  Motivated by recent advancements highlighting Ta as a promising material in
low-loss superconducting circuits and showing long coherence times in
superconducting qubits, we have explored the effect of cryogenic temperatures
on the growth of Ta and its integration in superconducting circuits. Cryogenic
growth of Ta using a low temperature molecular beam epitaxy (MBE) system is
found to stabilize single phase $\alpha$-Ta on several different substrates,
which include Al$\mathrm{_2}$O$\mathrm{_3}$(0001), Si(001), Si(111), SiN${_x}$,
and GaAs(001). The substrates are actively cooled down to cryogenic
temperatures and remain < 20 K during the Ta deposition. X-ray
$\theta$-2$\theta$ diffraction after warming to room temperature indicates the
formation of polycrystalline $\alpha$-Ta. The 50 nm $\alpha$-Ta films grown on
Al$\mathrm{_2}$O$\mathrm{_3}$(0001) at a substrate manipulator temperature of 7
K have a room temperature resistivity ($\mathrm{\rho _{300 K}}$) of 13.4
$\mathrm{\mu \Omega}$cm, a residual resistivity ratio (RRR) of 17.3 and a
superconducting transition temperature (T$_C$) of 4.14 K, which are comparable
to bulk values. In addition, atomic force microscopy (AFM) indicates that the
film grown at 7 K with an RMS roughness of 0.45 nm was significantly smoother
than the one grown at room temperature. Similar properties are found for films
grown on other substrates. Results for films grown at higher substrate
manipulator temperatures show higher $\mathrm{\rho _{300 K}}$, lower RRR and
Tc, and increased $\beta$-Ta content. Coplanar waveguide resonators with a gap
width of 3 $\mathrm{\mu}$m fabricated from cryogenically grown Ta on Si(111)
and Al$\mathrm{_2}$O$\mathrm{_3}$(0001) show low power Q$_i$ of 1.9 million and
0.7 million, respectively, indicating polycrystalline $\alpha$-Ta films may be
promising for superconducting qubit applications even though they are not fully
epitaxial.
