USE OF THE « BREMSSPECTRUM » FOR PHONON SPECTROSCOPY ON Al2O3 : V3+ AND FOR A STUDY OF THE PHONON PROPAGATION IN GRANULAR ALUMINIUM

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USE OF THE “ BREMSSPECTRUM ” FOR PHONON SPECTROSCOPY ON Al2O3 : V3+ AND FOR A

STUDY OF THE PHONON PROPAGATION IN GRANULAR ALUMINIUM

H. Kinder

To cite this version:

H. Kinder. USE OF THE “ BREMSSPECTRUM ” FOR PHONON SPECTROSCOPY ON Al2O3 : V3+ AND FOR A STUDY OF THE PHONON PROPAGATION IN GRANULAR ALUMINIUM.

Journal de Physique Colloques, 1972, 33 (C4), pp.C4-21-C4-23. �10.1051/jphyscol:1972405�. �jpa-

00215082�

JOURNAL DE PHYSIQUE Colloque C4, szdgplkment au no 10, Octobre 1972, page C4-21

USE OF THE BREMS SPECTRUM >>

FOR PHONON SPECTROSCOPY ON A120, : V3+

AND FOR A STUDY OF THE PHONON PROPAGATION IN GRANULAR ALUMINIUM

H. KINDER

Institut fur Festkorperforschung, Kernforschungsanlage Julich, Germany

RburnB. - A I'aide d'une m6thode de modulation nous avons pu isoler la discontinuit6 dans le spectre du rayonnement de freinage des phonons 6mis par une jonction tunnel supraconduc- trice. De cette f a ~ o n nous avons obtenu une source de phonons monochromatiques de frkquence variable. La premiere application de cette technique a kt8 1'6tude de la diffusion rtsonnante dans le systBme A1203 : V3

a 248 GHz. Nous avons aussi examin6 la propagation des phonons dans des films d'aluminium granul6. L'interfkrence de phonons observ6e a permis de dkterminer les vitesses du son. Quelques observations concernant I'interaction entre electrons et phonons transverses a w > 2 AD seront discutees.

Abstract. - The sharp edge of the phonon bremsspectrum ^>> of a superconducting tunnel junction was isolated by modulation. Thus a tunable source of monochromatic phonon pulses was obtained. As a first application, the resonant scattering of A1203 : V3

at 248 GHz was investi- gated. With this technique the phonon pr~pagation in granular aluminium films was studied. Pho- non interference was observed, and from this, the velocities of sound were measured. Some findings on the transverse phonon-electron interaction at w > 2 AD are discussed.

Monochromatic phonon pulses with tunable fre- quency were generated using a superconducting tunnel junction [I]. A1203 : V3" was investigated as the first example of phonon spectroscopy. In addition we report here on experiments concerning the propagation of phonons in the granular aluminium films used for the detector junctions.

In a superconducting tunnel junction a continuous phonon spectrum is generated due to quasiparticle decay [2]. This we call the bremsspectrum )) since its origin is similar to that of x-ray bremsstrahlung.

Numerical calculations [3] have shown that the bremsspectrum exhibits a sharp edge at the maximum frequency

(Vis the battery voltage, 2 A , is the energy gap of the generator junction).

We modulate the edge by additional, small voltage pulses. The rest of the spectrum remains nearly unmodulated [I]. Thus, in addition to the continuous, constant bremsspectrum we generate pulses of the differential bremsspectrum at the frequency ^co,.

Taking from the detector response the time varying component only, the differential spectrum is isolated.

Thus we can consider the junction as a source of mono- chromatic phonon pulses tuned by the dc voltage.

The frequency range available for spectroscopy is limited at the lower end by the detector threshold given by its energy gap 2 A, [2]. The upper limit is set

to 2 A , for most materials by reabsorption of the phonons of higher frequency within the generator [3].

In our experiments we used Sn-Oxide-Sn junctions as the generator and Al-Oxide-A1 junctions as detector.

The aluminium was made granular by oxygen to raise its T, to about 2 K [4]. Thus we obtained a frequency range from 150 to 280 GHz. Samples of sapphire containing 200 ppm V 3 + were used. The experiments were mainly planned to investigate the phonon reso- nant scattering of the V3+ ground state which is split by spin orbit coupling. The splitting wc.2 measured to be 8.25 cm-' by Joyce and Richards [5] using far infrared techniques. At the corresponding frequency of 248 GHz a dip in the detected differential phonon intensity was obtained. This is seen in figure 1 for various phonon modes. From the width of the observed dips we deduced a half width of about 9 GHz for the differential bremsspectrum emitted by the tin generator junctions [I].

Thus the new method is now well established. Use of this method was made for a study of the phonon propagation within the detector films of granular aluminium. For this purpose the thickness of the detec- tor films was made smaller than the phonon free path.

In this case, the phonon absorption is incomplete.

Thus after reflection from the back side of the detector the greater part of the phonons again escapes into the sapphire. Only the absorbed phonons, however, contribute to the detector signal. Hence, the latter now reflects the absorption probability of phonons in the granular aluminium films as a function of frequency.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972405

H. KINDER

LONGITUDINA L

0 50 100 150 200 250 280 FREQUENCY f (GHzI

FIG. 1. - Differential intensity of detected phonons as a func- tion of the frequency f~ = (eV- 2 d ~ ) / h . All measurements at

1.02 ... 1.05 K.

The result obtained for a detector, 630 A in total thickness, is shown in figure 2 for longitudinal phonons

h ^I I I I I I

0 50 100 150 200 250 280 FREQUENCY f (GHzl

FIG. 2. - Solid trace : frequency dependent response of a 620 A thick detector on longitudinal phonons. Dashed line : same detector with a droplet of silicone oil on back. The dotted lines are corrected for the V3+ absorption in the sapphire.

(solid line). A large oscillatory structure is seen in the frequency range from 2 AD to 2 A,. This we attribute to the thickness resonances (phonon interference) of the detector which are excited successively by tuning the frequency. To prove this we put a droplet of silicone oil on the back of the detector (after carefully warming to room temperature). Afterwards, the dashed curve of figure 2 was obtained [6]. The oscillation is clearly more damped. This indicates that the phonons now escape partially into the silicone oil, being lost for the interference which modulates the escape at the alumi- nium-sapphire interface.

Direct confirmation of the phonon interference was obtained from a second sample with a detector of 920 A total thickness and the same generator thickness.

The resulting trace is shown in figure 3. Clearly, the spacing Af of the oscillations is closer than in figure 2.

I I I I I I J

0 50 100 150 200 250 280 FREQUENCY f l G H z l

FIG. 3. - Phonon interference in a 920 A thick detector. The longitudinal phase velocity is obtained from the spacing Af

of the interference maxima.

Using the relation Af = v,/2 d (d = thickness of the detector) we obtain from figure 3 the longitudinal sound velocity

v, = (6.44 5 0.3) x lo5 cm/s.

This is, to our knowledge, the first measurement of the velocity of sound in granular aluminium. Since the aluminium had a T, of 2.0 K, it should consist of grains of an average size of 100 A [4]. In spite of this the sound velocity is equal to the one in bulk poly- crystalline A1 at ultrasonic frequencies, 6.6 x 10' cm/s

[18], within experimental error.

For thicker detector films the phonon interference vanishes since the absorption becomes complete. Still some small wiggles, for instance, are distinguishable in figure Ib where a detector of 1 600 A thickness had been used.

The case of transverse waves is shown in figure 4 for the 630 A thick detector. The interference structure is rather weak. This is probably due to diffuse scatter- ing which is more pronounced because of the shorter wave lengths. Again the structure is even weaker with the silicone oil on back (dashed line) [6]. From figure 4, the transverse velocity is

This is again coincident with the ultrasonic bulk velo- city (3.3 x 10-5cm/s [IS]).

Apart from the structure due to interference and due to the V3+ ions, the detector signal is proportional t o the integral absorption probability exp(a. d) - 1, where a is the attenuation and d is the effective thick- ness of metal where the phonons have to pass through.

In case of weak absorption, exp(cr. d) - 1 E a . d, so that a . d can be taken directly from the measured trace.

This case is best fulfilled for the dashed trace of figure 4, since the silicone oil further reduces the effective thickness.

In absence of a theory of transverse wave attenuation

applicable to frequencies exceeding 2 A we shall discuss

this trace qualitatively.

USE OF THE ^(< BREMSSPECTRUM >> FOR PHONON SPECTROSCOPY ON AI2O3 : V3+ C4-23

0 50 100 150 200 250 280 FREQUENCY f I G H z )

FIG. 4. - Transverse wave response of the 620 A thick detector, without (solid) and with (dashed) silicone oil.

1) The increase at 2 A , exhibits a step like behaviour (followed, of course, by some smooth further increase).

In contrast, a square root increase would have been expected for the electromagnetic interaction [7], on grounds of the coherence factors. Hence, a potential interaction is predominant here which is known from longitudinal waves to yield a step [S], [9], [lo]. This is consistent with Pippard's statement that the electro- magnetic interaction dies out at high frequencies, when the skin depth exceeds the wave length. Two different potentia1 interactions are known from the residual attenuation a t low frequencies, the cc real metal ⁾⁾ (electron umklapp) interaction, analysed in detail by Yokota et al. [12], and the cc collision drag ^)> effect [13], the role of which is not clear at the high frequencies.

2) To the smooth increase between 2 AD and 2 A, Refer [I] KINDER (H.), Phys. Rev. Lett., 1972, 28, 1564.

r21 EISENMENGER (W.) and DAYEM (A. H.). Phvs. Rev.

- - ,, -

Lett., 1967, 18, 125.

[3] KINDER (H.), LASZMANN (K.) and EISENMENGER (W.), Phvs. Lett.. 1970. 31A. 475.

[4] A B E L E ~ (B.), ^COHEN (R. w.) and CULLEN (G. W.), Phys. Rev. Lett., 1966, 17, 632.

[5] JOYCE (R. R.) and RICHARDS (P. L.), Phys. Rev., 1969, 179, 375.

[6] The intensity scale was adjusted arbitrarily.

[7] SCHARNBERG (K.), private communication.

[8] TSUNETO (T.), Phys. Rev., 1961, 121, 402.

[9] TEWORDT (L.), Phys. Rev., 1962, 127, 371.

[lo] BOBETIC (V. M.), Phys. Rev., 1964, 136, A 1535.

[1 11 PIPPARD (A. B.), Phil. Mag., 1955, 46, 1104.

[12] YOKOTA (M.), KUSHIBE (H.) and TSUNETO (T.), Progr. Theoret. Phys., Kyoto, 1966, 36, 237.

one can closely fit a w3 law, as shown by the dash- dotted line. Such a strong power law is not expected from the c( real metal N interaction, even for ql < 1 (q = w/u ; I ⁼ electronic free path). The meaning of I is, of course, not quite significant in the case of granular aluminium. Also, the cc collision drag ⁾⁾ effect should require a special model for the granular structure. There may be, however, a more trivial explanation by assuming an enhancement of the effec- tive thickness d due to diffusive (elastic) scattering.

This should increase in strength with decreasing pho- non wave length.

Additional information on the over all electron phonon interaction was obtained by a direct measure- ment of the recombination life time [14], [15] using short pulses. The life time turned out to be less than 100 ns at 1.05 K for our detectors (T, = 2.0 K).

This is rather small compared to the measurements of Gray et al. [16] on purer aluminium films on sapphire.

Even if one uses, for the worst case, a A - 4 law for the extrapolation, our value is at least fife times too small.

This fact indicates an enhancement of the electron- phonon interaction in granular aluminium. Indeed a corresponding enhancement of the cc low frequency tail ^)> of the quantity a2(w) F(w) was observed by Leger and Klein [17] in granular aluminium. Since in the Debye limit the phonon density of states is determined by the sound velocities, our measurements indicate that F(w) is essentially unchanged. Thus the enhance- ment should be due to a2(w), the average electron- phonon interaction, in accordance with our findings on the recombination life time.

I am deeply indebted to W. Buckel, H. Wiihl and W. Eisenmenger for valuable discussions on the pre- sented subjects.

[13] CLAIBORNE (L. T.) and MORSE (R. W.), Phys. Rev., 1964, 136, A 893.

[14] EISENMENGER (W.), Tunneling Phenomena in Solids, eds. E. Burstein and B. Lundqvist, Plenum Press, New York, 1969.

[I51 GRAY (K. E.), Phil. Mag., 1969, 20, 267.

[16] GRAY (K. E.), LONG (A. R.) and ADKINS (C. J.), Phil. Mag., 1969, 20, 273.

[17] LEGER (A.) and KLEIN (J.), Phys. Lett., 1969, 28A, 751, in this paper, az(w).F(co) was loosely called F(w).

[18] KAMM (G. N.) and ALERS ( G . A.), J. Appl. Phys., 1964, 35, 327. See also ANDERSON (0. L.), Phy- sical Acoustics Vol IIIB, ed. W. P. Mason (Aca- demic Press, New York-London 1965.

DISCUSSION

LONG. ^- Could Dr. Kinder say something about LONG. - Could Dr. Kinder explain, why the reso- the quasiparticle lifetime in his tunnel junctions ? nance structure for longitudinal phonons is stronger

KINDER. - We observed a life time less than 100 ns than for the transverse ?

where as an extrapolation using the measurements of _{KINDER. -} The of transverse phonons and Atkin% and a ' ^{-- A - 4 law in} is about half that of the longitudinal. Therefore they worst case of Unklapp according to Gray are more strongly scattered by the surface roughness.

theory, leads to a life time greater than 500 ns.