Numerical modeling of the V(z) curve for a thin-layer/substrate configuration

A numerical model is presented to calculate V(z) curves for a line-focus acoustic microscope and the specimen configuration of a thin isotropic elastic layer deposited on an isotropic elastic substrate. In this model, a Gaussian beam which is tracked through the lens into the coupling fluid, interacts with the thin-layer/substrate system. The numerical approach is based on the solution of singular integral equations by the boundary element method. The system of singular integral equations follows from the conditions at the interface of the coupling fluid and the thin layer and the interface of the thin layer and the substrate. An electrochemical reciprocity relation is used to express the voltage at the terminals of the microscope's transducer in terms of the calculated incident and back-scattered fields. V(z) curves are presented for various layer thicknesses and various combinations of the elastic constants of the layer and the substrate. The oscillations of the V(z) curves are related to the modes of wave propagation in a thin layer in contact with a solid half-space on one side and a fluid half-space on the other side. Calculated V(z) curves have also been compared with experimentally obtained curves, and good agreement is observed.     

Ray representation of longitudinal lateral waves in acoustic microscopy

For object materials having a large enough Rayleigh velocity, the V(z) (where V is the output voltage and z is the defocus distance) variation is mainly due to interference between the fields of the geometrically reflected wave and the leaky Rayleigh wave. However, for materials, such as organic compounds, having a low Rayleigh velocity, the leaky Rayleigh wave is not excited. For this case, the lateral wave resulting from propagation along the surface of the longitudinal wave plays a significant role in determining the V(z) dependence. The effect of the lateral wave contribution on V(z) is studied. Ray optics is to derive an expression giving the influence of the longitudinal lateral wave. Good agreement is found between the theory and measurements for z not near zero. Because of the ease with which the longitudinal wave velocity can be obtained from V(z), one can conveniently determine the elastic constant c(11 ) of isotropic materials using the acoustic microscope.     

Transient elastic waves in a wedge-shaped layer

Summary The theory of generalized ray is applied to analyzing transient elastic waves in a layered half-space with non-parallel interface. The propagation, reflection and refraction of longitudinal (P-) and transverse (SV-) waves which are generated by a line source in the surface layer of a two layer model are considered, each of the two homogeneous and isotropic layers having different density and inverse of wave speeds. Generalized ray integrals for multi-reflected rays in the top layer are formulated by using two rotated coordinate systems, one for each interface, and are expressed in terms of local wave slowness along each interface. Through a series of transformations of the local slowness, all ray integrals are expressible in a common slowness variable. Special attention is given to wave mode changes during reflection. The arrival time of each ray is then determined from the stationary value of the phase function with common slowness of the ray integral. Arrivals of head waves corresponding to rays refracted at a fast bottom are calculated from proper branch points of the Cagniard-mapping.With 3 FiguresPresented by F. Ziegler at the 16 th IUTAM Congress ICDAM Lyngby, Denmark, August 19–25, 1984.     

Acoustic microscopy measurement of elastic constants and massdensity

A method is presented to determine the elastic constants and the mass density of isotropic and anisotropic solids and anisotropic thin films. The velocity and attenuation of leaky surface acoustic waves (SAWs) have been obtained for specified propagation directions from V(z) curves measured by line-focus acoustic microscopy (LFAM). The experimentally obtained velocities have been compared to velocities obtained from a measurement model for the V(z) curve which simulates the experiment. Since the measured and simulated V(z) curves have the same systemic errors, the material constants are free of such errors. For an isotropic solid, Young's modulus E, the shear modulus G and the mass density ρ have been determined from the leaky Rayleigh wave velocity and attenuation, measured by LFAM, and a longitudinal wave velocity measured by a pulse-echo transit-time technique. For a cubic-crystalline solid, the ratios of the elastic constants to the mass density (c₁₁ /ρ, c₁₂/ρ, c₄₄/ρ) have been determined from the directional variation of measured SAW velocities, using a preliminary estimate of ρ. The mass density ρ has subsequently been determined by additionally using the attenuation of leaky SAWs in crystal symmetry directions. For a cubic-crystalline thin film deposited on a substrate, the elastic constants and the mass density (c₁₁, c₁₂, c₄₄, ρ) of the film have been determined from the directional variation of the measured SAW velocities, and a comparison of the corresponding attenuation coefficient with the measured attenuation coefficient has been used to verify the results     

Describing isotropic and anisotropic out-of-plane deformations in thin cubic materials by use of Zernike polynomials

Isotropic and anisotropic out-of-plane deformations induced by thin-film residual stress on thin cubic materials are studied. By transforming the compliance tensor, an analytical expression can be derived for the biaxial stiffness modulus for all directions in any given cubic crystal plane. A modified Stoney's equation, including both isotropic and anisotropic terms, can be formulated to predict the anisotropic out-of-plane deformation. The isotropic and anisotropic deformations are then described using the Zernike polynomials U21 and U22, respectively. Experimental results from (100) and (110) silicon wafers confirm the model by quantitatively comparing the changes in Z21 and Z22 coefficients due to thin-film stress.     

Surface acoustic waves in a gallium arsenide-conducting layerstructure

The electron attenuation and SAW velocity versus the surface conductivity and magnetic field induction for the structure consisting of the (001) cut anisotropic GaAs substrate and an isotropic conducting layer was calculated. The SAW propagated along the [110] piezoactive direction distinguished by the greatest electromechanical coupling coefficient     

Dissolution slowness surfaces of cubic crystals

The first part of this paper offers a tensorial method that gives analytical equations for the dissolution slowness surface of cubic crystals. Conditions for the proposed equations are outlined. The non-centrosymmetric class 23 is treated as an example. The evolution of the shape of the slowness surface with the higher rank of the dissolution tensors is studied, using in particular a three-dimensional graphical representation of the slowness surface. The conditions for obtaining slowness surfaces with a complex shape and an increasing number of extrema are discussed.     

铜铟硒薄膜的外延生长和表面重构及其电池性能研究

在GaAs的(110)、(001)和(111)A、(111)B等极性晶面上, 通过铜铟共溅-硒蒸镀的方法, 分布外延生长出(220/204)、(001)和(112)结晶取向的单晶CIS薄膜. 系统考察了CIS薄膜外延生长的结晶取向和表面微结构, 发现了这些CIS外延薄膜均需表面重构化而形成比表面能低的CIS(112)晶面, 结合晶体结构研究了各种晶面和比表面能的相关性. 通过各种衬底下不同结晶取向的CIS薄膜的太阳能电池组装, 发现当CIS薄膜生长具有(220/204)结晶取向时电池器件性能最好、效率最高, 说明可通过控制CIS薄膜的沉积条件和选用合适取向的衬底, 增加吸收层(220/204)的结晶取向, 从而显著提高CIS薄膜太阳电池的光电性能.     

Growth dynamics of GaAs, AlAs and (Al, Ga)As on GaAs (110) and (111)A substrates during molecular beam epitaxy

The growth dynamics of GaAs, AlAs and (Al, Ga)As films grown by molecular beam epitaxy (MBE) on GaAs(110) and (111)A substrates have been studied using reflection high energy electron diffraction (RHEED) intensity oscillations and scanning tunnelling microscopy (STM). In contrast to growth on (001) oriented substrates, the period of the RHEED intensity oscillation does not in general provide a measure of the growth rate. This is explained by the very different surface chemistry involved, since the short lifetime of arsenic molecules (As₂ or As₄) on non-(001) surfaces results in cation-stable surface conditions, which generate arsenic (anion)- induced intensity oscillations, whereas on (001) surfaces they are cationinduced under all normal growth conditions. The effects of this behaviour on surface morphology are illustrated, as are the relative influences of Ga and Al. STM images obtained during the first few monolayers of growth provide a detailed indication of the growth mode and in particular explain in a simple manner the origin of bilayer period RHEED intensity oscillations obtained during growth on GaAs (110).     

Thickness measurement of a thin-film layer on an anisotropic substrate by phase-sensitive acoustic microscope

Complex V(z) curves for single thin-film layers on anisotropic substrates are studied both experimentally and theoretically, and the application of V(z) measurement to the determination of film thickness on anisotropic substrates is discussed. Complex V(z) curves for aluminum layers (with thicknesses between 0.5 and 2 mum) on a silicon wafer have been calculated. The inverse Fourier transform of the V(z) curves, which corresponds to the reflection coefficient, shows sharp changes at critical angles of pseudosurface waves, pseudo-Sezawa waves, and Rayleigh surface waves. These critical angles strongly depend on the thickness. Complex V(z) curves for these specimens have been measured using a phase-sensitive acoustic microscope with a point focus lens at 400 MHz. The critical angles of the surface waves obtained from the measured V(z) curves are in good agreement with those obtained from the calculated V(z) curves. On the basis of this result, it is shown that the V(z) measurement is applicable to the determination of film thickness on an anisotropic substrate.     

Some dynamic properties of incompressible,transversely isotropic elastic media

Summary This paper investigates various dynamic properties of incompressible, transversely isotropic elastic media. The propagation condition for such materials allows the wave speeds to be obtained in explicit form. An examination of the slowness surface and direction of energy flux as the extensional modulus along the fibre tends to infinity is then easily carried out. The paper also includes an investigation of the dynamic response of such materials to a particular line impulsive force. This is done using integral transforms. These transforms are invertible in closed form.     

Effect of periodic surface roughness on V(z) curves for the line-focus acoustic microscope

A specimen with a periodic surface profile is considered to estimate the effect of surface roughness on the V(z) curve for the line-focus acoustic microscope. The Fourier optics approach is used to obtain the response of the lens and the Rayleigh-Fourier method is used to obtain the reflection coefficients for plane wave incidence from the fluid side on the periodic surface. An integral expression is obtained to calculate V(z) curves for periodic surface profiles. The V(z) curves are used to calculate the leaky Rayleigh wave velocities by applying the fast Fourier technique. Numerical results are presented to display the effect of sinusoidal surface roughness on the V(z) curves and the corresponding leaky Rayleigh wave velocities.     

Morphology- and orientation-controlled gallium arsenide nanowires on silicon substrates

GaAs nanowires were epitaxially grown on Si(001) and Si(111) substrates by using Au-catalyzed vapor-liquid-solid (VLS) growth in a solid source molecular beam epitaxy system. Scanning electron microscopy analysis revealed that almost all the GaAs nanowires were grown along <111> directions on both Si substrates for growth conditions investigated. The GaAs nanowires had a very uniform diameter along the growth direction. X-ray diffraction data and transmission electron microscopy analysis revealed that the GaAs<111> nanowires had a mixed crystal structure of the hexagonal wurtzite and the cubic zinc-blende. Current-voltage characteristics of junctions formed by the epitaxially grown GaAs nanowires and the Si substrate were investigated by using a current-sensing atomic force microscopy.     

GaMnAs with high Mn composition grown in Stranski-Krastanov mode

GaMnAs diluted magnetic semiconductor (DMS) thin films with high Mn compositions were grown on (001) GaAs substrate by low-temperature molecular beam epitaxy (LT-MBE) after inserting an InAs wetting layer onto the GaAs buffer. The growth follows the Stranski-Krastanov mode, which brings about special magnetic characteristics of Ga_0.88Mn_0.12As. The insulating-DMS-like M(T) relation of the as-grown sample indicates the existence of a high proportion of interstitial Mn atoms. The magnetization is greatly improved after annealing, and the low Curie temperature is suggested to be due to the surface hole-localization effect. The investigation on the magnetic anisotropy shows an almost isotropic characteristic of the magnetic properties, which is ascribed to the S-K growth mode.     

Experimental determination of the valence band structure of the InxGa1-x-As(001) surface

In_xGaj_1-xAs layers were grown on GaAs(00l) substrates by molecular beam epitaxy. The structure and quality of the surface and the layer thickness were monitored in situ by dynamical reflection high-energy electron diffraction (RHEED oscillations). Angle-resolved photoemission spectroscopy studies using He-I radiation were performed on the epitaxial layers. The energy-distribution curves of the photoelectrons were determined along the high symmetric directions in the surface Brillouin zone. The experimental band structure of In_xGa_1-xAs was determined with the help of the experimental and theoretical band structures of GaAs and In As. This article was submitted by the author in English.     

Physical consequences of the equivalence of conditions for the steady-state growth of nanowires and the nucleation on triple phase line

A new theoretical model describing the steady-state growth and crystalline structure of semiconductor nanowires (NWs) is proposed and its physical consequences are considered. It is demonstrated that the Nebol’sin-Shchetinin condition (nonwetting of the NW side surface by the liquid drop) necessary for the steady-state growth of NWs according to the vapor-liquid-solid (VLS) mechanism is equivalent to the Glas condition of nucleation on the triple phase line for the monocentric NW growth. An energy criterion for the steady-state growth of NWs is formulated in the general case of faceted NW side surface. Effective surface energies are found that determine the activation barrier for nucleation at the NW top. Based on the proposed model, the issue of determining the III–V semiconductor NW crystal structure (cubic zinc blende type versus hexagonal wurtzite type) is considered. In particular, it is shown that a decrease in the surface energy of a catalyst must lead to the predominant formation of a cubic phase, which is confirmed by experimental data on the growth of GaAs nanowires according to the VLS mechanism with Au and Ga catalysts.     

Effects of notch radius and anisotropy on the crack tip plastic zone

Factors which influence the shape and size of the plastic zone in the immediate vicinity of a crack tip in isotropic materials at small loads are investigated. The plastic zone dimensions for the opening mode (Mode I) have been calculated over a range of values for the crack tip radius. An increase in tip radius results in an increase in the plastic zone dimension. In anisotropic materials, the orientation of crack slit and the anisotropic yield constants are other factors that affect the plastic zone size and shape. In this paper, typical curves for the shape and size of plastic zone are given to illustrate the influence of normal or shear anisotropic yield constants. For sheet metals the effects of anisotropy on the plastic zone dimensions can be evaluated in terms of R values. Suggested values of constant b for isotropic materials are given if the “radius” approximation is employed for small applied stresses.     

A Monte Carlo investigation of growth and characterization of heteroepitaxial thin films

We investigate the growth of mismatched thin films by a kinetic Monte Carlo computer simulation and including a local photoemission model with reflection high-energy electron diffraction (RHEED) intensity for comparison. The strain is introduced through an elastic energy term based on a valence force field approximation. We describe an atomistic mechanism for dislocation nucleation during first stage of GaSb/GaAs (001) growth and in situ variations of photoemission current (PE) and RHEED intensity are reported. We have shown the formation of grooves corresponding to (111) facets, a precursor to the formation of misfit defects. The surface roughening and facetting by creation of grooves explain the absence of photoemission and RHEED oscillations in accordance with experimental observations [J.J. Zinck and D.H. Chow, J. Cryst. Growth, 175/176 (1997) 323, J.J. Zinck and D.H Chow, Appl. Phys. Lett. 66 (1995) 3524].     

Frequency modulated atomic force microscopy on MgO(001) thin films: interpretation of atomic image resolution and distance dependence of tip-sample interaction

Atomically resolved images on a MgO(001) thin film deposited on Ag(001) obtained in ultrahigh vacuum by frequency modulated atomic force microscopy at low temperature are presented and analysed. Images obtained in the attractive regime show a different type of contrast formation from those acquired in the repulsive regime. For the interpretation of the image contrast we have investigated the tip-sample interaction. Force and energy were recovered from frequency shift versus distance curves. The derived force curves have been compared to the force laws of long-range, short-range and contact forces. In the attractive regime close to the minimum of the force-distance curve elastic deformations have been confirmed. The recovered energy curve has been scaled to the universal Rydberg model, yielding a decay length of l = 0.3?nm and ΔE = 4.2?aJ (26?eV) for the maximum adhesion energy. A universal binding-energy-distance relation is confirmed for the MgO(001) thin film.