Fluoroethylene carbonate (FEC) and vinylene carbonate (VC) are widely used as electrolyte additives in lithium ion batteries. Here we analyze the solid electrolyte interphase (SEI) formed on binder-free silicon nanowire (SiNW) electrodes in pure FEC or VC electrolytes containing 1 M LiPF6 by solid-state NMR with and without dynamic nuclear polarization (DNP) enhancement. We find that the polymeric SEIs formed in pure FEC or VC electrolytes consist mainly of cross-linked poly(ethylene oxide) (PEO) and aliphatic chain functionalities along with additional carbonate and carboxylate species. The formation of branched fragments is further confirmed by 13C-13C correlation NMR experiments. The presence of cross-linked PEO-type polymers in FEC and VC correlates with good capacity retention and high Coulombic efficiencies of the SiNWs. Using 29Si DNP NMR, we are able to probe the interfacial region between SEI and the Si surface for the first time with NMR spectroscopy. Organosiloxanes form upon cycling, confirming that some of the organic SEI is covalently bonded to the Si surface. We suggest that both the polymeric structure of the SEI and the nature of its adhesion to the redox-active materials are important for electrochemical performance.