  With the aim of improving predictions on far infrared (FIR) line emission
from Giant Molecular Clouds (GMC), we study the effects of photoevaporation
(PE) produced by external far-ultraviolet (FUV) and ionizing
(extreme-ultraviolet, EUV) radiation on GMC structure. We consider three
different GMCs with mass in the range $M_{\rm GMC} = 10^{3-6}\,\rm{M_{\odot}}$.
Our model includes: (i) an observationally-based inhomogeneous GMC density
field, and (ii) its time evolution during the PE process. In the fiducial case
($M_{\rm GMC}\approx10^5 M_{\odot}$), the photoevaporation time ($t_{pe}$)
increases from 1 Myr to 30 Myr for gas metallicity $Z=0.05-1\,\rm Z_{\odot}$,
respectively. Next, we compute the time-dependent luminosity of key FIR lines
tracing the neutral and ionized gas layers of the GMCs, ([CII] at $158\,\rm{\mu
m}$, [OIII] at $88\,\rm \mu m$) as a function of $G_0$, and $Z$ until complete
photoevaporation at $t_{pe}$. We find that the specific [CII] luminosity is
almost independent on the GMC model within the survival time of the cloud.
Stronger FUV fluxes produce higher [CII] and [OIII] luminosities, however
lasting for progressively shorter times. At $Z=Z_{\odot}$ the [CII] emission is
maximized ($L_{\rm CII}\approx 10^4\,\rm{L_{\odot}}$ for the fiducial model)
for $t<1\,\rm{Myr}$ and $\log G_0\geq 3$. Noticeably, and consistently with the
recent detection by Inoue et al. (2016) of a galaxy at redshift $z\approx 7.2$,
for $Z\leq 0.2\,\rm{Z_{\odot}}$ the [OIII] line might outshine [CII] emission
by up to $\approx 1000$ times. We conclude that the [OIII] line is a key
diagnostic of low metallicity ISM, especially in galaxies with very young
stellar populations.
