Numerical modeling of a two-coil apparatus for measuring the magnetic penetration depth in superconducting films and arrays

We determine the magnetic penetration depth λ(T) in superconducting films by measuring the mutual inductance of two coils located on opposite sides of the films. The apparatus is designed to produce an accurate value for λ(0) without any assumptions about the dependence of λ(T/Tc)/λ(0) on T/Tc. In a typical configuration of coils and a 100±10 nm thick by 6 mm radius film, λ can be measured to better than ±12% as long as λ≳1500 Å. The noise level is typically ±2 Å. If two films are made the same way, so that they have the same thickness d, and they are measured in the same apparatus, then the relative uncertainty in λ between the two films is only ±9%, because uncertainties in d, the coil dimensions, etc., are eliminated. This article describes the apparatus and a detailed numerical model which illustrates the induced current density in the film and establishes the sources of uncertainties. The accuracy of the model is demonstrated through comparison with measurements on 0.15 mm thick circular Pb disks.