Hagen Schmidt

Surface acoustic wave scattering from steps, grooves, and strips on piezoelectric substrates

The paper studies, by the finite element method, the reflection of surface acoustic waves from single obstacles of regular shapes on the surface of piezoelectric materials. The so-called perfectly matched layer is used to truncate the computational domain. The following types of imperfections are considered: single steps, grooves, and projections, as well as metallic strips overlaying the substrate or inset into it. The absolute values and the phases of the reflection coefficients are computed for YZ and 128°YX LiNbO3 substrates as functions of the height-to-wavelength and the width-to-wavelength ratios. In addition, the reflectivity of gratings comprising a finite number of grooves or electrodes is computed and compared with the analytic estimations based on the coupling-of-modes theory.

Elastic and piezoelectric properties of AlN and LiAlO 2 single crystals

We have successfully grown high-quality AlN piezoelectric single crystal using the sublimation technique. Transparent crack-free boules of approximately 15 mm in diameter and 25 mm in length along the [0001] direction were obtained, with coloring from amber to dark brown depending on growth temperature. Full sets of material parameters of grown AlN and commercially available LiAlO2 bulk crystals were measured at room temperature. Temperature coefficients of the material parameters of LiAlO2 were also obtained in a temperature range from -70 to +50°C.

Rayleigh wave reflection from single surface imperfections on isotropic substrates

The specific features of the Rayleigh wave reflection from single surface imperfections of an isotropic substrate are studied by the finite element method. Six types of the imperfections are considered, namely, upstep and downstep, projection and groove, and strip of foreign material coating the substrate and buried into it. The dependence is found and analyzed of the absolute value and the phase of the reflection coefficients on the geometrical parameters of defects and the angle of incidence. Numerical results are compared to analytical predictions based on a development of the reflection coefficient in powers of the defect height to wavelength ratio h/λ and limited to the first-order term. In particular, this comparison reveals that in some cases approximate expressions are able to provide a good precision. At the same time situations are met when the linear approximation fails to describe the behavior of the reflection coefficient even at fairly small h/λ.

Detection and characterization of carbon contamination on EUV multilayer mirrors

In this paper, we detect and characterize the carbon contamination layers that are formed during the illumination of extreme ultraviolet (EUV) multilayer mirrors. The EUV induced carbon layers were characterized ex situ using spectroscopic ellipsometry (SE) and laser generated surface acoustic waves (LG-SAW). We show that both LG-SAW and SE are very sensitive for measuring carbon layers, even in the presence of the highly heterogeneous structure of the multilayer. SE has better overall sensitivity, with a detection limit of 0.2 nm, while LG-SAW has an estimated detection limit of 2 nm. In addition, SE reveals that the optical properties of the EUV induced carbon contamination layer are consistent with the presence of a hydrogenated, polymeric like carbon. On the other hand, LG-SAW reveals that the EUV induced carbon contamination layer has a low Youngs modulus (<100 GPa), which means that the layer is mechanically soft. We compare the limits of detection and quantification of the two techniques and discuss their prospective for monitoring carbon contamination build up on EUV optics.

Gyroscopic effect for SAW in common piezoelectric crystals

In the present work, using the well-known numerical procedure for SAW calculation in arbitrary crystals the gyroscopic effect is investigated. To take into account the medium rotation the Coriolis and centrifugal forces are introduced into the piezoelectric medium equations of motion. As a result of the standard procedure, the SAW velocity is calculated as a function of the medium rotation rate about each coordinate axis. A shift of such velocity due to rotation is determined for isotropic Al, STX-quartz, 128°YX-LiNbO3, YZ-LiNbO3, X112°Y-LiTaO3, and Z-cut of AlN substrates.

Usage of symmetry in the simulation of interdigital transducers

This paper discusses the application of the finite element method to the simulation of surface acoustic wave generation on piezoelectric substrates and the possibility of reducing the number of computations by taking into account the symmetry of the problem. It is shown that the computations can be performed in only one half of the structure provided that the substrate assumes particular orientations. The class of allowed orientations encompasses the majority of crystal cuts used in practice. A test computation of the electric admittance agrees well with experimental results. The perfectly matched layer method is implemented to truncate the computational domain.

Rayleigh wave scattering from a vertical edge of isotropic substrates.

The paper numerically studies the harmonic Rayleigh wave scattering at the 90-degree corner of isotropic substrate. The finite element method is used. The main attention is paid to two cases. The first one is the apex of the substrate corner is rounded off. The second one consists in that a layer of foreign material is deposited on the face which scatters the Rayleigh wave. The dependence of the reflection and the transmission coefficients on the Poisson ratio, the angle of incidence, the fillet radius, and the layer thickness are obtained. It is found that if the Rayleigh wave is incident perpendicularly to the substrate border, then the fillet of small radius as compared to the wavelength increases the reflection coefficient and decreases the transmission coefficient by factors 1.3-1.8. At normal incidence, the Poisson ratio does not change qualitatively the dependence of the reflection and transmission coefficients on the fillet radius. But the Poisson ratio can substantially affect the angle dependence of these coefficients if the wave is incident obliquely on the corner rounded off. It is also found out that a layer can modify the conditions of scattering such that the incident wave is totally reflected without transmission and conversion into bulk waves in a wide interval of angle of incidence, although, in principle, the bulk wave generation is allowed within a part of this angle interval.

Mutual conversion of bulk and surface acoustic waves in gratings of finite length on half-infinite substrates. I. FE analysis of surface wave generation

The paper studies numerically the bulk acoustic wave generation by the surface acoustic wave propagating across a grating created on the surface of an elastically anisotropic half-infinite substrate. The computations are fully based on the finite element method. Applying the discrete Fourier transformation to the displacement field found inside the substrate and using an orthogonality relation valid for plane modes we determine separately the spatial spectrum of the quasi longitudinal and the quasi transverse bulk waves, that is, the dependence of the amplitudes of these waves on the tangential component of the wave vector. The dependence is investigated of the central spectral peak height and shape on the frequency of the incident surface wave as well as on the thickness, the width, and the number of strips forming the grating. In particular, it is found that under certain conditions the central peak can be approximated fairly precisely by the central peak of a sinc-function describing the spectrum of the bounded acoustic beam of rectangular shape and of width equal to the length of the grating.

Anisotropy effects in the reflection of surface acoustic waves from obstacles

The paper studies the difference between the reflection coefficients of a surface acoustic wave incident on a groove or strip along the inverse directions. This difference occurs because of the crystallographic anisotropy of the substrate and/or the asymmetry of the shape of the obstacle. The numerical computations are carried out by the finite element method. A perfectly matched layer is implemented to truncate the computational domain. Some general properties of the transmission and reflection coefficients of surface acoustic waves are also discussed.

Damaging of metallization layers by high power surface acoustic wave fields

Similar to interconnection lines in integrated circuits patterned metallization structures are used as electrodes and reflecting elements in surface acoustic wave (SAW) devices. As electromigration is known to be a damaging mechanism in interconnects also the metallization of SAW devices tends to be degraded under high power conditions. Corresponding to the source of degradation, namely the elastic waves, the latter is called acoustomigration. Aim of this work is an approach to understand damage mechanisms by corresponding loading conditions and failure occurrences in the metallization. Our work is focused on in situ experiments with standing SAWs combining electrical measurements and different microscopic investigations (OM, SEM, FIB), detailed consideration of SAW stress field structure in connection with model experiments, and making use of the route of Cu technology. First results of a comparative study of fully metallized Al and Cu areas supporting high amplitude travelling SAWs are presented showing...