The current through the interface should be a combination of these effects, so if you plot J vs position you could get it. Both models must be activated in order to be included in the simulations, please see how to do it in the section dedicated to heterojunction simulations. Moroever, to consider field emission (tunnel) through the interface, you must specify this parameter in the interface statement. Hope this helps.
I advise that you check that TE is modelled correctly. Check the position of the Fermi-level up to the interface. If TE is modelled correctly, it should be flat up to the interface. If not, it will droop down and join the metal Fermi-level (diffusion mechanism).