  We present a numerical investigation of directly fiber-coupled hybrid
circular Bragg gratings (CBGs) featuring electrical control for operation in
the application relevant wavelength regimes around 930 nm as well as the
telecom O- and C-band. We use a surrogate model combined with a Bayesian
optimization approach to perform numerical optimization of the device
performance which takes into account robustness with respect to fabrication
tolerances. The proposed high-performance designs combine hCBGs with a
dielectric planarization and a transparent contact material, enabling >86%
direct fiber coupling efficiency (up to >93% efficiency into NA 0.8) while
exhibiting Purcell Factors >20. Especially the proposed designs for the telecom
range prove robust and can sustain expected fiber efficiencies of more than
$(82.2\pm4.1)^{+2.2}_{-5.5}$% and expected average Purcell Factors of up to
$(23.2\pm2.3)^{+3.2}_{-3.0}$ assuming conservative fabrication accuracies. The
wavelength of maximum Purcell enhancement proves to be the most affected
performance parameter by the deviations. Finally, we show that electrical field
strengths suitable for Stark-tuning of an embedded quantum dot can be reached
in the identified designs.
