On electron transport across interfaces connecting materials with different effective masses

We reconsider the problem of electronic transport across a heterojunction interface connecting two materials with different effective masses. Thermionic current does not remain invariant when the position X_int of the interface is shifted relative to that of the potential energy maximum, X_max, even if the shift is smaller than the carrier mean free path. We analyze every situation that arises when X_max=X_int, as well as the limiting case X_max→X_int. Besides the effective mass discontinuity at the interface, we allow for a band-edge discontinuity within a potential barrier of arbitrary shape. In most practical situations, the effective Richardson constant governing thermionic emission over a heterointerface barrier is determined by the effective mass in the material that contains X_max. This statement is rigorously true when the effective mass at X_max is lower than that in the other material, otherwise it is an approximation dependent on the value of the interface potential. The issue clarified in this work has relevance to theoretical constructs involving model boundary conditions at heterojunction interfaces