Anisotropic Effective Mass Research Articles

THE DENSITY MATRIX FOR AN ELECTRON CONFINED IN QUANTUM DOTS UNDER A UNIFORM MAGNETIC FIELD

By using unitary transformation and representation theory of quantum mechanics, we obtain two forms of density matrix respectively in (x1, p2) and (x1, x2) representations for an electron, with an anisotropic effective mass, confined in quantum dots under a uniform magnetic field (UMF). We find that both forms of density matrix can play an implemental role in the thermodynamical calculation. But, in order to calculate thermal average of angular momentum in z direction for this system, the density matrix in (x1, p2) representations is a more convenient form. When the confinement to electron in quantum dots disappears, we encounter a divergence problem of thermal average for some physical quantities. However, in the calculation of the thermal average of Hamiltonian, these divergent quantities cancelled each other out. And we eventually obtain a reasonable result.

Anisotropy of the Γ‐point effective mass and mobility in hexagonal InN

AbstractWe determine the anisotropic electron effective mass and mobility parameters in wurtzite InN thin films with free electron concentration N from 1.8 × 1017 cm–3 to 9.5 × 1018 cm–3 using Infrared Magneto‐optic Generalized Ellipsometry. The room‐temperature measurements were carried out with magnetic fields up to 4.5 T. For the Γ‐point we estimate m *⊥ = 0.047m 0 and m *‖ = 0.039m 0 for polarization perpendicular and parallel to the c ‐axis, respectively. Scattering by impurities or ionized donors may explain the decrease of mobility for polarization parallel to the c ‐axis from 1600 cm2/(Vs) to 800 cm2/(Vs) with increase in N , where the perpendicular mobility is further decreased, likely caused by additional grain boundary scattering. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Silicon quantum dot superlattices: Modeling of energy bands, densities of states, and mobilities for silicon tandem solar cell applications

Quantum dot superlattices offer prospects for new generations of semiconductor devices. One possible recently suggested application is in tandem solar cells based entirely on silicon, using confinement in the quantum dot to control the cell band gap. In this paper, we use the effective mass approach to calculate the conduction band structure of a three-dimensional silicon quantum dot superlattice with the dots embedded in a matrix of silicon dioxide, silicon nitride, or silicon carbide. The quantum dot superlattice is modeled as a regularly spaced array of equally sized cubic dots in the respective matrix. Incorporating the effect of silicon anisotropic effective mass is shown to reduce both the degeneracies of the isotropic solutions and the energy separation between states. Electron densities of state and mobilities are derived from the band structure data. Theoretical results for the effect of dot size, interdot distance, and matrix material have been obtained. These results clarify the required design features of silicon quantum dot superlattices for the proposed all-silicon tandem solar cells.

Enhancement of the Electron–Hole BCS Order by Energy Band Anisotropy in Highly Photoexcited Semiconductors

We discuss the enhancement effects of the electron–hole BCS order due to the effective-mass anisotropy in highly photoexcited semiconductors. The present study provides us with a new possibility to experimentally observe a macroscopic quantum state by applying the uniaxial stress to semiconducting materials with high density electrons and holes. It is quantitatively shown that this enhancement due to the stress induced mass anisotropy can exceed the reduction of the order arising from the temperature effect and to from the difference in valence- and conduction-band structures.

Biexciton recombination rates in self-assembled quantum dots

The radiative recombination rates of interacting electron-hole pairs in a quantum dot are strongly affected by quantum correlations among electrons and holes in the dot. Recent measurements of the biexciton recombination rate in single self-assembled quantum dots have found values spanning from two times the single exciton recombination rate to values well below the exciton decay rate. In this paper, a Feynman path-integral formulation is developed to calculate recombination rates including thermal and many-body effects. Using real-space Monte Carlo integration, the path-integral expressions for realistic three-dimensional models of $\mathrm{In}\mathrm{Ga}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$, $\mathrm{Cd}\mathrm{Se}∕\mathrm{Zn}\mathrm{Se}$, and $\mathrm{In}\mathrm{P}∕\mathrm{In}\mathrm{Ga}\mathrm{P}$ dots are evaluated, including anisotropic effective masses. Depending on size, radiative rates of typical dots lie in the regime between strong and intermediate confinement. The results compare favorably to recent experiments and calculations on related dot systems. Configuration interaction calculations using uncorrelated basis sets are found to be severely limited in calculating decay rates.

Hc2 of anisotropy two-band superconductors by Ginzburg–Landau approach

The purpose of this research is to study the upper critical field Hc2 of two-band superconductors by two-band Ginzburg–Landau approach. The analytical formula of Hc2 included anisotropy of order parameter and anisotropy of effective-mass are found. The parameters of the upper critical field in ab-plane (Hc2∥ab) and c-axis (Hc2∥c) can be found by fitting to the experimental data. Finally, we can find the ratio of upper critical field that temperature dependent in the range of experimental result.

Effects of Effective Mass Anisotropy and Effective Mass Difference in Highly Photoexcited Semiconductors

We analyze the effects of effective mass anisotropy and the effective mass difference between electrons and holes on the electron–hole ( e – h ) BCS state in highly excited semiconductors at various temperatures. The present analysis is based on the BCS-like pairing theory for finite temperatures. We find that, at sufficiently low temperatures, the e – h BCS state is stable even in the case of differing electron and hole effective masses. On the other hand, the difference in effective mass anisotropy between electrons and holes significantly suppresses the e – h BCS order. We have also found that, in the case where electrons and holes have the same mass anisotropy, the e – h BCS order becomes more stable with increasing the anisotropy.

110]-surface strained-SOI CMOS devices

We have newly developed [110]-surface strained-silicon-on-insulator (SOI) n- and p-MOSFETs on [110]-surface relaxed-SiGe-on-insulator substrates with the Ge content of 25%, fabricated by applying the Ge condensation technique to SiGe layers grown on [110]-surface SOI wafers. We have demonstrated that the electron and the hole mobility enhancement of [110]-surface strained-SOI devices amounts to 23% and 50%, respectively, against the mobilities of [110]-surface unstrained MOSFETs. As a result, the electron and the hole mobility ratios of [110]-surface strained-SOI MOSFETs to the universal mobility of (100)-surface bulk-MOSFETs increase up to 81% and 203%, respectively. Therefore, the current drive imbalance between n- and p-MOS can be reduced. Moreover, both the electron and the hole mobilities of the [110]-surface strained-SOIs strongly depend on the drain current flow direction, which is qualitatively explained by the anisotropic effective mass characteristics of the carriers on a [110]-surface Si. As a result, the [110]-surface strained-SOI technology with optimization of the current flow directions of n- and p-MOS is promising for realizing higher speed scaled CMOS.

INTERBAND MAGNETO-SPECTROSCOPY OF A HIGH-DENSITY TWO-DIMENSIONAL ELECTRON GAS IN A STRONG IN-PLANE MAGNETIC FIELD

We report results of temperature and field dependent studies of interband optical absorption and photoluminescence in a two-dimensional electron gas in a strong in-plane magnetic field (up to 45 T). We observe a field dependent shift of the Fermi energy with both the magnitude and sign of the shift varying with magnetic field. Simultaneous low temperature magneto-photoluminescence measurements reveal a monotonically increasing blue shift accompanied by a quenching of the intensity. A theoretical treatment based on a single particle picture and taking into account the diamagnetic shift as well as a shift due to an anisotropic effective mass cannot qualitatively reproduce our experimental results, indicating that many-body interactions may be important.

High-performance (1 1 0)-surface strained-SOI MOSFETs

We have studied (1 1 0)-surface strained-SOI n- and p-MOSFETs on (1 1 0)-surface relaxed Si 0.75Ge 0.25-on-insulator structures, applying the Ge condensation technique to SiGe layers grown on (1 1 0)-surface SOI wafers. We have demonstrated that the electron and the hole mobility enhancement of (1 1 0)-surface strained-SOI devices amounts to 23% and 50%, respectively, against the mobilities of (1 1 0)-surface unstrained MOSFETs. As a result, the electron and the hole mobility ratios of (1 1 0)-surface strained-SOI MOSFETs to the universal mobility of (1 0 0)-surface bulk-MOSFETs increase up to 81% and 203%, respectively. Therefore, the current drivability unbalance between n- and p-MOS can be reduced. Moreover, both the electron and the hole mobilities of the (1 1 0)-surface strained-SOIs strongly depend on the drain current flow direction, which is explained by anisotropic effective mass characteristics of the carriers. We have also introduced a simple model for electric field dependence of hole mobility of (1 1 0)-surface strained- and unstrained-MOSFETs. (1 1 0)-surface strained-SOI technology is also the candidate for higher speed scaled CMOS, optimizing the current flow directions of n- and p-MOS.

Electronic Structure and Electrical Conductivity of Undoped LiFePO[sub 4

The electronic structure of LiFePO 4 underpins transport properties important to its use as a lithium storage electrode. Here we have calculated the electronic structure of LiFePO 4 in the ordered olivine structure by a first-principles method to determine (i) the effective mass of carriers and (ii) the nature of the band structure. The electrical conductivity in high purity undoped LiFePO 4 has also been measured experimentally. Spin-polarized calculations show a large electron effective mass and a much smaller but highly anisotropic hole effective mass, suggesting that hole-doped compositions should have the greater electronic conductivity. More surprisingly, the calculations show that this polyanion compound is a half-metal with spin-sensitive band structure, like some other oxides being studied for spintronics applications. This previously unappreciated aspect of the LiFePO 4 electronic structure may play a role in determining transport properties including those relevant to electrochemical applications.

Surface‐induced broadening and shift of exciton ground‐state resonance in quantum wells

Basing on the Green's function method for the study of disordered systems, we propose a simple model that describes the shift and broadening of excitonic resonance in interface-corrugated quantum wells. This model employs the original microscopic excitonic Hamiltonian and is applicable in a wide region of varying parameters from the sharp resonance to the classical limit. The relaxation frequency and the shift of exciton ground-state resonance are calculated analytically for realistic quantum wells with finite potential barriers and anisotropic effective masses of the electron and hole. It is shown that the type of the excitonic resonance and its line-shape are mainly controlled by the competition between the correlation properties of surface disorder and finite height of potential barriers. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Vertically polarized lasing and photoluminescence in a ridge quantum-wire laser

We study vertically polarized lasing and spontaneous emissions in a ridge quantum-wire (QWR) laser. In particular, we find that most of emissions with energies near the band edge are vertically polarized. We make numerical calculation of oscillator strength for optical transitions between various combinations of electron and hole states, and indeed show oscillator strength of vertically polarized transitions is stronger in our QWR structure. We find that the different effective mass of electrons and holes, especially anisotropic effective mass of holes causes different shapes of wave functions between electrons and holes, which results in larger oscillator strength of vertically polarized transition.

Anisotropic size quantization and semimetal–semiconductor phase transition in bismuth-like cylindrical nanowires

The electronic subband structure of carriers in bismuth-like cylindrical nanowires is investigated analytically, using an anisotropic effective mass model. Quantum confinement effects are found to be significantly enhanced over the results of a quasi-isotropic approach, due to the correct consideration of both the mass anisotropy and the boundary shape of the wire. The size quantization problem for a carrier with anisotropic effective mass parameters in a cylindrical well is shown to be equivalent to that of a carrier with some isotropic effective mass in an elliptical well. Detailed study of the energy levels reveals their orbital degeneracy is lifted by the elliptic symmetry, where the degree of ellipticity corresponds to the mass anisotropy. Carrier motion is analysed by analogy to the geometrical optics of elliptic waveguides, with bounding caustic curves defining two groups inside the wire that correspond to ‘whispering gallery’ and ‘jumping ball’ modes. The additional confinement, arising from the mass anisotropy, leads to larger critical wire diameters for the semimetal-to-semiconductor transition, which is investigated for wires of different crystallographic orientation.

Conduction-band anisotropy effects in spherical semiconductor nanocrystals: atheoretical study

The quantum confinement for a conduction-band electron within a sphericalquantum dot is investigated in the framework of the effective-mass approximation.The conduction-band effective-mass anisotropy is fully taken into account. Theexact solution for the electronic spectrum is provided, showing how the‘isotropic’ mass levels map into the new spectrum which accounts for theanisotropy. The removal of degeneracies typical of the spherical dot, aswell as its effects on the infrared transition energies, are discussed.

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.

Screening and in-plane magnetoresistance of an anisotropic two-dimensional gas

In order to split the influence of the orbital and spin effects on the inplane magnetoresistance of a quasi two-dimensional gas we derive its linear response function and dielectric function for the case of anisotropic effective mass. This result is used for the calculation of elastic transport relaxation time of a quasi two dimensional system in a parallel magnetic field. The relaxation time is proved to be isotropic in the low density limit for the case of charged impurity scattering, allowing to separate the two contributions.

Anisotropy in Thermoelectric Properties of CsBi4Te6

ABSTRACTCsBi4Te6 (ZT ∼ 0.8 at 225 K) shows highly anisotropic features in its crystal morphology and structure as expressed by the parallel infinite [Bi4Te6] rods which are linked via Bi-Bi bonds. Band calculations also point to a significant anisotropy in the carrier effective masses, and for this reason we examined the anisotropic thermoelectric properties of CsBi4Te6. The electrical conductivity, thermopower and thermal conductivity were measured along the three different crystallographic directions of the monoclinic structure of CsBi4Te6. These measurements were performed on samples with different degrees of doping. The strong charge transport anisotropy of these samples was confirmed and also observed that the thermopower values along the c-axis direction (which is perpendicular to the layer of Cs atoms) was negative (-80 μV/K) while those along the needle direction (b-axis) and parallel to the [Bi4Te6] layers (a-axis) were p-type (50–100 μV/K at room temperature. Other anisotropic features in the crystal growth habit, electronic band structure, and electrical and thermal conductivities are also presented.

Anisotropy and reversible magnetization of the infinite-layer superconductorSr0.9La0.1CuO2

We present reversible magnetization measurements of a c-axis aligned ${\mathrm{Sr}}_{0.9}{\mathrm{La}}_{0.1}{\mathrm{CuO}}_{2}$ infinite-layer superconductor with ${T}_{c}\ensuremath{\simeq}43\mathrm{K}.$ The magnetization measured as a function of temperature and angle between the c axis and the external magnetic field are analyzed in terms of the Hao-Clem model. Consequently, the critical fields $[{H}_{c}(0),$ ${H}_{c1}^{c}(0),$ and ${H}_{c2}^{c}(0)]$ and the characteristic lengths $[{\ensuremath{\xi}}_{\mathrm{ab}}(0)$ and ${\ensuremath{\lambda}}_{\mathrm{ab}}(0)]$ are derived. We introduce a novel technique to describe the angular dependence of magnetization using the Hao-Clem model by employing the effective mass anisotropy. The anisotropy ratio $\ensuremath{\gamma}=9.3$ and the zero-temperature coherence length along the c axis ${\ensuremath{\xi}}_{c}(0)=5.2\AA{}$ are obtained by the technique. The coherence length ${\ensuremath{\xi}}_{c}(0)$ is longer than the c-axis lattice parameter $c=3.41\AA{},$ which implies three-dimensional coupling between ${\mathrm{CuO}}_{2}$ planes even at zero temperature.

Gigantic anisotropy of the harmonics generation efficiency in the semiconductors with effective mass anisotropy

The dependencies of third harmonic generation due to electron scattering by charged impurities versus electron effective mass, electron temperature and infrared radiation intensity and frequency are derived. For semiconductors with strong electron effective mass anisotropy, a gigantic anisotropy in the generation efficiency is found.