  Graphene based sensor to gas molecules should be ultrasensitive and ultrafast
because of the single-atomic thickness of graphene, while the response is not
fast. Usually, the measured response time for many molecules, such as CO, NH3,
SO2, CO2 and NO2 and so on, is on the scale of minutes or longer. In the
present work, we found via \emph{ab initio} calculations there exists a
potential barrier larger than 0.7 eV that hinders the gas molecule to land
directly at the defective sites of graphene and retards the response. An
efficient approach to the problem is suggested as modifying the graphene sheet
with other molecules to reduce the potential barrier and was demonstrated by a
graphene sheet modified by Fe2O3 molecules that shows fast response to H2S
molecule, and the calculated response time is close to the measured one, 500
$\mu$s.
