Victor P. Plessky

Surface Acoustic Waves in Inhomogeneous Media

This monograph covers important problems caused by the interaction of different types of surface acoustic waves with surface inhomogeneities. The problem of surface acoustic wave interaction with periodic topographic gratings, widely used in filters and resonators, is given careful consideration. The most important results of surface wave scattering by local defects such as grooves, random roughness and elastic wedges are described. Different theoretical approaches and practical rules for solving the surface wave problems are also presented.

Impedance Method in the Theory of Surface Waves in Inhomogeneous and Layered Media

This chapter deals with the impedance method for analysing surface waves in inhomogeneous piezoelectric structures. This analysis is based on the following arguments. We do not construct wave field solutions in the whole inhomogeneous structure by joining these fields on boundaries of irregularity, but consider only the fields on a certain convenient plane and describe the half-spaces (bordering this plane) by surface impedance matrices; the form of these matrices is defined not only by the medium character, but also by the properties of scattering inhomogeneities. This approach is quite natural because of the plane character of typical structures and allows us to split a complicated boundary-value problem of obtaining fields into two simpler independent problems: a problem of finding the surface impedances independent of fields and a problem of solving equations of motion on a plane with given impedances of adjusting half-spaces. And in this case a minimal number of variables is used for the description of both problems, and the problems themselves are posed in a compact form convenient for constructing both exact and approximate solutions by means of methods of perturbations.

Comparative analysis of synchronous "hiccup" and nonsynchronous saw resonators on quartz

Designed and measured characteristics of hiccup and non-synchronous surface acoustic wave resonators on quartz are presented and analyzed. In hiccup configuration basic periodicity of interdigital transducer and reflectors is the same except for additional distance of a quarter of wavelength in between neighboring electrodes at the center of transducer. The configuration with different periods of transducer and reflectors is called as non-synchronous. The hiccup SAW resonators show significant degradation of quality factor that can be attributed to radiation of bulk waves. Measured characteristics of non-synchronous resonators agree well with calculations.

Scattering of Surface Waves by Local Irregularities

Here the impedance approach to the analysis of wave propagation in inhomogeneous media presented in the previous chapter is used to investigate the scattering of these waves by a specific local boundary or bulk irregularities. The boundary irregularities of small height or depth in the form of groups of extended projections or hollows are the main functional elements of a large class of signal processing acoustoelectronic devices with reflecting gratings [4.1, 2]; band-pass or dispersion filters [4.3, 4], resonators [4.5], structural transducers [4.6, 7]. The boundary irregularities of finite dimensions are used as elements of two-periodic structures [4.8, 9], and the analysis of their scattering properties is also necessary for investigation of the surface wave propagation along rough surfaces [4.10-12]. The parameters of surface wave scattering by bulk inclusions in the acoustic lines material are used in seismology [4.13].

Interaction Between Electrode Structures and Surface Waves in Piezoelectrics

A system of thin electrodes on a piezoelectric surface is one of the main elements of all practical acoustoelectronic SAW signal processing devices [14.1-3]. Because the boundary value problem describing the interaction between SAW and electrode structures is extremely complicated and at the same time very important for practical applications, a great deal of literature has been occupied with this problem for different model assumptions and approximations. Here we list the main papers where the known calculation methods are given.

Mutual Transformation of Bulk and Surface Acoustic Waves by Periodic Irregularities

If the frequency becomes greater than the Bragg frequency, for a certain critical frequency ( {f_{sc}} = 2{f_0}{v_t}/({v_R}{v_t}) )(vt is the shear bulk wave velocity), the surface acoustic waves begin to scatter into bulk waves by the surface irregularities (Fig. 8.la). First, a shear bulk wave scattered backwards appears, and if the frequency continues to grow, a longitudinal wave appears.For λ=l the scattered waves propagate along the normal to the surface (Fig. 8.lb). If the wavelength continues to decrease (Fig. 8.1c), some scattered waves appear.

Basic Types of Surface Acoustic Waves in Solids

At present there exist about ten thousand books and papers dealing with the subject of surface acoustic waves in solids first described by Rayleigh in 1885 [1.1], and it is impossible even to mention all of them. But it is hardly necessary to do this, since there exist a great number of reviews [1.2-5] and monographs [1.6-18] concerning both the properties of surface acoustic waves and their application in special signal processing devices. Therefore, in this review chapter we present only the basic properties of the Rayleigh waves, Gulyaev—Bleustein waves, and waves of certain other types that are very often referred to in original chapters of this monograph.

Waves in a Half-space with Account of Surface Effects

Up to this point we considered the surface acoustic waves propagating in one or another inhomogeneous medium and did not concern ourselves with either the methods for producing the solid surfaces or their influence on the surface wave properties. Meanwhile, even in the case when a free surface is formed by cutting along the cleavage planes, i.e., when the surface is perfect, there is always a near-surface imperfect layer with properties which differ from those of the bulk medium since the upper surface atoms are under different conditions than those in the bulk media [15.1-4]. In this case there is a stressed state within the layer, and the near-surface atoms are characterized by other constants of elastic interaction. The thickness of a disturbed near-surface layer usually has the order of interatomic distance in a crystal lattice, i.e., is equal to 2-5 A.

Propagation of Surface Acoustic Waves in Small Scale Periodic Structures

This chapter, as well as the next two chapters, will be devoted to the surface acoustic wave (SAW) propagation along the surface of an acoustic line with periodic systems of irregularities having the shape of etched grooves, bars of metal, etc. (Fig. 6.1). Such periodic structures placed in the way of the wave propagation are the basic elements for many SAW devices. The main reason to use the gratings is that in order to get certain performances of devices, it is necessary to be able to control the wave propagation: to reflect the wave with small losses, to change the direction of the wave propagation, to scatter the waves, to transform bulk waves into surface waves, etc. Because of the complicated structure of SAW (Chap. 1), these operations cannot, as a rule, be performed by means of a single (local) scattering element and only a large number of perturbations placed periodically (or quasi-periodically) on the acoustic line surface allow us to obtain the required control of SAW propagation. In this case the influence of each separate element on the wave propagation can be small, but in the whole their influence can be essential. The separation of functions of SAW excitation and reception (by means of interdigital transducers) and forming the device performances by using quasi-periodic reflecting structures also has certain advantages. Nowadays, resonators and dispersion delay lines with unique characteristics are designed on the base of reflecting structures.

Thin-Film Waveguides for Surface Acoustic Waves

Thin-film waveguides for surface acoustic waves (strip or slot waveguides) [11.1, 2] (Figure. 11.1) keep the SAW beams from diverging, and allow us to use the area of substrata more effectively and to change the direction of wave propagation. Therefore, they are widely used for improving the parameters of acoustoelectronic devices. The waveguide effect appears due to the existence of a slow wave region in the substrate [11.3].