  The efficiencies of solar cells based on kesterite Cu$_2$ZnSnS$_4$ (CZTS) and
Cu$_2$ZnSnSe$_4$ (CZTSe) are limited by a low open-circuit voltage due to high
rates of non-radiative electron-hole recombination. To probe the origin of this
bottleneck, we calculate the band offset of CZTS(Se) with CdS, confirming a
weak spike of 0.1 eV for CZTS/wurtzite-CdS and a strong spike of 0.4 eV for
CZTSe/wurtzite-CdS. We also consider the effects of temperature on the band
alignment, finding that increasing temperature significantly enhances the
spike-type offset. We further resolve an outstanding discrepancy between
measured and calculated phonon frequencies for the kesterites, and use these to
estimate the upper limit of electron and hole mobilities based on optic phonon
Fr\"ohlich scattering, which uncovers an intrinsic asymmetry with faster
(minority carrier) electron mobility.
