Thin Lead Films Research Articles

Nucleation and growth of thin lead films on amorphous substrates

Experiments are described in which lead was deposited, by evaporation in vacuum, on to SiO-covered glass substrates along which a temperature gradient was maintained. Below the bulk melting point of lead (320 °C) at a substrate temperature of 189 ± 2 °C a transition was observed in the structure of the films. This transition corresponded to the one observed by Palatnik and Komnik at a temperature designated by them as T d. It was found that for any thickness of discontinuous lead film T d was constant, but that it showed a rapid change to about 245 °C at a critical pressure of oxygen in the vacuum chamber. This critical pressure could be varied by altering the lead deposition rate. An explanation for the transition is given in terms of surface melting of small islands, and the effect of oxygen interpreted in terms of its changing the effective surface energy of the particles.

Far-Infrared Absorption in Thin Superconducting Lead Films

We describe measurements of the far-infrared conductivity ${\ensuremath{\sigma}}_{1}\ensuremath{-}i{\ensuremath{\sigma}}_{2}$ of thin superconducting lead films with resistances of about $\frac{200\ensuremath{\Omega}}{\mathrm{square}}$ in the normal state. The conductivity is inferred from measurements of the transmittance and reflectance of a thin film of lead which has been evaporatively deposited on a quartz crystal. We report results for the real part of the conductivity of lead over the frequency range 9 to 120 ${\mathrm{cm}}^{\ensuremath{-}1}$. From these we infer an energy gap for lead films at $T=0$ of 22.5\ifmmode\pm\else\textpm\fi{}0.5 ${\mathrm{cm}}^{\ensuremath{-}1}$, or $(4.5\ifmmode\pm\else\textpm\fi{}0.1)k{T}_{c}$, where $k$ is the Boltzmann constant and ${T}_{c}$ is the superconducting transition temperature. The measurements were made at 2.0, 4.3, and 5.5\ifmmode^\circ\else\textdegree\fi{}K, and the energy gap varies with temperature in the manner predicted by the Bardeen-Cooper-Schrieffer theory. The frequency dependence of the real part of the conductivity also is in good agreement with the theory. No evidence is found of the strong precursor absorption which had been previously reported in the energy gap in lead, but ${\ensuremath{\sigma}}_{2}$ is found to be anomalously low (by \ensuremath{\sim}25%) near and below the gap frequency. This is believed to result from the strong-coupling anomalies discussed by Nam. This anomalously low ${\ensuremath{\sigma}}_{2}$ would also account for the anomalously steep absorption edge observed in other experiments on lead.

Preparing thin films of lead by diffusion evaporation

Preparing thin films of lead by diffusion evaporation

Influence d'un courant continu ou alternatif (50 Hz) sur le champ critique de films de plomb A 4.2 °K

In a perpendicular magnetic field larger than 0.3 H c2, the critical current of a thin lead film fits the empirical expression I c ∞ (H> c2−H) 3 2 . In a.c. current the transition appears when the peak current reaches the critical d.c. value.

TUNNELING MEASUREMENTS ON SUPERCONDUCTORS WITH ISOTROPIC ENERGY GAPS

The energy-gap anisotropy found in bulk superconductors is considerably reduced in thin films whose thickness, d, is much less than the range of coherence, ξ0, of the pure metal from which they are fabricated. By preparing such thin films of tin, indium, and lead, we have been able to examine the temperature dependence of the energy gap in each above 1.2 °K, using the tunneling technique. Values of the energy-gap parameter 2Δ(0)/kTe are given as 3.67 ± 0.07 and 3.87 ± 0.08, for tin and indium respectively, while the energy gap for lead is estimated to be 2ΔPb(0) = 2.70 ± 0.02 meV.

Critical-Current Behavior in Narrow Thin-Film Superconductors

Critical currents in planar thin films of tin and lead have been measured as a function of temperature using very narrow strip samples. There is a critical sample width of the order of one micron above which the critical-current behavior is dominated by flux-flow processes. For narrower samples the temperature dependence of the average critical current density is in excellent agreement with the usual relation deduced from free-energy consideration, and the low-temperature values are in good agreement with the simple depairing criterion. At higher temperatures the observed critical current densities are significantly larger than the Bardeen-Rogers predictions based on calculations of the BCS energy-gap variation with current. It is proposed that in these narrow films flux vortices due to the self-field of the current at the film edges are too large to enter the film and by their subsequent motion degrade the critical current. The approximate size of such vortices is calculated and good agreement with the experimental critical widths is obtained. The observation, in wide films only, of "training" phenomena similar to those seen in bulk type-II superconductors also tends to support this hypothesis.

1759. Columnar structure in thin vacuum-condensed lead films: R H Wade and J Silcox,Appl Phys Letter,8(1), 1966, 7–10

1759. Columnar structure in thin vacuum-condensed lead films: R H Wade and J Silcox,Appl Phys Letter,8(1), 1966, 7–10

Photoetching of thin lead films with nitromethane : L. H. Kaplan. J. Phys. Chem.68, 94 (1964)

Photoetching of thin lead films with nitromethane : L. H. Kaplan. J. Phys. Chem.68, 94 (1964)

710. Photoetching of thin lead films with nitromethane: L. H. Kaplan, J. Phys. Chem., 68, Jan. 1964, 94–100

710. Photoetching of thin lead films with nitromethane: L. H. Kaplan, J. Phys. Chem., 68, Jan. 1964, 94–100

Effect of Magnetic Field on Thermal Conductivity and Energy Gap of Superconducting Films

We have measured the change in the thermal conductivity of superconducting tin, indium, and lead films upon application of a magnetic field in the plane of the film. These experiments were undertaken to explore the dependence of the energy gap upon magnetic field and to determine the thermodynamic order of the field-induced transition in films. Within the range of temperatures available to us ($0.35{T}_{c}$ to $0.65{T}_{c}$) the thermal conductivity of indium and tin films increases nearly as ${H}^{2}$. In films of thickness $d\ensuremath{\geqq}2800$ \AA{} the thermal conductivity jumps at ${H}_{c}$ to the normal state value, indicating a first-order phase transition in thin films, consistent with the Ginzburg-Landau (GL) theory. If the effect of a field upon the superconducting state can be adequately represented as a change of the ${\ensuremath{\epsilon}}_{0}$ of BCS, we may use the theory of Bardeen, Rickayzen, and Tewordt to compute ${\ensuremath{\epsilon}}_{0}(H)$ from our data. At $T=0.65{T}_{c}$ we find $\frac{{\ensuremath{\epsilon}}_{0}(H)}{{\ensuremath{\epsilon}}_{0}(H=0)}={[1\ensuremath{-}{(\frac{H}{{H}_{c}})}^{2}]}^{\frac{1}{2}}$ in agreement with the GL prediction. At $T=0.35{T}_{c}$ however, $\frac{{\ensuremath{\epsilon}}_{0}(H)}{{\ensuremath{\epsilon}}_{0}(0)}=1\ensuremath{-}{(\frac{H}{{H}_{c}})}^{2}$ provides a more satisfactory fit to our data. Orientation of the field \ensuremath{\perp} and \ensuremath{\parallel} to the direction of heat flow produces the same effect on the thermal conductivity to \ifmmode\pm\else\textpm\fi{}1%. This is interesting in view of Bogoliubov's prediction of a ${\mathrm{p}}_{F}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{v}}_{\mathrm{drift}}$ term in the excitation spectrum of a current-carrying superconductor. When the field is not parallel to the surface of the film the thermodynamic transition is still sharply defined, but ${H}_{c}$ is reduced. Thin lead films gave results similar to those of indium and tin films except that at low fields the field-dependent conductivity increased more slowly than ${H}^{2}$ at low temperatures.

Photoetching of Thin Lead Films with Nitromethane

Photoetching of Thin Lead Films with Nitromethane

Penetration of magnetic fields into superconductors III. Measurements on thin films of tin, lead and indium

The magnetic moments of thin superconducting films of tin, lead and indium, obtained by evaporation of the metal in vacuo, have been measured by a ballistic method. Values of the penetration depth, λ 0 , at absolute zero, derived from them by extrapolation, are estimated as 5.0 ± 0.1 x 10 -6 cm. for tin, 3.9 ± 0.3 x 10 -6 cm. for lead, and 6.4 ± 0.3 cm. for indium. Within the limits of experimental error the results agree with the penetration law of London & London. From the areas of the magnetization curves, estimates of the difference in surface energy (α n – α 5 ) per unit area between free surfaces of the normal and superconducting phases respectively are derived, which are smaller than those previously assumed. No evidence is found for an increase in penetration depth at low temperatures and high fields such as that suggested by the theories of Heisenberg and Koppe.

Conductivity and Mobility of Thin Lead Films

From measurements of electric conductivity made on thin films of Pb obtained by condensing the metal on cooled glass surfaces at rates from 5\ifmmode\times\else\texttimes\fi{}${10}^{12}$ to 100\ifmmode\times\else\texttimes\fi{}${10}^{12}$ atoms ${\mathrm{sec}.}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}2}$ under high vacuum conditions designed to eliminate contamination, the following results are obtained: The critical film thickness (${d}_{c}$) at which the (specific) conductivity ($\ensuremath{\sigma}$) begins changing rapidly from its low value ($\ensuremath{\approx}{10}^{\ensuremath{-}6}$ mho\ifmmode\cdot\else\textperiodcentered\fi{}${\mathrm{cm}}^{\ensuremath{-}1}$) in the thinnest films to that of the bulk metal (${\ensuremath{\sigma}}_{0}$, $\ensuremath{\approx}{10}^{6}$ mho\ifmmode\cdot\else\textperiodcentered\fi{}${\mathrm{cm}}^{\ensuremath{-}1}$) is in the neighborhood of 60A for room temperature films, and of 30A for films cooled with liquid air. The mutual configuration of the condensed Pb atoms is unstable and changes with time, shown by a decrease observed in the conductivity when the film is isolated from external influences, and in the eventual appearance of a granular structure visible under the ultramicroscope. In some cases a reproducible dependence of the conductivity on the applied potential difference was observed. These effects are in harmony with the mechanism expected from considerations of the thermodynamic stability of such films, i.e., with a tendency toward aggregation resulting in the removal of mobile atoms into crystallization centers, and thus in formation of gaps which obstruct the conduction electrons. Certain deficiencies in quantitative reproducibility are ascribed to variations in the physical surface conditions on the plate where the film is condensed, presumably affecting the mobility of the layers condensed first.

Superconductivity of thin films. I. Mercury

This paper describes the results of measurements of the superconductive properties of thin films of mercury prepared according to the method described in a previous publication (Appleyard and Bristow 1939). Previous workers on the superconductivity of thin films (Sizoo and Onnes 1925; Burton, Wilhelm and Misener 1934; Misener, Smith and Wilhelm 1935; Misener 1936; and Shalnikov 1938) have not been able to distinguish definitely between the effect of the finite size of their specimens (which is the feature primarily interesting from the theoretical point of view), and effects due to their uncertain structure which is often profoundly affected by the methods of preparation of the films. In particular they have not been able to show that the magnetic threshold value of their films approaches the value for the bulk metal when the thickness of the films is sufficiently increased except at very great thicknesses. Shalnikov (1938), for example, has performed a series of experiments on superconducting thin films of lead and tin. But his thickest films seem to have had a critical field 2-3 times in excess of the bulk metal, and his results seem not to have been very reproducible (Shoenberg 1938). Pontius (1937) also obtained definite indications of a size effect with fine wires of very pure lead, but the difference in behaviour from that of the bulk metal was small. Results from wires are certainly reliable for the dimensions obtainable, but the difficulty of drawing a wire thinner than about 10 -4 cm. sets a limit to the scope of the method.

The True Absorption Coefficients for the Elements from Gold to Bismuth in the Neighborhood of theL-Absorption Edges

The $L$ x-ray absorption spectra of the metals gold to bismuth were examined with a calcite crystal spectrometer and ionization chamber. Thin films of thallium, lead and bismuth were evaporated onto very thin sheets of mica. The true absorption coefficients $\ensuremath{\tau}({L}_{\mathrm{I}})$, $\ensuremath{\tau}({L}_{\mathrm{II}})$, and $\ensuremath{\tau}({L}_{\mathrm{III}})$ corresponding to the photoelectric absorption by the three types of $L$ electrons were found to vary approximately as ${\ensuremath{\lambda}}^{2.56}$ for each of the five elements gold to bismuth. With this relation the coefficients were computed for a given wave-length. Their ratio $\ensuremath{\tau}({L}_{\mathrm{I}}):\ensuremath{\tau}({L}_{\mathrm{II}}):\ensuremath{\tau}({L}_{\mathrm{III}})$ (which is therefore independent of the wave-length) was found to be constant over the range 0.5 to 1.5A and to have approximately the same value for each of the five elements. The value of the ratio was found to be 19: 32: 49. This ratio also gives the relative numbers of photoelectrons ejected from the three $L$ shells by radiation of a given frequency. Ratios of $\ensuremath{\tau}({L}_{\mathrm{I}})$, $\ensuremath{\tau}({L}_{\mathrm{II}})$ and $\ensuremath{\tau}({L}_{\mathrm{III}})$ which are evaluated at their respective absorption edges ${L}_{\mathrm{I}}$, ${L}_{\mathrm{II}}$ and ${L}_{\mathrm{III}}$ were also determined. This ratio of $\frac{\ensuremath{\tau}({L}_{\mathrm{II}})}{\ensuremath{\tau}({L}_{\mathrm{III}})}$ was found to be approximately 0.45 for each element and is in good agreement with the value predicted by relativistic theory. The ratio $\frac{\ensuremath{\tau}({L}_{\mathrm{I}})}{[\ensuremath{\tau}({L}_{\mathrm{II}})+\ensuremath{\tau}({L}_{\mathrm{III}})]}$ has been found theoretically only by means of a nonrelativistic treatment of absorption. The experimental value, 0.163, is not in good agreement with the predicted value.