  Rare-earth ions (REI) have emerged as an attractive candidate for solid-state
qubits, particularly as a quantum memory. Their 4f-4f transitions are shielded
by filled 5s and 5p orbitals, offering a degree of protection from external
electric fields. Embedded within a thin film oxide host, REIs could enable a
qubit platform with significant memory capabilities. Furthermore, a
silicon-compatible thin film form factor would enable the use of standard
semiconductor fabrication processes to achieve chip-based integrability and
scalability for functional quantum networks. Towards this goal, we have carried
out optical and microstructural studies of erbium-doped polycrystalline and
epitaxial TiO$_2$ thin films on Si (100), r-sapphire, and SrTiO$_3$ (100). We
observe that the inhomogeneous optical linewidth of the Er photoluminescence is
comparable or better for polycrystalline Er:TiO$_2$(grown on Si) in comparison
to single crystal epitaxial films on sapphire or SrTiO$_3$, implying a relative
insensitivity to extended defects. We investigated the effect of the
film/substrate and film/air interface and found that the inhomogeneous
linewidth and spectral diffusion can be significantly improved via bottom
buffer and top capping layers of undoped TiO$_2$. Using such approaches, we
obtain inhomogeneous linewidths of 5.2 GHz and spectral diffusion of 180 MHz in
Er:TiO$_2$ /Si(100) films and have demonstrated the engineerability of
quantum-relevant properties in these thin films.
