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SUPERCONDUCTING TRANSITION
TEMPERATURES OF ULTRATHIN AMORPHOUS FILMS
C. Granqvist, T. Claeson
To cite this version:
C. Granqvist, T. Claeson. SUPERCONDUCTING TRANSITION TEMPERATURES OF ULTRA- THIN AMORPHOUS FILMS. Journal de Physique Colloques, 1974, 35 (C4), pp.C4-301-C4-303.
�10.1051/jphyscol:1974457�. �jpa-00215648�
JOURNAL DE PHYSIQUE Colloque C4, suppliment au no 5, Tome 35, Mai 1974, page C4-301
SUPERCONDUCTING TRANSITION TEMPERATURES OF ULTRATHIN AMORPHOUS FILMS
(*)C. G. GRANQVIST and T. CLAESON Physics Dept., Chalmers University of Technology
Fack, S-402 20 Gothenburg, Sweden
RBsumB. - La temperature de transition de supraconductivite des films amorphes de Bi et Ga, evaports sur support refroidi, est diminuee par un facteur deux quand 1'6paisseur est rdduite de SO a 3 nm.
La dependance d'kpaisseur est en accord avec un modkle base sur I'effet de proximite, dans lequel le film consiste en une couche mince non supra-conductive mise en contact avec la couche supra-conductive restante.
Abstract. - The superconducting transition temperature of vapour-quenched, amorphous films of Bi and Ga is suppressed by a factor of two as the thickness is decreased from 50 to 3 nm.
The thickness dependence agrees with a proximity type model in which the film consists of a thin, non-superconducting, surface layer in contact with a remaining, bulk superconducting part.
We will report upon measurements of the super- conducting transition temperature, T,, of amorphous Bi and Ga films, that have been extended to the ultrathin limit. The results are in accord with a model explaining the depression of Tc as due to the proximity between the bulk part of the superconductor and a normal surface layer.
It has long been known [I-61 that the Tc : s of ultra- thin films can be appreciably depressed compared to the thick-limit transition temperatures (T,,). A large number of theories and ideas have been given to explain this effect. They include modifications of the phonon spectrum [7], fluctuations of the order para- meter 14, 8-10], quantization of electronic levels in minute metallic particles 1 1 and substrate effects [4, 51. Several of these models are discussed by Strongin et al. [4].
It is experimentally documented [5] that relatively thick vapour quenched Bi and Ga films (being amor- phous [12] and superconducting [13]) display a Tc depression (T,, - T,) approximately proportional to the inverse film thickness (t-I). The dependence was described in terms of a modification of the boundary condition for the superconducting order parameter [5]. This approach assumes that the film thickness is much larger than the superconducting coherence length (t $ 5,).
The opposite limit (t 4
5,)
is valid for the experi- ments with ultrathin films of Pb and Bi by Strongin(*) Supported by the Swedish Natural Science Research Council.
et al. [4]. They interpret their results in terms of a model where the superconducting interaction is lowered within a surface sheath (of thickness b).
When t
< 5,
one can simply use an effective interaction strength being a weighed average of the values in the bulk and the surface layer as suggested by Cooper [14].Our Tc measurements on Bi and Ga were done in the thickness range 3 < t < 50 nm. Since
5,
for amorphous Bi has been estimated to be 7.2 nm 1151 (and a similar value ought to be valid for Ga), neither of the extreme limits discussed above can be applied directly.Our conceptual model is essentially the same one as used by Naugle et al. [5] and Strongin et al. [4].
The main part of the thin film is assumed to behave as a bulk superconductor with transition tempe- rature T,,. At the film surfaces the electron density of states drops [16, 171, and we assume that super- conductivity is lost in a layer of thickness b (of the order of a few times the Thomas-Fermi screening length). A proximity effect then lowers the Tc of the superconducting part and induces superconductivity in the normal one. The de Gennes-Werthamer theory of the superconducting proximity effect [18-201 is valid when the electron mean free path, 1, is much smaller than
t,.
This is certainly true for our amor- phous films and we extract from that theory :Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974457
C4-302 C. G. GRANQVIST AND T. CLAESON The subscript s(n) refers to the cr superconducting ))
(cc normal ))) part of the film, q-' is the (c extrapo- lation length )) of de Gennes [18], N is the electron density of states at the Fermi energy, and
where Y(z) is the digamma function [21].
The coherence length is given by
5
= (hop 116 nk, T,)'/~ (3) where v, is the Fermi velocity, k, is Bolzmann's constant, and A is (Planck's constant)/2 n.The low temperature conductivity, a, and the coefficient of the electronic specific heat, y, are related by
Assuming that a, z a, and observing that y cc N we get :
Eq. (2) can now be written
q, tan q,(t - b) = c (6) where the constant c only depends upon the properties of the normal layer and not upon the film thickness.
Eq. (1) and (6) finally give us Tc as a function of t with only two parameters, b and c. In the thin film limit, the result is the same as for the Cooper model [14].
The predicted values (with reasonable parameters) are compared with experimentally determined Tc : s of thin, amorphous Bi and Ga films in figure 1 . The agreement is good for films thicker than 5 nm, while the experimental Tc : s drop below the theoretical curve for the thinnest films. This is, however, reasonable both on experimental and theoretical grounds.
Firstly, the very thinnest films are not even but patchy. The transition widths increase with decreasing thickness and the normal film resistivity rises sharply.
The patchiness implies that relatively thick islands are connected by weak links which determine the resistive transition. Secondly, pair breaking due to fluctuations and due to quantization effects is likely to occur in this regime. Thus it is no surprise that Tc in the thinnest films is depressed more than expected from the proximity type model only.
Nevertheless it is striking that such a simple theory treating the film as consisting of two distinctly different layers can describe the depression in Tc over such a wide range as it does.
If T, 1s depressed by a proximity mechanism the pair breaking should have an very profound effect upon the energy gaps and the density of excited states [24]. Preliminary tunnel measurements do indicate that the density of states is more smeared than
expected from the Tc (and corresponding energy gap) decrease.
5 N Bi and Ga are evaporated from resistively heated Mo boats onto a liquid 3 ~ e cooled single quartz substrate (upon which a layer of Ge had previously been evaporated at room temperature) [23]. The
FIG. 1 . - ( 7 , - Tco)/Tco vs. t-1 for amorphous Ga and Bi films. The curves are derived from a numerical solution of eq. (1) and (6) using the indicated values of TCo, b and c. Our Tco : s agree very well with measurements on thick films by others
[5, 13, 221. We have used ts = 7.2 nm (applying to amorphous Bi [15]) also for Ga.
substrate and film surface temperatures. remain below 0.4 and 2 K resp. during the evaporation. The deposition rate is about 0.1 nm/s. The thickness is measured by a quartz crystal oscillator micro-balance (resolution about 0.1 nm ; absolute accuracy 10 to 15
%).
The Tc : s are measured resistively in situ with a current of 1 or 10 PA. The midpoint of the normal-superconducting transition is taken to define Tc *SUPERCONDUCTING TRANSITION TEMPERATURES OF ULTRATHIN AMORPHOUS FILMS C4-303
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