Singlet exciton fission has the potential to increase the efficiency of crystalline silicon solar cells beyond the conventional single junction limit. Perhaps the largest obstacle to achieving this enhancement is uncertainty about energy coupling mechanisms at the interfaces between silicon and exciton fission materials such as tetracene. Here, the previously reported silicon-hafnium oxynitride-tetracene structure is studied and a combination of magnetic-field-dependent silicon photoluminescence measurements and density functional theory calculations is used to probe the influence of the interlayer composition on the triplet transfer process across the hafnium oxynitride interlayer. It is found that hafnium oxide interlayers do not show triplet exciton sensitization of silicon, and that nitrogen content in hafnium oxynitride layers is correlated with enhanced sensitization. Calculation results reveal that defects in hafnium oxynitride interlayers with higher nitrogen content introduce states close to the band-edge of silicon, which can mediate the triplet exciton transfer process. Some defects introduce additional deleterious mid-gap states, which may explain observed silicon photoluminescence quenching. These results show that band-edge states can mediate the triplet exciton transfer process, potentially through a sequential charge transfer mechanism.