Optical and microstructural characterization of Er$^{3+}$ doped epitaxial cerium oxide on silicon

Rare-earth ion dopants in solid-state hosts are ideal candidates for quantum communication technologies such as quantum memory, due to the intrinsic spin-photon interface of the rare-earth ion combined with the integration methods available in the solid-state. Erbium-doped cerium oxide (Er:CeO$_2$) is a particularly promising platform for such a quantum memory, as it combines the telecom-wavelength (~1.5 $\mu$m) 4f-4f transition of erbium, a predicted long electron spin coherence time supported by CeO$_2$, and is also near lattice-matched to silicon for heteroepitaxial growth. In this work, we report on the epitaxial growth of Er:CeO$_2$ thin films on silicon using molecular beam epitaxy (MBE), with controlled erbium concentration down to 2 parts per million (ppm). We carry out a detailed microstructural study to verify the CeO$_2$ host structure, and characterize the spin and optical properties of the embedded Er$^{3+}$ ions. In the 2-3 ppm Er regime, we identify EPR linewidths of 245(1) MHz, optical inhomogeneous linewidths of 9.5(2) GHz, optical excited state lifetimes of 3.5(1) ms, and spectral diffusion-limited homogenoeus linewidths as narrow as 4.8(3) MHz in the as-grown material. We test annealing of the Er:CeO$_2$ films up to 900 deg C, which yields modest narrowing of the inhomogeneous linewidth by 20% and extension of the excited state lifetime by 40%. We have also studied the variation of the optical properties as a function of Er doping and find that the results are consistent with the trends expected from inter-dopant charge interactions.