  Novel wide-band-gap semiconductors are needed for next-generation power
electronic but there is a gap between a promising material and a functional
device. Finding stable contacts is one of the major challenges, which is
currently dealt with mainly via trial and error. Herein, we computationally
investigate the thermochemistry and phase co-existence at the junction between
three wide gap semiconductors, $\beta$-Ga$_{2}$O$_{3}$, GeO$_2$, and GaN, and
possible contact materials. The pool of possible contacts includes 47 elemental
metals and 4 common $n$-type transparent conducting oxides (ZnO, TiO$_2$,
SnO$_2$, and In$_2$O$_3$). We use first-principles thermodynamics to model the
Gibbs free energies of chemical reactions as a function of the gas pressure
(p$_{\mathrm{O}_2}$/p$_{\mathrm{N}_2}$) and equilibrium temperature. We deduce
whether a semiconductor/contact interface will be stable at relevant
conditions, possibly influencing the long-term reliability and performance of
devices. We generally find that most elemental metals tend to oxidize or
nitridize and form various interface oxide/nitride layers. Exceptions include
select late- and post-transition metals, and in case of GaN also the alkali
metals, which are predicted to exhibit stable coexistence, although in many
cases at relatively low gas partial pressures. Similar is true for the
transparent conducting oxides, for which in most cases we predict a preference
toward forming ternary oxides when in contact with $\beta$-Ga$_{2}$O$_{3}$ and
GeO$_{2}$. The only exception is SnO$_2$, which can form stable contacts with
both oxides. Finally, we show how the same approach can be used to predict gas
partial pressure vs. temperature phase diagrams to help direct synthesis of
ternary compounds. We believe these results provide a valuable guidance in
selecting contact materials to wide-gap semiconductors and suitable growth
conditions.
