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Experimental evidence for superconductivity enhancement mechanism
EXPERIMENTAL
EVIDENCE ENHANCEMENT J. KLEIN
Groupe
de Physique SNRS.
des Solides
Fact&
FOR SUPERCONDUCTIVITY MECHANISM and A. LEGER
de I’Ecole Normale
des Sciences.
Sup&ewe.
Tour 23. PARIS
Labomtoire
ussociP au
V”. France.
Synopsis
It is known that metallic films composed of small grains have an enhanced transition temperature. Many theoretical explanations have been proposed but none have yet received direct experimental confirmation. In this work, we believe to have shown, by tuneling experiments, that the enhancement of T, in granular Al films is related to the appearance of low frequency modes in the phonon density of states F(w). Using the results of McMillan’s theory, we can calculate T, and comparison with the experimental value is quite good.
It has been found that superconducting films consisting of very small crystallites, referred to as granular superconductors, have anomalously high transition temperatures T,. In order to prepare such films, Al being the metal studied, we adopt a method described by Cohen and Abel&s’) which consists of evaporating Al from Tungsten filaments with alumina boat inserts providing an internal supply of oxygen. We can modify the grain size of our Al films by varying the substrate temperature. These films exhibited increases in their Tc’s. Many explanations of this effect have been proposed but none has yet received direct experimental confirmation. McMillan’s theory*) relates the increase of T, to a modification of the phonon spectrum at low frequencies. He finds: 8D
T, =Gexp-
1.04(1+x) A--*(1+0.62h)‘
where k* is the coulomb pseudopotential and A = N(0) (J2)/M(~*), N(0)(52) is constant for a given structure of materials. So, in our experimental case of granular Al, T, is determined by (o’) (average value over the phonon density of states spectrum F(w)). The question now is to determine experimentally F(w). If we measure the tunnel current between two normal metals (Al-Al in our case) and if we plot dZZ/dI’/2versus I/ curves, we can observe structure closely related to the phonon spectrum of bulk Al as obtained from neutron diffraction data3). Such an effect has also been observed by Lambe and Jaklevic4) and Rowel15). This might be due to a real emission of phonons close to the Al740
SUPERCONDUCTIVITY
ENHANCEMENT
MECHANISM
741
Aloxide interface of the junction. Actually, there is no theoretical explanation of this fact and it seems hazardous to speculate on what one measures exactly. What we assume in this work is that the second derivative is proportional to the phonon density of states F(o). This hypothesis is supported by the fact mentioned above that the observed structure is close to the phonon spectrum of bulk Al. Thus, we use this phonon effect in order to study possible modification of the phonon spectrum for different kinds of Al-Al junctions made of granular aluminium with different values of T,. Three types of junctions have been considered in this work: Al-Al (ordinary) Al-Al (granular) Al-Al (granular)
T, = 1.3 K; T, = 2.3 K; T, = 3.66 K.
In all three cases we have plotted d21/dV2 zxxsus V, shown in fig. 1. At first, what we observed on the experimental curves labeled A is that the phonon structure is superimposed on a background which must be substracted in order to analyze the experimental results. This procedure yields curves C. The choice of this background is somewhat arbitrary but we have taken this fact into account and indicate the uncertainty of the results deduced. Now, we can compare curves C among themselves. A striking effect is the appearance of a low frequency tail in F(w) which is stronger in the films of higher T,. Let us point out that this low frequency tail exist always independently of the choice of the background specially between C, and Ct. Now, starting from curves C, we can calculate from McMillan’s formula a value of T,. We choose C1 as reference and we compare the others curves to C,. Thus, we calculate (02) and A, and then deduce T,. The results are summed up in table I. The uncertainty given in the calculated T, takes into account the ambigous choice of background and the spread observed in samples of the same type. Let us discuss the interpretation of the results. It seems clear that there is a shift of the phonon spectrum towards low frequencies in our granular film. Is the observed spectrum related to the bulk properties of the material? This is difficult to answer without any good theory ot the effect. What we can say is that the peaks observed are close to the known values for bulk phonons. If, on the other hand we observed phonons of Al-Aloxide interface, there must be a strong correlation with all the phonons of the grains constituting the Al films. This hypothesis is supported by the following independent result. Assuming that the low frequency tail is due to surface phonons, taking one “surface mode” per surface atom (as a consequence of the Dickey and Paskin calculation% we can estimate a grain size of our films (table I) and these results agree with the direct electron microscopy observation.
J. KLEIN
AND A. LEGER
~
modulation H
Ordinary
Al
Granular
Al
Granular
Al
Tc = 3.66”K
b/y; ,/f.y -_____---- \ I
0
I
20
I
I
I I
40
0
,’ ,
I
I
:
_-
20
40
E( meV)
V(mV)
Fig. 1. Phonon distribution function F(o) of Al from tunneling d*lldV* characteristics having different T,. (A) Experimental curves (B) Superimposed structure when Al is the superconducting (C) Phonon distribution function F(w) deduce from (A)
state
for films
SUPERCONDUCTIVITY
ENHANCEMENT
MECHANISM
743
TABLEI
Al Film Ord (I) Gran (2) Gran (3)
(&) 849
T’“” e
Grain diam. (A) talc Microscopy
758
1.3 K 1.3Km reference 2.4kO.3 K 2.30K 40
70
703
3.4kO.3 K 3.66K
30
20
p
Thus the experimental observation of the softening of the phonon spectrum (within our assumptions) due to the appearance of surface phonons in granular Al seems to confirm McMillan’s model for T, enhancement in these films. Further work is currently being done in order to optimize the surface to volume ratio of our samples. Acknowledgements. We thank Mr. Belin for his expert sample preparation and Miss Gauthier for her collaboration. We also thank Professors J. Bok and J. P. Burger for many suggestions and valuable discussions.
REFERENCES 1) 2) 3) 4) 5) 6)
Cohen, R. W. and Abel&s, B., Phys. Rev. 168 (1968)444. McMillan, W. L., Phys. Rev. 167 (1968) 33 I. Klein, J. and Ltger, A., Phys. Letters 28A (1968) 134. Lambe, J. and Jaklevic, R. C., Bull. Am. Phys. Sot. 14 (1969)43. Rowell, J. M., McMillan, W. L. and Feldmann, W. L., Phys. Rev. 180 (1969) 658. Dickey, J. M. and Paskin A., Phys. Rev. Letters 21(1968) 1441.
EVIDENCE ENHANCEMENT J. KLEIN
Groupe
de Physique SNRS.
des Solides
Fact&
FOR SUPERCONDUCTIVITY MECHANISM and A. LEGER
de I’Ecole Normale
des Sciences.
Sup&ewe.
Tour 23. PARIS
Labomtoire
ussociP au
V”. France.
Synopsis
It is known that metallic films composed of small grains have an enhanced transition temperature. Many theoretical explanations have been proposed but none have yet received direct experimental confirmation. In this work, we believe to have shown, by tuneling experiments, that the enhancement of T, in granular Al films is related to the appearance of low frequency modes in the phonon density of states F(w). Using the results of McMillan’s theory, we can calculate T, and comparison with the experimental value is quite good.
It has been found that superconducting films consisting of very small crystallites, referred to as granular superconductors, have anomalously high transition temperatures T,. In order to prepare such films, Al being the metal studied, we adopt a method described by Cohen and Abel&s’) which consists of evaporating Al from Tungsten filaments with alumina boat inserts providing an internal supply of oxygen. We can modify the grain size of our Al films by varying the substrate temperature. These films exhibited increases in their Tc’s. Many explanations of this effect have been proposed but none has yet received direct experimental confirmation. McMillan’s theory*) relates the increase of T, to a modification of the phonon spectrum at low frequencies. He finds: 8D
T, =Gexp-
1.04(1+x) A--*(1+0.62h)‘
where k* is the coulomb pseudopotential and A = N(0) (J2)/M(~*), N(0)(52) is constant for a given structure of materials. So, in our experimental case of granular Al, T, is determined by (o’) (average value over the phonon density of states spectrum F(w)). The question now is to determine experimentally F(w). If we measure the tunnel current between two normal metals (Al-Al in our case) and if we plot dZZ/dI’/2versus I/ curves, we can observe structure closely related to the phonon spectrum of bulk Al as obtained from neutron diffraction data3). Such an effect has also been observed by Lambe and Jaklevic4) and Rowel15). This might be due to a real emission of phonons close to the Al740
SUPERCONDUCTIVITY
ENHANCEMENT
MECHANISM
741
Aloxide interface of the junction. Actually, there is no theoretical explanation of this fact and it seems hazardous to speculate on what one measures exactly. What we assume in this work is that the second derivative is proportional to the phonon density of states F(o). This hypothesis is supported by the fact mentioned above that the observed structure is close to the phonon spectrum of bulk Al. Thus, we use this phonon effect in order to study possible modification of the phonon spectrum for different kinds of Al-Al junctions made of granular aluminium with different values of T,. Three types of junctions have been considered in this work: Al-Al (ordinary) Al-Al (granular) Al-Al (granular)
T, = 1.3 K; T, = 2.3 K; T, = 3.66 K.
In all three cases we have plotted d21/dV2 zxxsus V, shown in fig. 1. At first, what we observed on the experimental curves labeled A is that the phonon structure is superimposed on a background which must be substracted in order to analyze the experimental results. This procedure yields curves C. The choice of this background is somewhat arbitrary but we have taken this fact into account and indicate the uncertainty of the results deduced. Now, we can compare curves C among themselves. A striking effect is the appearance of a low frequency tail in F(w) which is stronger in the films of higher T,. Let us point out that this low frequency tail exist always independently of the choice of the background specially between C, and Ct. Now, starting from curves C, we can calculate from McMillan’s formula a value of T,. We choose C1 as reference and we compare the others curves to C,. Thus, we calculate (02) and A, and then deduce T,. The results are summed up in table I. The uncertainty given in the calculated T, takes into account the ambigous choice of background and the spread observed in samples of the same type. Let us discuss the interpretation of the results. It seems clear that there is a shift of the phonon spectrum towards low frequencies in our granular film. Is the observed spectrum related to the bulk properties of the material? This is difficult to answer without any good theory ot the effect. What we can say is that the peaks observed are close to the known values for bulk phonons. If, on the other hand we observed phonons of Al-Aloxide interface, there must be a strong correlation with all the phonons of the grains constituting the Al films. This hypothesis is supported by the following independent result. Assuming that the low frequency tail is due to surface phonons, taking one “surface mode” per surface atom (as a consequence of the Dickey and Paskin calculation% we can estimate a grain size of our films (table I) and these results agree with the direct electron microscopy observation.
J. KLEIN
AND A. LEGER
~
modulation H
Ordinary
Al
Granular
Al
Granular
Al
Tc = 3.66”K
b/y; ,/f.y -_____---- \ I
0
I
20
I
I
I I
40
0
,’ ,
I
I
:
_-
20
40
E( meV)
V(mV)
Fig. 1. Phonon distribution function F(o) of Al from tunneling d*lldV* characteristics having different T,. (A) Experimental curves (B) Superimposed structure when Al is the superconducting (C) Phonon distribution function F(w) deduce from (A)
state
for films
SUPERCONDUCTIVITY
ENHANCEMENT
MECHANISM
743
TABLEI
Al Film Ord (I) Gran (2) Gran (3)
(&) 849
T’“” e
Grain diam. (A) talc Microscopy
758
1.3 K 1.3Km reference 2.4kO.3 K 2.30K 40
70
703
3.4kO.3 K 3.66K
30
20
p
Thus the experimental observation of the softening of the phonon spectrum (within our assumptions) due to the appearance of surface phonons in granular Al seems to confirm McMillan’s model for T, enhancement in these films. Further work is currently being done in order to optimize the surface to volume ratio of our samples. Acknowledgements. We thank Mr. Belin for his expert sample preparation and Miss Gauthier for her collaboration. We also thank Professors J. Bok and J. P. Burger for many suggestions and valuable discussions.
REFERENCES 1) 2) 3) 4) 5) 6)
Cohen, R. W. and Abel&s, B., Phys. Rev. 168 (1968)444. McMillan, W. L., Phys. Rev. 167 (1968) 33 I. Klein, J. and Ltger, A., Phys. Letters 28A (1968) 134. Lambe, J. and Jaklevic, R. C., Bull. Am. Phys. Sot. 14 (1969)43. Rowell, J. M., McMillan, W. L. and Feldmann, W. L., Phys. Rev. 180 (1969) 658. Dickey, J. M. and Paskin A., Phys. Rev. Letters 21(1968) 1441.