ULTRASONIC EXPERIMENTS WITH PICOSECOND TIME RESOLUTION

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ULTRASONIC EXPERIMENTS WITH PICOSECOND

TIME RESOLUTION

C. Thomsen, H. Grahn, H. Maris, J. Tauc

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C10, supplement au n012, Tome 46, ddcembre 1985 page C10-765

ULTRASONIC EXPERIMENTS WITH PICOSECOND TIME RESOLUTION C. THOMSEN, H.T. GRAHN', H.J. MARIS AND J. TAUC

Department of Physics and Division

of

Engineering,

Brown

University, Providence, Rhode Island 02912, U.S.A.

R6sum6 - Nous prkentons une nouvelle m ~ t h o d e pour faire des mesures ultrasonores avec une r6solution temporelle de I'ordre de la picoseconde. La m'ethode peut Ctre utilis6e avec des 6chantillons tres mince, aussi bien dans les cas oii I'attenuation est tres elev6e. Nous preentons la thCorie du processus de la g'en6ration et de la detection, et nous montrons plusieurs re'sultats experimentaux pour I'attenuation et la vitesse obtenus par cette nouvelle mdthode.

Abstract - We describe a new method which can be used t o make ultrasonic measurements with picosecond time resolution. The method can be used t o study samples in which the acoustic path length is very short and the ultrasonic attenuation very large. We describe the theory of the generation and detection process, and present some-attenuation and velocity measurements we have made by this method.

I

-

INTRODUCTION

In experiments using the ultrasonic pulse-echo technique the acoustic path length is usually between a few mm and a few cm. The lower limit on the path length is set by the response time r,, of the trans- ducers and the associated electronics. The acoustic path length 1 has t o be such t h a t the round-trip time in the sample l/v (v = sound velocity) is larger than r,,. In a typical case r,, is 1 psec, and so if the sound velocity is 3x10' cm sec-', 1 must be greater than 0.3 cm. With special effort r,, and 1 may be reduced by 10 or 100 below these values / I / .

There are many applications in which it is necessary t o work with much smaller path lengths. The attenuation may be large, e.g., 10' dB cm-'. I t may be impossible t o prepare a large sample. For example, there are many amorphous materials which can only be prepared as thin films. Another important application is the use of ultrasonics as a nondestructive probe of small structures. One would like t o be able to test the bonding of metallic coatings to substrates, and to characterize thin films in VLSI circuits. T o perform experiments on films of thickness 3000 requires a time resolution of

-

0.1 nsec, which is beyond the capability of conventional transducers and electronics.

In this paper

we describe a new method we have developed /2/. This method has an effective time resolution of

-

10 psec (lo-" sec) and hence is ideally suited for measurements with very short acoustic path lengths.

I1 - GENERATION

In the last few years much progress has been made in the of ultrashort light pulses. It is now possible to generate pulses /3,4/ with duration less than 0.1 psec a t a high repetition rate (e.g., 100 MHz). This technology is the natural one t o consider a s the basis for a n ultrasonic system with resolu-

IBM Predoctoral Fellow.

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C10-766

JOURNAL

DE PHYSIQUE

tion in the picosecond range. A strain pulse is easily generated from a light pulse. The light is directed a t the surface of an absorbing material. It is absorbed within some characteristic absorption length f, whose magnitude depends on the material and on the light wavelength. When photons are absorbed in a semiconductor

c

is typically 200

-

2000

A,

provided that the photon energy is greater than the bandgap. For visible light absorbed in a metal $ is typically between 100 and 300

A.

T h e energy deposited per unit volume in the material a t a depth z below the surface is

where Q is the total energy absorbed and A is the area of the beam. This energy raises the temperature of the material and sets up a stress which is

where C is the specific heat per unit volume, ,9 is the thermal expansion coefficient, and B is the bulk modulus. If the duration of the light pulse is 1 psec or less, the material does not have time t o move while the light is being absorbed. Hence, we may assume t h a t immediately after the absorption of the light pulse the elastic strain is zero. T h e inhomogeneous stress (2) causes an elastic strain t o develop. The spatial form of this strain a t various times after excitation is shown in Fig. 1. For time much larger than q/v the strain may be considered t o be the sum of two contributions. There is a time- independent component which decays exponentially with distance from the surface. This is caused by the expansion of the heated material near the surface t o a stress-free state. The other contribution is a strain pulse which propagates into the material. It has a characteristic shape given by

e(z,t) m - exp(-

1 z

- v t

1

/c) sgn(z - vt) ₍₃₎

Thus, the effective duration of this pulse is roughly rt

-

2f/v. If we take as representative values

c

= 300

A,

v = 3 X 10' cm sec-', r* is 20 psec.

This description of the generation process ignores several effects which may be important. The heat is assumed t o be deposited in the surface layer instantaneously, i.e., the duration of the laser pulse is much less than r'. It is assumed t h a t the system can be described by a temperature, i.e., that the electrons and phonons in the material reach equilibrium before

i.

This is a good approximation in metals. In semiconductors the incident photons excite long-lived electron-hole pairs which make an extra contribution t o the stress /2/. Finally, one must consider the possibility t h a t heat may diffuse a significant distance while the strain pulse is being formed and leaving the heated region /5/. This effect is important in metals where 5 is small and the thermal diffusivity is high.

DISTANCE FROM SURFACE z

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In the experiments we have performed the energy in each light pulse is typically 0.1 nJ, and the area is 40 g m X 40 pm. The amplitude of the strain pulse is then in the range

lo-'

to

lo-'.

I11

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DETECTION

A detection scheme we have used in our first experiihents /2/ is shown schematically in the inset of Fig. 2. In these experiments the strain pulse was generated by a light pulse (the pump pulse) absorbed a t the interface between a film of the material t o be studied and a sapphire substrate. For this geometry the generated strain pulse has a different shape from that indicated in Fig. 1, but this is not important for the following discussion. After generation the strain pulse bounces back and forth in the film. Each time it is reflected from the substrate its amplitude decreases because some of its energy is transmitted into the substrate. A second, and smaller, light pulse is passed through the film a t a later time t . This pulse, which we call the probe pulse, is produced by dividing off about 10% of the energy in the pump pulse, and then introducing an extra optical path before the pulse reaches the samgle. The transmission of the probe pulse through the film is studied as a function of the time delay t. The strain pulse in the film changes the optical constants (refractive index n, absorption coefficient a ) of the film, and this alters the transmission of the probe pulse by an amount AT(t). Results we have obtained in this way for a film of amorphous AslTeJ on sapphire are shown in Fig. 2. The oscillations can be understood a s follows. The change in the transmission of the probe pulse is principally caused by the strain-induced change A a in the absorption coefficient. Hence

where the integral is over the film thickness d, and <r(z,t)> is the average strain in the film a t time t. While the strain pulse is propagating in the film, < r > is constant. However, when the pulse is reflected from the free surface the propagating strain pulse changes sign and this changes < c > . Since this sign change occurs once for each time interval 2d/v, the transmission oscillations should be periodic with time 4d/v. This is in agreement with our results.

2 0 0 4 0 0 TIME t (psec) --- PROBE PUMP --- SAPPHIRE As,Te, SUBSTRATE I I I I

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This detection method based on the measurement of light transmission has two disadvantages. A T is sensitive only t o the averaee strain in the sample, whereas a conventional transducer measures strain a t a specific point. The technique can only be used for samples which are not too thick, since they must be partially transparent. We have developed an alternative method which avoids these problems. In this technique we measure the change in reflection AR(t) of the delayed probe pulse. The origin of these reflectivity changes is interesting. A t a free surface the normal stress is always zero. Hence, the strain pulse echoing back and forth in the sample does not produce a time-varying stress or strain a t the surface. Thus, the optical ['constants" n and a a t the surface are truly constant, and so it might seem that there should be no time-dependence t o the reflectivity. However, the probe beam actually penetrates a distance

-

c

into the sample, and the reflectivity can be influenced by changes in strain within this distance. We can write

where f(z) is a measure of the sensitivity of the reflectivity t o strain a t a depth z. An estimate of f(z) for As,Te, is shown in Fig. 3. We see that the reflectivity measurement probes the strain over a dis- tance

of

approximately the penetration depth from the surface. For a metal the absorption length

c

is less and so the thickness of the region probed is smaller. The change in AR is of the same order of magnitude as the strain. Thus, it is necessary t o use signal-averaging techniques t o determine these small reflectivity changes.

IV

-

RESULTS

In Fig. 4 we show results obtained for an amorphous AszTeS film of thickness

-

2400 A on a sapphire substrate. Immediately after the pump pulse the reflectivity undergoes a rapid increase followed by a rapid decrease. These changes are due to the electrons and holes excited by the light pulse, and t o the heating of the surface layer. Three echoes of the strain pulse are clearly seen, and have a round trip time in the sample of

-

220 psec.

In the inset of Fig. 4 we show the shape of the first echo on an expanded scale. Note t h a t this echo is an

even

function of time with respect t o an origin taken a t its midpoint. We can explain this pulse shape and the width of the pulse in terms of the spatial shape of the propagating strain pulse (Fig. 1) and the "sensitivity function" f(z) (Fig. 3). The strain pulse is an function of distance from its midpoint. However, the sign of the strain changes on reflection a t the.free surface, and this means t h a t the strain c(z,t) for any given distance z from the surface is actually an even function of time. Hence, from Eq. 5 AR(t) is also an even function of time as is observed. Note t h a t the second echo is inverted with respect t o the first, since it has undergone an extra reflection a t a free surface.

Fig. 3 The sensitivity of the reflection coefficient t o strain as a function of distance z from the surface.

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20 psec

rn

TIME t (psec)

Fig. 4 Acoustic echoes in a 2400

A

film of amorphous As2Te3 on a sapphire substrate a t 300

K.

The echoes are detected by observing changes in the reflectivity of the film surface as measured by a probe pulse. The inset shows an expanded view of the first echo.

T o make a quantitative measurement of ultrasonic loss we need t o study the attenuation of strain waves of a definite frequency. T o do this we take the Fourier transforms Al(w) and A2(w) of the first and second echoes. The magnitude of Al(w) is shown in Fig. 5. The spectrum peaks a t a frequency of

25 GHz. The attenuation per unit distance of the Fourier component of frequency w in the strain pulse, which is the same as the ultrasonic attenuation, is then

Notice that it is not necessary to know the sensitivity function to carry out the analysis. However, a(w) as given by Eq. 6 must be corrected for the partial transnlission of energy into the substrate. This method can be used t o measure ~ ( w ) over the range of frequency where Al(w) and A2(w) are appre- ciable. For As,Te, this is roughly from 5 t o 50 GHz. In Fig. 8 we show the temperature dependence of the attenuation a t 30 GHz determined in this way.

Fig. 5 Magnitude Fig. 4.

FREQUENCY (GHz)

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JOURNAL DE PHYSIQUE

100 200

TEMPERATURE ( K )

Fig. 6 Ultrasonic attenuation a t 30 GHz in amorphous As2Te3. The sample was a film of thickness 4150

A.

It is straightforward t o use this technique to measure the sound velocity and its dependence on temperature. The simplest approach is to measure the time between corresponding points of the first and second echoes. This gives the results shown in Fig. 7. These results have been calculated using the film thickness as measured a t 300 K, i.e., no correction has been applied for the thermal contraction of the film. One can certainly use more elaborate techniques t o calculate the sound velocity from the raw data, and this will make it possible t o increase the accuracy. For example, the velocity, and its dependence on frequency, can be found from the relative phase of the Fourier transforms of the first and second echoes. We have not yet carried o u t this type of analysis, but we have seen qualitative indica- tions of velocity dispersion. The dispersion makes itself evident as differences between the shapes of the first and the subsequent echoes.

We have so far used this technique to generate and detect strain pulses in amorphous and crystalline As2Te3, amorphous germanium, polyacetylene /6/, and copper. Wiesenfeld /7/ has recently performed experiments with GaAs and InGaAsP. We have also used amorphous As2TeS as

a

transducer t o generate a pulse which propagated through an SiOz film and, after reflection, was then detected in the As2Te3 film /2/. In this way it was possible t o measure the sound velocity in S O z . It is not possible t o generate and detect acoustic pulses directly in SiOa because this material is optically transparent t o the wavelength of our light pulses.

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We show in Fig. 8 an example of the resolution of the technique when used for studies of very thin films. Fig. 8 a shows the shape of the first received echo in a 2400

&

film of As2Te3 on sapphire a t a nominal temperature of 15 K. (The actual temperature may be higher because of the heating by the light pulses). Air was then allowed t o leak into the apparatus and a very thin film condensed on the free surface of the As2Te3. This caused a drastic change in the echo shape (Fig. 8b). Results obtained after a.dding more air are shown in Fig. 8c. From the change in the pulse shape, and the sound velocity in solid nitrogen /8/ of 1.8X105 cm sec-', we estimate t h a t the thickness of the air layer in Fig. 8c is 100 t o 150

A.

This indicates the ability of this technique t o probe extremely small structures.

V - DISCUSSION

We have shown here some examples of what can be done with our picosecond ultrasonic system. The technique makes it possible to extend ultrasonic measurements into regions which have been previously inaccessible. One can make attenuation and velocity measurements in samples whose thickness is very small, i.e., 1000

ft

or less. Materials in which the attenuation is very large (e.g., 10' dB cm-I) can be studied. These features make possible room-temperature ultrasonic measurements a t frequencies a t 30 GHz. The length of the generated strain pulse is determined by the absorption length

c

of the light in the sample. This length determines the position of the peak in the Fourier spectrum of the pulse. Through the use of a tunable light source, it will be possible t o change

c,

and hence make measurements over a wider range of frequencies. The shortest pulses, and hence the highest frequencies, should be obtainable in metals since

c

can then be as short as 100

8.

These pulses should have Fourier com- ponents wich extend into the range above 100 GHz, and will make possible ultrasonic measurements a t these frequencies.

The detection scheme relies on the change in the optical constants with elastic strain, and the resulting change in the optical reflection coefficient. The sensitivity can be increased by an appropriate choice of the photon energy in the probe beam. This energy should ideally be chosen t o lie in a range where the reflectivity is changing rapidly with photon energy.

This technique should also make possible ultrasonic studies of non-equilibrium phenomena. These might include ultrasonic attenuation due t o photo-excited electrons and holes, the electron-hole plasma, non-equilibrium superconductivity, and non-equilibrium phonon distributions.

We thank T . R. Kirst for technical assistance, J. Strait for valuable discussions, and J. J. Hauser and D. Young for supplying us with some of the thin-film samples. This work was supported in part by the National Science Foundation through the Materials Research Laboratory a t Brown University.

TIME

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JOURNAL

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PHYSIQUE

REFERENCES:

Kushibiki, J., Sannomiya, T., and Chubachi, N., IEEE Trans. Son. Ultrason.

w,

338 (1982); Nikoonahad, M., Yue, G-Q., Ash, E. A., IEEE Trans. Son. Ultrason.

SU-32.

152 (1985). Thomsen, C., Strait, J., Vardeny,

Z.,

Maris, H. J., Tauc, J. and Hauser, J. J., Phys. Rev. Lett. 53, 989 (1984).

-

Fork, R. L., Greene, B. I., Shank, C. V., Appl. Phys. Lett.

36, 671 (1981).

Ultrafast Phenomena IV, Proceedings of the Fourth International Conference, edited by D. H.

Auston and V. B. Eisenthal (Springer-Verlag, Berlin, 1984). White, R. M., J. Appl. Phys.

a,

3559 (1963).

Thomsen, C., Strait, J., Vardeny,

Z.,

Maris, H. J., Tauc, J., and Hauser, J. J.,

in

Ultrafast Phenomena IV, ref. 4, p. 133.

Wiesenfeld, J. M., Appl. Phys. Lett., t o be published.