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Thin film MgB2 is a promising material for technical improvements in superconducting radio frequency (SRF) technology and applications. At present, bulk niobium SRF accelerating cavities suffer from a fundamental upper limit in maximally sustained accelerating gradients; however, a scheme involving multilayered superstructures consisting of superconducting-insulating-superconducting (SIS) layers has been proposed to overcome this fundamental material limit of 50 MV/m. The SIS multilayer paradigm is reliant upon implementing a thin shielding material with a suitably high HC1, which may prevent early field penetration in a bulk material layer and consequently delay the high field breakdown. It has been predicted that for thin superconducting films - thickness less than the London penetration depth ( ~ 120 nm in the case of MgB2) - the lower critical field HC1 can be enhanced with decreasing thickness. Thus, MgB2, with a high TC and relatively low HC1 value, as compared with Nb, is a prime candidate for such SIS structures. Here we present our study on the microstructure, surface morphology, and superconducting properties on a thickness series of MgB2 thin films and correlate the effects of film thickness and surface morphology on HC1.