  The Lyman-Werner (LW) radiation field is a key ingredient in the
chemo-thermal evolution of gas in the Early Universe, as it dissociates H2
molecules, the primary cooling channel in an environment devoid of metals and
dust. Despite its important role, it is still not implemented in cosmological
simulations on a regular basis, in contrast to the ionising UV background. This
is in part due to uncertainty in the source modelling, their spectra and
abundance, as well as the detailed physics involved in the propagation of the
photons and their interactions with the molecules. The goal of this work is to
produce an accurate model of the LW radiation field at $z\geq6$, by
post-processing the physics-rich high-resolution FiBY simulation. Our novelties
include updated cross sections for H$_2$, H$^-$ and H$^+_2$ chemical species,
IGM absorption by neutral Hydrogen and various spectral models for Population
III and Population II stars. With our fiducial set of parameters, we show that
the mean LW intensity steadily increases by three orders of magnitude from
$z\sim23$ to $z\sim6$, while spatial inhomogeneities originate from massive
star-forming galaxies that dominate the photon budget up to a distance of
$\sim100$ proper kpc. Our model can be easily applied to other simulations or
semi-analytical models as an external radiation field that regulates the
formation of stars and massive black hole seeds in high-$z$ low-mass halos.
