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 Si-SOI layers using such structures. 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 2 V/m to be applied across the SOI layer. Utilizing this structure we measure the Stark shift parameters of arsenic donors embedded in the Si SOI layer and find a contact hyperfine Stark parameter of $\eta_a=-1.9\pm0.2\times10^{-3} \mu^2^2$. We also demonstrate electric-field driven dopant ionization in the SOI device layer, measured by electron spin resonance.

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