction (MTJ) with double MgO barriers were investigated by tunneling magnetoresistance (TMR) measurements of patterned cells across an 8-inch wafer. The MTJ structure was designed to have two CoFeB free layers and one bottom pinned layer, separated by MgO tunnel barriers. The observed resistance showed three types of TMR curves depending on the crystallization of the middle CoFeB layer. From the analysis of TMR curves, coherent crystallization of the middle CoFeB layer with the top and bottom MgO barriers was found to occur non-uniformly: About 80% of the MTJ cells in the wafer exhibited coherent crystallization of the middle CoFeB layers with the bottom MgO tunnel barrier, while others had coherent crystallization with the top MgO tunnel barrier or both barriers. This non-uniform crystallization of the middle CoFeB layer in a double MTJ was also clearly observed in tunneling electron microscopy images. Thus, control of the crystallization of the middle CoFeB layer is important for optimizing the MTJ with double MgO barriers, and especially for the fabrication of double barrier MTJ on a large area substrate.     

Fano resonances and electron localization in heterobarriers

A study is made of electron tunneling in semiconductor heterostructures having a complex dispersion law. A generalized Fabry-Perot approach is used to describe tunneling across the barrier. Mixing of electron states at the heterojunctions is responsible for the asymmetric resonant structure of the transmission which is characterized by a resonance-antiresonance pair. The resonance corresponds to a pole while the antiresonance corresponds to a zero of the scattering amplitude in the complex energy plane, i.e., near the pole and the zero the transmission of the heterobarrier has a Fano resonance structure. It is shown that for certain barrier parameters the resonances may collapse and localized states may appear in the heterobarrier, which is observed on the current-voltage characteristics of the barriers. The two-valley model of a GaAs/Al_xGa_1?x As/GaAs heterostructure is considered as an example. An analysis is made of the resonance structure in the barrier as a function of the type of boundary conditions used for the heterojunctions. The low-temperature current-voltage characteristic of the barrier is calculated.     

Synthesis of web-like-structured ZnO cluster with strong photoluminescence intensity

A web-like-structured ZnO cluster (WLSZC) has been prepared by applying ultrasonic treatment for 70 min during the co-precipitation process. These samples were subsequently characterized by high-resolution transmission electron microscopy (TEM) and photoluminescence (PL) spectroscopy. In WLSZC, we observed homogeneous polygons, which consist of one single-crystal particle at each side. The PL intensity of the WLSZC is 8-14 times greater than that of nano-particle samples, most likely due to the resonant effect of the polygonal pores (about 100 nm wide). In addition, four blue peaks appeared in the prepared samples indicates that variable defects may be produced during the ultrasonic treatment.     

Co-doped (La, Sr)TiO(3-delta) : a high Curie temperature diluted magnetic system with large spin polarization

We report on tunneling magnetoresistance (TMR) experiments that demonstrate the existence of a significant spin polarization in Co-doped (La, Sr)TiO(3-delta) (Co-LSTO), a ferromagnetic diluted magnetic oxide system (DMOS) with high Curie temperature. These TMR experiments have been performed on magnetic tunnel junctions associating Co-LSTO and Co electrodes. Extensive structural analysis of Co-LSTO combining high-resolution transmission electron microscopy and Auger electron spectroscopy excluded the presence of Co clusters in the Co-LSTO layer and thus, the measured ferromagnetism and high spin polarization are intrinsic properties of this DMOS. Our results argue for the DMOS approach with complex oxide materials in spintronics.     

Local super-saturation dependent synthesis of MgO nanosheets

Well-crystallized MgO nanosheets have been prepared with MgB₂ as a precursor without any catalyst via a simple chemical vapor deposition (CVD) method. The nanosheets are grown parallel to (2 0 0) plane according to the high-resolution transmission electron microscopy profiles. At the same time, MgO nanowires are formed in the different area of substrate, which is the result of the difference in local super-saturation. Consequently, we propose that the growth mechanism depends on the surface energy and the local super-saturation in the system.     

Resonance energy level selection in symmetrical rectangular quadruple-barrier structures

Resonant tunneling is studied theoretically in symmetrical rectangular quadruple-barrier structures by taking into account mass difference between the well layer and the barrier layer. Analytical expressions for the transmission coefficient and the resonance condition are derived. Especially, it is obtained that two independent resonance energies can be determined analytically as a function of the outer and the central well widths, which may be very useful for resonant tunneling device fabrications. Furthermore, the variation of the resonance energy with the outer barrier width is investigated. It is found that the resonance level is rarely affected with a small change of the outer barrier width. It is derived analytically that the transmission peak is decreased to less than unity when the outer barrier width becomes thinner than a critical value.