Ultrasonics 36 ( 1998) 317~ 321

Anisotropic elastic characterization of surfaces from 2 MHz to 20 GHz

Andrew Briggs *, Oleg Kolosov

D~~purtlent of’Muteriu1.s. Purks Roud, O.ufbrd Univrrsity. O.Ffbrd, OXI 3PH, UK

Abstract

A range of techniques is now available to characterise the elastic properties of surfaces and surface layers. Applications include

measurement of stress, subsurface damage, layer thickness and bonding, and the elastic properties of thin layers. At the bottom of the frequency range, group velocity measurements can be made by timing the transit of pulses between knife edges. Over a range of higher frequencies acoustic microscopy can be used to measure the interference between specular and surface waves, using the V(Z) technique with cylindrical (line-focus-beam) lenses or transducers. For dispersive surfaces L’(,f‘) techniques can be used, either in an acoustic microscope with V-groove lenses, or in an ultrasonic microspectrometer with a spherical-planar pair. Surface Brillouin spectroscopy enables the frequency range to be extended to 20 GHz, with acoustic wavelengths less than 300 nm and sensitivity to surface layers considerably thinner than that. All of these techniques can give azimuthal resolution on anisotropic surfaces. The near field technique of ultrasonic force microscopy is able to give information about anisotropic structures on surfaces with nanometre resolution. The user is now in a strong position to choose the technique most appropriate to the material which he wishes to study or characterise, and a growing range of applications is becoming established. 0 1998 Elsevier Science B.V.

Kcywrds; Surface acoustic wave; Scanning interference fringe; Ultrasonic microspectrometer; Acoustic microscopy; Brillouin spectroscopy; Ultrasonic force microscopy

1. Measuring surface elastic properties

Surface elastic properties may be measured using surface acoustic waves, since these have longitudinal and transverse components which decay exponentially with depth. By making measurements as a function of propagation direction it is possible to characterise the

elastic properties of anisotropic surfaces. Generally the depth sampled is comparable with the wavelength, and therefore by choosing the appropriate frequency it is possible to sample a given depth of interest. A range of techniques is now available covering four orders of magnitude in frequency, and therefore probing a corre- sponding range of depths.

Coupling to surface vibrations may be via a solid contact. by using laser excitation and detection, or a through coupling fluid such as water. The progression

from the greatest depth sampled to the smallest is characterized by a sequence first in that order, and then by a sequence in the reverse order, rather like a hierarchy of brackets in algebra. In the following headings an

* Corresponding author: Fax: (44) 1865 273783;

e-mail: andrew.briggs(cumaterials.ox.ac.uk

0041-624)</98;‘$19.00 0 I998 Elsevier Science B.V. All rights reserved. PII SO041 -624X( 97 )00090-5

indication is given of the frequency or range of frequen-

cies at which a technique has been demonstrated or is

commonly used. These frequencies are illustrative only;

it may be quite possible to use the techniques at other

frequencies. Generally the higher the frequency the

shallower the depth sampled, though the final technique

listed shows how to beat this rule.

Many of the papers in this proceedings issue of

Ultrusonics deal with one or two of the techniques listed

here, such as acoustic microscopy, surface Brillouin

spectroscopy, and the family of scanning probe micro-

scopies with ultrasonic excitation. It is hoped that this

synopsis will help to indicate how each technique relates

to others included in this issue. Some other ultrasonic

surface characterization techniques such as ultrasonic

microspectroscopy and scanning interference fringes do

not have dedicated papers in this issue at all, and it is

hoped that their mention here may help to fill such lacunae. Space does not permit the inclusion of original

figures and tables, which may be readily consulted in

the references given. These references are illustrative

only and are far from exhaustive; they should certainly be supplemented for specific enquiries by a literature

survey using a current database.

2. Contact transducers (2-20 MHz)

A direct way to measure the Rayleigh velocity on the surface of a sample is to launch a Rayleigh wave, either

with a wedge transducer or with a laser source, and then to measure the difference in the time of arrival at two transducers a calibrated distance apart. This method

is commonly used at traditional NDT frequencies (typi- cally a centre frequency of 5 MHz), and so conventional

NDT circuits can be used. Detection can be by transduc- ers with either a pyramid or cone type point contact, or

a wedge type line contact. The line contact is more demanding in alignment and surface finish, but gives a

stronger signal. For non-contact applications EMATs (electromagnetic acoustic transducers) can be used; these require careful calibration to determine a value for the

effective separation of the transducers. Anisotropy can be measured by rotating the alignment of the transducer array. Unfortunately, this does not provide a method

of eliminating effects of texture when measuring residual stresses with Rayleigh waves, since only shear horizontal waves are degenerate with respect to a 90’ change in propagation direction in an unstressed anisotropic

surface. Unlike the other Rayleigh methods commonly used

at higher frequencies, all methods based on the difference between two arrival times measure the group velocity of surface waves. For materials which may be regarded

as a half-space with properties which do not change with depth, this will be the same as the phase velocity, but in many cases of practical interest with layered structures the difference may be important.

Both wedge transducers and EMATs can be used to make measurements with sufficient accuracy to detect changes in Rayleigh velocity due to residual stress, and this may be an important area of application. In one particular study comparison was made between the changes in Rayleigh velocity due to stresses applied to an aluminium alloy [ 11. The change in velocity with stress measured by wedge contact transducers was dv/drr= -0.061 m SC’ MPa-‘, which compared with dv/da = -0.062 m s-r MPa-’ measured by acoustic microscopy. This agreement is well within experimental error, given that range of stress applied was + 200 MPa, and the accuracy of the contact transducer measure- ments was about +5m s-l.

3. Scanning interference fringes ( 110 MHz)

If you take a coherent beam of light and allow it to

pass through two closely spaced slits, the resulting interference pattern exhibits periodic fringes. The phe- nomenon was observed by Thomas Young, though he little anticipated either the conceptual controversy that would not be resolved until Paul Dirac developed

quantum electrodynamics, nor the ease with which the phenomenon could be seen following the invention of the laser. If you introduce a frequency shift into one of the two beams of light, at any point on the screen the

intensity will be modulated at that frequency, and the overall pattern will appear to move at a speed equal

to the frequency multiplied by the fringe spacing. If the laser intensity is high enough to cause local heating, then this periodic source can generate acoustic waves

[2]. By arranging the speed at which the interference

fringes move across the surface to be equal to a surface wave mode, then that mode can be excited with sufficient amplitude to be detected by, for example, a probe laser

beam with a knife edge detector. This is the principle of measurement of Rayleigh waves by scanning interference fringes [3].

Since the scanning interference fringe method excites waves in a defined direction in the surface, it can be used to measure anisotropic surfaces. In this way meas-

urements have been made of an Si(OO1) surface. The results are in good agreement with those obtained by line-focus-beam acoustic microscopy, except that in this case there is no fluid loading. The SIF measurements gave vRtrl,,, = 5085 f 5 m s- ‘, compared with vR,rrO, = 509Ok 1 m SC’ measured by acoustic microscopy [4],

and dependence on azimuthal angle of both Rayleigh and pseudo-Rayleigh waves is almost identical in the two techniques. Scanning interference fringes can be expected to find applications in cases where this kind of

measurement is needs to be made without contact to the specimen, for example during processing at elevated

temperature.

4. Ultrasonic microspectrometer (20-300 MHz)

For layered surfaces a powerful way to characterise the elastic structure and properties of the surface is to measure the reflection coefficient of acoustic waves inci- dent from a fluid (almost always water) at a given angle, and to measure the frequencies at which dips occur [5]. An experimental apparatus which has been developed for this purpose is know as the ultrasonic microspec- trometer (USMS) [6]. It has two transducers which are arranged on a goniometer, one to transmit a broadband pulse, and the other to receive it. The instrument exploits benefits developed for confocal microscopes, in which advantages can be gained by having different pupil functions for the two lenses. In USMS one of the transducers is planar to give angular resolution, and the other can be spherical to give spatial resolution. In this way lateral resolution of 10 urn has been achieved. The wide angle of acceptance of the second transducer has the further benefit that by tilting the spherical-planar pair of transducers the response at a range of incident angles can be measured. The reflected broadband signal

can be digitised and Fourier transformed to measure the

frequency response. In a series of experiments the response of an X-cut

quartz crystal has been measured over a range of incident angles from 20-32” over 180” scan of azimuthal angles. Excellent agreement was found both in combinations of

angles at which marked changes in phase and magnitude occurred and in the actual values of the phase and magnitude [5], and such agreement gives a high level of

confidence in the technique. For many practical purposes it may be sufficient simply to find the frequencies at

which dips occur in the reflected wave; indeed, since the

reflection coefficient often undergoes a marked phase change around these frequencies the dips may be enhanced experimentally by the finite angular aperture of the planar transducer, with consequent phase cancel- lation. Although a broadband pulse is used, since the results are analysed as a function of frequency the measurements correspond more directly to phase veloci-

ties at each frequency than to a dispersive group velocity, a point that will be elaborated in the next section. All the measurements correspond to propagation in the direction defined by the component in the surface of the

normal to the planar transducer, and so by rotating the sample azimithally anisotropic surfaces can be measured; this has been experimentally confirmed with X-cut quartz at 140 MHz. A delightful application of this technique is to the propagation of leaky wedge acoustic waves in fused quartz.

5. Acoustic microscopy (225 MHz)

Quantitative acoustic microscopy depends on the vari- ation of the video signal V in an acoustic microscope with the defocus --I of the lens towards the sample [7]. Oscillations appear in the resulting V(L) curve due to interference between the specularly reflected ray and rays associated with propagation as leaky Rayleigh waves in the surface of the sample. This phenomenon occurs with spherical lenses used for imaging, and can

be modelled for anisotropic materials. By using a cylin- drical lens Rayleigh waves can be excited in one direction only in an anisotropic surface. and measurements can then be made with azimuthal resolution [8]. In certain anisotropic materials, either surface or pseudosurface waves can be generated, and in some orientations both can be seen at once. The best known implementation is

at 225 MHz, although early work at 30 MHz (in Russian) also demonstrated azimuthal resolution on LiNbO, and on quartz [9]. Sophisticated techniques are available for relating the data to layered surfaces (for which it is also possible to use broadband V-groove lenses [lo] in a way similar to USMS) and even to surface stress [4,1 I]. Measurements of a layer on an anisotropic substrate yields the full range of azimuthal

data, and this increase in data more than outweighs the

larger number of unknown elastic constants. so that

elastic properties of anisotropic layered surfaces can

generally be determined with greater confidence than those of isotropic layered structures.

Like other high frequency Rayleigh wave techniques,

acoustic microscopy measures phase velocity. For practi- cal reasons a pulse must be used in the experiment

(though the pulse length in the LFB microscope contains many more oscillations than in an imaging microscope).

and therefore more than one frequency is present. But no attempt is made to measure the group velocity of

the pulse, and in more advanced microscopes special electronic circuits are used to ensure that the measure- ment is made on a single frequency component of the spectrum within the pulses. The propagation direction

arises as a further question in anisotropic materials, since even when there is no dispersion with frequency, the Pointing vector (which gives the direction of the

group velocity) is not in general parallel to the wave vector (which gives the direction of the phase velocity). In the LFB microscope it is again the phase velocity

that is measured. since the nature of the cylindrical lens means that while beam steering by the anisotropy may affect the strength of the oscillations in the lens signal V(Z), it cannot affect their period. Thus the azimuthal

propagation angle of the surface waves measured in an LFB microscope refers to the direction of the wave vector (which is perpendicular to the axis of the cylindri- cal lens), and not the direction of group velocity. In this context the ray model of the I’(:) etfect may seem a little confusing at first, since rays are associated with

energy how, but more careful analysis shows that any deviation of the ray in the surface from the wave vector cancels out, and it is indeed the phase velocity (in the

direction of the wave vector) that is being measured. An accuracy better than 0.1% is now routine. and accuracies of 0.005% are reported for the characteriza- tion of anisotropic materials such as LiNbO, and LiTaO, wafers for SAW devices [ 121.

6. Brillouin spectroscopy (2-20 GHz)

With the remorseless advance of nanotechnological industrial processes. there are ever increasing applica- tions that require the characterization of thinner and thinner surface treatments and coatings. There are severe practical limitations on the ability of any of the above

methods to give accurate results at frequencies above a few hundred megahertz, at which the Rayleigh wave- length is several microns in most materials. The measure- ment frequency can be increased by up to two orders of magnitude by using surface Brillouin spectroscopy [ 131. A beam of light is directed at the surt’ace at an oblique angle. Most of the light is scattered specularly, but a

small fraction will be scattered inelastically, with the excitation or absorption of a thermal phonon. The inelastic process causes a change in the frequency of the

light, equal to the frequency of the phonon. The corre- sponding change in wavelength is small, but by using a sufficiently sophisticated Fabry-Perot interferometer the

relevant spectrum of frequency shifts can be measured.

Knowing the wavevector of the incident light, and the angles of the incident and scattered beam, the velocity

of surface waves can be measured. The relevant signal from transparent materials can be greatly enhanced by applying a layer of aluminium to the surface a few

nanometres thick. Rayleigh waves are detected in one direction only in the surface, and so anisotropic surfaces can readily be measured by azimuthal rotation of

the sample; indeed a commercially available surface Brillouin spectrometer has this facility built in [ 141.

In all calculations of waves in layered structures use can be made of the continuity of the tangential compo- nent of the wave vector. This is simply a statement of Snell’s law, and can be written

k, sin (1, = k, sin 0,

where the subscripts refer to any incident or reflected or refracted beam. In surface Brillouin spectroscopy the tangential components of the various wave vectors are

also of crucial importance, but now the equation is one of conservation rather than continuity, and can be thought of equally as diffraction by a surface grating

associated with the surface phonon, or in terms of conservation of momentum, so that the phonon wave vector is equal to the difference between the tangential components of the scattered and incident wave vectors:

* Q = k, sin 0, -k, sin 0,

the sign depending on whether a phonon is annihilated or created. In the backscattering geometry commonly used 0 2 z -8,. and k, zk,. Surface Brillouin spectro- scopy is becoming established for a range of industrial problems [ 151, and is proving particularly significant in the characterization of layered nanocomposites.

7. Ultrasonic force microscopy ( l-200 MHz)

Focused acoustic microscopy is limited in its reso- lution by attenuation in the coupling fluid. Moreover, the greatest quantitative accuracy is obtained with the line-focus-beam technique, in which spatial resolution is sacrificed in the interests of quantitative accuracy with azimuthal resolution. Smaller depths can be sampled by using the gigahertz frequencies which Brillouin spectro- scopy offers, and for uniform nanolayers this is the preferred technique. But in Brillouin spectroscopy there is a Fourier compromise between the angular resolution and spatial resolution. Is it possible to characterise

surface elastic properties with nanoscale depth and lateral resolution? The breakthrough in this came with

the invention of the ultrasonic force microscope ( UFM ) [ 161, which exploits the principle that the resolution of a near field system is not limited by the wavelength. The family of related scanning probe microscope techniques

which has grown up includes atomic force acoustic

microscopy [ 17,181 and scanning local acceleration microscopy [ 191.

The UFM is based on an atomic force microscope, in which a tip on the end of a cantilever is in contact with the sample, with a feedback loop to maintain constant cantilever deflection. The sample is mounted on an ultrasonic transducer which causes surface

vibrations. The mechanical interaction between the tip and the surface is extremely nonlinear. At high enough

frequencies the inertia of the tip means that its response at the ultrasonic frequency is weak, but the nonlinear interaction leads also to a quasi-static deflection. This deflection would not be easy to measure, partly because of thermal drift and also because when imaging there

may also be topographical effects. Therefore the ultra- sonic vibration is modulated at a frequency of a feu kilohertz, at which the cantilever can readily respond. and this frequency is detected through a lock-in circuit. The tip-sample contact is thus acting rather like a mechanical diode, with the whole system behaving like a mechanical crystal radio. By measuring the nonlinear behaviour of the deflection as a function of the ultrasonic

amplitude it is possible to learn about the stiffness of the tip-sample contact, and hence (given certain other parameters) the local sample stiffness.

It might seem that the only elastic information that

could be obtained by UFM would be the value of the plane strain modulus E/( I -?), but in fact remarkable

contrast has been found from single crystal germanium quantum dots grown on Si(OO1) [20]. Comparison with electron microscopy suggests that indeed anisotropic effects are being imaged, possibly associated with the

shape of the dots and the mismatch strain responsible for their formation.

8. No excuse

Even within the family of ultrasonically excited scan- ning probe microscopy. the particular technique can be matched to the user’s particular requirement [21]. In principle almost all the techniques described here can be scaled up for larger applications, what is remarkable is that techniques are available to cover very small applications and layer thicknesses, right down to the nano scale. For robust quantitative measurements of anisotropic surfaces there is a range of Rayleigh wave techniques, for most of which commercial instruments are readily available, and the user is in a strong position

to adopt the technique most appropriate for his specific

need [22]. A sophisticated array of mathematical tools

is available for relating surface wave propagation data to the elastic properties and structure. There is no excuse for being unable to characterise the elastic properties of

anisotropic surfaces of interest.

[I ] T. Berruti. M.M. Cola. G.A.D. Brigs, Acoustoelastic measure-

ments in aluminium alloy specimens by means of a contact and

the non-contact LFB acoustic microscopy technique, J. Acoust.

Sot. Am. ( 1997) in press.

[2] H. Nishino. Y. Tsukahara. Y. Nagata. T. Koda, K. Yamanaka.

Excitation of high-frequency surface acoustic waves by phase

velocity scanning of a laser interference fringe, Appl. Phys. Lett.

62 ( 1993) 2036 2038.

[3] K. Yamanaka. New approaches in acoustic microscopy for non-

contact measurement and ultra high resolution, in: G.A.D. Brig&s

(Ed.). Advances in Acoustic Microscopy I. Plenum Press. New

York. 1995, pp. 301 342.

[4] Z. Sklar. P. Mutti, N.C. Stoodley, G.A.D. Brig@. Measuring the

elastic properties of stressed materials by quantitative acoustic

microscopy. in: G.A.D. Brigs (Ed.). Advances in Acoustic

Microscopy I. Plenum Press. New York. 1995, pp. 209-247.

[5] Y. Tsukahara, N. Nakaso. K. Ohira. M. Yanaka. Interaction of

acoustic waves with solid surfaces. in: G.A.D. Brigs. W. Arnold

(Eds.), Advances in Acoustic Microscopy 2. Plenum Press, 1996.

pp. 10% 165.

[h] N. Naknso. K. Ohira and Y. Tsukahara, Reflection coefficient

measurement of anisotropic materials by ultrasonic micro-spec-

trometer. in: Proc. 1990 IEEE Ultrason. Symp.. IEEE. 1991.

pp. 713 71x.

[7] G.A.D. Brigs. Acoustic Microscopy, Clarendon Press, Oxford,

1992.

[S] J. Kushibiki. N. Chubachi. Material characterisation by line-focus

beam acoustic microscope. IEEE Trans. Sonics Ultrason. 32

(1985) I89 212.

[9] S.I. Berezina. Acoustic microscope applications to the measure-

ment of the orientation dependencies of SAW-velocity in crystals.

Proc. Soviet Union Conf. Acoustoelectronics and Quantum

Acoustics. Dushanbe. 1981, pp. 84 X5.

[IO] A. Atalar. H. Kiiymen. A. Bozkurt. G. Yaralioglu. Lens gcomc-

tries for quantitative acoustic microscopy. in: G.A.D. Brigs

(Ed.). Advances in Acoustic Microscopy I Plenum Press. New

York. 1995. pp. ll7- 151.

[I I] J.D. Achenbach. J.O. Kim. Y.-C. Lee, Measuring thin-film elastic

constants by line-focus acoustic microscopy. in: G.A.D. Brigs

(Ed.). Advances in Acoustic Microscopy I. Plenum Press, New

York. 1995, pp. 153-208.

[I21 J. Kushibiki. H. Ishiji. T. Kobayashi. N. Chubachi. I. Sahashi.

T. Sasamata, Characterization of 36 ~ YX LiTaO, wafers by linc-

focus beam acoustic microscopy. IEEE Trans. Ultrason. Fcrro.

Freq. Control 42 ( 1995) 83.

[ 131 P. Mutti. C.E. Bottani. G. Ghislottl. M. Beghi, G.A.D. Brigs.

J.R. Sandercock. Surface Brillouin scattering Extending surface

ua\e measurements to 20 GHr. in: G.A.D. Briggs (F.d.l.

Advances in Acoustic Microscopy I. Plenum Press. New York.

1995. pp. 249 300.

[ 141 BriSc. Bede Scientilic Instruments Ltd.. Lindsey Park. Bowburn.

Durham DH6 5PF. UK; http:,‘:www.bede.co.uk.

[ 151 P.D. Warren, C. Pecorari. O.V. Kolosov. S.G. Roberts. G.A.D.

Briggs. Characterisation of surface damage via hurl:dce acoustic

waves. Nanotechnology 7 ( 1996) 295 301.

[ 161 0. Kolosov, K. Yamanaka. Nonlinear detectjon of ultrasonIc

vibrations in an atomic force microscope. Jpn. J. ,Appl. Phys. Lett.

32 (1993) LlOY5.

[ 171 U. Rabe. W. Arnold. Atomic-force microhcopy at MHz frequen-

cies. Annalen der Physik 3 (1994) 589 5Y8.

[IS] II. Rabe, V. Sherer. S. Hirsekorn, W. Arnold, Nanomechanical

surface characterization by atomic force microscopy. Journal of

Vacuum Science & Technology Bl5 ( 1997) I506 I51 I.

[I91 N.A. Burnham. A.J. Kulik, G. Gremaud. P.J. Gallo. F. Oulcvey.

Scanning local-acceleration microscopy, Journal of Vacuum Sci-

ence 6i Technology 814 ( 1996) 794 7Y9.

[20] 0. Kolohov, M.R. Castell. C. Marsh, G.A.D. Briggs. T. Kamins.

S. Williams. Direct imaging of elastic nanobtructure of Ge islands

by ultrasonic force microscopy. ( I997) submitted for publication.

[2l] N.A. Burnham. G. Gremaud, A.J. Kulik. P..I. Gallo. F. Oulevey.

Materials properties measurements choosing the optimal scan-

ning probe microscope configuration. Journal of Vacuum Science

&Technology 814 (1996) I308 1312.

[22] T.E. Matikas. R.L. Crane. Ultrasonic nondestructive techniques

for materials characterization. MRS Bulletin 21 ( IO) ( 1996)

IX 21