  We have been developing X-ray SOIPIXs for next-generation satellites for
X-ray astronomy. Their high time resolution ($\sim10~\mu$s) and
event-trigger-output function enable us to read out without pile-ups and to use
anti-coincidence systems. Their performance in imaging spectroscopy is
comparable to that in the CCDs. A problem in our previous model was degradation
of charge-collection efficiency (CCE) at pixel borders. We measured the
response in the sub-pixel scale, using finely collimated X-ray beams at
$10~\mu$m\Phi$ at SPring-8, and investigated the non-uniformity of the CCE
within a pixel. We found that the X-ray detection efficiency and CCE degrade in
the sensor region under the pixel circuitry placed outside the buried p-wells
(BPW). A 2D simulation of the electric fields shows that the isolated
pixel-circuitry outside the BPW creates local minimums in the electric
potentials at the interface between the sensor and buried oxide layers. Thus, a
part of signal charge is trapped there and is not collected to the BPW. Based
on this result, we modified the placement of the in-pixel circuitry so that the
electric fields would converge toward the BPW. We confirmed that the CCE at
pixel borders is successfully improved with the updated model.
