Phonon States and Dispersive Spectra of Polar Optical Phonons in Quasi-One-Dimensional Nanowires of Wurtzite ZnO and Zinc-Blend MgO Semiconductors

Within the framework of the macroscopic dielectric continuum model and Loudon's uniaxial crystal model, the phonon modes of a wurtzite/zinc-blende one-dimensional (1D) cylindrical nanowire (NW) are derived and studied. The analytical phonon states of phonon modes are given. It is found that there exist two types of polar phonon modes, i.e. interface optical (IO) phonon modes and the quasi-confined (QC) phonon modes existing in 1D wurtzite/zinc-blende NWs. Via the standard procedure of field quantization, the Fröhlich electron-phonon interaction Hamiltonians are obtained. Numerical calculations of dispersive behavior of these phonon modes on a wurtzite/zinc-blende ZnO/MgO NW are performed. The frequency ranges of the IO and QC phonon modes of the ZnO/MgO NWs 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 properties of the IO and QC modes on the free wave-number k_z and the azimuthal quantum number m arediscussed. The analytical Hamiltonians of electron-phonon interaction obtained here are quite useful for further investigating phonon influence on optoelectronics properties of wurtzite/zinc-blende 1D NW structures.     

Impact of anisotropy on polar optical vibration in a wurtzite cylindrical nanowire with ring geometry

The quasi-confined (QC) phonon modes, surface optical (SO) phonon modes and corresponding Fröhlich-like Hamiltonian in a wurtzite cylindrical nanowire with ring geometry are investigated in the framework of the dielectric continuum model and Loudon’s uniaxial crystal model. Numerical calculations are focused on the dispersion relations of the SO phonons and the electron–SO phonon coupling strength. Results show that there are only two branches of SO phonon modes. The dispersions of the two branches of SO phonon modes are obvious when the phonon wave-number k_z or the azimuthal quantum number m is small. Typical degenerating behavior of the SO modes is evidenced due to the anisotropic effect of wurtzite crystal. Moreover, when k_z or m are large enough, the frequencies of the two branches of SO modes converge to a definite limiting frequency in single planar heterostructure. The calculations of the electron–SO phonon coupling strength reveal that the high-frequency SO modes (SO₊) play a more important role in the coupling strength than the low-frequency ones (SO₋). Furthermore, the long-wavelength SO phonons with small m are the main factor contributing to the electron–phonon interaction.     

Polar interface and surface optical vibration spectra in multi-layer wurtzite quantum wires： transfer matrix method

The polar interface optical （IO） and surface optical （SO） phonon modes and the corresponding Froehlich electron phonon-interaction Hamiltonian in a freestanding multi-layer wurtzite cylindrical quantum wire （QWR） are derived and studied by employing the transfer matrix method in the dielectric continuum approximation and Loudon＇s uniaxial crystal model. A numerical calculation of a freestanding wurtzite GaN/AlN QWR is performed. The results reveal that for a relatively large azimuthal quantum number m or wave-number kz in the free z-direction, there exist two branches of IO phonon modes localized at the interface, and only one branch of SO mode localized at the surface in the system. The degenerating behaviours of the IO and SO phonon modes in the wurtzite QWR have also been clearly observed for a small kz or m. The limiting frequency properties of the IO and SO modes for large kz and m have been explained reasonably from the mathematical and physical viewpoints. The calculations of electron-phonon coupling functions show that the high-frequency IO phonon branch and SO mode play a more important role in the electron phonon interaction.     

Thermal conductivity of VLS-grown rough Si nanowires with various surface roughnesses and diameters

In this paper, we synthesize VLS-grown rough Si nanowires using Mn as a catalyst with various surface roughnesses and diameters and measured their thermal conductivities. We grew the nanowires by a combination vapor-liquid-solid and vapor-solid mechanism for longitudinal and radial growth, respectively. The surface roughness was controlled from smooth up to about 37 nm by the radial growth. Our measurements showed that the thermal conductivity of rough surface Si nanowires is significantly lower than that of smooth surface nanowires and decreased with increasing surface roughness even though the diameter of the smooth nanowire was lower than that of the rough nanowires. Considering both nanowires were grown via the same growth mechanism, these outcomes clearly demonstrate that the rough surface induces phonon scattering and reduces thermal conductivity with this nanoscale-hole-free nanowires. Control of roughness induced phonon scattering in Si nanowires holds promise for novel thermoelectric devices with high figures of merit.     

A search for high frequency vibrational modes at a stepped surface

In this paper we present a theory of the vibrations of atoms in the vicinity of a stepped surface on a Bravais crystal. The static relaxations in the positions of the atoms in the crystal are determined, and the atomic force constants are then calculated in the relaxed atomic configuration. The general theory is applied to a simple stepped surface, and the local phonon density of states is carried out for atoms at several points on the stepped surface by the real space continued fraction recursion method. No evidence is found for high frequency surface phonons.     

Molecular dynamics study of the equilibrium flux of gas molecules to a fractal/rough surface: Effects of gas atom diameter

The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using the random deposition technique. By applying various depositions the surface roughness was controlled and, as a measure of irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in ideal gas and the numbers of collisions with these surfaces were counted. The calculations were carried out using the simplified molecular dynamics simulation technique (only hard core repulsions were assumed). The calculations were performed for various ratios of gas phase atoms diameter to the surface substrate atoms diameter. The results obtained showed that the size of a gas phase atom has crucial influence on the relation between the frequency of collision and the surface fractal dimension     

The physical process of melting and freezing

It is suggested that at the melting temperature the wavelength of the average thermal phonon vibration is equal to or is a harmonic of the distance separating the atomic layers in the crystal. This resonance between the phonon and lattice vibrations equals out the energy of the vibrating atoms in the surface layer. If this “uniform” energy is higher than the energy corresponding to the metastable transition state then all the surface atoms lose its position stability. In order to make the jump to the next potential well energy is required to overcome on the viscous resistance of the liquid. If this energy, latent heat of fusion, is supplied then the atomic/molecular sheet or platelets from the surface are detached and melting occurs. The proposed model is consistent with all of the characteristic features of melting and freezing. Equations calculating the average phonon wavelength and the corresponding lattice distance at the melting temperature are derived from fundamental thermodynamic relationships. The required thermodynamic parameters are determined from experiments of the nine selected highly symmetrical solids. The calculated wavelengths of the phonon vibration are equal to or is a harmonic of the $d$-spacing of the atomic/molecular layers in agreement with theory.     

应用碳化硅表面改性技术降低全息-离子束刻蚀光栅刻槽的粗糙度

采用具有良好比刚度和热稳定性的碳化硅材料作为基底,使用全息-离子束刻蚀技术制作了光栅。碳化硅材料表面固有缺陷导致制作的光栅刻槽表面粗糙度高,槽底和槽顶粗糙度分别达到了29.6 nm和65.3 nm (R_q)。通过等离子辅助沉积技术在碳化硅表面镀制一层均匀的硅改性层,经过抛光可以获得无缺陷的超光滑表面。XRD测试表明制备的硅改性层为无定形结构。原子力显微镜的测试结果表明:经过抛光后,表面粗糙度为0.64 nm(R_q)。在此表面上制作的光栅刻槽表面粗糙度明显降低,槽底和槽顶粗糙度分别为2.96 nm和7.21 nm,相当于改性前的1/10和1/9。     

Interface-Optical-Phonon Modes in Quasi-one-dimensional Wurtzite Rectangular Quantum Wires

By employing the dielectric continuum model and Loudon's uniaxial crystal model, the interface optical (IO) phonon modes in a freestanding quasi-one-dimensional (Q1D) wurtzite rectangular quantum wire are derived and analyzed. Numerical calculation on a freestanding wurtzite GaN quantum wire is performed. The results reveal that the dispersion frequencies of IO modes sensitively depend on the geometric structures of the Q1D wurtzite rectangular quantum wires, the free wave-number k_z in z-direction and the dielectric constant of the nonpolar matrix. The degenerating behavior of the IO modes in Q1D wurtzite rectangular quantum wire has been clearly observed in the case of small wave-number k_z and large ratio of length to width of the rectangular crossing profile. The limited frequency behaviors of IO modes have been analyzed deeply, and detailed comparisons with those in wurtzite planar quantum wells and cylindrical quantum wires are also done. The present theories can be looked on as a generalization of that in isotropic rectangular quantum wires, and it can naturally reduce to the case of Q1D isotropic quantum wires once the anisotropy of the wurtzite material is ignored.     

Double-layer structural-acoustic coupling for cylindrical shell by using a combination of WDA and BIE

This work formulates the double-layer structural-acoustic coupling problem for cylindrical shell by using a combination of the wave-number domain approach (WDA) and the boundary integral equation (BIE). Expressions for the spectral radial velocity of the outer surface of a finite fluid-filled/submerged (FFS) cylindrical thin shell are formulated by means of the transfer matrix equation in wave-number domain. It is shown that the spectral variables on the inner surface of the shell are related to those on the outer surface of the shell. The far field sound radiation from this kind of shell is numerically evaluated for various fluid cases. An experimental verification is performed, and a good correlation between the theoretical results and the experimental results shows that the theoretical study work in this paper is correct.     

Application of a multiregion model to the EM scattering from a rough surface with or without a target above it

An efficient multiregion model is introduced to calculate the electromagnetic scattering from a perfectly electrical conducting(PEC) rough surface with or without a PEC target above it.In the multiregion model,the rough surface is split into multiple regions depending on their position along the rough surface.Two intermediate regions are chosen as the dominant region.If a target is located above the rough surface,the target will also be included in the dominant region.The method of moments(MOM) is only adopted on the dominant region to ensure validity.Hence,the new model can greatly reduce the number of unknowns associated with full MOM analysis.The induced electric currents on the other regions are obtained by approximately considering the mutual coupling between different regions along the rough surface.Compared with the published hybrid method,this new model is not only suitable for EM scattering from a target above a rough surface but also applicable for just rough surfaces.Several numerical simulations are presented to show the validity and efficiency of the multiregion model.     

Theoretical study of the Kirchhoff integral from a two-dimensional randomly rough surface with shadowing effect: application to the backscattering coefficient for a perfectly-conducting surface

In this paper, the backscattering coefficient of a two-dimensional randomly rough perfectly-conducting surface is investigated using the Kirchhoff approach with a shadowing function. The rough surface height/slope correlations assumed to be Gaussian are accounted for in this analysis. The scattering coefficient is then formulated in terms of a characteristic function for the integrations over the surface heights, in terms of expected values for the integrations over the surface slopes. Numerical comparisons of Kirchhoff's approach (KA) with the stationary-phase (SP) approximation are made with respect to the choice of the one-dimensional surface height autocorrelation function and the shadowing effect. For an isotropic surface the results show that SP underestimated the incoherent backscattering coefficient compared with KA. Moreover, when the correlation between the slopes and the heights is neglected, the shadowing effect may be ignored.     

Electromagnetic scattering from two-layered rough interfaces with a PEC object: vertical polarization

Electromagnetic(EM) scattering from a stack of two rough interfaces separating a homogeneous medium with a perfectly electric conducting(PEC) object has been calculated through the method of moments for vertical polarization.Theoretical formulations of EM scattering from multi-layered rough interfaces with a PEC object have been derived in detail and the total fields and their normal derivatives on the rough interfaces are solved.The two-layered model is a special case.In this work,a Gaussian rough surface was applied to simulate the rough interface.A cylinder was located above,between or below the two-layered rough interfaces.Through numerical simulations,the validity of this work is demonstrated by comparing it with existing scattering models,which are special cases that include a PEC object located above/below a single-layered rough interface and two-layered rough interfaces without an object.Subsequently,the influences of characteristic parameters,such as the relative permittivity of the medium,as well as the average height between the two rough surfaces,on the bistatic scattering coefficient are discussed.     

Relation between statistical properties of surface roughness and the averaged speckle intensity in the diffraction field

A theoretical and experimental investigation is made on the relation between the statistical properties of a rough surface and the averaged speckle intensity in the diffraction field. The theoretical analysis is performed in some detail over a wide range of the random phase variation for various illuminated objects. The result gives an interpretation for the behavior of the averaged speckle intensity obtained experimentally for various states of rough surfaces.     

Observation of increase in Raman intensity of surface phonon polaritons on rough surfaces of ZnTe

An increase in Raman intensity of surface phonon polaritons has been observed in free-standing thin slabs (thickness ～ 7 μm) of single- crystal ZnTe with rough surfaces by a conventional Raman-scattering technique at room temperature. The samples with various root-mean- square roughness heights have been prepared by making use of final polishing powders with different mean-grit sizes, and the surface roughness has been confirmed by measuring the intensities of the diffuse scattering of the laser light. The increase of the Raman intensity is proportional to the mean-square height of the surface roughness, and the shift of the dispersion relation is also proportional to it. The frequency shift is explained by a perturbation theory of the surface-roughness-induced scattering.     

Theoretical study of the Kirchhoff integral from a two-dimensional randomly rough surface with shadowing effect: application to the backscattering coefficient for a perfectly-conducting surface

Abstract

In this paper, the backscattering coefficient of a two-dimensional randomly rough perfectly-conducting surface is investigated using the Kirchhoff approach with a shadowing function. The rough surface height/slope correlations assumed to be Gaussian are accounted for in this analysis. The scattering coefficient is then formulated in terms of a characteristic function for the integrations over the surface heights, in terms of expected values for the integrations over the surface slopes. Numerical comparisons of Kirchhoff's approach (KA) with the stationary-phase (SP) approximation are made with respect to the choice of the one-dimensional surface height autocorrelation function and the shadowing effect. For an isotropic surface the results show that SP underestimated the incoherent backscattering coefficient compared with KA. Moreover, when the correlation between the slopes and the heights is neglected, the shadowing effect may be ignored.     

Nonlinear dynamics for proper ferroelastic transitions for which the landau condition is violated

On the basis of a lattice model the domain structure for ferroelastic transformations is examined. The model accounts for both strongly nonlinear and competing interactions which allow for, in some situations, the propagation of nonlinear excitations. The model can be mostly applied to proper ferroelastic transformations of which In-Tl, Ti-Ni, etc.… are good prototypes. The phonon dispersion of the transverse acoustic waves obtained in the linearized case is discussed and the results show first a phonon softening at nonzero wave-number and next an upwards convexity of the phonon branch near the long-wavelength limit. This can be seen as pre-transitional effects. In a fully nonlinear case we consider vanishing dilatation transformations and the continuum approximation is applied to the one-dimensional version. Then, we investigate nonlinear excitations; three main classes of solution are found: i) quasi-harmonic solutions corresponding to periodically modulated structures in space which is a precursor effect of the elastic transformation, ii) an array of solitons made of periodic arrangements of parent-elastic domains and iii) a moving strain soliton. All the significant results are numerically illustrated by means of the microscopic model. Finally, the similarity to martensitic transformations and some extensions of the model are outlined.     

Interface Optical Phonon Modes and Frohlich Electron-Phonon Interaction Hamiltonian in a Multi-shell Spherical Nanoheterosystem

Under dielectric continuum approximation, interface optical (IO) phonon modes and the Frohlich electron-IO phonon interaction Hamiltonian in a multi-shell spherical nanoheterosystem were derived and studied. Numericalcalculations on three-layer and four-layer CdS/HgS spherical nanoheterosystems have been performed. Results revealthat there are four IO phonon modes for the three-layer system and six IO phonon modes for the four-layer system.On each interface, there are two IO phonon modes, the frequency of one is between WTO,CdS and WLO,CdS, and that ofthe other is between WTO,HgS and WLO,HgS. With the increasing of quantum number l, the frequency of each IO modeapproaches one of the two frequency values of the single CdS/HgS heterostructure, and the potential for each IO modeis more and more localized at a certain interface, furthermore, the coupling between the electron-lO phonons becomes weaker.     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

极性晶体中强耦合表面磁极化子特性

研究极性晶体中表面磁极化子的特性。采用Huybrechts线性组合算符和幺正变换方法,导出了晶体中强耦合表面磁极化子处于基态的振动频率和有效哈密顿量,讨论了坐标z的两种极限情况,对RbCl晶体进行了数值计算。结果表明:振动频率和平行有效哈密顿量随磁场的增加而增大。