The energy diagram of the contact of two different semiconductors and, thus the height of the potential barrier can be determined from the band structure for each material in first approximation using the Anderson’s model, which does not take into account the presence of interface states and electric dipoles at the heterojunction interface. The detail information can be found, for example, in the following book:
B. L. Sharma, R. K. Purohit “Semiconductor heterojunctions”
The calculated height of the potential barrier is equal to the difference between the work functions of each semiconductor material. Therefore, it is necessary to know the doping level (the location of the Fermi level) additionally to the band structure of the semiconductors under investigation. Unfortunately, as usually, the actual height of the potential barrier differs from its calculated value according the Anderson’s model, since the effect of interface states can not be neglected. However it is another long story :-).
Jaafar Jalilian just scooped me. ;) That's a good paper. There *is* a right way to do it. Note that there are subtleties related to cases where polarization, hence electric fields, are present, and asymmetric interfaces. Some of those are explained in the attached paper.
Some other issues relate to composition as determined by growth conditions, e.g. attachment. Anyway the key point is that the difference of bulk energies must be supplemented by actual interface dipole induced jumps.