  Optical emission line diagnostics, which are a common tool to constrain the
properties of the interstellar medium (ISM) of galaxies, become progressively
inaccessible at higher redshifts for ground-based facilities. Far-infrared
(FIR) emission lines, which are redshifted into atmospheric windows accessible
by ground-based sub-millimeter facilities, could provide alternative ISM
diagnostics to optical emission lines. We investigate FIR line ratios involving
[CII]$\lambda 158 \mu$m, [OIII]$\lambda 88 \mu$m, [OIII]$\lambda 52 \mu$m,
[NII]$\lambda 122 \mu$m and [NIII$\lambda 57 \mu$m, using synthetic emission
lines applied to a high-resolution (m$_{\rm gas}$= 883.4 M$_{\odot}$)
cosmological zoom-in simulation, including radiative-transfer post processing
with KramsesRT at z = 6.5. We find that the [CII]/[NII]122 ratio is sensitive
to the temperature and density of photo-dissociation regions, and thus could be
a useful tool to trace the properties of this gas phase in galaxies. We also
find that [NII]/[NIII] is a good tracer of the temperature and
[OIII]52/[OIII]88 a good tracer of the gas density of HII regions. Emission
line ratios containing the [OIII]$\lambda 88 \mu$m line are sensitive to high
velocity outflowing gas.
