HAL Id: jpa-00217657
https://hal.archives-ouvertes.fr/jpa-00217657
Submitted on 1 Jan 1978
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
PHONON EFFECTS IN MICROWAVE-ENHANCED
SUPERCONDUCTIVITY
T. Klapwijk, H.B. van den Heuvell, J. Mooij
To cite this version:
JOURNAL DE PHYSIQUE Colfoque C6, supplement au no 8, Tome 39, aozit 1978, page C6-525
PHONON EFFECTS I N MICROWAVE-ENHANCED SUPERCONDUCTIVITY
T.M. Klapwijk, H.B.van Linden van den Heuvell and J.E. Mooij
Depar-tment of App Zied Physics, De Z f t U n i v e r s i t y of Techno Zogy, De Z f t , The Netherlands
RQsum6.- Le courant critique de rubans d'aluminium ddposl sur un substrat de silice est mesur6 en pr6sence d'un champ microonde 3 3 GHz. L'bchantillon est placl soit dans un bain dlh&lium liquide soit dans le vide. On montre que le courant critique slaccro?t plus rapidement avec la puissance microonde lorsque l'bchantillon est plongb dans l1h8lium liquide.
Abstract.- The microwave-enhanced critical current of aluminum strips on silicon substrates has been measured in vacuum and immersed in liquid helium. In helium the enhancement is larger.
Microwave-enhanced superconductivity has been observed in aluminum and in tin with different methods of measurement / 1-41. The phenomenon is explained by Eliashberg's theory of gap enhancement
151, which shows that the presence of a microwave
field of suitable frequency leads to a nonequili- brium distribution of quasiparticles. Relaxation of the quasiparticles occurs by means of inelastic electron-phonon scattering. Eliashberg et alneglec- ted the effects of this interaction on the phonon bath which they assumed to remain in equilibrium at the bath temperature. Chang and Scalapino / 6 /
performed numerical calculations in which the pho- non distribution is followed. They find that the phonons are driven out of equilibrium as well, which will in turn effect the quasiparticle dis- tribution and the gap enhancement. The magnitude
of this effect depends on the coupling of the pho- non system in the metal to the surroundings. A pa- rameter r is introduced by Chang and Scalapino
esc
which gives the average liftime of phonons spent in the sample if no interactions occur. r de-
esc pends on sample thickness but also on the efficien- cy of the transfer of phonons across the interfa-
ces with substrate and helium bath. resc is scaled with rg, the lifetime of phonons of energy 2A
against pair breaking (at T = 0). If T esc"~ <<
the phonons in the superconductor will remain in thermal equilibrium at the bath temperature. Apart
from this microscopic approach Latyshev and Nad'
/ 2 / have pointed out that, due to the dissipation caused by the microwaves, the effective temperature of the metal will he higher than the bath tempera- ture.
In order to obtain an impression of the importance of phonon non-equilibrium effects, we have investigated microwave enhancement while chan-
ging the thermal coupling to the bath. The experi- ments have been arranged in such a way that r
esc (the heat transfer rate in macroscopic terms) could be varied in situ by positioning the sample in a vacuum can which could subsequently be filled with liquid helium.
We have measured the critical current of narrow aluminum strips to observe the gap enhance- ment. Mono-crystalline silicon was used as the substrate. The vacuum can was filled with liquid helium by controlled condensation from the gas. The can could also be evacuated again without leaving the helium temperature range. In the top of the can a carbon resistor was used as a liquid level indicator. The bath temperature was measured with a germanium thermometer outside the can, carefully shielded from the microwave field
.
The temperature was controlled to within 0.1 mK. The 3 GHz micro- wave radiation was applied through a coaxial cable, terminated in the can with a loop. The critical current was measured by displaying the current- voltage characteristic on an oscilloscope screen. Previously we found that this method leads to a premature maximum of the amount of enhancement of the critical current that can be observed. Thisis due to heating of the sample after the criti- cal current has been exceeded. We have now employed the method indicated by Pals 131 to continue the measurements at higher power levels.
Figure 1 gives results obtained with an aluminum strip on silicon, 2,5 pm wide, 0.1 um
thick and 250 m long. The bath temperature is 1.1720 K and the equilibrium critical temperature 1.2130 K. As shown the critical current increases with increasing microwave power (3 GHz).
we obtain for A1 : rB = 2 . 4 ~ 1 0 - ~ ~ s . We therefore estimate that for our film in vacuum T e s c / ~ B = 25 and in liquid helium T ~ ~= ~6. For these values / T ~ Chang and Scalapino find results which are compa- rable to those of figure 1, at T/Tc = 0.9 and a frequency of 20 GHz. The calculations predict a
Fig. 1 : Critical current of an aluminum strip on silicon as a function of microwave power (frequency
3 GHz). The same sample was investigated in vacuum (drawn line) and immersed in liquid helium (dotted line).
In contact with liquid helium the increase is subs- tantially higher than in vacuum. The maximum value of the critical current in liquid is obtained at lower power levels than in vacuum. As the presence of liquid helium will not make any difference as
respects the microwave coupling, we expect the power levels to be identical for the two cases. Similar results are obtained for different bath temperatures and for other samples.
For a comparison with Chang and Scalapi- no's calculations, T~~~ can be estimated in both cases. From the results of Smith and Mochel 171 we calculate with the aid of the results of Kaplan et al. /8/ that
rest =
2 x 1 0 - ~ s for an aluminum film,0.1 um thick, on glass. The same value is obtained $or the aluminum-helium interface. From acoustic mismatch calculations of the kind performed by Little /g/ we estimate that the transfer effiency for phonons across an aluminum-silicon interface is a third of the efficiency for crossing an alu- minum-glass interface. From reference 181 we
maximum for A(or I ) as a function of power, as is observed experimentally. The maximum should be higher at smaller values of T ~ ~ ~ / T ~ . However, at those smaller values of T e s c / ~ B the maximum should occur at a higher power level. This is in contra- diction with our measurements.
We have also analysed our experimental re- sults on the basis of the phenomenologicalapproach
of Latyshev and Nad', assuming the sample tempera- ture to be higher than the bath temperature. From
our data we estimate that the effective sample temperature at the highest power levels is very significantly higher than the bath temperature
(more than 500 mK, Teff = 1.4 Tc). These data re- quire a more detailed analysis which will be pu- blished elsewhere.
References
/l/ Klapwijk, T.M. and Mooij J.E., Physica
81B
(1976) 132. Klapwijk T.M., van den Bergh J.N., and Mooij, J.E., J. Low Temp. Phys.2
(1977) 385./2/ Latyshev, Yu.1. and Nad', F.Ya., Zh. Eksp.Teor. Fiz.
2
(1976) 2158 (Sov.Phys. JETP 44 (1976)-
1136.
/3/ Pals, J.A., Phys. Letters
G
(1977) 975. Pals, J.A., Phys. Letters63A
(1977) 141. /4/ Kommers, T., and Clarke, J., Phys. Rev.Letters38 (1977) 1091. -
/5/ Ivlev, B.I., Lisitsyn, S.G. and Eliashberg,G.M. J. Low Temp. Phys.
10 (1973) 449.
161 Chang, J.J., Scalapino, D.J., J. Low Temp. Phys.
9
(1977) 477./7/ Smith, L.N., Mochel, J.M., Phys. Rev. Letters (1975) 1597.
/ S / Kaplan, S.B., Chi, C.C., Langenberg, D.N., Chang, J.J., Jafarey, S., and Scalapino, D.J., Phys. Rev. B
