Kinetic Inductance and nonlinearity of MgB2 Films at 4K

We report on the fabrication and characterization of superconducting magnesium diboride (MgB$_2$) thin films intended for quantum-limited devices based non-linear kinetic inductance (NLKI) such as parametric amplifiers with either elevated operating temperatures or expanded frequency ranges. In order to characterize the MgB$_2$ material properties, we have fabricated coplanar waveguide (CPW) transmission lines and microwave resonators using $\approx$ 40 nm thick MgB$_2$ films with a measured kinetic inductance of $\sim$ 5.5 pH/$\square$ and internal quality factors, $Q_i \approx 3 \times 10^4$ at 4.2 K. We measure the NLKI in MgB$_2$ by applying a DC bias to a 6 cm long by 4 $μ$m wide CPW transmission line, and measuring the resulting phase delay caused by the current dependent NLKI. We also measure the current dependent NLKI through CPW resonators that shift down in frequency with increased power applied through the CPW feedline. Using these measurements, we calculate the characteristic non-linear current parameter, $I_*$, for multiple CPW geometries. We find values for corresponding current density, $J_* = 12-22$~MA/cm$^2$ and a ratio of the critical current to the non-linear current parameter, $I_C/I_* = 0.14-0.26$, similar to or higher than values for other superconductors such as NbTiN and TiN.