Disorder in carbon-doped HPCVD MgB$_{2}$ thin films

Carbon-doped MgB$_{2}$ films prepared by hybrid physical-chemical vapor deposition have the highest $H_{c2}$ ($\sim $70 T at 0 K for H parallel to \textit{ab} plane) of all MgB$_{2}$ materials. We have characterized the nanoscale structure and chemistry of one such film by TEM and STEM. The C concentration in the Mg(B$_{1-x}$C$_{x})_{2}$ grains from EELS is not dramatically higher than that of C-doped bulk MgB$_{2}$, so doping does not explain the high $H_{c2}$. Instead, the doped film has a variety of forms of structural disorder at length scales down to 5 nm, which may be sufficient to explain the $H_{c2}$ of these films. These include MgB$_{2}$ domains with a 30 degree rotation about the $c$-axis, small angle rotations about $c$-axis, and a small tilt of the $c$-axis. There are also amorphous, C-rich regions between some MgB$_{2}$ domains. The amorphous phase comes from the oversupply of C during growth, which may also cause the other disorder by interrupting epitaxial film growth. This work is supported by the FRG on MgB$_{2}$, NSF DMR-0514592.