  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 $4{\rm ~\mu m\phi}$ 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.
