Effective Mass Calculations Research Articles

Optical transitions in quantum ring complexes

Making use of a droplet-epitaxial technique, we realize nanometer-sized quantum ring complexes, consisting of a well-defined inner ring and an outer ring. Electronic structure inherent in the unique quantum system is analyzed using a micro-photoluminescence technique. One advantage of our growth method is that it presents the possibility of varying the ring geometry. Two samples are prepared and studied: a single-wall ring and a concentric double-ring. For both samples, highly efficient photoluminescence emitted from a single quantum structure is detected. The spectra show discrete resonance lines, which reflect the quantized nature of the ring-type electronic states. In the concentric double--ring, the carrier confinement in the inner ring and that in the outer ring are identified distinctly as split lines. The observed spectra are interpreted on the basis of single electron effective mass calculations.

Tuning ofg-factor in self-assembled In(Ga)As quantum dots through strain engineering

We have investigated the effect of strain on the $g$-factors of self-assembled In(Ga)As dots by single-dot spectroscopy and an eight-band effective mass calculation taking into account the influence of the strain distribution and the Zeeman effect. The strain and its distribution in and around the quantum dots are varied by thermal annealing or by introducing an strain reducing layer. Thermal annealing produces a graded composition profile due to $\mathrm{In}\mathrm{Ga}$ intermixing. The graded composition profile reduces both hydrostatic and biaxial strain near the bottom of the dot, and enhances them near the top. This strain variation results in a large reduction of the absolute hole $g$-value and a small reduction of the absolute electron $g$-value. On the other hand, the covering of InAs dots with an ${\mathrm{In}}_{0.17}{\mathrm{Ga}}_{0.83}\mathrm{As}$ strain reducing layer decreases mainly the hydrostatic strain. The variation of the strain and the band edge alignment enhance the electron $g$-value while they reduce the hole $g$-value. These results should provide insights to control the $g$-factors in pyramidal self-assembled dots.

First-principle calculations of structural properties and effective-mass of zinc-blende ZnTe and CdTe

The electronic band structures of zinc-blende ZnTe and CdTe are calculated by using a self-consistent full-potential linearized augmented plane-wave method within the first-principle formalism. In order to clarify the electronic properties near the Brillouin-zone (BZ) center and give an effective guideline on the material design for electronic and optical devices, we link the first-principle band calculations with the effective-mass approximation. The electronic properties are analytically studied on the basis of the effective-mass Hamiltonian for zinc-blende symmetry. The effective-mass parameters, such as crystal-field splitting, spin-orbit splitting, electronic effective mass,and the hole effective mass and the corresponding Luttinger-like parameters, are determined by reproducing the calculated band structures near the BZ center. The obtained results are in good agreement with available experimental and theoretical values.

Changes in elastic deformation of strained Si by microfabrication

We have investigated microfabrication-associated changes in the elastic deformation of strained Si films by Raman microscopy. The Raman frequency of the Si–Si vibration mode of microstructured strained Si differed from that of the as-deposited film. This result was attributed to the relaxation of the strain by the appearance of the free surface of the structure. Strain parameters were calculated from the observed Raman frequency, with the asymmetric shape of the structure being taken into account. Dependences of the degree and symmetry of the strain, as well as their spatial distributions, on sample dimensions are discussed. Theoretical calculations of energy bands and hole effective mass were carried out to determine the effect of the fabrication-associated relief of elastic strain on the band structures.

Stripes and holes in a two-dimensional model of spinless fermions or hardcore bosons

We consider a Hubbard-like model of strongly-interacting spinless fermions and hardcore bosons on a square lattice, such that nearest neighbor occupation is forbidden. Stripes (lines of holes across the lattice forming antiphase walls between ordered domains) are a favorable way to dope this system below half-filling. The problem of a single stripe can be mapped to a spin-1/2 chain, which allows understanding of its elementary excitations and calculation of the stripe's effective mass for transverse vibrations. Using Lanczos exact diagonalization, we investigate the excitation gap and dispersion of a hole on a stripe, and the interaction of two holes. We also study the interaction of two, three, and four stripes, finding that they repel, and the interaction energy decays with stripe separation as if they are hardcore particles moving in one (transverse) direction. To determine the stability of an array of stripes against phase separation into particle-rich phase and hole-rich liquid, we evaluate the liquid's equation of state, finding the stripe-array is not stable for bosons but is possibly stable for fermions.

Magnesium Acceptor Energy Levels in Cubic GaN

Intra-impurity transitions of the Mg acceptor in cubic phase GaN were measured with the use of photothermal ionization spectroscopy. Apart from the photoionization band several sharp features were detected, related to internal Mg-acceptor transitions. The transitions were identified with the help of effective-mass model calculations involving light- and heavy-hole as well as spin-orbit split-off bands. Transitions to resonant states, associated with the spin-orbit split-off valence band, were also identified. The determined hole binding energy of the Mg acceptor in zinc-blende GaN is 236 ′ 1 meV.

Large Resonant Stokes Shift in CdS Nanocrystals

The electronic spectrum of CdS colloidal quantum dots (QDs) with a radius of 1.0−2.3 nm is studied by low-temperature photoluminescence excitation spectroscopy. CdS QDs are found to exhibit a resonant Stokes shift of ∼20−70 meV, which is ∼4 times larger than similarly sized CdSe QDs. This effect can be reproduced by an effective-mass theoretical calculation, which reveals that the hole ground state (or highest occupied molecular orbital, HOMO) in CdS QDs is a P state and the ground-state exciton is an optically passive state. Compared to CdSe, in CdS, the smaller spin−orbit splitting causes the orbital-symmetry-forbidden dark exciton in a QD and its larger resonant Stokes shift. The band-edge photoluminescence in CdS QDs exhibits a lifetime of ∼200 ns at 10 K, which is consistent with the dark exciton mechanism.

Full-relativistic calculations of the SrTiO3 carrier effective masses and complex dielectric function

We perform fully relativistic band-structure calculations for cubic SrTiO3, which are used to obtain carrier effective masses and the frequency behavior of its complex dielectric function ε(ω). The obtained values and anisotropy of the carrier effective masses are shown to be highly influenced by the relativistic contributions. In order to evaluate the static dielectric constant, the low-frequency behavior of ε(ω) is obtained by taking into account also the optical phonon contributions to the imaginary part of ε(ω), adopting a simplified classical oscillator dispersion model. It is found that the phonon contribution leads to about 240 times (at T=85 K) the value of the bare electronic contribution to the dielectric constant. The calculated temperature dependence of the dielectric constant is shown to be consistent with that observed in bulk SrTiO3 static permittivity measurements.

Coulomb correlations in semiconductors

We use tight-binding theory to demonstrate how $k\ensuremath{\cdot}p$ theory and local-density approximation (LDA) energies should be corrected to incorporate Coulomb correlation corrections. Applications to the enhanced band gap for the creation of quasiparticles, to the effective mass of carriers, and to the static dielectric susceptibility are given. We find that, in the $k\ensuremath{\cdot}p$ calculations of effective masses, use of the enhanced gap is only accurate for small-gap semiconductors. In the expression for the static dielectric constant, one should use the unenhanced LDA gap for the leading term and the enhanced gap for the metallization term.

Comparison between asp3d5tight-binding and an effective-mass description of silicon quantum dots

This paper presents a tight-binding approach to the calculation of the electronic structure of small silicon nanocrystals. It is based on a nearest-neighbor ${\mathrm{sp}}^{3}{d}^{5}$ Hamiltonian. This Hamiltonian is designed to give accurate results in the limit of a bulk Si crystal and more exactly to reproduce as much as possible the Si band structure. This method is then compared with an effective-mass calculation in order to apprehend the limit of this simplified technique widely used to study the electrical properties of devices based on silicon quantum dots.

Optical properties of bulk and epitaxial unordered GaxIn1−x P semiconductor alloys

The electron band structure of GaxIn1−xP bulk solid solutions was calculated by the local model pseudopotential method taking into account lattice mismatch. The resulting local strain of the lattice was taken into account in calculations of effective mass and deformation potential. The main optical characteristics of GaxIn1−xP alloys can be explained by the presence of internal local strains and antisite defects. In comparison with bulk samples, the concentration dependences of the spectral peaks E1 and E1+Δ1 in pseudomorphic thin films were found to be more sensitive than the fundamental absorption edge E0 to deformations caused by the substrate.

Electric Field Effects in Stacked Dots

We present the results of effective mass calculations for the optical properties of single and stacked InGaAs quantum dots (QD) in the presence of a longitudinal electric field. We have empirically included the effect of inhomogeneity in the In distribution. This effect leads to inverted electron-hole mean vertical positions (i.e. the holes lay above the electrons). We have calculated the variation of the fundamental interband transitions with the electric field, as well as the absorption spectrum, taking into account Gaussian fluctuations in the vertical and lateral dimensions.

Optical properties of InAs/InP ultrathin quantum wells

The optical properties of ultrathin InAs impurity layers embedded in bulk InP are investigated. Our calculations are based on a tight-binding description of the electronic structure, with spin-orbit interactions and strain effects included in a consistent manner. It is shown that the energy gap increases with decreasing number of InAs monolayers. In the limit of a single InAs monolayer, the energy gap is found to be 120 meV less than that of bulk InP. Our results are in good agreement with experimental data as far as the heavy-hole–electron transition is concerned. The energy difference between optical transitions is, however, in disagreement with both experiment and effective-mass calculations.

Stark effects and electro-optical properties of strongly stacked dots

We present the results of effective mass calculations for the optical properties of stacked quantum dots in the presence of a longitudinal electric field. Attention is focused on strongly stacked dots structures where we show that a vertical field acts on the electron much in the same way as found in one-dimensional quantum well structures. As a consequence their Stark tunability can be made much larger than their inhomogeneous broadening. The electro-optical absorption probabilities of stacked dots for intraband and interband transitions are quantitatively calculated taking into account gaussian fluctuations in the vertical and lateral dimensions.

Electronic Structure, Stark Effect and Optical Properties of Multistacked Dots

We present the results of effective mass calculations for the electronic structure and optical properties of stacked quantum dots in the presence of a longitudinal electric field. Attention is focussed on strongly stacked dot structures, in which a vertical field acts on the electron in the same way as found in a quantum well. We have studied the dipole selection rules and oscillator strengths of stacked dots for intraband transitions (far-infrared absorption). In the case of interband transitions, we have studied the effect of a longitudinal electric field on the overlap between electron and hole wavefunctions. We have also calculated the absorption spectrum for structures of attached dots, taking into account Gaussian fluctuations in the vertical and lateral dimensions.

Calculation of the Infrared Optical Transitions in Semiconductor Ellipsoidal Quantum Dots

We report on our effective mass calculations for a particle confined in an ellipsoidal quantum dot. Upon using a curvilinear coordinates system, the single particle exact eigenvalues and eigenfunctions have been numerically calculated. Dielectric image effects have been properly taken into account. It is shown that on keeping the volume constant, the confinement energies depend only on the dot shape. The implications of this shape dependence are analyzed for the infrared optical properties.

Zeeman spin splittings in semiconductor nanostructures

A systematic theoretical and experimental study of Zeeman spin splittings and g factors in semiconductor nanostructures is given. Six-band effective-mass calculations of electron, hole, and exciton spin splittings are made and are shown to account for experimental results presented here on ${\mathrm{In}}_{0.10}{\mathrm{Ga}}_{0.90}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ systems for the size dependences of g factors in deep-etched quantum dots and wires and for the magnetic-field dependences of the Zeeman splittings in quantum wells. These effects are traced to band mixing, and an analytic form of the results is given that connects these two effects and describes their dependences on dimensionality.

Stabilized electronic state and its luminescence at the surface of oxygen-passivated porous silicon

Photoluminescence (PL) spectra of as-made porous Si samples were obtained in a wide peak-wavelength range. After exposure to air or coupling with ${\mathrm{C}}_{60}$ molecules, the PL peak shifts to a pinning wavelength within the range of 610--630 nm. This pinning wavelength is almost independent of the size of the original porous Si nanocrystallites and both redshifting and blueshifting can occur for different sizes. A self-consistent effective-mass calculation shows that the $\mathrm{Si}=\mathrm{O}$ binding states are responsible for the radiation of this pinning wavelength and the blueshift for the large nanocrystallites is due to the additional potential modulation within the Si nanocrystallite by the long-range Coulomb interaction of oxygen ions.

L−to−Xcrossover in the conduction-band minimum of Ge quantum dots

Screened-pseudopotential calculations of large ((less-or-similar sign)3000 atoms) surface-passivated Ge quantum dots show that below a critical dot diameter that depends on the passivant, the character of the lowest conduction state changes from an L-derived to an X-derived state. Thus, in this size regime, Ge dots are Si-like. This explains the absence, in a pseudopotential description, of a crossing between the band gaps of Si and Ge dots as a function of size, predicted earlier in single-valley effective-mass calculations. The predicted L{yields}X crossing suggests that small Ge dots will have an X-like, red shift of the band gap with applied pressure, as opposed to an L-like blue shift of large dots. (c) 2000 The American Physical Society.

Optical transitions of Al0.35Ga0.65As/GaAs asymmetric double quantum wells grown on GaAs(n11)A (n≤4) substrates

The optical transitions in Al0.35Ga0.65As/GaAs asymmetric double quantum wells (ADQWs) grown on GaAs(n11)A (n≤4) substrates were studied by photoluminescence at low temperatures. The redshift of two PL peaks for substrate orientation far from the (100) plane is attributed to the large anisotropy of the heavy-hole band in the different GaAs orientations. The energy difference of the two transitions also shows a similar shift. By comparing the PL measurements with a simple effective mass calculation, the effective mass of the heavy hole on GaAs(n11)A (n=1, 2, 3, 4) planes is found to be about 0.95, 0.73, 0.54 and 0.41m0, respectively. The effect of As pressures on PL peak energies in ADQWs is also studied. The As pressure-dependence of PL peak energies is attibuted to a decrease of the Ga desporption rate with increasing As pressures on GaAs(n11)A substrates.