  Si$_3$N$_4$ waveguides, pumped at 1550 nm, can provide spectrally smooth,
broadband light for gas spectroscopy in the important 2 ${\mathrm{\mu}}$m to
2.5 ${\mathrm{\mu}}$m atmospheric water window, which is only partially
accessible with silica-fiber based systems. By combining Er+:fiber frequency
combs and supercontinuum generation in tailored Si$_3$N$_4$ waveguides, high
signal-to-noise dual-comb spectroscopy (DCS) spanning 2 ${\mathrm{\mu}}$m to
2.5 ${\mathrm{\mu}}$m is demonstrated. Acquired broadband dual-comb spectra of
CO and CO$_2$ agree well with database line shape models and have a
spectral-signal-to-noise as high as 48$/\sqrt{\mathrm{s}}$, showing that the
high coherence between the two combs is retained in the Si$_3$N$_4$
supercontinuum generation. The DCS figure of merit is 6$\times
10^6/\sqrt{\mathrm{s}}$, equivalent to that of all-fiber DCS systems in the 1.6
${\mathrm{\mu}}$m band. Based on these results, future DCS can combine fiber
comb technology with Si$_3$N$_4$ waveguides to access new spectral windows in a
robust non-laboratory platform.
