Aa. Grinberg et S. Luryi, ON ELECTRON-TRANSPORT ACROSS INTERFACES CONNECTING MATERIALS WITH DIFFERENT EFFECTIVE MASSES, I.E.E.E. transactions on electron devices, 45(7), 1998, pp. 1561-1568
We reconsider the problem of electronic transport across a heterojunct
ion 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 fre
e 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 situ
ations, the effective Richardson constant governing thermionic emissio
n over a heterointerface barrier is determined by the effective mass i
n 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 mater
ial, otherwise it is an approximation dependent on the value of the in
terface potential. The issue clarified in this work has relevance to t
heoretical constructs involving model boundary conditions at heterojun
ction interfaces.