Common Gate Transimpedance Amplifier Transfer Function
I finally got the reason or the assumption used in the paper.
The assumption is
$$ R_{D}r_{o} \approx R_{D}(r_{o} + R_{D})$$ for $$  r_{o} &gt;&gt; R_{D} $$
Continuing from my result above.
$$ \frac{v_{out}}{i_{pd}} = \frac{(1 + g_{m}r_{o})R_{D}}
{sC_{PD}R_{D} + \left[ (sC_{o}R_{D} + 1)(sC_{PD}r_{o} + g_{m}r_{o} +1 ) \right]   }$$
the denumerator can be written fully as follow:
$$s^2C_{o}R_{D}C_{PD}r_{o} + s (C_{PD}R_{D} + C_{PD}r_{o} + C_{o}R_{D}g_{m}r_{o} + C_{o}R_{D}) + (g_{m}r_{o} +1)  $$
then when we want to factor it, it can be written as
$$ \left(sC_{o}R_D + 1 \right) \left[ sC_{PD}(r_{o}+ {\color{brown} R_{D} } ) + g_{m1}r_{o} + 1 \right] $$
The additional  \$ {\color{brown} R_{D}} \$ is intentionally added to make factorization easy.
In my case, \$ {\color{brown} R_{D}} \$ is ~5% of \$ r_{o} \$. So it does not affect too much.