  Protoplanetary disks are thought to have lifetimes of several million years
in the solar neighborhood, but recent observations suggest that the disk
lifetimes are shorter in a low metallicity environment. We perform a suite of
radiation hydrodynamics simulations of photoevaporation of protoplanetary disks
to study the disk structure and its long-term evolution of $\sim 10000$ years,
and the metallicity dependence of mass-loss rate. Our simulations follow
hydrodynamics, extreme and far ultra-violet radiative transfer, and
non-equilibrium chemistry in a self-consistent manner. Dust grain temperatures
are also calculated consistently by solving the radiative transfer of the
stellar irradiation and grain (re-)emission. We vary the disk gas metallicity
over a wide range of $10^{-4}~ Z_\odot \leq Z \leq 10 ~Z_\odot$. The
photoevaporation rate is lower with higher metallicity in the range of $10^{-1}
\,Z_\odot \lesssim Z \lesssim 10 \,Z_\odot$, because dust shielding effectively
prevents far-ultra violet (FUV) photons from penetrating into and heating the
dense regions of the disk. The photoevaporation rate sharply declines at even
lower metallicities in $10^{-2} \,Z_\odot \lesssim Z \lesssim
10^{-1}\,Z_\odot$, because FUV photoelectric heating becomes less effective
than dust-gas collisional cooling. The temperature in the neutral region
decreases, and photoevaporative flows are excited only in an outer region of
the disk. At $10^{-4}\,Z_\odot \leq Z \lesssim 10^{-2}\,Z_\odot$, HI
photoionization heating acts as a dominant gas heating process and drives
photoevaporative flows with roughly a constant rate. The typical disk lifetime
is shorter at $Z=0.3~Z_\odot$ than at $Z = Z_\odot$, being consistent with
recent observations of the extreme outer galaxy.
