Devices incorporating nanoscale materials, particularly carbon nanotubes (CNTs), offer exceptional electrical performance. Absent, however, is an experimentally backed model explaining contact-metal work function, device layout, and environment effects. To fill the void, this report introduces a surface-inversion channel model based on low temperature and electrical measurements of a distinct single-walled semiconducting CNT contacted by Hf, Cr, Ti, and Pd electrodes. Anomalous barrier heights and metal-contact dependent band-to-band tunneling phenomena are utilized to show that, dependent upon contact work function and gate field, transport occurs either directly between the metal and CNT channel or indirectly via injection of carriers from the metal-covered CNT region to the CNT channel. The model is consistent with previously contradictory experimental results, and the methodology is simple enough to apply in other contact-dominant systems.