We have been developing the X-ray silicon-on-insulator (SOI) pixel sensor called XRPIX for future astrophysical satellites. XRPIX is a monolithic active pixel sensor consisting of a high-resistivity Si sensor, thin SiO$_2$ insulator, and CMOS pixel circuits that utilize SOI technology. Since XRPIX is capable of event-driven readouts, it can achieve high timing resolution greater than $sim 10{rm ~mu s}$, which enables low background observation by adopting the anti-coincidence technique. One of the major issues in the development of XRPIX is the electrical interference between the sensor layer and circuit layer, which causes nonuniform detection efficiency at the pixel boundaries. In order to reduce the interference, we introduce a Double-SOI (D-SOI) structure, in which a thin Si layer (middle Si) is added to the insulator layer of the SOI structure. In this structure, the middle Si layer works as an electrical shield to decouple the sensor layer and circuit layer. We measured the detector response of the XRPIX with D-SOI structure at KEK. We irradiated the X-ray beam collimated with $4{rm ~mu mphi}$ pinhole, and scanned the device with $6{rm ~mu m}$ pitch, which is 1/6 of the pixel size. In this paper, we present the improvement in the uniformity of the detection efficiency in D-SOI sensors, and discuss the detailed X-ray response and its physical origins.
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