THE TUNNELING DENSITY OF STATES OF SUPERCONDUCTIVE Nb-Sn

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THE TUNNELING DENSITY OF STATES OF SUPERCONDUCTIVE Nb-Sn

D. Moore, M. Beasley, J. Rowell

To cite this version:

D. Moore, M. Beasley, J. Rowell. THE TUNNELING DENSITY OF STATES OF SUPER- CONDUCTIVE Nb-Sn. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-1390-C6-1394.

�10.1051/jphyscol:19786577�. �jpa-00218068�

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JOURNAL DE PHYSIQUE Colloque C6, suppl&ment au no 8, Tome 39, aoat 1978, page

C6-1390

THE

TUNNELING

DENSITY

OF STATES OF SUPERCONDUCTIVE ~ b - ~ n ~ D.F. ~ o o r e ~ , M.R. Beasley and J.M. Rowell s

Department of AppZied Physics and EZectricaZ Engineering, Stanford U n i v e r s i t y , CA. 94305, U.S.A.

*

EeZZ Laboratories, Murray H i Z Z , NJ, 07974, U.S.A.

Rdsumd.- Nous mesurons les dgviations de la densitd d16tats BCS induites par les phonons B l'aide de jonctions tunnel Pb sur Nb Sn. L'amplitude globale des ddviations ddcroit mais la forme ne varie pas de fagon apprdciable pour Qes compositions allant de 25 _%at Sn (haut Tc), fort couplage) P 20 % at Sn (bas Tc, faible couplage).

Abstract.- Using Pb on Nb,Sn tunnel junctions we measure the phonon-induced deviations from the BCS density of states. The overall strength of the deviations decreases but the shape does not change appreciably over the composition range from 25 at.% Sn (high Tc, strong-coupling) to 20 at.% Sn (low Tc, weak-coupling)

.

As a class the A15 materials include most of the known high transition temperature superconductors, and consequently they have been studied from many points of view. Electron tunneling measurements, which are well known to provide a wealth of funda- mental information about the microscopic properties of superconductors, have not been generally possible with these superconductors, however, because of the problems of making good junctions on such difficult materials. Of particular interest from tunneling studies is the tunneling density of states and the detailed information it contains in principle about the electron-phonon interaction responsible for superconductivity.

In the past, despite much hard work, the only really successful quantitative tunneling study

(i.e. good enough to yield a tunneling density of states) on any A15 superconductor has been the work of Shen on NbsSn formed by reacting Sn on a bulk Nb substrate /I/. Recently, however, with the availabi- lity of VP--v high quality vapor-deposited A15 thin films, greatly improved tunneling measurements have become possible /2,3,4,5/. These studies have provi- ded useful information about the dependence of the energy gap on composition, important diagnostic information about the quality and nature of the films, and even an unambiguous confirmation of a substan- tial varrier to flux entry when a magnetic field is applied parallel to the surface of Nb,Sn / 6 / . More

ft

Work at Stanford initiated under support of the U.S. National Science Foundation. Presently sup- ported by the U.S. Office of Naval Research

? Present Address : Bell Laboratories, Murray Bill, NJ 07974, U.S.A.

recently the pair (Josephson) tunneling noted ear- lier 121 has been studied in detail for the case of Nb Sn and found to have some technological interest

3

171. In this paper, however, we focus on the density of states and the electron-phonon spectral function obtained from tunneling on a series of Nb-Sn films with various compositions.

The films of interest were deposited by means of dual electron beam codeposition of the ele- ments using the techniques developed by Hammond

/8,9/, and the tunneling barriers were formed either using the thermal oxide of the as-deposited A15 film or using an evaporated layer of Si deoosited on the film before exposure to the atmosphere / 4 / . In all cases reported here the counter-electrodes were Pb.

We note that the success of this work is highly de- pendent on the quality of the thin films that can be obtained with coevaporation. The surface region near the barrier is crucial because of the short sampling depth of the tunneling electrons

(QJ

C0

= 5 nm) in the A15 superconductors. At high bias voltages this sampling depth is even shorter and the tunneling measurements are sensitive to at most the first few atomic layers.

The current-voltage characteristic, I@), of a typical Nb Sn/oxide/Pb tunnel junction is presen-

3

ted in figure 1. The quasiparticle (Giaever) tunneling curve is excellent and the leakage conduction at voltages below the gap is low, there being a small onset at the lead gap, $b, probably indica- tive of a finite density of states within the niobium-tin gap. [~ncidentl~, the dc pair (Josephson) tunneling current has been suppressed by application of a small magnetic field.] We obtain a preliminary

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786577

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Fig. 1 : Current-voltage characteristic at 1.5 K of a Nb ~n/~xide/Pb tunnel junction

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estimate of A Nb-Sn by measuring the voltage corresponding to the point of maximum slope in I(V) and subtracting the known energy gap of the counter- electrode, APb (1.5 K) = 1.35meV. For the junction of figure I , A = 3.25 meV yielding a

Nb 3Sn

2A/kBTcZ 4.3. More details of the material properties of the films and the procedures for making junctions are given elsewhere / 5 / .

Figure 2 shows the dynamic resistance, dV/dI, as measured on the junction shown in figurel.

Curve (A) shows data taken at 1.5 K, the superconduc tivi ty of the Pb counter-electrode having been suppressed in a magnetic field of 210 mT. Curve (B) is the corresponding data taken at 20 K in the nor- mal state, and displaced slightly in dV/dI to match up at high bias voltages. The phonon-induced structure in (A) is clearly evident.

To illustrate this phonon-induced structure in more useful quantitative form, we reduce the data by calculating the normalized tunneling conduc- tance d ~ / d ~ l s / d ~ / d ~

I n

⁽ⁱ. e . the tunneling density of states for the superconductor) and subtracting from this the BCS density of states expected for a superconductor with the measured energy gap. The resulting deviation from the BCS density of states, o(w), is shown in figure 3. To illustrate the effect of choosing a smaller energy gap, we also show the data reduced using Am Sn = 2.8 meV.

The electron-pionon spectral function, a2(w)F(w), has been calculated from A and o(w) using both the McMillan-Rowell /lo/, and the alternative

Fig. 2 : The dynamic resistance, dV/dI, of the junction shown in figure 1, (A) at 1.5 K in a magnetic field to quench the superconductivity of the Pb, and (B) at 20 K

method proposed by Galkin et al. /I]/ and implemen- ted at Stanford by D.B. Kimhi. The results obtained using the former procedure are shown in figure 4.

There are clearly resolved peaks in a2 (w)F(w) near 9, 18 and 25 meV. Moreover the overall shape is not sensitive to the gap value chosen. From the a2(w)F(w) obtained using the measured gap of 3.15 meV, we cal- culate A

-

²

I

a2(w)F(w)w-l dw = 0.76 and the Coulomb pseudopotential p P =

-

0.10. In fact all junctions analyzed to date give p* < 0 indicating that the observed deviation from the BCS density of states is not strong enough to give an a2(w)~(w) consistent with the gap estimated from I(V) within the framework of the Eliashberg gap equation. The origins of this problem are not clear, but we sus- pect our surfaces and/or barriers are still not ideal. We note, however, that certain useful. inte- gral averages over the electron-phonon spectral function do not depend strongly on the choice of A and the resulting value of u". Such integrals should be physically meaningful and are summarized intable I. Moreover, keeping this same shape of a2 (w)F(w) and fixing u* = + 0.11 we obtain X = 1.6 ?r 0.1.

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JOURNAL DE PHYSIQUE

( A ) A = 3.15 mV ( B ) d'2.8 mV

- 0.04

Fig

- ^-

I I

oLt:.'

^, ^I ^I ^J

0 10 2 0 30

ENERGY ( m V )

0 10 20 30 4 0

VOLTAGE ( m V ) ABOVE GAP

Fig. 3 : The tunneling density of states expressed as the deviation from the BCS density of states using the gap parameter (i) A = 3.1 meV (ii) A = 2.8 meV

.

⁴^:The electron-phonon spectral function,

ci2 (w)F(w)

,

calculated from the tunneling density of states using two values of the gap parameter

Schweiss et al. /12/ have reported inelastic neutron scattering experiments which give G(w) for Nb3Sn, a function which is closely related tothepho- non spectral function,F(w). They observe on the basis of their data and that of Shen on ol?w)F(w) that CL'(W) is a decreasing function of energy. A comparison of a2(w)F(w) from our improved tunneling data with G(w) of Schweiss et al. leads to the same conclusion. Ho-

wever, we can not rule out the possibility that the residual surface problems mentioned above may result in some distortion of o(w) at high energies wherethe sampling depth is shortest. This in turn would affect a 2 (w)F(w).

Table I

Some weighted average phonon frequencies of NbgSn

KWlog ⁼exp [(2/~)

i

a2(w)~(w)w-l ₌log w dw] _9.7₂_0.3_meV.

With the electron beam coevaporation method of film deposition it is simple to obtain a series of samples with a systematic variation of composition. Some current-voltage characteristics of junctions fabricated using Si barriers from a typicalse- ries are shown in figure 5. From these curves we have obtained the variation of A Nb-Sn with composition

151. The single-phase A15 region (18-25 % Sn) is particularly interesting because the superconductive properties are very sensitive to composition. The 25 at.% Sn material has Tc s 18 K and is strong-coupling, 2A/k T = 4.3 f 0.1. In contrast, with 20 at.% Snthe

B c

material has Tc % 8 8 and is weak-coupling 2A/kBTc = 3.4

+

^0.2.

From the dynamic resistance, dV/dI, of junctions (a), (b) and (c) in figure 5 we have also calculated the corresponding a(w) which are shown in figure 6. The overall strength of a(w) is reduced in sample (c) with 21.5

+

1.5 at.% Sn as compared with stoichiometric Nb Sn. For purposes we prefer

3

to compare the shapes of o(w) rather than $(w)~(w) because there is an unambiguous procedure for redu- cing the data as far as o(u).

We can summarize the result by stating that as the Sn concentration is reduced from the 25 at.%

in NbjSn there is a reduction in the magnitude of ~(0) and hence also in the electron-phonon coupling. re- flecting the fact that the superconductive proper-

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Fig. 5 : Current-voltage characteristics of a series of ~b-Sn/Si/Oxide/Pb tunnel junctions. The curves are normalized at 7 meV and the ori- gin progressively shifted for clarity

ties become steadily weaker. We do not observe a dramatic change in the position of any particular feature in the electron-phonon spectral function, however. [~ote that peaks in a2F(w) correspond to regions of negative du(w)/dw]. If anything, thepeak near 9 meV is shifted to higher energies as the Sn concentration is reduced. The drop in the densityof states between 5 and 10 meV becomes smaller as the Sn concentration is reduced, but changes at lower energies are difficult to quantify and interpret because of the width of the rise in the I(V) at the gap. Taking the behaviour between 5 and 1 0 meV at face value there is an implied decrease in the weight of a2(w)~(w) below 10 meV, hence a stiffening of the lattgce or a decrease in coupling strengthat these frequencies.

In conclusion, tunneling measurements are clearly now yielding valuable information about the A 1 5 superconductors and hopefully more rapid progress

towards understanding these interesting materials will be possible.

I I I

I

0 10 2 0 3 0 4 0

VOLTAGE (mV) ABOVE GAP

0.02

..

^' Î Î Î

Fig. 6 : The deviation from the BCS density of states of junctions (a), (b) and (c) in figure 5

0.01

We thank R.B. Zubeck and R.R. Hammond for

NIOBIUM TIN

#G.77.35

- ..

( S i Overlay) -

help preparing the A 1 5 films, and, along with T.H. Geballe, for many useful discussions.

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JOURNAL DE PHYSIQUE

References

/I/ Shen, L.Y.L., Phys. Rev. Lett.

9

(1972) 1082 /2/ Moore, D.F., Rowell, J.M., and Beasley, M.R.,

Solid State Commun.

0

(1976) 305

/ 3 / Rowell, J.M., and Schmidt, P.H., Appl. Phys.

Lett.

3

(1976) 622

/4/ Moore, D.F., Zubeck, R.B., and Beasley, M.R., Bull. Am. Phys. Soc.

22

(1977) 289

/5/ Moore, D.F., Rowell, J.M., and Beasley, M.R., to be published

/6/ Moore, D.F., and Beasley, M.R., Appl. Phys.

Lett.

30

(1977) 494

/7/ Howard, R.E., Rudman, D.A., and Beasley, M.R., submitted for publication

/8/ Hammond, R.H., IEEE Trans. Mag-Il (1975) 201 /9/ Hamond, R.H., J. Vac. Sci. Technol.

15

⁽¹⁹⁷⁸⁾

382

/lo/ McMillan, W.L., and Rowell, J.M., in Superconductivity, Parks, R.D., Ed.

(Marcel Dekker, New York) 1969, p. 561 / 1 I/ Galkin, A.A., D'Yachenko, A.I., and

Svistunov, V.M., Sov. Phys.- JETP

2

(1974) 1 1 15

/12/ Schweiss, B.P., Renker, B., Schneider, E.. and _. _. Reichardt, W., ~uperconductivit~ in d- and f- Band Metals, Douglass, D.H., Ed., Proc. Second Rochester Conf. (Plenum Press, New York) 1976, p. 189