  We developed a 2-mm-thick CdTe double-sided strip detector (CdTe-DSD) with a
250 um strip pitch, which has high spatial resolution with a uniform large
imaging area of 10 cm$^2$ and high energy resolution with high detection
efficiency in tens to hundreds keV. The detector can be employed in a wide
variety of fields for quantitative observations of hard X-ray and soft
gamma-ray with spectroscopic imaging, for example, space observation, nuclear
medicine, and non-destructive elemental analysis. This detector is thicker than
the 0.75-mm-thick one previously developed by a factor of $\sim$2.7, thus
providing better detection efficiency for hard X-rays and soft gamma rays. The
increased thickness could potentially enhance bias-induced polarization if we
do not apply sufficient bias and if we do not operate at a low temperature, but
the polarization is not evident in our detector when a high voltage of 500 V is
applied to the CdTe diode and the temperature is maintained at -20 $^\circ$C
during one-day experiments. The ''Depth Of Interaction'' (DOI) dependence due
to the CdTe diode's poor carrier-transport property is also more significant,
resulting in much DOI information while complicated detector responses such as
charge sharings or low-energy tails that exacerbate the loss in the energy
resolution.
  In this paper, we developed 2-mm-thick CdTe-DSDs, studied their response, and
evaluated their energy resolution, spatial resolution, and uniformity. We also
constructed a theoretical model to understand the detector response
theoretically, resulting in reconstructing the DOI with an accuracy of 100 um
while estimating the carrier-transport property. We realized the detector that
has high energy resolution and high 3D spatial resolution with a uniform large
imaging area.
