Magnetoelectric Cr<Subscript>2</Subscript>O<Subscript>3</Subscript> and relativity theory

Based on the dielectric continuum phonon model, uniaxialmodel and force balance equation the mobility of two dimensional electrongas in wurtzite Al_xGa_1-xN/GaN/Al_xGa_1-xN quantum wells isdiscussed theoretically within the temperature range dominated by opticalphonons. The dependences of the electron mobility on temperature, Al molarfraction and electron sheet density are presented including hydrostaticpressure effect. The built-in electric field is also taken into account. Itis found that under normal pressure the main contribution to the mobility isfrom the scattering of interface optical phonons in narrow (for well widthd < 12 Å) and wide (for d > 117 Å and d > 65 Å for finitelythick barriers and infinitely thick ones, respectively) wells, whereas thatis from the scattering of confined optical phonons in a well with anintermediate width. It is shown that the electron mobility decreases withincreasing Al molar fraction and temperature, whereas increases obviouslywith increasing electron sheet density. The theoretical calculated electronmobility is 978 cm²/V?s which is higher than an available experimentaldata 875 cm²/V?s when x equals to 0.58 at room temperature. Theresults under hydrostatic pressure considering the modification of strainindicate that the mobility increases slightly as hydrostatic pressureincreases from 0 to 10 GPa.     

Interface polarons in a heterojunction with triangular bending-band

The interface polaron states in a heterojunction are discussed by considering an energy-band bending near the interface and the influence of an image potential. The ground state energy and the effective mass of a polaron are variationally calculated. The numerical results for the GaAs/ heterojunction are given. It is shown that even though the influences from bulk longitudinal optical (LO) phonons are more important for the heterojunctions with lower Al composition, the contributions from two branches of interface optical (IO) phonons are not negligible. For the heterojunctions with higher Al composition, both the influences from LO phonons and two branches of IO phonons are important. The band-bending plays an important role for the interface localization of polarons, but the influence of the image potential is not essential. Received: 4 November 1997 / Revised and Accepted: 9 March 1998     

Hydrostatic pressure effect on the electron mobility in a ZnSe/Zn1－xdx Se strained heterojunction

With a memory function approach, this paper investigates the electronic mobility parallel to the interface in a ZnSe/Zn1-xCdxSe strained heterojunction under hydrostatic pressure by considering the intersubband and intrasubband scattering from the optical phonon modes. A triangular potential approximation is adopted to simplify the potential of the conduction band bending in the channel side and the electronic penetrating into the barrier is considered by a finite interface potential in the adopted model. The numerical results with and without strain effect are compared and analysed. Meanwhile, the properties of electronic mobility under pressure versus temperature, Cd concentration and electronic density are also given and discussed, respectively. It shows that the strain effect lowers the mobility of electrons while the hydrostatic pressure effect is more obvious to decrease the mobility. The contribution induced by the longitudinal optical phonons in the channel side is dominant to decide the mobility. Compared with the intrasubband scattering it finds that the effect of intersubband scattering is also important for the studied material.     

Pressure effect on the electron mobility in AlAs/GaAs quantum wells

By taking the influence of optical phonon modes into account, this paper adopts the dielectric continuum phonon model and force balance equation to investigate the electronic mobility parallel to the interfaces for AlAs/GaAs semiconductor quantum wells (QWs) under hydrostatic pressure. The scattering from confined phonon modes, interface phonon modes and half-space phonon modes are analysed and the dominant scattering mechanisms in wide and narrow QWs are presented. The temperature dependence of the electronic mobility is also studied in the temperature range of optical phonon scattering being available. It is shown that the electronic mobility reduces obviously as pressure increases from 0 to 4GPa, the confined longitudinal optical (LO) phonon modes play an important role in wide QWs, whereas the interface optical phonon modes are dominant in narrow QWs, the half-space LO phonon modes hardly influence the electronic mobility expect for very narrow QWs.     

Interface polarons in a realistic heterojunction potential

The ground states of interface polarons in a realistic heterojunction potential are investigated by considering the bulk and the interface optical phonon influence. A self-consistent heterojunction potential is used and an LLP-like method is adopted to obtain the polaron effect. The numerical computation has been done for the Zn_1-xCd_xSe/ZnSe system to obtain the polaron ground state energy, self energy and effective mass parallel to the interface. A simplified coherent potential approximation is developed to obtain the parameters of the ternary mixed crystal and the energy band offset of the heterojunction. It is found that at small Cd concentration the bulk longitudinal optical phonons give the main contribution for lower areal electron densities, whereas the interface phonon contribution is dominant for higher areal electron densities. The interface polaron effect is weaker than the effect obtained by the three dimensional bulk phonon and by the two dimensional interface phonon models. Received 17 September 1998     

Impurity band in SnBi<Subscript>4</Subscript>Se<Subscript>7</Subscript>: thermoelectric power and electrical resistivity measurements

Thermoelectric power and electrical resistivity measurements on polycrystalline samples of Bi₂Se₃ and stoichiometric ternary compound in the quasi-binary system SnSe–Bi₂Se₃ in the temperature range of 90–420 K are presented and explained assuming the existence of an impurity band. The variation of the electron concentration with temperature above 300 K is explained in terms of the thermal activation of a shallow donor, by using a single conduction band model. The density of states effective mass m ^*=0.15m ₀ of the electrons, the activation energy of the donors, their concentration, and the compensation ratio are estimated. The temperature dependence of the electron mobility in conduction band is analyzed by taking into account the scattering of the charge carriers by acoustic phonon, optical phonon, and polar optical phonon as well as by alloy and ionized impurity modes. On the other hand, by considering the two-band model with electrons in both the conduction and impurity bands, the change in the electrical resistivity with temperature between 420 and 90 K is explained.     

Electron–phonon interaction in fan-shaped quantum dot and quantum wire

The optical phonon modes and electron–optical-phonon interaction in fan-shaped quantum dot and quantum wire are studied with the dielectric continuum (DC) model and separation of variables. The explicit expressions for the longitudinal optical (LO) and interface optical (IO) phonon eigenmodes are deduced. It is found that there exist two types of IO phonon modes: top interface optical (TIO) phonon mode and arc interface optical (AIO) phonon mode, in a fan-shaped quantum dot. After having quantized the eigenmodes, we derive the Hamiltonian operators describing the LO and IO phonon modes as well as the corresponding Fröhlich electron–phonon interaction. The potential applications of these results are also discussed.     

Polarons in a cylindrical quantum well wire with finite confining potential

The polaron self-energy and the correction to the electron effective mass in a cylindrical quantum well wire (QWW) are studied by the perturbation approach. The interactions of electrons with different phonon modes in the QWW system, including the confined longitudinal optical phonon modes, in the wire (LO1), in the barrier materials (LO2) and in the interface optical (IO) phonon modes, are considered. The result shows that the LO1 phonon’s contribution to the polaron self-energy increases gradually as the radius of the wire increases, and finally reaches that of the three-dimensional limit, while the LO2 phonon contributes only when the radius of the wire is very small. Also, the contribution of the IO phonon modes first increases quickly as the wire radius increases and soon reaches a maximum, then reduces to zero monotonically.     

Electron-phonon interaction in hemispherical quantum dot

Within the framework of the dielectric continuum (DC) model, the optical phonon modes and electron-optical-phonon interaction in hemispherical quantum dot are investigated. The proper eigenfunctions for longitudinal optical (LO) and interface optical (IO) phonon modes are constructed. After having quantized the eigenmodes, we derive the Hamiltonian operators describing the LO and IO phonon modes as well as the corresponding Fröhlich electron-phonon interaction. The dispersion relation of IO phonon modes is size independent. The potential applications of these results are also discussed.     

Polar Oscillation of Interface and Surface Optical Phonons in Free-Standing Cylindrical Quantum-Well Wires

Under dielectric continuum approximation, interface optical (IO) and surface optical (SO) phonon modes as well as the corresponding Fro^ehlich electron-phonon interaction Hamiltonian in a free-standing cylindrical quantum-well wire (QWW) are derived and studied. Numerical calculations on GaAs/AlzGa1-x As cylindrical QWW are performed. Results reveal that there are two branches of IO phonon modes and one branch of SO phonon mode, and the dispersion frequencies of IO or SO phonon modes sensitively depend on the Al mole fraction x in AlzGa1-x As material and the wavevector in z direction, kz. With the increasing of kz and quantum number m, the frequency of each IO mode approaches one of the two frequency values of the single GaAs/AlxGa1-x As heterostructure, and the electrostatic potential distribution of the phonon mode tends to be more and more localized at a certain interface or surface, meanwhile, the coupling between the electron-IO and -SO phonons becomes weaker.     

Acoustic and optical phonons and their dispersion in model ferroelastics Hg<Subscript>2</Subscript>Cl<Subscript>2</Subscript>

Thefrequency dispersion curve of acoustic and optical phonons are calculated and constructed, and the density of states of the phonon spectrum is obtained for Hg₂Cl₂ crystals. The influence of the hydrostatic pressure on the frequencies of acoustic and optical phonons and their dispersion is analyzed theoretically. It is revealed that an increase in the pressure leads to a considerable softening of the slowest acoustic TA branch (soft mode) at the X point of the Brillouin zone boundary. This behavior is consistent with the phenomenological Landau theory and correlate with experiments.     

The phonon effects on the impurity states in cylindrical quantum wire with a finite confining potential

The variational method and the effective mass approximation are applied to calculate the binding energies of the hydrogenic impurity states in a cylindrical quantum wire with finite deep potential well. The phonon effects on the impurity states are considered by taking both the couplings of the electron-phonon and the impurity ion-phonon into account. The numerical results for the GaAs cylindrical quantum wire are given and discussed. It is found that the ion-phonon interaction reduces the impurity binding energy and supplies key contribution to the energy shift, but the electron-phonon coupling enhances the binding energy less. Longitudinal optical (LO) phonons play more important role than interface optical (IO) phonons in the impurity potential screening. The polaron effect caused by LO phonons is more important when the wire is thinner, otherwise the LO phonons are dominant for the thicker wires.     

弱耦合多原子半无限晶体中的表面极化子的有效势

本文研究弱耦合多原子半无限晶体中表面极化子的性质。采用线性组合算符和幺正变换导出表面极化子的的有效势。     

Potentials induced by the electron-optical-phonon interaction in a quantum well

The potential induced by the electron-optical-phonon interaction in a quantum well (QW) is investigated by means of the perturbation theory. We consider the interactions of an electron with both bulklike confined longitudinal optical (LO) phonons and four branches of interface optical (IO) phonons. The spatial distributionV _i(z) of the induced potential for QW structures with different heterolayer compositions and different well widths is calculated in detail. The numerical results show that the heterolayer composition of the QW plays an important role in determining the shape ofV _i(z) and that the existence of IO-phonons is important to the electronic states in QWs.     

Ternary mixed crystal effects on interface optical phonon and electron-phonon coupling in zinc-blende GaN/AlxGa1−xN spherical quantum dots

The theoretical investigations of the interface optical phonons, electron–phonon couplings and its ternary mixed effects in zinc-blende spherical quantum dots are obtained by using the dielectric continuum model and modified random-element isodisplacement model. The features of dispersion curves, electron–phonon coupling strengths, and its ternary mixed effects for interface optical phonons in a single zinc-blende GaN/Al_xGa_1−xN spherical quantum dot are calculated and discussed in detail. The numerical results show that there are three branches of interface optical phonons. One branch exists in low frequency region; another two branches exist in high frequency region. The interface optical phonons with small quantum number l have more important contributions to the electron–phonon interactions. It is also found that ternary mixed effects have important influences on the interface optical phonon properties in a single zinc-blende GaN/Al_xGa_1−xN quantum dot. With the increase of Al component, the interface optical phonon frequencies appear linear changes, and the electron–phonon coupling strengths appear non-linear changes in high frequency region. But in low frequency region, the frequencies appear non-linear changes, and the electron–phonon coupling strengths appear linear changes.     

Fröhlich electron-interface and -propagating optical phonon interactions in a wurtzite multi-shell cylindrical heterostructure

Under the dielectric continuum model and Loudon's uniaxial crystal model, the polar optical phonon modes in a wurtzite multi-shell cylindrical heterostructure are analyzed and discussed. The analytical electrostatic potential functions are presented for all the five types of polar optical phonon modes including the interface optical (IO) modes, the propagating (PR) modes, the quasi-confined (QC) modes, the half-space-like (HSL) modes and the exactly confined (EC) modes. By adopting a transfer matrix method, the free IO and PR phonon fields and corresponding Fröhlich electron -IO and -PR interaction Hamiltonians are obtained via the method of electrostatic potential expansion. The analytical formulas are universal and can be applied to single, double and some complex cylindrical wurtzite quantum systems.     

One-phonon-assisted resonant electron Raman scattering of GaAs quantum dots in an AlAs matrix

We have presented a theoretical calculation of the differential cross section (DCS) for the electron Raman scattering (ERS) process associated with the bulk-like longitudinal optical (LO) and interface optical (IO) phonon modes in semiconductor quantum dots (QDs). Electron states are considered to be confined within the QDs. We consider the Fröhlich electron-phonon interaction in the framework of the dielectric continuum approach. We study selection rules for the processes. Some singularities in the Raman spectra are found and interpreted. A discussion of the phonon behavior for QDs with large and small size is presented. The numerical results are also compared with that of experiments.     

Polar optical phonon states and dispersive spectra of wurtzite ZnO nanocrystals embedded in zinc-blende MgO matrix

Based on the macroscopic dielectric continuum model and Loudon’s uniaxial crystal model, the polar optical phonon modes of a quasi-0-dimensional (Q0D) wurtzite spherical nanocrystal embedded in zinc-blende dielectric matrix are derived and studied. It is found that there are two types of polar phonon modes, i.e. interface optical (IO) phonon modes and the quasi-confined (QC) phonon modes coexisting in Q0D wurtzite ZnO nanocrystal embedded in zinc-blende MgO matrix. Via solving Laplace equations under spheroidal and spherical coordinates, the unified and analytical phonon states and dispersive equations of IO and QC modes are derived. Numerical calculations on a wurtzite/zinc-blende ZnO/MgO nanocrystal are performed. The frequency ranges of the IO and QC phonon modes of the ZnO/MgO nanocrystals are analyzed and discussed. It is found that the IO modes only exist in one frequency range, while QC modes may appear in three frequency ranges. The dispersive frequencies of IO and QC modes are the discrete functions of orbital quantum numbers l and azimuthal quantum numbers m. Moreover, a pair of given l and m corresponds to one IO mode, but to more than one branches of QC. The analytical phonon states and dispersive equations obtained here are quite useful for further investigating Raman spectra of phonons and other relative properties of wurtzite/zinc-blende Q0D nanocrystal structures.     

One phonon-assisted electron Raman scattering in a wurtzite cylindrical quantum well wire

We report the electron resonant Raman scattering (ERRS) process related to the longitudinal optical (LO), interface optical (IO) and quasi-confined (QC) phonons in a cylindrical GaN-AlN quantum well wire (QWW). We present the differential cross-section (DCS) and study the selection rules. Results reveal that the emitted photon frequency decreases with increasing the radius because of the size-selective Raman scattering effect and the built-in electric field. The contribution to the DCS mainly stems from the GaN-type LO (LO1), QC and IO phonons when the wire is thin, but the LO1 and QC phonons are dominant for the thick wire.