Impedance mismatch: a new length scale in the electrodynamics of a superconductor–metal system

Effective surface impedance of Y Ba2Cu3O7−δfilms on silicon substrates

“…The temperature dependence for ω p and τ can be obtained from conductivity and Hall mobility making use of textbook formulae for the Drude model. Taking typical data for a lightly doped n-type silicon material (sample '131' from the seminal paper of Morin and Maita [19]) like our substrate, we obtain a typical dependence of R d using equations (10) and (8). The result is reported in figure 6, together with the bulk surface impedance R d as obtained from equation (9).…”

“…Exceptions can arise when the dielectric has a strong temperature dependence in its dielectric constant, showing 'dramatic' resonance phenomena at certain temperatures [4,7,8] or when the film and the substrate characteristic impedances combine together so as to give frequency-dependent peaks in R s [9]. On the other hand, metallic substrates are always in their bulk limit with small surface impedance values, a characteristic which does not allow us to neglect their contribution to the effective superconducting film impedance [10]. Finally semiconductors, the most common being silicon, are an intermediate case, and are more rich in phenomenology [5].…”