  The vertical structure of debris disks provides clues about their dynamical
evolution and the collision rate of the unseen planetesimals. Thanks to the
ever-increasing angular resolution of contemporary instruments and facilities,
we are beginning to constrain the scale height of a handful of debris disks,
either at near-infrared or millimeter wavelengths. Nonetheless, this is often
done for individual targets only. We present here the geometric modeling of
eight disks close to edge-on, all observed with the same instrument (SPHERE)
and using the same mode (dual-beam polarimetric imaging). Motivated by the
presence of CO gas in two out of the eight disks, we then investigate the
impact that gas can have on the scale height by performing N-body simulations
including gas drag and collisions. We show that gas can quickly alter the
dynamics of particles (both in the radial and vertical directions), otherwise
governed by gravity and radiation pressure. We find that, in the presence of
gas, particles smaller than a few tens of microns can efficiently settle toward
the midplane at the same time as they migrate outward beyond the birth ring.
For second generation gas ($M_\mathrm{gas} \leq 0.1$ $M_\oplus$), the vertical
settling should be best observed in scattered light images compared to
observations at millimeter wavelengths. But if the gas has a primordial origin
($M_\mathrm{gas} \geq 1$ $M_\oplus$), the disk will appear very flat both at
near-infrared and sub-mm wavelengths. Finally, far beyond the birth ring, our
results suggest that the surface brightness profile can be as shallow as $\sim
-2.25$.
