  In this work, we show that spectroscopic ellipsometry can be combined with
photoemission spectroscopy to obtain complete interface band diagrams of
non-ideal semiconductor heterointerfaces, such as interfaces between thin-film
polycrystalline materials. The non-destructive ellipsometry measurement probes
the near-interface band gap of the two semiconductors (including the buried
semiconductor) after the interface has formed. This is important in the
non-ideal case where chemical processes during interface growth modify the
electronic properties of the two separated surfaces. Knowledge of
near-interface band gaps improves accuracy in conduction band offset
measurements of non-ideal interfaces, and it sheds light on their device
physics. Both of those positive outcomes are demonstrated in the
Cu$_2$ZnSnS$_4$/CdS interface used here as a case study, where the band gap of
both materials decreases by up to 200 meV from the bulk to the near-interface
region. This finding reveals a preferential electron-hole recombination channel
near the interface, and it yields corrected values for the interfacial
conduction band offset.
