Triangular Potential Research Articles

Energy dependence of the effective mass in the envelope-function approximation

Results of a study on the tunneling electron effective mass as a function of energy and barrier width are reported. A system with a highly selective transmission factor, a double barrier, has been chosen in order to be able to define a particular energy. As the energies of the resonant transmission peaks are mostly determined by the effective mass of the material forming the well, while the transmission-peak width mostly depends on the barrier effective mass, both masses are obtained separately by fitting results for transmission using layers of periodic lattices and using the simplification allowed by the effective-mass approximation. The central well width has been varied and several transmission maxima have been considered, thus covering a wide energy range. The effective-mass in the relatively large barrier is shown to be much lower than the bulk-conduction-band value. For very thin barriers, when the decay length of tunneling electrons becomes of the same order as the barrier width, an anomalous increase in the effective mass is observed for high energies. Finally, we obtain the behavior of the effective mass as a function of energy in a one-dimensional triangular potential profile.

Temperature dependent tunnelling current at metal/polymer interfaces—potential barrier height determination

It has been demonstrated that the expression for the temperature dependent tunneling current through a triangular potential barrier at metal/polymer interfaces fits experimental data including the deviation from a straight line observed in Fowler–Nordheim plots. The fitting parameters can be used to calculate the potential barrier height at the metal/polymer interface, which is of crucial importance for the control of charge injection in organic light emitting diodes. The tunneling current density expression reproduces the observed dependence of the current with temperature.

Behavior of a frustrated quantum spin chain with bond dimerization

We clarified behavior of the excitation gap in a frustrated S=1/2 quantum spin chain with bond dimerization by using the numerical diagonalization of finite systems and a variational approach. The model interpolates between the independent dimer model and the S=1 spin chain by changing a strength of the dimerization. The energy gap is minimum at the fully-frustrated point, where a localized kink and a freely mobile anti-kink govern the low-lying excitations. Away from the point, a kink and an antikink form a bound state by an effective triangular potential between them. The consequential gap enhancement and the localization length of the bound state is obtained exactly in the continuous limit. The gap enhancement obeys a power law with exponent 2/3. The method and the obtained results are common to other frustrated double spin-chain systems, such as the one-dimensional J_1 - J_2 model, or the frustrated ladder model.

Validity of the JWKB formula for a triangular potential barrier

The JWKB approximation is extensively used in tunnelling probability calculations. We apply the JWKB formula to a triangular potential barrier and test its accuracy. Zusammenfassung. Die JWKB-Methode wird extensiv benutzt bein Berechnungen von Tunnel-Wahrscheinlichkeiten. Wir wenden die JWKB-Formel auf eine dreieckige Potentialschwelle an und testen ihre Genauigkeit.

A novel preparation of gold films by electrodeposition at the interface between a Na(AuCl4)-CuSO4 aqueous phase and an immiscible hexyl acetate organic phase

Electrolysis at the interface between a Na(AuCl4)–CuSO4 aqueous phase and an immiscible hexyl acetate phase resulted in continuous growth of gold films along the interface. To maintain filmy growth of gold, it was effective to stimulate displacement of predeposited copper with gold by applying a rectangular or triangular potential in a given range. Two types of electrodes were applied: from a point electrode the film grew concentrically like a blooming flower, and from a line electrode the film grew unidirectionally toward the counter electrode as a spreading wave. A long time electrolysis could be performed by circulating and filtering the aqueous solution. The film contained no trace of copper and was very thin (<1μm).

An exact formulation for the electromagnetic fields of a cylindrical antenna with a triangular current distribution

A mathematically exact formulation for the vector potential and corresponding electromagnetic fields of a triangular current cylindrical dipole are presented for the first time in this paper. These exact expressions converge rapidly in the near‐field region of the antenna allowing them to be used for the efficient and accurate computational modeling of electrically short cylindrical antennas. The exact series expansion of the triangular current vector potential is shown to contain two fundamental exponential integrals and their higher‐order associated integrals. Numerically stable forward recurrence relations have been derived which may be used for the efficient evaluation of these higher‐order integrals in addition to the cylindrical wire kernel. These recursions may also be employed in the computation of the electric and magnetic fields. It is demonstrated that the classical thin wire forms of the vector potential and electromagnetic fields are actually special cases of the more general exact expansions. Finally, the exact formulation was used to investigate the near‐field behavior of traditional thin wire as well as moderately thick wire dipoles. Several near‐field plots are presented including a vector plot of the total electric field in the vicinity of a moderately thick quarter‐wavelength dipole.

Self-excited oscillation and non-linear anelasticity of In20 at.% Tl due to transformation twins

Non-linear anelasticity of In20 at.% Tl thermoelastic martensite is studied by measuring self-excited oscillations and resonance curves. The self-excited frequency is of the order of one-tenth of the driving frequency, and thus the fundamental wave is amplitude-modulated by the self-excited oscillation. The modulation frequency depends on temperature and shows a maximum near 5°C. The activation energies estimated are roughly half of the activation energy for impurity diffusion of Tl in In. The experimental results obtained are similar to those of In-19.1 at.% Tl by Wuttig and Lin. The impurity drag effect, as applied to the twin anelasticity in InTl by Wuttig and Lin, and the effects of assumed triangular and rectangular potentials between Tl atom and twin boundary on the temperature dependence of the maximum modulation frequency are discussed.

Piezoreflectance study of a GaAs/Al0.23Ga0.77As asymmetric triangular quantum well heterostructure

We have studied the Piezoreflectance (PZR) spectra at 300 K, 80 K and 20 K related to the intersubband transitions from a GaAs/Al0.23Ga0.77As asymmetric triangular quantum well heterostructure fabricated by molecular beam epitaxy using the digital alloy compositional grading method. A comparison of the relative intensity of heavyand light-hole related features in the PZR spectra and those in the photoreflectance emphasizes the contribution of the strain dependence of the energies of the confined states, which allows us to identify unambiguously the features associated with the heavy- and light-hole valence bands. Comparison of the observed intersubband transitions with an envelope function calculation provided a self-consistent verification that the digital alloy composition grading method generated the desired effective linearly graded asymmetric triangular potential profile.

Static SIMS: Surface charge stabilization of insulators for highly repeatable spectra when using a quadrupole mass spectrometer

AbstractSurface charge stabilization is important to achieve stable static SIMS spectra from insulators. For static SIMS using a quadrupole mass spectrometer, the problem is exacerbated by the narrow spread of ion energies passed by the quadrupole system. Here, for a positive ion beam we study three methods of electron beam surface charge neutralization and compare their effectiveness for large‐area static SIMS analysis. These methods are: a traditional low‐energy flood source aimed at the sample; a 500 eV electron beam aimed at the sample; and a low‐energy source of scattered electrons placed between the sample and the quadrupole‐based static SIMS entrance ion optics. The latter method is shown to be efficient, easy to use and reliable. Variations in the surface potential are considerably reduced but small variations still show an effect leading to variable intensities in different peaks. This variation is reduced a further order of magnitude so that, in the static mode, final scatters for poly(tetrafluoroethene) have standard deviations below 2%. This final reduction is achieved by the application of a triangular waveform potential of 32 V peak‐to‐peak amplitude at 6.5 kHz frequency, to the sample holder and the sample environment. The mass spectra are then equivalent to the results for a mass spectrometer with a 32 eV wide energy acceptance window.

Dipole spectra of holes in quantum dots.

The eigenenergies and the dipole excitation spectrum of a single hole in a quantum dot is calculated as a function of a magnetic field. To describe a realistic dot based on an ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/GaAs heterostructure we use a triangular subband potential and a parabolic lateral confinement. The bulk valence band structure is considered by using the Luttinger Hamiltonian. In the absence of band mixing, the parabolic confinement would lead to only two dipole transitions, with the well known resonance frequencies previously established for dots containing electrons. The strong coupling of light- and heavy-hole states leads to a substantial shift of these resonance frequencies and introduces new features at transition energies comparable to the heavy-hole--light-hole subband separation.

Photoreflectance characterization of an InAlAs/InGaAs heterostructure bipolar transistor

We have measured the photoreflectance spectrum at 300 K from a lattice-matched InAlAs/InGaAs heterostructure bipolar transistor grown by molecular beam epitaxy. The energy features of photoreflectance spectra have been identified and the built-in dc electric fields and associated doping profiles have been evaluated in the n-InAlAs emitter from the observed Franz–Keldysh oscillations. The undoped InGaAs spacer between emitter and base was added on to change the built-in electric field. The results showed that the energy features above the InGaAs band gap are the transitions from the valence band to the quantized state of the conduction band. The quantum well of the conduction band is in the interface of the InAlAs and InGaAs heterojunction. The interface charge densities in the spacer channel are determined to be 3.54×1011 cm−2 and 4.22×1011 cm−2, corresponding to the samples with spacer thicknesses of 300 and 500 Å, respectively. A triangular potential profile model was used to calculate the microstructure in the potential well and electron energy transition. The theoretical and experimental results were compared and good agreements were also found.

Molecular beam epitaxy for high electron mobility modulation-doped two-dimensional electron gases

Spatial separation of the electrons participating in conduction from the corresponding donor impurities is possible by modulation doping of a heterojunction. The most common modulation-doped heterojunction that has been studied in n-AlGaAs/i-GaAs. The electrons transfer from the AlGaAs to the GaAs, where they collect in the triangular potential well at the AlGaAs/GaAs heterojunction, forming a two-dimessional electron gas (2DEG). This spatial separation of the conduction electrons and the ionized donors results in a reduction of the ionized impurity scattering. In addition, the scattering due to phonons can be reduced by cooling the sample. Several groups, using the advanced film growth technique of molecular beam epitaxy, have reported 2DEG mobilities in the range (1–10)×10 6 cm 2V −1S −1 with carrier concentrations of (1–5)×10 11 cm −2 at temperatures of 0.35−4.2 K. These electron mobilities and carrier densities translate into electrons traveling distances greater than 10 μm between collisions. Since photolithographic capabilities allow much smaller device geometries, devices based on the wave nature of the electron are now possible and several have been demonstrated. A discussion of molecular beam epitaxy techniques to obtain such high mobility modulation-doped 2DEGs will be presented, together with a review of what other groups have reported.

Delayed rectifier outward current and repolarization in human atrial myocytes.

Previous work has suggested that the primary time-dependent repolarizing current in human atrium is the transient outward current (Ito), but interventions known to alter the magnitude of the delayed rectifier current (IK) affect atrial electrophysiology and arrhythmias in humans. To explore the potential role of IK in human atrial tissue, we used the whole-cell configuration of the patch-clamp technique to record action potentials and ionic currents in isolated myocytes from human atrium. A delayed outward current was present in the majority of myocytes, activating with a time constant ranging from 348 +/- 61 msec (mean +/- SEM) at -20 mV to 129 +/- 25 msec at +60 mV. The reversal potential of tail currents was linearly related to log [K+]o with a slope of 55 mV per decade, and fully activated tail currents showed inward rectification. The potassium selectivity, kinetics, and voltage dependence were similar to those reported for IK in other cardiac preparations. In cells with both Ito and IK, IK greatly exceeded both components of Ito (Ito1 and Ito2) within 50 msec of a voltage step from -70 to +20 mV. Based on the relative magnitude of Ito and IK, three types of cells could be distinguished: type 1 (58% [73/126] of the cells) displayed a large Ito together with a clear IK, type 2 (13% [17/126] of the cells) displayed only IK, and type 3 (29% [36/126] of the cells) was characterized by a prominent Ito and negligible IK. Consistent differences in action potential morphology were observed, with type 2 cells having a higher plateau and steeper phase 3 slope and type 3 cells showing a triangular action potential and lesser phase 3 slope compared with type 1 cells. We conclude that IK is present in a majority of human atrial myocytes and may play a significant role in their repolarization and that previously observed variability in human atrial action potential morphology may be partially due to differences in the relative magnitude of time-dependent outward currents.

Microbiosensors for acetylcholine and glucose

Microbiosensors based on carbon and platinum fibers are described. Carbon fibers were used to construct microelectrodes of 7 μm diameter. Electrochemical operations for pre-electrolysis and measuring were examined for the highly sensitive determination of hydrogen peroxide. A triangular potential (−2 to +2 V vs. Ag/AgCl) was applied before measuring each pair of double pulses (first pulse: 750 mV; second pulse: 1100 mV). The determination limit was 0·1 μ m of hydrogen peroxide. The reproducible determination of hydrogen peroxide is possible even in samples containing albumin protein. The separation of hydrogen peroxide from ascorbic acid is also possible because the oxidation potential of ascorbic acid is different from that of hydrogen peroxide. An acetylcholine microsensor was fabricated by immobilizing acetylcholine esterase and choline oxidase on the carbon fiber by entrapment with poly(vinyl alcohol)-quarternized stilbazole (PVA-SbQ). This sensor gave a linear calibration plot for the range 0·1–1·0 m m with a linear correlation coefficient of 0·9842. Glucose oxidase (GOD) and glucose dehydrogenase (GDH) immobilized cylindrical platinum microelectrodes were fabricated, and their characteristics were evaluated, respectively, by using 1,4-benzoquinone (BQ) and ferricyanide as electron mediators. Each enzyme was immobilized by using PVA-SbQ on a cylindrical microelectrode of 2 μm diameter. A linear range in the calibration curve of the GOD-based glucose microsensor was observed to be wider than that obtained using a disk electrode of 1 mm diameter. The mediated response of the 2 μm glucose sensor was compared with the response resulting from hydrogen peroxide detection. This result showed that a higher response and a wider linear range were observed with highly concentrated mediator. A much higher response of the GDH immobilized 2 μm microelectrode was obtained when not only ferricyanide but also diaphorase was employed to reoxidize the NADH produced by the enzyme reaction of GDH. The GDH-based glucose microsensor was found to be unaffected by the concentration of dissolved oxygen.

Simulation of transmission coefficient through a triangular potential barrier

An analytical expression of the transmission coefficient for the electron transport through a triangular potential barrier has been modified for solution using the method of numerical simulation. The triangular potential barrier has been modelled as a staircase function. The performance of this numerical simulation method is briefly described. The simulation has been developed for personal computer IBM PC AT.

Ultramicro acetylcholine sensor based on an enzyme-modified carbon fibre electrode

Carbon fibres are used to construct ultramicroelectrodes 7 μm in diameter. Electrochemical operations for pre-electrolysis and measurement were examined for the sensitive determination of hydrogen peroxide. When a triangular potential (−2 to +2 V vs. Ag/AgCl) was applied before every measuring double pulse (first pulse, 750 mV; second pulse, 1100 mV), the limit of detection was 0.1 μM hydrogen peroxide. Reproducible determination of hydrogen peroxide is possible even in samples containing albumin. The separation of hydrogen peroxide from ascorbic acid is also possible because the oxidation potential of ascorbic acid is different from that of hydrogen peroxide. An ultramicro acetylcholine sensor was fabricated by immobilizing acetylcholinesterase and choline oxidase on the carbon fibre by entrapment with poly(vinyl alcohol)-quaternized stilbazole (PVA-SbQ). This sensor gave a linear calibration plot for the range 0.1–1.0 mM with a linear correlation coefficient of 0.9842. A rapid determination in 5 s is possible because of the thin enzyme membrane on the carbon fibre.

Adjustable confinement of the electron gas in dual-gate silicon-on-insulator mosfet's

The confinement of the electron gas in MOS structures fabricated on thin silicon on insulator (SOI) layers is studied with emphasis on the principle of volume inversion. Analytical solutions are proposed for the potential distribution across the film and energy quantization. It is found that the triangular potential well approximation, which holds in bulk Si MOS systems, is no longer valid in SOI. Instead, the potential becomes parabolic, and even rather flat for SOI films which are very thin (30 – 100 nm) and not intentionally doped (10 15 cm −3). The energy separation of the lowest subbands is extremely small so that the quantum effects can be ignored. This confirms that the minority carriers are absolutely free in the volume of the film, their distribution being totally governed by the Poisson equation and current conservation equation. The presence of the natural back gate in SOI-MOS structures makes possible not only the volume inversion or accumulation but also the transition from 3-D to 2-D systems.

Photoreflectance of selectively doped n-AiGaAs/GaAs heterostructures

The two dimensional electron gas concentration dependence of photoreflectance of n-AIGaAs/GaAs heterostructures are reported and explained by analysing the physical process induced by photo-modulation. Comparison of the experimental results and energy level calculations basedon a triangular potential well approximation shows good agreement.

On the charge control of the two-dimensional electron gas for analytic modeling of HEMTs

A simple charge control model is developed for the two-dimensional electron gas (2-DEG) of high-electron-mobility transistors (HEMTs). This model explicitly takes into account the effective distance of the 2-DEG from the heterointerface and has been developed for use in analytic I-V and C-V modeling. In this model, the Fermi energy level versus the 2-DEG sheet carrier-concentration is represented by a simplified expression derived from the triangular potential well approximation and is shown to be dominated by terms with different functional forms in two distinct operation regions: a moderate carrier-concentration region and a subthreshold region. The validity of the analytic charge control model is supported by the calculated results of a self-consistent quantum mechanical model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Mechanism for high-T c superconductivity in the Hubbard model

A pair trapping mechanism for holes in a triangular potential well arising from a “string” of shifted spins is discussed in the context of experiments and related theories of the new high-T c superconductors. The mechanism involves anisotropic singlet pairing, of which the most simple candidate examined is d-wave pairing.