  Single rare-earth ions in solids show great potential for quantum
applications, including single photon emission, quantum computing, and
high-precision sensing. However, homogeneous linewidths observed for single
rare-earth ions are orders of magnitude larger than the sub-kilohertz
linewidths observed for ensembles in bulk crystals. The spectral broadening
creates a significant challenge for achieving entanglement generation and qubit
operation with single rare-earth ions, so it is critical to investigate the
broadening mechanisms. We report a spectral broadening study on a single
Er$^{3+}$ ion in a Si nano-transistor. The Er-induced photoionisation rate is
found to be an appropriate quantity to represent the optical transition
probability for spectroscopic studies, and the single ion spectra display a
Lorentzian lineshape at all optical powers in use. Spectral broadening is
observed at relatively high optical powers and is caused by spectral diffusion
on a fast time scale.
