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 28Si-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 2V/lm to be applied across the SOI layer. Utilizing this structure, we measure the Stark shift parameters of arsenic donors embedded in the 28Si-SOI layer and find a contact hyperfine Stark parameter of na=-1.9+/-0.7x10-3 lm2/V2. We also demonstrate electric-field driven dopant ionization in the SOI device layer, measured by electron spin resonance.