Finally, we considered tri-layer interfaces with a varying number of atomic layers of the ZnTe or CdSe tunnel barrier between the InAs and Al. We have found that the band gap of the barrier evolves as function of distance from the InAs and Al interfaces in a similar manner to the Insb/CdTe/α-Sn interface we had studied previously. Contrary to the expectation that the band gap of a very thin barrier would be wider than the bulk band gap because of the quantum size effect, in fact, it is narrowed owing to evanescent states penetrating from both the Al and InAs directions. Only with 24 atomic layers of either material the barrier band gap approaches the expected value about halfway between the Al and InAs. With 8 atomic layers of either ZnTe or CdSe, MIGS from the Al were found to penetrate through the entire width of the barrier into the InAs. 16 layers of either material were found to insulate the InAs from MIGS, which we interpret to mean that the InAs is effectively decoupled from the Al. Although ZnTe and CdSe behave similarly with respect to the barrier thickness, the two materials markedly differ in their band edge positions. As a result, we have found that ZnTe may provide an effective barrier mainly for electrons and to a lesser degree for holes, whereas CdSe only provides a barrier for holes.