Finite Barrier Research Articles

Linear intersubband optical absorption in the semiparabolic quantum wells based on AlN/AlGaN/AlN under a uniform electric field

The linear intersubband optical absorption in the polarization semiparabolic quantum wells (SPQWs) are investigated for typical AlN/AlxGa 1−x N/AlN. First, the one-dimensional Poisson and Schrödinger equations have been solved by the variational method within a finite potential barrier model and a bent band figured by all confinement sources (realistic model). Then, the intersubband optical absorption between the lowest two subbands has been theoretically studied under an uniform external electric field. Computed results including the effective confining potential profile, the wave function and the distribution of electron gas in quantum wells, intersubband optical absorption coefficient have been discussed. Our calculation shows that the positive interface polarization charges affect on the distribution of the two-dimensional electron gas (2DEG) in SPQWs so it has great influences on the total optical absorption coefficients significantly.

Stark effect in finite-barrier quantum wells, wires, and dots

The properties of confined carriers in low-dimensional nanostructures can be controlled by external electric fields and an important manifestation is the Stark shift of quantized energy levels. Here, a unifying analytic theory for the Stark effect in arbitrary dimensional nanostructures is presented. The crucial role of finite potential barriers is stressed, in particular, for three-dimensional confinement. Applying the theory to CdSe quantum dots, finite barriers are shown to improve significantly the agreement with experiments.

Intermolecular Charge Transfer Parameters, Electron–Phonon Couplings, and the Validity of Polaron Hopping Models in Organic Semiconducting Crystals: Rubrene, Pentacene, and C60

We evaluate the validity of the commonly assumed polaron hopping model for some of the most popular organic semiconductors, rubrene, pentacene, and C60. This model is based on the assumption that the charge carrier is localized, i.e., forms a polaron that hops from one molecule to the next. We have calculated the relevant intermolecular charge transfer parameters that determine whether a polaron forms or not: electronic coupling matrix element and reorganization energy for the above materials using quantum chemical calculations and molecular dynamics simulations. We find that neither for rubrene nor pentancene the hopping model is justified due to the relatively large electronic couplings between molecules in the respective herringbone layers. For C60 the coupling matrix elements are smaller, and a small but finite barrier for charge transport exists in any transport direction. Despite the theoretical problems surrounding the polaron transport model, we find that mobilities based on this model (as obtaine...

A modified 3D algorithm for road traffic noise attenuation calculations in large urban areas

The primary objective of this study is the development and application of a 3D road traffic noise attenuation calculation algorithm. First, the traditional empirical method does not address problems caused by non-direct occlusion by buildings and the different building heights. In contrast, this study considers the volume ratio of the buildings and the area ratio of the projection of buildings adjacent to the road. The influence of the ground affection is analyzed. The insertion loss due to barriers (infinite length and finite barriers) is also synthesized in the algorithm. Second, the impact of different road segmentation is analyzed. Through the case of Pearl River New Town, it is recommended that 5° is the most appropriate scanning angle as the computational time is acceptable and the average error is approximately 3.1 dB. In addition, the algorithm requires only 1/17 of the time that the beam tracking method requires at the cost of more imprecise calculation results. Finally, the noise calculation for a large urban area with a high density of buildings shows the feasibility of the 3D noise attenuation calculation algorithm. The algorithm is expected to be applied in projects requiring large area noise simulations.

Photo-ionization cross-section of donor-related in (In,Ga)N/GaN core/shell under hydrostatic pressure and electric field effects

Hydrogenic-like donor-impurity related self and induced polarizations, bending energy and photo-ionization cross section in spherical core/shell zinc blende (In,Ga)N/GaN are computed. Based on the variational approach and within effective-mass and one parabolic approximations, the calculations are made under finite potential barrier taking into account of the discontinuity of the effective-mass and the constant dielectric. The photo-ionization cross section is studied according to the photon incident energy considering the effects of hydrostatic pressure, applied electric field, structure's radius, impurity's position and indium composition in the core. It is obtained that the influences mentioned above lead to either blue shifts or redshifts of the resonant peak of the photo-ionization cross section spectrum. The unusual behavior related to the structure radius is discussed which is as a consequence of the finite potential confinement. We have shown that the photo-ionization cross section can be controlled with adjusting the internal and external factors. These properties can be useful for producing some device applications such as quantum dot infrared photodetectors.

Role of dissipation in realistic Majorana nanowires

We carry out a realistic simulation of Majorana nanowires in order to understand the latest high- quality experimental data [H. Zhang et al., arXiv:1603.04069 (2016)] and, in the process, develop a comprehensive picture for what physical mechanisms may be operational in realistic nanowires leading to discrepancies between minimal theory and experimental observations (e.g., weakness and broadening of the zero-bias peak and breaking of particle-hole symmetry). Our focus is on understanding specific intriguing features in the data, and our goal is to establish matters of principle controlling the physics of the best possible nanowires available in current experiments. We identify dissipation, finite temperature, multi-sub-band effects, and the finite tunnel barrier as the four most important physical mechanisms controlling the zero-bias conductance peak. Our theoretical results including these realistic effects agree well with the best available experimental data in ballistic nanowires.

Buffer layer influence on light absorption of electron intersubband transition in binary energy level systems of quantum wells

Due to the restriction of the ZnO buffer layer on the left barrier in a wurtzite asymmetric ZnO/MgxZn1-xO single quantum well (QWs) structure with finite barriers, the other factors such as the size of the well and right barrier, and Mg component, etc. will influence the critical value of the left barrier width to form a binary level energy system. By adopting a finite difference method to solve the Schrdinger equation, the eigenstates and eigenenergies of electrons in a two-dimensional electron gas are obtained, and the influences of buffer layer ZnO, size and ternary mixed crystal effects on the formation of binary energy level system in QW are discussed. In our computation, the influences of energy band bending, material doping and built-in electric fields on a realistic heterostructure potential are considered. Furthermore, based on the Fermi's golden rule, the optical absorption coefficient of electronic intersubband transition in QW and the influences of buffer layer thickness, the widths of left barrier, well and right barrier and ternary mixed crystal effects are discussed. Our results indicate that the critical width of left barrier increases with the increases of the right barrier width and buffer layer thickness for a binary energy level system of ZnO/MgxZn1-xO single quantum well with a ZnO buffer layer on the left side. However, the critical width of left barrier decreases with the increase of well width and Mg component. Besides, the buffer layer thickness, the widths of left barrier, well and right barrier and ternary mixed crystal also affect the light absorption induced by the electronic intersubband transitions. The increases of Mg component, the widths of right barrier and left barrier will increase the absorption peak and produce its blue-shift. Whereas, increasing well width will reduce the absorption peak and produce its red-shift. The above conclusions are expected to give theoretical guidance in improving the opto-electronic properties of materials and devices made of these heterostructures.

The Energy Levels Splitting Calculated for the Heavy and Light Holes in a Cd<sub>1-x</sub>Zn<sub>x</sub>S Double Quantum Dot

This work reports on a theoretical investigation of a double Cd_1-xZn_xS quantum dot embedded in an insulating material.The quantum dots are assumed to have a flattened cylindrical geometry with a finite barrier at the boundary.The energy levels splitting has been computed, using the tight binding approximation, in the case of the heavy and light holes, as a function of zinc composition for different inter-quantum dot separations. An analysis of the results shows that, for the light holes, the coupling is maximum when x=0.8. Moreover, it has been demonstrated the strong localization character of the heavy holes in this nanostructure.

Multigap superconductivity and barrier-driven resonances in superconducting nanofilms with an inner potential barrier

We study the crossover in a zero temperature superconducting nanofilm from a single to a double superconducting slab induced by a tunable insulating potential barrier in the middle. The single phase superconducting ground state of this heterostructure is shown to be intrinsically multigapped and to have a new type of resonance caused by the strength of the barrier, thus distinct from the Thompson-Blatt shape resonance which is caused by tuning the thickness of the film. Single particle electronic states are strongly or weakly affected according to their parity (even or odd) with respect to the insulating barrier. The lift of the parity degeneracy at finite barrier strength reconfigures the pairing interaction and leads to a multigapped superconducting state with interaction driven resonances.

Island nucleation inside a one-dimensional gap with hindered aggregation

The island formation process inside a one-dimensional gap with length L is studied. In the model i + 1 monomers are required to form an stable island. The aggregation of monomers to the islands at the ends of the gap is hindered by an additional attachment barrier Ea which reduces the hopping rate of the monomers to the island. Depending on Ea there are different regimes: zero and weak barriers, large but finite barriers and infinite barriers. The probability of nucleation at position n inside a gap with length L, , and the nucleation rate ω are studied. Both, and ω, are calculated by using two different analytical methods: exact master equation for the time evolution of i + 1 monomers deposited simultaneously and mean field approximation. In all cases the results are compared with Kinetic Monte Carlo simulations to explore the range of applicability of both methods.

A full-Newton step interior-point algorithm for linear optimization based on a finite barrier

In this paper, we propose a finite barrier kernel function for primal–dual interior-point algorithm in linear optimization with a full-Newton step. To our best knowledge, it is the first time that the property of exponential convexity is used for full-Newton step interior-point methods(IPMs). Moreover, the analysis is simplified and the complexity of the algorithm coincides with the currently best iteration bound for linear optimization problems.

Analysis of Dual Gate Structures Using Double-Well and WKB Quantization Rules

An alternative method for direct calculation of energy levels for symmetric dual gate structures with body widths of 3–10 nm is presented in the current paper, using double well analysis and Wentzel-Kramers-Brillouin (WKB) quantization rules. The double well analysis explains the lower energy level splitting, as well as the twin shape of the corresponding wave function with odd–even symmetry. The potential is approximated using a parabolic potential. The perturbation analysis, which already gives good accuracy for higher energies and lower electron effective mass, is compared with the current approach. The combination of the double well and WKB method gives improved accuracy for energies below barrier maximum potential, over perturbation potential, while a simple analytic second-order WKB correction term is needed for energies just above the potential peak. Using the WKB representation of wave function, the effect of finite barrier height on wave function penetration and on energy levels is analytically treated, for all energy levels, with barriers as low as 0.5 eV. Theoretical models are verified using numerical eigenvalue/eigenvector solvers, while device modeling results are compared with self-consistent simulator.

Control of the binding energy by tuning the single dopant position, magnetic field strength and shell thickness in ZnS/CdSe core/shell quantum dot

Recently, the new tunable optoelectronic devices associated to the inclusion of the single dopant are in continuous emergence. Combined to other effects such as magnetic field, geometrical confinement and dielectric discontinuity, it can constitute an approach to adjusting new transitions. In this paper, we present a theoretical investigation of magnetic field, donor position and quantum confinement effects on the ground state binding energy of single dopant confined in ZnS/CdSe core/shell quantum dot. Within the framework of the effective mass approximation, the Schrödinger equation was numerically been solved by using the Ritz variational method under the finite potential barrier. The results show that the binding energy is very affected by the core/shell sizes and by the external magnetic field. It has been shown that the single dopant energy transitions can be controlled by tuning the dopant position and/or the field strength.

Periodic barrier structure in AA-stacked bilayer graphene

We study the charge carriers transport in an AA-stacked bilayer graphene modulated by a lateral one-dimensional multibarrier structure. We investigate the band structures of our system, that is made up of two shifted Dirac cones, for finite and zero gap. We use the boundary conditions to explicitly determine the transmission probability of each individual cone () for single, double and finite periodic barrier structure. We find that the Klein tunneling is only possible when the band structure is gapless and can occur at normal incidence as a result of the Dirac nature of the quasiparticles. We observe that the band structure of the barriers can have more than one Dirac points for finite periodic barrier. The resonance peaks appear in the transmission probability, which correspond to the positions of new cones index like associated with . Two conductance channels through different cones () are found where the total conductance has been studied and compared to the cases of single layer and AB-stacked bilayer graphene.

Study of impedance model and water transport behavior of modified solvent-free epoxy anticorrosion coating by EIS

This work studied the evolution of an impedance model of 60 μm modified solvent-free epoxy anti-corrosion coating on a Q235 steel surface in 3.5% NaCl solution using electrochemical impedance spectroscopy. The electrochemical process of the system was divided into five stages. During the early stage of immersion, water absorption occurred mainly at the coating, coating resistance decreased, and coating impedance deviated from purely capacitive characteristics. The corrosion reaction started after water permeated into the metal/coating interface. During the mid-immersion stage, the electrochemical reaction at the coating/metal interface was controlled by semi-infinite diffusion of corrosion products due to the barrier effect of the coating. The types of corrosion product diffusion gradually became finite layer diffusion and barrier layer diffusion with the clogging of coating pores. Logarithm of coating capacitance and the square root of time showed a linear relationship in the early immersion stage, which was a typical characteristic of Fick’s diffusion. Afterwards, increase in the coating capacitance slowed down, and a non-Fickian diffusion process occurred, which presented the two-stage absorption characteristics. Water diffusion coefficient in coating was calculated to be 2.95 × 10−10 cm2/s, while volume fraction and total water absorption at saturation of coating were 2.3% and 185 μg, respectively, indicating good water resistance and protective properties of the coating. The water kinetic equation in the coating which can reflect the whole Fick diffusion process of water and containing time and location variables was obtained via the Fick diffusion equation and three-dimensional images of water distribution in the coating were drawn by transforming the dynamic equation into programs.

Analytic solutions of tunneling time through smooth barriers

In the discussion of temporary behaviors of quantum tunneling, people usually like to focus their attention on rectangular barrier with steep edges, or to deal with smooth barrier with semi-classical or even numerical calculations. Very few discussions on analytic solutions of tunneling through smooth barrier appear in the literature. In this paper, we provide two such examples, a semi-infinite long barrier V(x)=A2[1+tanh(x/a)] and a finite barrier V(x) = A sech2(x/a). To each barrier, we calculate the associated phase time and dwell time after obtaining the analytic solution. The results show that, different from rectangular barrier, phase time or dwell time does increase with the length parameter a controlling the effective extension of the barrier. More interestingly, for the finite barrier, phase time or dwell time exhibits a peak in k-space. A detailed analysis shows that this interesting behavior can be attributed to the strange tunneling probability Ts(k), i.e., Ts(k) displays a unit step function-like profile Θ(k − k0), especially when a is large, say, a ≫ 1/κ, 1/k. And k0≡mA/ħ is exactly where the peak appears in phase or dwell time k-spectrum. Thus only those particles with k in a very narrow interval around k0 are capable to dwell in the central region of the barrier sufficiently long.

Design of all-optical, hot-electron current-direction-switching device based on geometrical asymmetry.

We propose a nano-scale current-direction-switching device(CDSD) that operates based on the novel phenomenon of geometrical asymmetry between two hot-electron generating plasmonic nanostructures. The proposed device is easy to fabricate and economical to develop compared to most other existing designs. It also has the ability to function without external wiring in nano or molecular circuitry since it is powered and controlled optically. We consider a such CDSD made of two dissimilar nanorods separated by a thin but finite potential barrier and theoretically derive the frequency-dependent electron/current flow rate. Our analysis takes in to account the quantum dynamics of electrons inside the nanorods under a periodic optical perturbation that are confined by nanorod boundaries, modelled as finite cylindrical potential wells. The influence of design parameters, such as geometric difference between the two nanorods, their volumes and the barrier width on quality parameters such as frequency-sensitivity of the current flow direction, magnitude of the current flow, positive to negative current ratio, and the energy conversion efficiency is discussed by considering a device made of Ag/TiO2/Ag. Theoretical insight and design guidelines presented here are useful for customizing our proposed CDSD for applications such as self-powered logic gates, power supplies, and sensors.

Many-electron atom confinement by a penetrable planar boundary

The role of spatial limitation by an inert geometric planar boundary with finite potential barrier height on the electronic properties of many-electron atoms is presented based on models of quantum confinement. The variational treatment of the Thomas–Fermi–Dirac–Weizsäcker density functional scheme is applied throughout. As a sample application of the model, results are presented for the barrier-height dependence of the atom–wall interaction in terms of the ground-state energy shift of a Ne atom close to an aluminum surface and its relation with the corresponding repulsive continuous planar potential. Also, within this model, neutralization close to a surface is shown to be more prompt than Ne ionization.

Kramers' Turnover Theory: Improvement and Extension to Low Barriers.

Kramers' turnover theory as derived by Pollak, Grabert, and Hänggi (PGH) suffers from a few drawbacks. First, the energy loss in PGH theory is not a monotonic function of the friction. Second, the theory is not applicable to surface diffusion, because the effective potential for the system does not conserve the periodicity of the potential. Third, when the reduced barrier height is low, it is rather inaccurate. In this paper, we present a modification of PGH theory that alleviates these drawbacks. We also introduce a finite barrier correction term which takes into consideration that the energy interval of the escaping particle is bounded from below. The resulting theory is tested for motion on a cubic potential and relatively low reduced barriers.

Polaronic effects on diamagnetic susceptibility of a hydrogenic donor in nanostructures

The binding energy and diamagnetic susceptibility of a hydrogenic donor in nanostructures like quantum well, quantum wire and quantum dot have been calculated for the finite and infinite barrier square well potential and are computed using variational technique. The binding energy of cubic nanostructures formed by GaAs/Ga1−x Al x As has also been obtained using conduction band non-parabolicity and polaronic correction. Our results demonstrate that the effect of polaronic mass and band non-parabolicity which exhibits effective binding energy and diamagnetic susceptibility for the nanostructures having narrow width sizes and it is not significant to the low dimensional nanostructures.