An analysis of the room-temperature dark conductivities and activation energies for doped μc-Si and μc-Si,C is used to develop a band alignment model which shows that the maximum attainable dark conductivities in these materials are determined by transport through, or over interfacial potential barriers between Si crystallites, c-Si, and the intervening amorphous regions: a-Si:H or a-Si,C:H, respectively. For all levels of doping in μc-Si,C, the transport is limited by thermionic emission over interfacial barriers at the c-Si/a-Si,C:H interface, placing a significant constraint on applications requiring both high optical transparency and high conductivity.