Anisotropic Effective Mass Research Articles

Wave propagation in an elastic metamaterial with anisotropic effective mass density

The effect of anisotropic mass density on wave propagation in acoustic/elastic metamaterials is presented in this research. The use of microstructures to achieve mass anisotropy in metamaterials is an intensive field of study. In this work, a numerical continuum model, based on a recently developed cantilever-in-mass model, is proposed. Mass anisotropy in this model is derived based on analytical calculations of a two-dimensional (2D) ‘mass-in-mass’-spring lattice system. The mass–spring lattice is able to portray anisotropic effective mass density in two orthogonal principal directions. Effective mass density along each direction is frequency-dependent. A strong “effective mass anisotropy” is accomplished within the frequency band gap or just below the frequency range of negative effective mass. The proposed mass–cantilever continuum model is used to examine 2D wave propagation. Results show that wave attenuation in a metamaterial with 2D anisotropic mass density is dependent on both input frequency and wave input angle. This study demonstrates a case whereby wave attenuation is achieved by selecting wave input frequency in the band gap region to enact “negative effective mass density”, thereby mitigating wave propagation. In this case, the most efficient attenuation performance is achieved at an input wave angle of 0°. This study also illustrates another case whereby wave attenuation is obtained by mass anisotropy at a frequency just below the local resonance frequency. Wave attenuation is achieved by redirecting wave propagation along the transverse direction, particularly prominent at an input wave angle of 70°. Both numerical calculations of mass–spring lattice model and continuum cantilever-in-mass model show excellent agreement with each other.

Accurate electronic and optical properties of hexagonal germanium for optoelectronic applications

High-quality defect-free lonsdaleite Si and Ge can now be grown on hexagonal nanowire substrates. These hexagonal phases of group-IV semiconductors have been predicted to exhibit improved electronic and optical properties for optoelectronic applications. While lonsdaleite Si is a well-characterized indirect semiconductor, experimental data and reliable calculations on lonsdaleite Ge are scarce and not consistent regarding the nature of its gap. Using ab initio density-functional theory, we calculate accurate structural, electronic, and optical properties for hexagonal Ge. Given the well-known sensitivity of electronic-structure calculations for Ge to the underlying approximations, we systematically test the performance of several exchange-correlation functionals, including meta-GGA and hybrid functionals. We first validate our approach for cubic Ge, obtaining atomic geometries and band structures in excellent agreement with available experimental data. Then, the same approach is applied to predict electronic and optical properties of lonsdaleite Ge. We portray lonsdaleite Ge as a direct semiconductor with only weakly dipole-active lowest optical transitions, small band gap, huge crystal-field splitting, and strongly anisotropic effective masses. The unexpectedly small direct gap and the oscillator strengths of the lowest optical transitions are explained in terms of symmetry and back-folding of energy bands of the diamond structure.

Transverse to longitudinal mode conversion via nonlinear inertial effects in a locally resonant metamaterial plate

Acoustic and elastic metamaterials have potential for tailoring wave propagation in ways beyond the capabilities of conventional materials and have been shown to exhibit a myriad of rich dynamical effects, such as negative effective properties, cloaking, extreme damping, and non-reciprocity. However, most of the existing literature has been focused on linear dynamics in which these behaviors are restricted to narrow frequency bands. More recently, nonlinearity has been investigated as a method of increasing this bandwidth, as well as a means to broaden the palette of available dynamics. Past studies on nonlinear acoustic and elastic metamaterials have demonstrated effects not easily accessible in the linear regime, including harmonic generation, mode hopping and conversion, tunable band gaps, chaos, and intrinsic localized modes. In this work, we present a model for a nonlinear elastic plate metamaterial that exhibits mode conversion between transverse and longitudinal waves. The mode conversion is enabled by cantilevered beam attachments undergoing large-angle out-of-plane oscillations. By analyzing the unit cell of this locally-resonant plate, we interpret the transverse-longitudinal coupling as a nonlinear, anisotropic effective mass density. The mode conversion effect is demonstrated via direct numerical simulations. [Work supported by NSF and ARL:UT.]

Spatial imaging of charge transport in silicon at low temperature

We present direct imaging measurements of charge transport across a 1 cm × 1 cm × 4 mm crystal of high purity silicon (∼20 kΩ cm) at temperatures between 500 mK and 5 K. We use these data to determine the intervalley scattering rate of electrons as a function of the electric field applied along the ⟨111⟩ crystal axis, and we present a phenomenological model of intervalley scattering which explains the constant scattering rate seen at low-voltage for cryogenic temperatures. We also demonstrate direct imaging measurements of effective hole mass anisotropy, which is strongly dependent on both temperature and electric field strength. The observed effects can be explained by a warping of the valence bands for carrier energies near the spin-orbit splitting energy in silicon.

Viscoelastic response of quantum Hall fluids in a tilted field

In this paper, we examine the viscoelastic properties of integer quantum Hall (IQH) states in a tilted magnetic field. In particular, we explore to what extent the tilted-field system behaves like a two-dimensional electron gas with anisotropic mass in the presence of strain deformations. We first review the Kubo formalism for viscosity in an external magnetic field, paying particular attention to the role of rotational symmetry and contact terms. Next, we compute the conductivity, stress, and viscosity tensors for IQH states in the presence of a tilted field and vertical confining potential. By comparing our results with the recently developed bimetric formalism, we show that, at the level of the contracted Hall viscosity tensor, the mapping between tilted field and effective mass anisotropy holds only if we simultaneously modify the background perpendicular magnetic field; in other words, a simultaneous measurement of the density, contracted Hall viscosity, and Hall conductivity at fixed particle number can distinguish between tilted field and effective mass anisotropy. Additionally, we show that in the presence of a tilted magnetic field, the stress tensor acquires an unusual anisotropic ground state average, leading to anomalous elastic response functions. We develop a formalism for projecting a three-dimensional Hamiltonian with confining potential and magnetic field to a two-dimensional Hamiltonian in order to further address the phenomenology of the tilted-field IQH fluid. We find that the projected fluid couples non-minimally to geometric deformations, indicating the presence of internal geometric degrees of freedom.

An accurate and compact tight-binding model for GeS

In this work we calculate the bands structure for the GeS monolayer from a multi-orbital tight-binding model, where the effect of s-p mixing are considered in slater-Koster equations. The model parameters are adjusting and optimising compared with the band structure obtained by density-functional theory calculation based on the hybrid HSE06 functional. It reproduces the conduction and valence bands as well as the orbital compositions. The anisotropic effective masses and Fermi velocities are identified directly from the anisotropy bands structure.

Strain-engineering the anisotropic electrical properties of low-symmetry bilayer GeSe

As an isostructural analog of black phosphorus, GeSe has attracted considerable attention recently due to its intriguing in-plane anisotropic optical, vibrational, and electrical properties stemming from the low-symmetry two-dimensional crystal structure. However, there has been no report about the anisotropy tuning of GeSe, hampering its further applications in optoelectronics and electronics. Here, we systematically investigate the change of electronic properties of the bilayer GeSe with different stacked crystal structures under strain through first-principles calculation. Notably, the anisotropy of electron effective mass can be controlled and even rotated by 90° in a slipping process of one crystallographic period along the armchair direction. These plentiful strain-engineering properties of the bilayer GeSe would render it useful for the exploration of novel GeSe-based optoelectronic and electronics applications.

Stacking effect on electronic, photocatalytic and optical properties: A comparison between bilayer and monolayer SnS

In this work, the stacking-dependent optoelectronic performances of a bilayer SnS were explored based on density functional theory (DFT). The results demonstrated that an AB-stacking induces an indirect-to-direct transition, a feature that is capable of vanquishing electron transition impediment from an intrinsic indirect monolayer SnS. An anisotropic and small carrier effective mass exists in all the stacking models, among which the AB-stacking with the lowest value favors high carrier mobility. Calculated band alignments are indicative of acceptable and adjustable photocatalytic activity for all the stacking models, unlike the monolayer SnS. The AB-stacking configuration possesses the strongest redox power, which facilitates it to be a potential candidate for photocatalytic water splitting. Additionally, the AB-stacking does effectively improve optoelectronic properties. The study demonstrated that layer-stacking is an availably adjustable method in the fields of sunlight-driven photocatalysis for nano-optoelectronic devices.

Energy filtering in silicon nanowires and nanosheets using a geometric superlattice and its use for steep-slope transistors

This paper investigates energy filtering in silicon nanowires and nanosheets by resonant electron tunneling through a geometric superlattice. A geometric superlattice is any kind of periodic geometric feature along the transport direction of the nanowire or nanosheet. Multivalley quantum-transport simulations are used to demonstrate the manifestation of minibands and minibandgaps in the transmission spectra of such a superlattice. We find that the presence of different valleys in the conduction band of silicon favors a nanowire with a rectangular cross section for effective energy filtering. The obtained energy filter can consequently be used in the source extension of a field-effect transistor to prevent high-energy electrons from contributing to the leakage current. Self-consistent Schrödinger-Poisson simulations in the ballistic limit show minimum subthreshold swings of 6 mV/decade for geometric superlattices with indentations. The obtained theoretical performance metrics for the simulated devices are compared with conventional III-V superlatticeFETs and TunnelFETs. The adaptation of the quantum transmitting boundary method to the finite-element simulation of 3-D structures with anisotropic effective mass is presented in Appendixes A and B. Our results bare relevance in the search for steep-slope transistor alternatives which are compatible with the silicon industry and can overcome the power-consumption bottleneck inherent to standard CMOS technologies.

Valence band tomography of wurtzite GaN by spectroscopic ellipsometry

The effective hole masses of wurtzite GaN are determined experimentally by an all-optical method. Therefore, we measure interband transitions as a function of the degenerate free-electron density and analyze the different many-body contributions arising from the Burstein–Moss effect and band-gap renormalization. When the known anisotropic effective electron mass is taken into account, the shape of the valence band can be reconstructed. Here, nonpolar GaN thin films doped with germanium or silicon at 9 × 1018 ≤ n ≤ 1.5 × 1020 cm−3 are investigated. Effective hole masses of , for the A valence band and for the B valence band are found (for 0.3 nm−1 < |k| < 2 nm−1) .

Ab initio and semiempirical modeling of excitons and trions in monolayer TiS3

We explore the electronic and the optical properties of monolayer ${\mathrm{TiS}}_{3}$, which shows in-plane anisotropy and is composed of a chain-like structure along one of the lattice directions. Together with its robust direct band gap, which changes very slightly with stacking order and with the thickness of the sample, the anisotropic physical properties of ${\mathrm{TiS}}_{3}$ make the material very attractive for various device applications. In this study, we present a detailed investigation on the effect of the crystal anisotropy on the excitons and the trions of the ${\mathrm{TiS}}_{3}$ monolayer. We use many-body perturbation theory to calculate the absorption spectrum of anisotropic ${\mathrm{TiS}}_{3}$ monolayer by solving the Bethe-Salpeter equation. In parallel, we implement and use a Wannier-Mott model for the excitons that takes into account the anisotropic effective masses and Coulomb screening, which are obtained from ab initio calculations. This model is then extended for the investigation of trion states of monolayer ${\mathrm{TiS}}_{3}$. Our calculations indicate that the absorption spectrum of monolayer ${\mathrm{TiS}}_{3}$ drastically depends on the polarization of the incoming light, which excites different excitons with distinct binding energies. In addition, the binding energies of positively and the negatively charged trions are observed to be distinct and they exhibit an anisotropic probability density distribution.

Radii of Rydberg states of isolated silicon donors

We have performed high field magnetoabsorption spectroscopy on silicon doped with a variety of single and double donor species. The magnetic field provides access to an experimental magnetic length, and the quadratic Zeeman effect, in particular, may be used to extract the wave-function radius without reliance on previously determined effective mass parameters. We were, therefore, able to determine the limits of validity for the standard one-band anisotropic effective mass model. We also provide improved parameters and use them for an independent check on the accuracy of effective mass theory. Finally, we show that the optically accessible excited-state wave functions have the attractive property that interactions with neighbors are far more forgiving of position errors than (say) the ground state.

Sp3s∗ tight-binding calculation of band edges and effective masses of InAs/GaSb superlattices with different interface structures

The band edge energy and effective mass of InAs/GaSb type II superlattices on a (001) GaSb substrate have been investigated using the empirical sp3s∗ tight-binding method. The influence of interfacial bonds on electronic properties has been clarified in typical superlattices of (InAs)n(GaSb)n with C2v point group symmetry and both (InAs)n(InSb)(GaSb)n and (InAs)n(GaSb)n(GaAs) superlattices with D2d point group symmetry. In the short period region of superlattices, we found that the band offsets in the vicinity of the hetero interfaces significantly impact on the band edges and that interfacial Ga-As bonds specifically cause large anisotropy of in-plane effective masses in (InAs)n(GaSb)n superlattices.

A Curved Noninteracting 2D Electron Gas with Anisotropic Mass

AbstractIn da Costa's thin‐layer approach, a quantum particle moving in a 3D sample is confined to a curved thin interface. At the end, the interface effects are ignored and the quantum particle is localized on a curved surface. A geometric potential arises and, since it is due to this confinement procedure, it depends on the transverse to the surface mass component. The effects due to an anisotropic effective mass on a noninteracting two‐dimensional electron gas confined to a curved surface are reported. By tailoring the mass, many investigations carried out in the literature can be improved, which in turn can be useful to better designing electronic systems without modifying the geometry of the given system. Some examples are examined, such as a particle on a helicoidal surface, on a cylinder, on a catenoid and on a cone, with some possible applications briefly discussed.

Excited states of neutral donor bound excitons in GaN

We investigate the excited states of a neutral donor bound exciton (D0X) in bulk GaN by means of high-resolution, polychromatic photoluminescence excitation (PLE) spectroscopy. The optically most prominent donor in our sample is silicon accompanied by only a minor contribution of oxygen—the key for an unambiguous assignment of excited states. Consequently, we can observe a multitude of Si0X-related excitation channels with linewidths down to 200 μeV. Two groups of excitation channels are identified, belonging either to rotational-vibrational or electronic excited states of the hole in the Si0X complex. Such identification is achieved by modeling the excited states based on the equations of motion for a Kratzer potential, taking into account the particularly large anisotropy of effective hole masses in GaN. Furthermore, several ground- and excited states of the exciton-polaritons and the dominant bound exciton are observed in the photoluminescence (PL) and PLE spectra, facilitating an estimate of the associated complex binding energies. Our data clearly show that great care must be taken if only PL spectra of D0X centers in GaN are analyzed. Every PL feature we observe at higher emission energies with regard to the Si0X ground state corresponds to an excited state. Hence, any unambiguous peak identification renders PLE spectra highly valuable, as important spectral features are obscured in common PL spectra. Here, GaN represents a particular case among the wide-bandgap, wurtzite semiconductors, as comparably low localization energies for common D0X centers are usually paired with large emission linewidths and the prominent optical signature of exciton-polaritons, making the sole analysis of PL spectra a challenging task.

Theoretical treatment of the processes involving the dipole transitions to the lowest exciton states in hexagonal semiconductors

The treatment of the two-photon transitions to the An=1 exciton level and the resonant Raman scattering of light by LO-phonons is given for the hexagonal semiconductors A2B6, taking into account the influence of the complex top valence band and anisotropy of the exciton effective mass.

Many-body theory of effective mass in degenerate semiconductors

We derive the many-body theory of the effective mass in the effective mass representation (EMR). In the EMR, we need to solve the equation of motion of an electron in the presence of electron–electron interactions, where the wavefunction is expanded over a complete set of Luttinger–Kohn wavefunctions. We use the Luttinger–Ward thermodynamic potential and the Green’s function perturbation to derive an expression for the band effective mass by taking into account the electron–electron interactions. Both quasi-particle and the correlation contributions are considered. We show that had we considered only the quasi-particle contribution, we would have missed important cancellations. Thus the correlated motion of electrons has important effects in the renormalization of the effective mass. Considering the exchange self-energy in the band model, we derive a tractable expression for the band effective mass. We apply the theory to n-type degenerate semiconductors, PbTe and SnTe, and analyze the impact of the theory on the anisotropic effective mass of the conduction bands in these systems.

On the behavior of acoustic/elastic metamaterials with anisotropic mass density

The effect of anisotropic mass density in acoustic/elastic metamaterials on wave propagation is presented in this research. The use of microstructures to achieve anisotropic physical properties in metamaterials is an intensive field of study. In this work, a two-dimensional (2D) ‘mass-in-mass’-spring lattice system is utilized to achieve anisotropic effective mass density in two orthogonal principal directions.In each direction, the effective mass density is frequency-dependent and can be “effectively negative” if it falls within the frequency bandgap region. A 2D numerical continuum model,based on a recently developed cantilever-in-mass model, is further presented and examined to study how wave input angles affect 2D wave propagation. Results show that wave attenuation is dependent on both input frequency and wave input angle in a 2D metamaterial. This study demonstrates a case whereby wave attenuation is achieved,by selecting wave input frequency in the bandgap region to enact “negative effective mass density”. This study also illustrates another case when wave attenuation is obtained for positive anisotropic mass density. This behavior is achieved by directing wave propagation to transverse direction at a specific input wave angle of 60°. Both numerical calculations of mass-spring lattice model and continuum cantilever-in-mass model show good agreement.

The inherent transport anisotropy of rutile tin dioxide (SnO2) determined by van der Pauw measurements and its consequences for applications

The anisotropic electron mobility of unintentionally doped, single crystalline, bulk, rutile SnO2(100) and (110) wafers is investigated by van der Pauw-Hall measurements. The room temperature average Hall electron mobility of μ ≈ 220 cm2/V s at a Hall electron concentration of n ≈ 1018 cm−3 suggests high-quality samples. The extracted 1.26 times higher mobility in the c-direction than perpendicular to it is in very good agreement with the corresponding anisotropy of the effective electron mass, which is 1.28 times higher perpendicular to c than parallel to c, suggesting rather isotropic scattering mechanisms. At temperatures below 100 K, a higher mobility anisotropy is found and tentatively attributed to low-angle grain boundaries with a surprisingly low energy barrier. Thus, the efficiency of mobility-sensitive applications, such as field effect transistors, increases by aligning the transport direction with the c-direction of the crystal. For transparent contact applications, such as Sb- or F-doped SnO2 (termed “ATO” or “FTO,” respectively), this benefit is expected to be even larger due to the increasing effective mass anisotropy with the increasing electron concentration.

Electron effective mass in In0.33Ga0.67N determined by mid-infrared optical Hall effect

Mid-infrared optical Hall effect measurements are used to determine the free charge carrier parameters of an unintentionally doped wurtzite-structure c-plane oriented In0.33Ga0.67N epitaxial layer. Room temperature electron effective mass parameters of m⊥*=(0.205±0.013) m0 and m∥*=(0.204±0.016) m0 for polarization perpendicular and parallel to the c-axis, respectively, were determined. The free electron concentration was obtained as (1.7 ± 0.2) × 1019 cm−3. Within our uncertainty limits, we detect no anisotropy for the electron effective mass parameter and we estimate the upper limit of the possible effective mass anisotropy as 7%. We discuss the influence of conduction band nonparabolicity on the electron effective mass parameter as a function of In content. The effective mass parameter is consistent with a linear interpolation scheme between the conduction band mass parameters in GaN and InN when the strong nonparabolicity in InN is included. The In0.33Ga0.67N electron mobility parameter was found to be anisotropic, supporting previous experimental findings for wurtzite-structure GaN, InN, and AlxGa1−xN epitaxial layers with c-plane growth orientation.