Surface Acoustic Waves in Inhomogeneous Media

397 Pages·1995·26.48 MB·English

by  Dr. Sergey V. Biryukov

Springer Series on
Wawe Phenomena 20
Springer Series on
Wa• • Ph. ...m en.
Editors: L.M. Brekhovskikh L.B. Felsen H.A. Haus
Managing Editor: H. K. V. Lotsch
Volume 19
Laser Ultrasonics
By L. M. Lyamshev
Volume 20
Surface Acoustic Waves in Inhomogeneous Media
By S. V. Biryukov, Y. V. Gulyaev, V. V. Krylov and V. P. Plessky
Volume 1-18 are listed at the end of the book
S.V. Biryukov YU.V. Gulyaev
V.V. Krylov V.P. Plessky
Surface Acoustic Waves
in Inhomogeneous Media
With 138 Figures and 5 Tables
Springer-Verlag Berlin Heidelberg GmbH
Dr. Sergey V. Biryukov Prof. Yuri V. Gulyaev, Academician
A.L. Mints Radiotechnical Institute Institute of Radioengineering
Russian Academy of Sciences and Electronics
10-12,8 Marta St. Russian Academy of Sciences
Moscow 125083, Russia 11, Mokhovaya St.
Moscow 103907, Russia
Prof. Victor V. Krylov Dr. Victor P. Plessky
Centre for Research into the Advanced SAW Products SA
Built Environment Case postale 415
Faculty of Environmental Studies Chemin des Chapons-des-Pres 11
The Nottingham Trent University CH-2022 Bevaix
Burton Street, Nottingham NGI 4BU Switzerland
UK
Series Editors:
Professor Leonid M. Brekhovskikh, Academician
P.P. Shirsov Institute of Oceanology, Russian Academy of Sciences,
Krasikowa Street 23, 117218 Moscow, Russia
Professor Leopold B. Felsen, Ph.D.
Boston University, Department of Aerospace and Mechanical Engineering,
110 Cummington Street, Boston, MA 02215, USA
Professor Hermann A. Haus, Ph.D.
Department of Electrical Engineering & Computer Science, MIT, Cambridge, MA 02139, USA
Managing Editor: Dr.-Ing. Helmut K.V. Lotsch
Springer-Verlag, Tiergartenstrasse 17, D-69121 Heidelberg, Germany
ISBN 978-3-642-63348-5
Library of Congress Cataloging-in-Publication Data. Biriukov, S. V. (Sergey Vladimirovich) Surface acoustic
wave in inhomogenous media I S.V. Biryukov , .. [et al.). p. cm. - (Springer series on wave phenom
ena; 20) Includes bibliographical references and index.
ISBN 978-3-642-63348-5 ISBN 978-3-642-57767-3 (eBook)
DOI 10.1007/978-3-642-57767-3
1. Surface acoustic waves. 2. Solids. 3. Surface waves. 1. Title.
II. Series. QC176.8.A3B57 1995530.4'16 - dc20 94-36945
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© Springer-Verlag Berlin Heidelberg 1995
Originally publisbed by Springer-Verlag Berlin Heidelberg l\ew York in 1995
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Preface
The study of propagation and scattering of Surface Acoustic Waves (SAW) in
inhomogeneous solids has become a wide and rapidly developing area of applied
physics. Work in this direction is stimulated to a large degree by the possibility
of using SAW to create new compact and effective acoustoelectronic signal
processing devices, as well as by the requirements of seismology, environmental
acoustics, ultrasonic nondestructive testing, and surface physics.
The interaction of SAW with various local irregularities such as steps,
grooves, surface electrodes, bulk inclusions, wedge edges and waveguide struc
tures forms the basis of operation of most SAW signal-processing devices,
including ones used in modern mobile phones. Certain irregularities can be of
a random nature such as rough surfaces and curved boundaries whose influence
must also be taken into account.
A consistent analysis of any SAW phenomena must be based on the solution
of the relevant boundary problem for elasticity equations, which in the case
of piezoelectric media are connected with Maxwell's equations. At the initial
stage of development of SAW applications even an approximate solution of
such problems appeared to be too complicated; due to practical reasons this led
to the development of a simplified serniempirical approach based on various
models. The few available monographs on the physics of surface acoustic waves
contain essentially the above mentioned approach, the rigorous methods being,
as a rule, described only and, at best, the end results given.
However, the natural extension of operating capacity of SAW devices and
increased requirements for their performances inevitably lead to the necessity
of a consistent analysis of typical inhomogeneous structures which would be
based on exact or approximate solutions of the equations of motion. The same
thing can also be said about the related problems of seismics and ultrasonic
nondestructive testing, where a variety of existing methods of design makes it
very urgent to develop a consistent approach to the problems of propagation
and scattering of surface waves in inhomogeneous media. Such an approach is
developed in this monograph which summarizes a good deal of original work
published lately.
The book deals with traditional and new methods of theoretical analysis
of the mechanisms of propagation of surface acoustic waves in inhomoge
neous solids. The processes of scattering, reflection and transformation of waves
by local and periodic discontinuities of various types, as well as SAW wave
guides, are considered. The propagation of SAW on smooth surfaces of variable
VI Preface
curvature and their scattering at the boundaries of wedge-like regions are exam
ined. Certain aspects of the effect of random irregularities on surface wave
propagation are touched upon. The book on the whole is of a theoretical nature;
however, the relevant experimental investigations are described as well.
The book, which represents a shortened and corrected version of the
first Russian edition, is based to a large extent on original works by the
authors although the results in this field obtained by other investigators are
also included; this helps to treat the problem under consideration all the more
fully. Chapters I, 2, 6-8 have been written jointly by Yu. V. Gulyaev and
V. P. Plessky, Chaps. 3-5, II, 14, by S. V. Biryukov, and Chaps. 9, 10, 12,
13, 15, by V. V. Krylov. All chapters of the book are mutually independent to
a large extent and can be read in an arbitrary order.
Since the first Russian edition in 1991, many changes have occured, par
ticularly in Moscow where this book was originally written. Two of the authors
(V.P.P. and V.V.K.) are now working in other countries facing new challenging
problems in surface wave theory and in acoustics generally.
Because of limited space in the book, we were not able to reflect many
interesting recent results in the field, in particular investigations of nonlinear
surface acoustic waves which have advanced in the past few years. To assist the
reader, some new references have been added to the original list of references.
The authors wish to thank their colleagues who at one time or an
other took part in discussions on various problems treated in this
book: I.D. Abrahams, c.K. Campbell, P. Cawley, l.R. Chamuel, D.P. Chen,
D.G. Crighton, c.c. Ferguson, L.L. Goryshnik, V.I. Grigorievsky, C.S. Hart
mann, l. Heighway, P. Hess, Yu.A Kosevich, V.A Krasil'nikov, OJ. Leroy,
AA. Maradudin, G. Martin, AP. Mayer, G.A Maugin, D.P. Morgan,
V.G. Mozhaev, A.I. Murdoch, D.F. Parker, V.G. Polevoy, S.M. Rytov,
B.K. Sinha, R.H. Tew, T. Thorvaldsson, H.F. Tiersten and M. Weihnacht.
Our special thanks are to Mrs. M.A. Shishkova for translating the manuscript
into English and to Dr. H.K. V. Lotsch for his careful and patient editing of the
book.
The authors hope that this book will be of use both for specialists in the
field of physics of surface acoustic waves and for students (postgraduates and
undergraduates) who undertake reading in the subject for the first time. The
authors are aware of the fact that the book may contain controversial assertions,
too subjective or one-sided arguments, and inaccuracies. All the remarks and
suggestions regarding the contents of the book will be fully appreciated.
Nottingham, UK Victor V. Krylov
November 1994
Contents
1 Basic Types of Surface Acoustic Waves in Solids .......... 1
1.1 Rayleigh Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Gulyaev-Bleustein Waves ........................ 5
1.3 Love Waves and Other Shear Surface Waves ........... 9
1.4 Waves in Plates and Layered Structures ............... 11
1.5 Surface Waves in Crystals ........................ 14
2 Interaction of Surface Acoustic waves With Electrons and
Influence of Substrate Environment on Wave Propagation 18
2.1 General ..................................... 18
2.2 Acoustoelectronic Amplification of Surface Waves ....... 20
2.3 Nonlinear Acoustoelectronic Effects ................. 24
2.4 Interaction of Surface Waves in Piezoelectrics
with Electron Beams in a Vacuum . . . . . . . . . . . . . . . . . . . 26
2.5 Acoustic Transfer of Charges ...................... 27
2.6 Rayleigh Wave Attenuation Caused by Gas Load ........ 29
2.7 Stoneley Waves on the Interface between a Solid and a Fluid 30
2.8 "Viscosity" Shear Surface Waves ................... 31
3 Impedance Method in the Theory of Surface Waves
in Inhomogeneous and Layered Media .................. 35
3.1 Concept of Surface Impedance ..................... 35
3.2 Equation for the Surface Impedance Matrix ............ 38
3.3 Layered Anisotropic Medium ...................... 45
3.4 Energy Relations ............................... 47
3.5 Layered Isotropic Elastic Medium ....... . . . . . . . . . . . . 53
3.6 Impedance of a Piezoelectric of Class C6v ..........•.. 57
3.7 Energy Flux and Density for Classical Types
of Surface Waves .............................. 60
3.8 Scattering of Surface Waves by Weak Inhomogeneities
in Born's Approximation ......................... 65
VIII Contents
4 Scattering of Surface Waves by Local Irregularities -. . . . . . . . 72
4.1 Impedance of a Layered Half-space
with a Thin Irregular Layer ....................... 72
4.2 Scattering by Irregularities of a Projection
and a Hollow Type ............................. 74
4.3 Angles of Zero Scattering . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4 Scattering of Rayleigh Waves ...................... 78
4.5 Transformation into Bulk Waves .................... 86
4.6 Scattering of Gulyaev-Bleustein Waves
by Two-dimensional Boundary Irregularities ........... 92
4.7 Impedance of Elastic Half-space with Bulk Irregularities ... 95
4.8 Scattering by Cylindrical and Wedge-like Irregularities 97
5 Second Order EtTects in Surface Wave Scattering
by a Rectangular Projection . . . . . . . . . . . . . . . . . . . . . . . . .. 105
5.1 Iteration Method ............................... 105
5.2 Equation for the Surface Impedance ................. 106
5.3 A Rectangular Projection in the Case of Horizontally
Polarized Waves: An Exact Solution for Surface Impedance 108
5.4 Second Order Effects in a Scattered Field
of Horizontally Polarized Waves .................... 11 0
5.5 Parameters of Scattering for Love Waves .............. 117
5.6 A Rectangular Projection in the Case
of Vertically Polarized Waves ...................... 119
5.7 Scattering of the Rayleigh Wave .................... 121
6 Propagation of Surface Acoustic Waves
in Small Scale Periodic Structures ..................... 124
6.1 General Notion ................................ 124
6.2 Surface Transverse Waves on a Rough Surface. . . . . . . . . . 127
6.3 Shear Waves on a Periodically Perturbed Interface ....... 131
6.4 Surface Skimming Bulk Waves
and Surface Transverse Waves in Crystals ............. 133
7 Bragg Reflection of Surface Waves . . . . . . . . . . . . . . . . . . . .. 139
7.1 Background of the Problem ....................... 139
7.2 Reflection of Rayleigh Waves from Sinusoidal Irregularities
on a Substrate Surface ........................... 141
7.3 Weighted Reflectors ............................. 146
7.4 Bragg Reflection in the Case of Oblique Incidence
on a Grating .................................. 150
7.5 Case of Finite Beam Aperture. . . . . . . . . . . . . . . . . . . . . . 157
Contents IX
7.6 Two-dimensional Reflecting Structures ............... 160
7.7 Bragg Reflection of Gulyaev-Bleustein Waves .......... 163
8 Mutual Transformation of Bulk and Surface Acoustic Waves
by Periodic Irregularities ............................ 175
8.1 Brekhovskikh Damping .......................... 175
8.2 Crystal Anisotropy Effect ......................... 178
8.3 Role of Second Order Effects ...................... 182
8.4 Structural Transducer ... . . . . . . . . . . . . . . . . . . . . . . . . . 184
8.5 Damping Interference of Scattered Waves
for Shear Surface Waves Propagating in Gratings
with Period Equal to Half the Wavelength ............. 193
9 Rayleigh Waves on Curved Surfaces of Arbitrary Form . . . . . 196
9.1 History of the Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . 196
9.2 Analysis of Rayleigh Wave Propagation along a Curved
Surface by the Method of Parabolic Equations .......... 198
9.3 Anisotropy of the Rayleigh Wave Velocity
due to Surface Curvature ......................... 202
9.4 Geometrical Acoustics of Curved Surfaces . . . . . . . . . . . .. 206
9.5 Rays and Caustics of Rayleigh Waves
on Surfaces of Varying Curvature ................... 208
10 Topographic Waveguides ............................ 217
10.1 Rectangular and Triangular Ridges on the Surface
of a Solid as Waveguides ........................ 217
10.2 Waves Propagating along the Edge of an Elastic Wedge
(Wedge Acoustic Waves) ........................ 220
10.3 Geometrical-acoustic Approach to the Theory
of Wedge Waves .............................. 224
10.4 Scattering of Wedge Acoustic Waves ... . . . . . . . . . . . .. 230
10.5 Smooth Topographic Waveguides .................. 233
11 Thin Film Waveguides for Surface Acoustic Waves ........ 243
11.1 Impedance Method for Determining Fields
and Dispersion Equations ........................ 244
11.2 Fundamental Rayleigh Mode . . . . . . . . . . . . . . . . . . . . .. 247
11.3 Fundamental Love Mode ........................ 253
11.4 Rayleigh Wave Radiation by a Thin Film Waveguide
in the Case of Love Wave Propagation .............. 255
X Contents
12 Scattering of Surface Acoustic Waves at the Boundaries
of Wedge-like Regions .............................. 260
12.1 History of the Problem . . . . . . . . . . . . . . . . . . . . . . . . .. 260
12.2 Rayleigh Wave Reflection and Transmission in Acute Angle
Elastic Wedge in the Case of Normal Incidence ........ 262
12.3 Rayleigh Wave Reflection from Wedge Edge in the Case
of Oblique Incidence: The Effects of Caustic Phase Shift . 267
12.4 On the Applicability Conditions for the Geometrical
Acoustics Approximation for Solid Wedges ........... 272
12.5 Characteristic Properties of Surface Wave Scattering
in Obtuse-angle Wedge . . . . . . . . . . . . . . . . . . . . . . . . .. 277
13 Waves on Rough Surfaces ........................... 282
13.1 Background.................................. 282
13.2 Statement of Surface Wave Scattering Problems
by Use of Integral Equation ...................... 283
13.3 Born series: The First and Higher Approximations
of the Theory of Scattering .... . . . . . . . . . . . . . . . . . .. 287
13.4 The Rayleigh Wave Attenuation on a Rough Surface .... 292
13.5 The Rayleigh Wave Dispersion due to Roughness ....... 297
14 Interaction Between Electrode Structures
and Surface Waves in Piezoelectrics ........... " . . . . . . .. 301
14.1 Statement of the Problem ........................ 302
14.2 Relation Between Surface Charge Distribution
and Parameters of Scattered Waves ................. 303
14.3 Integral Equation for Surface Charge Distribution ..... ,. 307
14.4 Approximate Methods for Solving the Integral Equation
for Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 310
14.5 Self-consistent Solution ......................... 312
14.6 Narrow-electrode Approximation . . . . . . . . . . . . . . . . . .. 316
14.7 A Single Electrode .. . . . . . . . . . . . . . . . . . . . . . . . . . .. 320
14.8 Two-electrode Transducer . . . . . . . . . . . . . . . . . . . . . . .. 324
14.9 Multi-electrode Structures . . . . . . . . . . . . . . . . . . . . . . .. 329
15 Waves in a Half-space with Account of Surface Effects ..... 330
15.1 Gibbs' Definition of Surface Effects ................ 331
15.2 Surface Stress Tensor: Surface Elasticity and Density .... 334
15.3 Nonclassical Boundary Conditions
Incorporating Surface Effects ..................... 338
15.4 Surface Effects and Rayleigh Waves ................ 345
References .......................................... 355
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
Subject Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385