  Aims: To trace the radial and vertical spatial distribution of H2CS, a key
species of the S-bearing chemistry, in protoplanetary disks. To analyse the
observed distributions in light of the H2CS binding energy, in order to discuss
the role of thermal desorption in enriching the gas disk component. Methods: In
the context of the ALMA chemical survey of Disk-Outflow sources in the Taurus
star forming region (ALMA-DOT), we observed five Class I or early Class II
sources with the o-H2CS(7_1,6-6_1,5) line on a 40 au scale. We estimated the
binding energy (BEs) of H2CS using quantum mechanical calculations, for the
first time, for an extended, periodic, crystalline ice. Results: We imaged H2CS
in two rotating molecular rings in the HL Tau and IRAS04302+2247 disks. The
outer radii are about 140 au (HL Tau), and 115 au (IRAS 04302+2247). The
edge-on geometry of IRAS 04302+2247 reveals that H2CS emission peaks, at radii
of 60-115 au, at z = +- 50 au from the equatorial plane. The column densities
are about 10^14 cm^-2. For HL Tau, we derive, for the first time, the
[H2CS]/[H] abundance in a protoplanetary disk (about 10^-14). The BEs of H2CS
computed for extended crystalline ice and amorphous ices is 4258 K and
3000-4600 K, respectively, implying a thermal evaporation where dust
temperature is larger than 50-80 K. Conclusions: H2CS traces the so-called warm
molecular layer, a region previously sampled using CS, and H2CO.
Thioformaldehyde peaks closer to the protostar than H2CO and CS, plausibly due
to the relatively high-excitation level of observed 7_1,6-6_1,5 line (60 K).
The H2CS BEs implies that thermal desorption dominates in thin, au-sized, inner
and/or upper disk layers, indicating that the observed H2CS emitting up to
radii larger than 100 au is likely injected in the gas due to non-thermal
processes.
