Anisotropic Effective Mass Research Articles

Excitonic terahertz absorption in semiconductors with effective-mass anisotropies

A microscopic approach is developed to compute the excitonic properties and the corresponding terahertz response for semiconductors characterized by anisotropic effective masses. The approach is illustrated for the example of germanium where it is shown that the anisotropic electron mass in the L-valley leads to two distinct terahertz absorption resonances separated by 0.8 meV.

First-principles cluster expansion study of functionalization of black phosphorene via fluorination and oxidation

We systematically explore chemical functionalization of monolayer black phosphorene via chemisorption of oxygen and fluorine atoms. Using the cluster expansion technique, with vary- ing concentration of the adsorbate, we determine the ground states considering both single- as well as double- side chemisorption, which have novel chemical and electronic properties. The nature of the bandgap depends on the concentration of the adsorbate: for fluorination the direct bandgap first decreases, and then increases while becoming indirect, with increasing fluorination, while for oxidation the bandgap first increases and then decreases, while mostly maintaining its direct nature. Further we find that the unique anisotropic free-carrier effective mass for both the electrons and holes, can be changed and even rotated by 90 degrees, with controlled chemisorption, which can be useful for exploring unusual quantum Hall effect, and novel electronic devices based on phosphorene.

Donor wave functions in Si gauged by STM images

The triumph of effective mass theory in describing the energy spectrum of dopants does not guarantee that the model wavefunctions will withstand an experimental test. Such wavefunctions have recently been probed by scanning tunneling spectroscopy, revealing localized patterns of resonantly enhanced tunneling currents. We show that the shape of the conducting splotches resemble a cut through Kohn-Luttinger (KL) hydrogenic envelopes, which modulate the interfering Bloch states of conduction electrons. All the non-monotonic features of the current profile are consistent with the charge density fluctuations observed between successive {001} atomic planes, including a counterintuitive reduction of the symmetry - a heritage of the lowered point group symmetry at these planes. A model-independent analysis of the diffraction figure constrains the value of the electron wavevector to $k_0 = (0.82 \pm 0.03)(2\pi/a_{Si})$. Unlike prior measurements, averaged over a sizeable density of electrons, this estimate is obtained directly from isolated electrons. We further investigate the model-specific anisotropy of the wave function envelope, related to the effective mass anisotropy. This anisotropy appears in the KL variational wave function envelope as the ratio between Bohr radii b=a. We demonstrate that the central cell corrected estimates for this ratio are encouragingly accurate, leading to the conclusion that the KL theory is a valid model not only for energies but for wavefunctions as well.

Double ellipsoid model for conductivity effective mass along [110] orientation in (100) Si-based strained p-channel metal-oxide-semiconductor

The performance of a Si metal-oxide-semiconductor field-effect transistor can be enhanced effectively by the strain technology and the orientation engineering. For example, the [110] direction is usually used as the channel direction in the Si p-channel metal-oxide-semiconductor (PMOS) on 100 oriented substrate. While SunEdison company rotates the channel direction 45 degrees to the [100] direction, its hole mobility is 1.15 times larger than the hole mobility of the former.The orientation engineering is based on the anisotropy of the hole effective mass along different directions. The enhancement of carrier mobility naturally occurs when we choose the direction with the smaller carrier effective mass as the channel direction.However, according to the reported results in the literature, the hole effective mass values along the [110] and [100] orientation are about 0.6m0 and 0.29m0, respectively. The former is twice larger than the latter, which cannot explain that the experimental result increases 1.15 times.We find that the effective mass values along both the long axis and the short axis should be taken into consideration, and the value of 0.6m0 can only represent the long axis term by observing the equivalent energy diagram of the first sub-band in Si PMOS.In view of this, the double ellipsoid model is given for the conductivity effective mass along the [110] direction in (100) Si PMOS, which explains the reason why the hole mobility along the [100] direction is 1.15 times larger than that along the [110] direction in Si PMOS. And then, based on the E-k relation of the inversion layer in Si-based strained PMOS, we study the conductivity effective mass along the [110] direction in (100) Si-based strained PMOS by the above method.The results show that 1) the [110] oriented hole conductivity effective mass of biaxially strained Si PMOS can be calculated directly by its spherical equivalent energy diagram; 2) in the case of biaxially strained Si1-xGex PMOS, its conductivity effective mass needs to be calculated by the double ellipsoid method; 3) the [110] oriented hole conductivity effective mass of uniaxially strained Si PMOS should be solved approximately by two different sizes of ellipsoid.Our valid models can provide the valuable references for studying and designing the Si-based strained PMOS device.

Microscopic model of the Knight shift in anisotropic and correlated metals

We present a microscopic model of nuclear magnetic resonance in metals. The spin-1/2 local nucleus and its surrounding orbital electrons interact with the arbitrary constant and perpendicular time-oscillatory magnetic inductions and with each other via an anisotropic hyperfine interaction. An Anderson-like Hamiltonian describes the excitations of the relevant occupied local orbital electrons into the conduction bands, each band described by an anisotropic effective mass with corresponding Landau orbits and an anisotropic spin tensor. Local orbital electron correlation effects are included using the mean-field decoupling procedure of Lacroix. The Knight resonance frequency and corresponding linewidth shifts are evaluated to leading orders in the hyperfine and Anderson excitation interactions. While respectively proportional to and a constant for weak , both highly anisotropic shifts depend strongly upon when a Landau level is near the Fermi energy. Electron correlations affect the anisotropy of the linewidth shift. The model is easily generalizable to arbitrary nuclear spin I.

Anisotropy of inter-band transitions and band structure of Cs3Zn6B9O21 nonlinear optical crystals

Polarized optical functions near the fundamental absorption edge of novel Cs3Zn6B9O21 nonlinear optical crystals possessing a wide UV transparency down to 190nm were investigated. The anisotropy of optical functions is not well studied yet which restrains the further strategy of the formation on its base of solid state compounds with desirable properties. The studies were performed using a band structure calculations as well as the experimental measurements of fundamental polarized UV absorption edge and X-ray photoelectron spectra of the studied crystals. The experimental data were used for evaluation of scissor factors of the band structure. The results of the calculations were compared with the XPS and polarized absorption optical spectra of the investigated crystals. The introduction of the scissor factor was performed in order to obtain a sufficient agreement with experiment. The observed anisotropy of absorption may be explained by the anisotropy of carrier effective masses.

Anisotropic Effective Mass, Optical Property, and Enhanced Band Gap in BN/Phosphorene/BN Heterostructures.

Phosphorene is receiving great research interests because of its peculiar physical properties. Nonetheless, the phosphorus has a trouble of degradation due to oxidation. Hereby, we propose that the electrical and optical anisotropic properties can be preserved by encapsulating into hexagonal boron nitride (h-BN). We found that the h-BN contributed to enhancing the band gap of the phosphorene layer. Comparing the band gap of the pristine phosphorene layer, the band gap of the phosphorene/BN(1ML) system was enhanced by 0.15 eV. It was further enhanced by 0.31 eV in the BN(1ML)/phosphorene/BN(1ML) trilayer structure. However, the band gap was not further enhanced when we increased the thickness of the h-BN layers even up to 4 MLs. Interestingly, the anisotropic effective mass and optical property were still preserved in BN/phosphorene/BN heterostructures. Overall, we predict that the capping of phosphorene by the h-BN layers can be an excellent solution to protect the intrinsic properties of the phosphorene.

Interplay between effective mass anisotropy and Pauli paramagnetic effects in a multiband superconductor: Application toSr2RuO4

We investigate the mixed state properties in a type II multiband superconductor with uniaxial anisotropy under the Pauli paramagnetic effects. Eilenberger theory extended to a multiband superconductor is utilized to describe the detailed vortex lattice properties, such as the flux line form factors, the vortex lattice anisotropy and magnetic torques. We apply this theory to Sr$_2$RuO$_4$ to analyze those physical quantities obtained experimentally, focusing on the interplay between the strong two-dimensional anisotropy and the Pauli paramagnetic effects. This study allows us to understand the origin of the disparity between the vortex lattice anisotropy ($\sim$60) and the $H_{\rm c2}$ anisotropy ($\sim$20). Among the three bands; $\gamma$ with the effective mass anisotropy $\sim$180, $\alpha$ with $\sim$120, and $\beta$ with $\sim$60, the last one is found to be the major band, responsible for various magnetic responses while the minor $\gamma$ band plays an important role in the vortex formation. Namely, in a field orientation slightly tilted away from the two dimensional basal plane those two bands cooperatively form the optimal vortex anisotropy which exceeds that given by the effective mass formula with infinite anisotropy. This is observed by small angle neutron scattering experiments on Sr$_2$RuO$_4$. The pairing symmetry of Sr$_2$RuO$_4$ realized is either spin singlet or spin triplet with the d-vector strongly locked in the basal plane. The gap structure is that the major $\beta$ band has a full gap and the minor $\gamma$ band has a $d_{x^2-y^2}$ like gap.

Effects of electron–optical phonon interactions on the polaron energy in a wurtzite ZnO/MgxZn1−xO quantum well**Project supported by the National Natural Science Foundation of China (Grant Nos. 11264027 and 11364030), the Project of Prairie Excellent Specialist of Inner Mongolia, China, and the “Thousand, Hundred and Ten” Talent Training Project Foundation of Inner Mongolia Normal University, China (Grant No. RCPY-2-2012-K-039).

We investigated the properties of polarons in a wurtzite ZnO/MgxZn1−xO quantum well by adopting a modified Lee–Low–Pines variational method, giving the ground state energy, transition energy, and phonon contributions from various optical-phonon modes to the ground state energy as functions of the well width and Mg composition. In our calculations, we considered the effects of confined optical phonon modes, interface-optical phonon modes, and half-space phonon modes, as well as the anisotropy of the electron effective band mass, phonon frequency, and dielectric constant. Our numerical results indicate that the electron–optical phonon interactions importantly affect the polaronic energies in the ZnO/MgxZn1−xO quantum well. The electron–optical phonon interactions decrease the polaron energies. For quantum wells with narrower wells, the interface optical phonon and half-space phonon modes contribute more to the polaronic energies than the confined phonon modes. However, for wider quantum wells, the total contribution to the polaronic energy mainly comes from the confined modes. The contributions of the various phonon modes to the transition energy change differently with increasing well width. The contribution of the half-space phonons decreases slowly as the QW width increases, whereas the contributions of the confined and interface phonons reach a maximum at d ≈ 5.0 nm and then decrease slowly. However, the total contribution of phonon modes to the transition energy is negative and increases gradually with the QW width of d. As the composition x increases, the total contribution of phonons to the ground state energies increases slowly, but the total contributions of phonons to the transition energies decrease gradually. We analyze the physical reasons for these behaviors in detail.

Anisotropic effective mass approximation model to calculate multiple subband structures at wide-gap semiconductor surfaces: Application to accumulation layers of SrTiO3 and ZnO

We propose a simplified theoretical model that well reproduces the dispersion curves of the multiple subbands in a two-dimensional electron gas in the accumulation layer at the surfaces of wide-gap semiconductors. The electronic band structures containing multiple subbands with different orbital characteristics are derived by self-consistently solving the Poisson–Schrödinger equations with anisotropic effective mass approximations. Calculations were carried out on the two-dimensional electron gas states formed at the surfaces of SrTiO3 and ZnO for comparison. The calculated subband structures at the SrTiO3 surface were in excellent agreement with available angle-resolved photoelectron spectroscopy data, confirming the validity of the present model. The calculations further indicate the existence of a high electron density, exceeding 2×1021cm−3 and a high electric field of 20MVcm−1 at the surface. Moreover, photoelectron-escape depths are discussed quantitatively and photoelectrons from the first subband are found to dominate the total photoelectron intensity in the spectra.

Landau levels and magneto-transport property of monolayer phosphorene.

We investigate theoretically the Landau levels (LLs) and magneto-transport properties of phosphorene under a perpendicular magnetic field within the framework of the effective k·p Hamiltonian and tight-binding (TB) model. At low field regime, we find that the LLs linearly depend both on the LL index n and magnetic field B, which is similar with that of conventional semiconductor two-dimensional electron gas. The Landau splittings of conduction and valence band are different and the wavefunctions corresponding to the LLs are strongly anisotropic due to the different anisotropic effective masses. An analytical expression for the LLs in low energy regime is obtained via solving the decoupled Hamiltonian, which agrees well with the numerical calculations. At high magnetic regime, a self-similar Hofstadter butterfly (HB) spectrum is obtained by using the TB model. The HB spectrum is consistent with the LL fan calculated from the effective k·p theory in a wide regime of magnetic fields. We find the LLs of phosphorene nanoribbon depend strongly on the ribbon orientation due to the anisotropic hopping parameters. The Hall and the longitudinal conductances (resistances) clearly reveal the structure of LLs.

The influence of growth method and conditions on the electrical properties of SnS<sub>2</sub> crystals

Узагальнено результати дослідження електропровідності, холлівської рухливості та ефективних мас електронів і дірок у шаруватих кристалах SnS2, вирощених методами хімічних транспортних реакцій, статичної сублімації й Бріджмена. Показано, що високе значення анізотропії електропровідності (с / ||с = 103-104) не зв’язане з анізотропією ефективних мас електронів, а зумовлене наявністю плоских протяжних дефектів упаковки шарів в реальних кристалах, які є потенціальними бар’єрами для електронів.

Validity of the acoustic approximation for elastic waves in heterogeneous media

The acoustic approximation of elastic waves is a very common approximation in exploration geophysics. The interest of the acoustic approximation in the inverse problem context lies in the fact that it leads to a much lower numerical cost than for the elastic problem. Nevertheless, the earth is not an acoustic body, and it has been found in the past that this approximation is not without drawbacks mainly because of P-to-S energy conversion and that anisotropy cannot be easily modeled. We studied a different issue of this approximation related to small heterogeneities with respect to the minimum wavelength of the wavefield. We first numerically found that elastic and acoustic waves behave differently with respect to small-scale heterogeneities, introducing differences in amplitudes but also in phase between elastic and acoustic signals. We then derived physical and mathematical interpretations of this phenomenon, developing the different nature of elastic- and acoustic-wave propagation that led to the conclusion that, in rough media, acoustic waves can only be a poor-quality approximation of elastic waves. Interestingly, we also found that, in the acoustic case, small-scale heterogeneities give rise to natural acoustic effective anisotropic media through an anisotropic effective mass matrix. Unfortunately, this anisotropy is of a different nature compared with the elastic effective anisotropy and can not be used to mimic elastic anisotropy.

Программа трехмерного моделирования и визуализации конформационной динамики биомакромолекул Maya-K-PDB

The work is devoted to obtaining the bipolaron functional in anisotropic crystals by Buimistrov-Pekar method for an arbitrary electron-phonon coupling. The effect of electron correlations related to the direct dependence of the wave function from the distance between the electrons on bipolaron energy is studied. The single-center and two-center (coaxial configuration) bipolaron models in crystals with anisotropic effective mass for the limiting case of quasi-systems (the system “light axis”) were compared.

Twin boundary effects on spontaneous half-quantized vortices in superconducting composite structures (d-dot’s)

We investigate effects of anisotropy of an orthorhombic structure in twin domains on spontaneous half-quantized vortices (SHQVs) in a d-dot, which is a nano-scaled composite structure that consists of a d-wave superconductor embedded in an s-wave matrix. Since YBa2Cu3O7−δ (YBCO) has the orthorhombic structure, there are twin domains separated by twin boundaries (TBs). In order to analyze effects of TBs on SHQVs, we derive two-component Ginzburg–Landau equations, in which electrons in YBCO have anisotropic effective mass. It is found that the magnitude of field around SHQVs is monotonically decreasing with increasing anisotropy of effective mass and finally peak values of the fields become zero. This means that anisotropy of the effective mass suppresses SHQVs and when the anisotropy is too large, SHQVs do not appear in d-dot’s.

Magnetic susceptibility of Bi2 − x Sb x Te3 (0 < x < 1) solid solution crystals in the range from 2 to 400 K

The magnetic susceptibility of single crystals of Bi2Te3-Sb2Te3 solid solutions containing 10, 25, and 50 mol % Sb2Te3 has been measured using a superconducting Josephson interferometer in the temperature range from 2 to 400 K at 3-K intervals in magnetic fields of up to 2.38 × 106 A/m at two orientations of the magnetic field H with respect to the trigonal axis C3 of the crystals (H ‖ C3 and H ⊥ C3) with a relative uncertainty within 2%. A new approach has been proposed for separately assessing the contributions of the ionic core and free charge carriers to the magnetic susceptibility, which uses experimental data on magnetic susceptibility and effective mass anisotropy. Analysis of the data obtained in this study demonstrates that the temperature variation of carrier susceptibility in the region of degenerate and nondegenerate states of the electronic system can be described in terms of the Pauli and Landau-Peierls approaches if one takes into account the complex structure of the valence band and “nonparabolicity” of the light hole energy spectrum.

ChemInform Abstract: Broken Symmetries in URu2Si2

AbstractReview: 52 refs.

Thomas-Fermi method for computing the electron spectrum and wave functions of highly doped quantum wires in n-Si

The application of the Thomas-Fermi method to calculate the electron spectrum in quantum wells formed by highly doped n-Si quantum wires is presented under finite temperatures where the many-body effects, like exchange, are taken into account. The electron potential energy is calculated initially from a single equation. Then the electron energy sub-levels and the wave functions within the potential well are simulated from the Schr?dinger equation. For axially symmetric wave functions the shooting method has been used. Two methods have been applied to solve the Schr?dinger equation in the case of the anisotropic effective electron mass, the variation method and the iteration procedure for the eigenvectors of the Hamiltonian matrix.

Control of a two-dimensional electron gas on SrTiO₃(111) by atomic oxygen.

We report on the formation of a two-dimensional electron gas (2DEG) at the bare surface of (111) oriented SrTiO3. Angle resolved photoemission experiments reveal highly itinerant carriers with a sixfold symmetric Fermi surface and strongly anisotropic effective masses. The electronic structure of the 2DEG is in good agreement with self-consistent tight-binding supercell calculations that incorporate a confinement potential due to surface band bending. We further demonstrate that alternate exposure of the surface to ultraviolet light and atomic oxygen allows tuning of the carrier density and the complete suppression of the 2DEG.

Effects of strong electron–hole exchange and exciton–phonon interactions on the exciton binding energy of aluminum nitride

In this study, the exciton binding energies of AlN are calculated by the anisotropic effective mass theory, which considers the strong electron–hole exchange and Fröhlich-type exciton–phonon interactions. Our calculated results are in good agreement with recent experimental results, indicating that the electron–hole exchange and exciton–phonon interactions play essential roles in describing the excitonic structure of AlN. We estimate that the exciton binding energies of AlN are 53.7 and 67.3 meV, for the spin-singlet and the spin-triplet states, respectively. In addition, a universal correlation has been found in compound semiconductors including AlN, where the effect of the electron–hole exchange and Fröhlich-type exciton–phonon interactions almost compensates each other on the binding energy of a spin-singlet exciton.