Anisotropic Effective Mass Research Articles

Super-resolution imaging by resonant tunneling in anisotropic acoustic metamaterials

The resonant tunneling effects that could result in complete transmission of evanescent waves are examined in acoustic metamaterials of anisotropic effective mass. The tunneling conditions are first derived for the metamaterials composed of classical mass-in-mass structures. It is found that the tunneling transmission occurs when the total length of metamaterials is an integral number of half-wavelengths of the periodic Bloch wave. Due to the local resonance of building units of metamaterials, the Bloch waves are spatially modulated within the periodic structures, leading to the resonant tunneling occurring in the low-frequency region. The metamaterial slab lens with anisotropic effective mass is designed by which the physics of resonant tunneling and the features for evanescent field manipulations are examined. The designed lens interacts with evanescent waves in the way of the propagating wavenumber weakly dependent on the spatial frequency of evanescent waves. Full-wave simulations validate the imaging performance of the proposed lens with the spatial resolution beyond the diffraction limit.

Giant and anisotropic magnetoresistances in p-type Bi-doped Sb2Te3 bulk single crystals

Antimony telluride (Sb2Te3) compounds are well known as excellent thermoelectric materials and have been recently confirmed as three-dimensional topological insulators. In this letter, we have investigated the anisotropic magneto-transport properties of p-type Bi-doped Sb2Te3 bulk single crystals over a broad range of temperatures, degrees and magnetic fields. Giant magnetoresistance (MR) of up to 230% was observed, which exhibits quadratic field dependences in low fields and becomes linear at high fields without any trend towards saturation. The giant MR also shows strong anisotropy with anisotropy ratio up to 210% in angle-dependent measurements. The giant MR might result from strong intervalley and intravalley scattering of holes and the strong anisotropy is attributable to the anisotropy of hole mobility, relaxation time and effective mass in the Fermi surface. The observed giant anisotropic MR could find applications in Sb2Te3-based anisotropic magneto-electronic devices.

Anisotropy of the carrier effective masses in bulk α-PbO

The electronic properties of an individual α-PbO layer and bulk material consisting of stacked interacting layers are studied with the first-principle calculations. It was found that while for an individual layer the top of the valence band is extremely flat, for stacked layers it becomes dispersive due to the interlayer interaction. As a result, an effective mass of holes drops from m*h = 38m0 in a single layer to m*h = 2.44m0 in bulk α-PbO. In contrast, the conduction band is almost independent of the layer interaction: for both individual layer and bulk material the bottom of the conduction band is characterized by sharp dispersion. The electron effective mass is practically unchanged and is about m*e = 0.4m0. The calculation of the electron density distribution suggests that heavy holes are a result of a strong localization of lone pair p electrons on the oxygen atom which form the top of the valence band. A similar effect of heavy holes is observed for another photoconductor like amorphous Se (Gobrecht H. and Tausend A., in Proceedings of the International Conference on the Physics of Semiconductor, Paris, 1964 (Academic Press Inc., New York) 1965, p. 1189) for which the lone pairs of the valence electrons play an important role in photo-generation.

Electron–hole transition in a spherical quantum dot confined at the center of a cylindrical nano-wire: Comparison of isotropic and anisotropic effective mass

Electronic structure of an InAs spherical quantum dot placed at the center of a GaAs cylindrical nano-wire is investigated. The Schrodinger equation within the effective mass approximation is solved and the energy eigenvalues and transition energies are calculated as a function of quantum dot and nano-wire radii using the finite element method. The two types of heavy holes, hhI and hhII, with isotropic and anisotropic effective masses are considered, respectively. The effect of spherical and nano-wire confining potentials, the size of the dot and the nano-wire on ground and first excited state energies of the electron, heavy hole I and heavy hole II are investigated. The results show that the electron and heavy holes energies decrease as the dot and the nano-wire radii increase. The emitted wavelength of transitions between el-hhI and el-hhII are also calculated and compared. The results show that the anisotropy of the effective mass has great effect on the emitted wavelength.

Multi-displacement microstructure continuum modeling of anisotropic elastic metamaterials

An elastic metamaterial made of lead cylinders coated with elliptical rubbers in an epoxy matrix is considered, and its anisotropic effective dynamic mass density tensor is numerically determined and demonstrated. To capture both dipolar resonant motion and microstructure deformation in the composite, a new multi-displacement microstructure continuum model is proposed. In the formulation, additional displacement and kinematic variables are introduced to describe global and local deformations, respectively. The macroscopic governing equations of the two-dimensional anisotropic elastic metamaterial are explicitly derived through a simplified procedure. To verify the current model, wave dispersion curves from the current model are compared with those from the finite element simulation for both longitudinal and transverse waves. Very good agreement is observed in both the acoustic and optic wave modes. This work could provide a benchmark of continuum modeling of elastic metamaterials with nonelementary microstructures.

The model of valence-band dispersion for strained Ge/Si1-xGex

Based on the kp theory, the valence-band dispersion model for biaxial strained Ge/Si1-xGex is derived by taking strained Hamiltonian perturbation into account. The model can be used to calculate the valence band structure and hole effective mass along arbitrarily k wavevector direction in strained Ge grown on arbitrarily oriented relaxed Si1-xGex virtual substrate. The MATLAB simulation results of the model show that by comparison with relaxed Ge, the more anisotropy of the hole effective mass occurs in strained Si1-xGex and the hole effective mass of the top valence band decreases with the increase of Ge fraction. The results can supply valuable references to the conduction channel design related to stress and orientation in the Si-based strained Ge MOS devices and integrated circuits.

Anisotropy and isotropy of hole effective mass of strained Ge

In this paper, the hole effective mass along arbitrarily k wavevector direction and the hole isotropic effective masses in strained Ge/(001)(101)(111)Si1-xGex are obtained with in the frame work of kp theory. It is found that the hole effective mass of the top valence band along [010] wave vector decreases obviously with stress increasing and its absolute value is smallest. The hole effective mass of the second valence band tends to gently decrease with stress increasing, and is not significant in magnitude. Compared with the existing isotropic effective quality, the result obtained in this paper is proved to be correct.

Anisotropy of Drift Velocity in Electron Transport Simulation in Silicon

Ensemble Monte Carlo simulation based on analytic band model has been researched and developed for electron transport in silicon. The simulation shows anisotropy of drift velocity for different directions of electric fields as in the case of full band model. This phenomenon is due to the anisotropy of electron effective masses in X valley.

Magnetic susceptibility of (Bi2 − x Sb x )Te3 (0 < x < 1) alloys in the temperature range 2 to 50 K

The superconducting quantum interferometer device with Josephson junctions (SQUID magnetometer) is used to study the temperature dependences of the magnetic susceptibility of (Bi2−x Sb x )Te3 (0 < x < 1) alloy crystals in the temperature range 2 to 50 K, at the magnetic field vector H orientations H | C 3 and H ⊥ C 3 with respect to the crystal trigonal axis C 3. It is found that the magnetic susceptibility of the ion core of the samples under study is χ G = −0.35 × 10−6 cm3/g, the contribution of lattice defects to magnetic susceptibility can be disregarded, and the contribution of free carriers is of a diamagnetic nature in the entire studied temperature range. It is shown that the contribution of free carriers to the resulting magnetic susceptibility and its anisotropy can be described within the Pauli and Landau-Peierls approach. In calculating the magnetic susceptibility, taking into account the constant concentration of free carriers in the state of pronounced degeneracy, it is found that the temperature dependence of the anisotropic effective masses varies with crystal chemical composition. This is possibly associated with the complex structure of the valence band and its variation as the Sb2Te3 content in the alloy increases.

Electronic Transports for Thermoelectric Applications on IV&amp;ndash;VI Semiconductors

Seebeck effect, Peltier effect, Thomson effect, electronic thermal conductivity, Hall effect, and Nernst effect are described on the basis of electronic conduction theory, taking account of effective mass anisotropy, nonparabolicity in E­k relation, and temperature dependent band gap. It is shown that the temperature dependence of the band gap does not modify the basic equations for the Seebeck coefficient, thermal conductivity, and Nernst coefficient. In narrow gap semiconductors, existence of minority carriers significantly enhances the electronic thermal conductivity, owing to the multiple carrier transport known as bipolar diffusion. Calibration coefficient £ for the Hall effect (RH ¼� £=en )i s increased by nonparabolicity in the E­k relation. Nernst coefficient gives useful information on scattering properties of the materials. [doi:10.2320/matertrans.E-M2012812]

The diamagnetic susceptibility of hydrogenic donor in two-dimensional semiconductors with anisotropic effective mass of carriers

In this study, the effects of quantum confinement and effective mass anisotropy parameter on the diamagnetic susceptibility of a hydrogenic donor placed in GaAs, Si, and Ge quantum wells with infinite confinement potential are investigated in the effective mass and parabolic band approximations by using two and one parameter trial wave functions. It is observed that the diamagnetic susceptibility of a hydrogenic donor in anisotropic quantum wells is essentially equal to the transverse diamagnetic susceptibility part when well widths are larger than L>100Å, and the impurity is located at center. Moreover, a two parameter trial wave function model gives higher values of diamagnetic susceptibility, except for χz (GaAs).

Analytical and numerical studies on strain and crystal-orientation effects on the valence bands in hexagonal semiconductor layers and quantum wells

The effects of strain and crystal orientation on the effective masses of holes in bulk layers and in quantum wells (QWs) of hexagonal semiconductors are studied systematically within a six-band effective-mass theory. Analytical expressions of the effective masses in strained bulk layers are derived in some specific cases. The sum rule among the inverse effective masses in bulk layers as well as that among the inverse quantization masses in QWs is proved. Numerically calculated results on GaN bulk layers grown on non-polar planes reveal that strain modifies anisotropy in zone-center effective masses. The quantization energies of holes in unstrained GaN QWs are calculated as a function of the growth direction. The calculated results are also shown for quantization masses in (0 0 0 1) and ( 1 0 1 ¯ 0 ) strained QWs as functions of the well width and strain.

Effective Mass Anisotropy of Hot Electrons in Nonparabolic Conduction Bands ofn-Doped InGaAs Films Using Ultrafast Terahertz Pump-Probe Techniques

The anisotropic effective mass of energetic electrons in an isotropic, nonparabolic conduction band is revealed using ultrafast THz-pump-THz-probe techniques in a n-doped InGaAs semiconductor thin film. A microscopic theory is applied to identify the origin of the observed anisotropy and to show that the self-consistent light-matter coupling contributes significantly to the THz response.

POLARONIC EFFECTS IN WURTZITE GaN/AlxGa1-xN QUANTUM WELLS

The properties of polarons in a wurtzite GaN / Al x Ga 1-x N quantum well (QW) are investigated by adopting an effective-mass approximation and a modified Lee–Low–Pines variational method. The ground-state energy, the transition energy and the phonon contributions due to various optical-phonon modes to the ground-state energy as functions of the well width are given. The effects of the confined (CF) optical phonon mode, interface (IF)-optical phonon modes, half-space (HS) phonon modes, the anisotropy of the electron effective band mass and the phonon frequency are respectively considered (or included) in the calculation. The results have been compared with those of the zinc-blende structure. The numerical result indicates that both the ground-state energies of polaron and the transition energy decrease with increasing well width. For QWs with larger well width (&gt; 10 nm), the total contribution to polaronic energy mainly comes from the confined mode, and for QWs with narrower well width (&lt; 2 nm), the total contribution to polaronic energy mainly comes from the IF-optical phonon and HS phonon modes. And the phonon contribution in GaN/Al x Ga 1-x N QW is much larger than that in GaAs/Al x Ga 1-x As QW. The two IF-optical phonon modes with lower frequency, the transverse optical-like CF and HS modes are extremely small so that they can be neglected in the further discussion.

Multiband superconductivity in LaFeAsO0.9F0.1single crystals probed by high-field vortex torque magnetometry

To probe manifestations of multiband superconductivity in oxypnictides, we measured the angular dependence of the magnetic torque $\tau(\theta)$ in the mixed state of LaO$_{0.9}$F$_{0.1}$FeAs single crystals as a function of temperature $T$ and magnetic fields $H$ up to 18 T. The paramagnetic contribution of the Fe ions is properly treated in order to extract the effective mass anisotropy parameter $\gamma=(m_c/m_{ab})^{1/2}$ from $\tau(\theta)$. We show that $\gamma$ depends strongly on both $T$ and $H$, reaching a maximum value of $\sim$ 10 followed by a decrease towards values close to 1 as $T$ is lowered. The observed field dependencies of the London penetration depth $\lambda_{ab}$ and $\gamma$ suggest the onset of suppression of a superconducing gap at $H \approx H_{c2}/3$.

Anomalies in Transport and Superconducting Properties of Ba1-xKxFe2As2 Single Crystals

The transport and superconducting properties of Ba1-xKxFe2As2 single crystals were studied. Both in-plane and out-of-plane resistivity were measured by Montgomery method. The in-plain resistivity temperature dependence was found to be nonlinear with the tendency to saturate at high temperature. We have found that the resistivity anisotropy is almost independent of temperature and lies in the range 10–40 for the studied samples. We explain this result by the extrinsic nature of high out-of-plane resistivity, which may be due to the presence of flat defects along Fe–As layers. This statement is supported by comparatively small effective mass anisotropy, obtained from the upper critical field measurements.

Photoabsorption oscillations in semiconductors with sharply anisotropic effective mass of electrons in quantizing magnetic fields

A theory of photoabsorption on magnetic-impurity states of carriers with sharply anisotropic effective mass is developed. Both in crossed and parallel electric and magnetic fields the photoabsorption coefficient is investigated for intraband (in terms of Landau bands) and interband transitions of an electron. It is shown that the resonant component of the photoabsorption coefficient at electron detachment and the resonant component of cyclotron resonance harmonics have periodically dependence by the magnetic field as √H. Influence of parity of the magnetic-impurity states on frequency dependence of the resonant component of photoabsorption coefficient is studied.

Determination of effective mass of heavy hole from phonon-assisted excitonic luminescence spectra in ZnO

Longitudinal optical (LO) phonon-assisted luminescence spectra of free excitons in high-quality ZnO crystal were investigated both experimentally and theoretically. By using the rigorous Segall–Mahan model based on the Green’s function, good agreement between the experimental emission spectra involving one or two LO phonons and theoretical spectra can be achieved when only one adjustable parameter (effective mass of heavy hole) was adopted. This leads to determination of the heavy-hole effective mass mh⊥ = (0.8 m0 and mh∥ = 5.0 m0) in ZnO. Influence of anisotropic effective masses of heavy holes on the phonon sidebands is also discussed.

Design and measurements of a broadband two-dimensional acoustic metamaterial with anisotropic effective mass density

We present the experimental realization and characterization of a broadband acoustic metamaterial with strongly anisotropic effective mass density. The metamaterial is composed of arrays of solid inclusions in an air background, and the anisotropy is controlled by the rotational asymmetry of these inclusions. Transmission and reflection measurements inside a one-dimensional waveguide are used to extract the relevant components of the effective density tensor together with the effective bulk modulus of the metamaterial. Its broadband anisotropy is demonstrated by measurements that span 500–3000 Hz. Excellent agreement between these measurements and numerical simulations confirms the accuracy of the design approach.

Locally resonant acoustic metamaterials with 2D anisotropic effective mass density

A two-dimensional (2D) lattice model with anisotropic resonant microstructures is found to provide an anisotropic band gap structure. A 2D continuum with anisotropic effective mass density is introduced to represent this lattice system. Two methods are proposed to derive the equivalent continuum. In the first method, the effective mass density of the equivalent continuum is obtained by matching the dispersion relations for harmonic waves propagating in the principal directions. The second approach employs an approximate estimation of the effective mass density by volume-averaging an effective mass that represents the resonant microstructure. For both equivalent continuum models, the effective mass density is frequency-dependent and may become negative in certain frequency ranges. Subsequently, the effective mass density of the equivalent continuum assumes the form of a second-order tensor. Thus, it suffices to determine the effective mass density tensor with respect to the principle directions. It is shown numerically that the local-resonance effect is accurately described by the equivalent continuum model. In addition, the effect of anisotropic mass density on wave propagation is numerically illustrated and discussed.