HI!

Refer a good book in Quantum Mech. for your problem " W. Heitler, Quantum Theory of Radiation, Ed. by N. F. Mott, E. C. Bullard, and D. H. Wilkinson, The University Press. Oxford, 1960". This ia a very nice book you can apply QM in any problem.

Tunneling of charge carriers is a major quatum phenomenon which occurs across hetero-interfaces and is a main concept in expalining the functioning of many heterostructure devices etc. Apart from this, as you also mentioned, scattering of these charge carrires and generation-recombination transitions are few other fundamental processes happening across interfaces. The physial and chemical properties/conditions at the interface control these processes. If your query is more into semiconductor heterointerfaces, I suggest you to see the book by D K Schroder and papers by H J Brillison.