We develop an efficient back gate for silicon-on-insulator (SOI) devices operating at cryogenic temperatures, and measure the quadratic hyperfine Stark shift parameter of arsenic donors in isotopically purified $^{28}$Si-SOI layers using such structu
res. The back gate is implemented using MeV ion implantation through the SOI layer forming a metallic electrode in the handle wafer, enabling large and uniform electric fields up to $sim$ 2 V/$mu$m to be applied across the SOI layer. Utilizing this structure we measure the Stark shift parameters of arsenic donors embedded in the $^{28}$Si SOI layer and find a contact hyperfine Stark parameter of $eta_a=-1.9pm0.2times10^{-3} mu$m$^2$/V$^2$. We also demonstrate electric-field driven dopant ionization in the SOI device layer, measured by electron spin resonance.
