Theoretical study of resonant tunneling in rectangular double-, triple-, quadruple-, and quintuple-barrier structures

The transmission coefficient and the resonance condition in the one-dimensional rectangular double-, triple-, quadruple-, and quintuple-barrier structures are derived theoretically under the assumption of the constant tunneling effective mass. It is found that the resonance energies are different from the eigenvalues in the quantum well due to coupling between wells in the multiple-barrier (much more than triple-barrier) structures. It is confirmed that the transmission spectrum is a Lorentzian near to energies of resonance.     

The effect of non-constant effective tunneling mass and asymmetry for resonant tunneling in double-barrier structures

We discuss the transmission coefficient τ_d in non-repetitive, one-dimensional, rectangular double-barrier structures without simplifications such as strongly attenuating barriers, strong localization, or overall constant effective tunneling mass of the electron. For resonance τ_d=1, we obtain two non-approximative conditions which require different resonance energies of the tunneling electron than previously reported in the literature. In fact, the resonance peaks are shifted to higher energy levels in the order of the width of the peaks due to the effect of non-constant tunneling mass. We investigate the dependence of the resonance condition and the shape of the resonance peaks in regard to perturbation of the electron energy, the gap width as well as the barrier width and height. Resonance is stable for variation of the barrier width but sensitive for variation of the barrier height and the gap width. Received: 9 December 1998 / Accepted: 5 January 1999 / Published online: 31 March 1999     

Two interacting electrons in a Gaussian confining potential quantum dot

Two interacting electrons in a Gaussian confining potential quantum dot are considered under the influence of a perpendicular homogeneous magnetic field. The energy levels of the low-lying states are calculated as a function of magnetic field. Calculations are made by using the method of few-body physics within the effective-mass approximation. A ground state behavior (singlet→triplet state transitions) as a function of the strength of a magnetic field has been found in the weak confinement case as a two-electron quantum dot with parabolic confining potential.     

A comparison of confining potentials in the quantum wire problem

A simple numerical method for solving a two-terminal quantum electronic waveguide problem is presented. The method can be adapted to a quantum wire cavity of irregular geometry and/or non-constant potential field. We compare the circular bend wire with parabolic confining potential profile to the commonly used hard wall confinement. We find an energy scaling which makes the results correspond closely.     

Expulsion of carriers from the double-barrier quantum well and investigation of its spectral consequences

We propose a simple procedure for evaluating the spontaneous (in absence of bias) expulsion of carriers from a nanostructure and exemplify it by computing the distribution of the net charge in the DBQW. We calculate the corresponding correction to the spectrum of this nanostructure and discuss lifting of degeneracy in narrow DBQWs. Numerical examples illustrate these effects in a wide range of temperatures, carrier densities, and widths of the quantum well.     

Density and well width dependences of the effective mass of two-dimensional holes in (100) GaAs quantum wells measured using cyclotron resonance at microwave frequencies

Cyclotron resonance at microwave frequencies is used to measure the band mass (m_b) of the two-dimensional holes (2DHs) in carbon-doped (100) GaAs/ Al_xGa_1−xAs heterostructures. The measured m_b shows strong dependences on both the 2DH density (p) and the GaAs quantum well width (W). For a fixed W, in the density range (0.4×10¹¹ to 1.1×10¹¹ cm⁻²) studied here, m_b increases with p, consistently with previous studies of the 2DHs on the (311)A surface. For a fixed , m_b increases from 0.22m_e at to 0.50m_e at , and saturates around 0.51m_e for .     

Effects of electric field and hydrostatic pressure on donor binding energies in a spherical quantum dot

The binding energies of a hydrogenic donor in a GaAs spherical quantum dot in the Ga_1−xAl_xAs matrix are presented assuming parabolic confinement. Effects of hydrostatic pressure and electric field are discussed on the results obtained using a variational method. Effects of the spatial variation of the dielectric screening and the effective mass mismatch are also investigated. Our results show that (i) the ionization energy decreases with dot size, with the screening function giving uniformly larger values for dots which are less than about 25 nm, (ii) the hydrostatic pressure increases the donor ionization energy such that the variation is larger for a smaller dot, and (iii) the ionization energy decreases in an electric field. All the calculations have been carried out with finite barriers and good agreement is obtained with the results available in the literature in limiting cases.     

Donor binding energies and spin-orbit coupling in a spherical quantum dot

The ground state and a few excited state energies of a hydrogenic donor in a spherical quantum dot (GaAs in a GaAlAs matrix) are computed. While the 1s and the 2s-state energies behave normally for dots of all radii, the 2p₀ and 2p_± states are unbound for most of the radii of interest. It is predicted that a semiconductor quantum dot with a hydrogenic donor will exhibit photoconductivity for a low threshold wavelength ∼12 μm. The spin-orbit coupling gives a contribution of the order of 10⁻⁵ meV for both 2p₀ and 2p_± states.     

Electronic conductance of a multi-channel point contact in a magnetic field

We present the numerical results of the electronic conductanceG of a quantum wire with a multichannel point contact structure in a perpendicular external magnetic fieldH at zero temperature, based on the rigorous quantum mechanics of a two-dimensional noninteracting electron gas. Computational results show the approximate quantization of the electronic conductance. WheH is weak,Ginteger multiples of 2e ²/h; and whenH is trong, Ginteger multiples of 2ne ²/h, wheren is the number of channels in the point contact structure of the quantum wire. Quantum leaps take place whenH±2m ^* E _F /[e(2j+1)], wherej is either zero or a positive integer small enough for the external magnetic fieldH to be strong, andm ^* is the effective mass of an electron in the device. To our knowledge, no report on this quantization of electronic conductance has been published. Oscillations are manifest in theGH curves for comparatively narrow channels because of the quantum size effect.     

Resonant tunneling and confining phenomena in symmetrical rectangular triple-barrier structures with c-type deep wells

Theoretical study of resonant tunneling is carried out in rectangular triple-barrier structures with C-type deep wells. Analytical expressions for the transmission coefficient and the resonance conditions are derived. Transmission characteristics versus electron energy are investigated and it is shown analytically that the transmission spectrum is a Lorentzian in form near energies of resonance. It is confirmed that the resonance energy is almost equal to the eigenenergy of the double-well structure. Moreover, wave functions of an electron at the resonance level are examined and the confining phenomenon is studied.     

Binding energy of an off-center hydrogenic donor in a spherical Gaussian quantum dot

The energy levels of an off-center hydrogenic donor confined by a spherical Gaussian potential have been calculated as a function of the potential radius for different donor position by exact diagonalization method. The results have clearly demonstrated the so-called quantum size effect. The binding energy is dependent on the dot radius R, the impurity ion distance D, and the confining potential depth V₀.     

Model calculations of diffusion limited trapping dynamics in quantum well laser structures

We present a phenomenological theoretical model to treat the trapping of carriers into quantum wells of semiconductor laser structures. We consider explicitely the transport within the barrier layers by solving the continuity equation with the appropriate boundary conditions taking into account surface recombination, radiative and nonradiative recombination in the barrier layers and trapping of carriers into the quantum wells. The experimental findings for the trapping dynamics in GaAs/AlGaAs quantum well structures can be consistently interpreted by the model calculations.     

Auger recombination with traps in quantum-well semiconductors

Auger recombination involving traps is calculated for quantum-well semiconductors. Apart from some modifications the results are analogous to those for bulk semiconductors. In particular, the lifetime of the recombination process is proportional to the inverse carrier density and independent of temperature.     

Structure and magnetic properties of Fe4/Cun (n=2,4) superlattices from first-principles study

The structures and magnetic properties of Fe4/Cun (n=2, 4) superlattices have been investigated by the first-principles pseudopotential plane-wave method based on spin density approximation. Compared with the ideal fcc-Cu bulk structure, for the optimized Fe4/Cu2 model, obvious contraction of interlayer distances occurs on the interior Fe layers, whereas the interlayer distances of Fe layers in Fe4/Cu4 are expanded. The anti-parallel alignment magnetic moment and negative polarization of the interior Fe layer have been found in the Fe4/Cu2 model. This can be explained in terms of the magnetic-volume effect, and the moment of anti-parallel alignment attributes to the contracted interlayer distances between the interior Fe layers. The MR ratio has also been evaluated by means of the two-current model. The MR ratio of the Fe4/Cu2 model (4.89%) is much small than that of the Fe4/Cu4 one (23.65%).     

Electronic band structures of low-dimensional adsorbate systems: Rare-gas adsorption on transition metals

Angle-resolved photoemission data are dis-cussed for five different Xe adlayers which exhibit electronic structures of different dimensionalities. Xe adsorption on Ni (110)-(1 × 2)-3Hand the (×) R30^° Xe layer on Ru (001) reveal two-dimensional (2D) Xe-derived band structures that are characteristic for hexagonal rare-gas layers. Different Xe 5p dispersion widths on Ni and on Ru are found due to the difference in the Xe-Xe nearest-neighbor distance. For three rare-gas systems (two different Xe coverages on hydrogen-modified Pt (110)-(1 × 2)-H and Kr step decoration on a Pt (997) surface) true one-dimensional (1D) band structures are found. For Xe step adsorption on Pt (997), electronic localized (0D) behavior is observed due to an enlarged Xe-Xe separation. The qualitative differences of the band structures in the case of 2D, 1D and 0D rare-gas systems are demonstrated and are explained by the different dimensionalities of the various structures. Received: 3 August 2000 / Accepted: 4 August 2000 / Published online: 7 March 2001     

Formation and charge control of a quantum dot by etched trenches and multiple gates

We have fabricated a GaAs/InGaAs/AlGaAs-based single-electron transistor (SET) formed by etched trenches and multiple gates. Clear Coulomb-blockade oscillations have been observed when the gate biases are scanned. By self-consistently solving three-dimensional Schr?dinger and Poisson equations, we have studied the energy-band structure and the carrier distribution of our SET. General agreement between numerical simulation results and measurement data has been obtained, thus indicating the effectiveness of our SET-device design as well as the necessity of a complete three-dimensional quantum-mechanical simulation. Received: 18 October 2001 / Accepted: 6 January 2002 / Published online: 20 March 2002     

Ground state energies of neutral and negatively charged donors in nanowire superlattice

Using the Bastard-type trial function for the neutral donor and the Hylleraas-type trial function for the negatively charged donor, we investigate the effect of donor positions inside the cylindrical GaAs/Ga(Al)As nanowire superlattice on their ground state energies. Results of calculation, presented in the form of contour plots of the energies corresponding to different donor positions along a cross section through symmetry axis, show a close relationship between the energies of the neutral and negatively charged donors and the charge distributions in one- and two-electron nanowire superlattices, respectively, at the point of their locations. The higher the charge density resulting from the unbound electron at a point in the heterostructure, the lower are the ground state energies of the neutral and negatively charged donors located at this point.     

Elementary excitations in nanochannel arrays of quantum wires

We present an analytical model for the Coulomb interaction effects in quantum wires forming a nanochannel array. We study the elementary excitations (plasmons and electron-hole excitations) of electron arrays forming three-dimensional structures. The plasmon spectrum of boson arrays is also calculated. Our model applies to bulk material with one-dimensional conduction channels as realized in organic or polymer crystals and in nanochannel array glasses.     

Effect of Hydrostatic Pressure on Interband Transitions in Coupled Quantum Wires

We calculate the exciton binding energy and interband optical absorption in a rectangular coupled quantum wire under the hydrostatic pressure in the effective-mass approximation, using the variational approach. It is found that the interband optical absorption strongly depend on the hydrostatic pressure and the coupling parameter, and that the magnitude of the absorption coefficient for the HH1-E1 transition in the coupled quantum wire is larger than that of the single quantum wire.