Norihiko Nishiguchi

Acoustic phonon modes of rectangular quantum wires

Acoustic phonon modes of a free-standing rectangular quantum wire composed of cubic crystals are theoretically investigated using an algorithm developed to analyse data from resonant ultrasound spectroscopy. The normal phonon modes are classified according to their spatial symmetries into a compressional mode termed the dilatational mode and non-compressional modes referred to as the flexural, torsional, and shear modes. The formalism that we present is quite general and can be applied to wires of any cubic material. As an example, the dispersion relations are obtained for square and rectangular wires of GaAs, taking into account the anisotropic elasticity of the material. The dispersion curves for a rectangular wire are compared with those of the approximate hybrid modes referred to as the thickness and width modes, and the validity of the modes is discussed. The existence of edge modes is confirmed by examining the spatial distribution of displacement vectors.

Vibrational dynamics of force microscopy: Effect of tip dimensions

The dynamics of a vibrating cantilever with an attached tip in contact with a solid is treated analytically. The tip length is shown to be crucial in determining the resonant response. The finite tip size changes the boundary conditions for the flexural motion, rendering the cantilever-tip-sample combination more rigid and implicating both the normal and lateral stiffnesses of the sample in the analysis. This is confirmed in an experiment with a silica sample, a sapphire tip, and a silicon cantilever. The theory has implications in the field of quantitative analysis with atomic ac force microscopy.

Vibrational spectrum and specific heat of fine particles

Abstract The vibrational spectrum for a fine particle is obtained by exactly solving the wave equation for a homogeneous elastic sphere with free surface. In terms of this frequency spectrum, enhancements in the specific heat of fine particles are calculated and compared with the experiments at low temperatures. Qualitative features of the experimental results are consistently explained in our theory.

Phonon-transmission rate, fluctuations, and localization in random semiconductor superlattices: Green's-function approach.

We analytically study phonon transmission and localization in random superlattices by using a Greens-function approach. We derive expressions for the average transmission rate and localiza- tion length, or Lyapunov exponent, in terms of the superlattice-structure factor. This is done by considering the backscattering of phonons, due to the complex mass-density fluctuations, which in- corporates all of the forward-scattering processes. These analytical results are applied to two types of random superlattices and compared with numerical simulations based on the transfer-matrix method. Our analytical results show excellent agreement with the numerical data. A universal relation for the transmission fluctuations versus the average transmission is derived explicitly, and independently confirmed by numerical simulations. The transient of the distribution of transmission to the log-normal distribution for the localized phonons is also studied. In a previous paper, 3 we studied phonon propagation through random SLs by means of the transfer-matrix method. The random SLs considered are the multilay- ered systems where two kinds of basic blocks of materi- als (which may or may not have internal structure) are stacked at random. Each sample has its own realization of randomness in the order of constituent layers, and the phonon-transmission rate versus frequency shows a fine spiky structure specific to the particular realization of disorder present in that given sample. This fluctuating transmission rate can be considered to be a fingerprint of the sample, like the reproducible conductance fluctu- ations found in electronic mesoscopic transport. The ensemble average of the transmission rate over possible configurations of the constituent layers smears out the fine structure, but still leaves global features of trans- mission dips and peaks. The dips arise from phonon localization due to the interference among backscattered phonons. The peaks arise from the resonance occurring when appropriate matching conditions are satisfied be- tween the phonon wavelength and the thickness of a basic layer. A significant result of Ref. 3 is that there exists a re- rnarkable correlation between the ensemble-averaged re- flection rate and the squared SL-structure factor calcu- lated analytically. The latter describes the sum of the phonon amplitudes reflected from SL interfaces. The smaller contributions coming from multiple-phonon re- fIections have been neglected. We find that at the fre- quencies where the maxima (minima) of the structure factor are attained, the reflection rate exhibits peaks (dips). The purpose of the present study is to establish quan- titatively the relation between the phonon-transmission rate and the SL-structure factor. Also, we examine in some detail the localization characteristic of phonons in- jected into random SLs. Our study is based on the Greens-function method which has originally been ap- plied to the electronic conductivity in one-dimensional metals. 4 In Sec. II we model the random SLs and formulate the phonon-transmission rate in terms of Greens func- tions. In Sec. III we derive integral equations for the Greens functions by introducing complex mass-density fluctuations which induce the backscattering of phonons. The solutions of these integral equations, satisfying ap-

Real-time imaging of acoustic rectification

We image gigahertz surface acoustic waves normally incident on a microscopic linear array of triangular holes—a generic “acoustic diode” geometry—with a real-time ultrafast optical technique. Spatiotemporal Fourier transforms reveal wave diffraction orders in k-space. Squared amplitude reflection and transmission coefficients for incidence on both sides of the array are evaluated and compared with numerical simulations. We thereby directly demonstrate acoustic rectification with an asymmetric structure.

Lattice thermal conductivity in superlattices: molecular dynamics calculations with a heat reservoir method

We report on a molecular dynamics study of the cross-plane lattice thermal conductivity in GaAs/AlAs superlattices. The layers of the superlattice are modelled by a three-dimensional face centred cubic lattice with cubic anharmonicity, and with atomic scale roughness at the interfaces. We perform the simulation of heat flow for a section of a superlattice with high- and low-temperature thermal reservoirs attached to opposite ends. The calculation reproduces qualitatively the features observed experimentally, i.e., the dramatic reduction of the conductivity relative to the conductivity of the bulk constituent materials, and the variation of the thermal conductivity with the superlattice repeat distance. The results are also in agreement with those obtained previously by Daly et al (2002 Phys. Rev. B 66 024301) who determined the thermal conductivity from the time taken for an initially inhomogeneous temperature distribution to relax.

Charging Effect of InAs Dots in Split-Gate High Electron Mobility Transistor Structure

We report on a series of distinct current oscillations due to charging of InAs dots in a GaAs double heterojunction field-effect transistor (DHFET) with self-assembled InAs dots formed on the bottom of the channel. These peaks can be interpreted by the tunneling of electrons from the channel to the InAs dots resulting in the threshold voltage shift. Observed number of currrent peaks suggests that each dot can accomodate up to six electrons. Based on the InAs dot size estimated by Transmission Electron Microscope (TEM) observation, relatively large effective mass of 0.06 m0–0.08 m0 were estimated in order to account for accomodation of six electrons per dot.

Rectification of elastic waves in a thin plate

We propose a rectifier of elastic waves in a thin plate, which is made of an elastically isotropic material containing a periodic array of triangular holes as scatterers, and demonstrate numerically that it works both for the symmetric and anti-symmetric Lamb waves as well as shear horizontal waves. The rectification is caused by the geometric effects on wave scattering due to the asymmetric scatterers, while the interplay between the mode conversion and interference effects among the scattered waves owing to the periodic arrangement of scatterers complicates it. The mechanism makes it possible to rectify the typical elastic waves in the system above the threshold frequency corresponding to the wavelength equivalent to the periodicity of scatterers.

Guided acoustic phonons in quantum wires : theory of phonon fiber

Acoustic phonon modes confined to a GaAs cylindrical quantum wire within AlAs are analytically investigated within the context of an elastic continuum model. Elastic properties are assumed to be isotropic for both materials for mathematical convenience. The displacement vector is expressed by the scalar potential and two vector potentials. The confined acoustic phonon modes are classified into three types according to the rotational symmetry of the potential functions: dilatational, torsional, and flexural modes. Dispersion curves of the modes show phonon subband structures with finite cutoff frequencies due to confinement of waves in lateral directions. The density of the confined phonon modes accordingly appears as staircaselike structures.

Acoustic phonon modes and dispersion relations of nanowire superlattices

We study theoretically acoustic phonon modes in nanowire superlattices (NWSLs) composed of cubic materials. We classify the acoustic phonon modes in rectangular and square cross-section NWSLs, based on group theory. For NWSLs consisting of GaAs and AlAs, we calculate numerically the dispersion relations of each phonon mode and corresponding displacement fields. We examine the effects of both the lateral confinement and superlattice modulation along the wire axis. The results suggest that peculiar electron-phonon interactions occur because the vibrations of both the lateral and longitudinal confining potentials induce scattering potential in addition to the deformation and piezoelectric potentials.