Single-wall carbon nanotubes (SWCNTs) of varied polydispersity (length, electronic type and chirality) are used to study the impact of SWCNT purity and processing on both the durability of freestanding SWCNT nanosheets and the performance of SWCNT-silicon heterojunctions. Solution-processed SWCNT films are deposited on n-doped silicon substrates and p-doped to yield photovoltaic devices with competitive photo-conversion efficiency, fill factor and open-circuit voltage. The temperature dependence of the dark-current density and its transient recovery after an abrupt change in bias are used to clarify the nature of the junctions over a broad range of SWCNT polydispersity and processing schemes, where the latter varies from the vacuum filtration of aqueous colloidal SWCNTs to the flow-deposition of aligned nanotube super-acid suspensions. As an intermediate step in all of these processes, the durability of freestanding SWCNT nanosheets in a variety of solvents is considered in the context of large-deformation elasticity and plasticity.