  (Abridged) We present the results from the X-ray spectral analysis of high-z
AGN in the CDFS, making use of the new 4Ms data set and new X-ray spectral
models from Brightman & Nandra, which account for Compton scattering and the
geometry of the circumnuclear material. Our goals are to ascertain to what
extent the torus paradigm of local AGN is applicable at earlier epochs and to
evaluate the evolution of the Compton thick fraction (f_CT) with z, important
for XRB synthesis models and understanding the accretion history of the
universe. In addition to the torus models, we measure the fraction of scattered
nuclear light, f_scatt known to be dependant on covering factor of the
circumnuclear materal, and use this to aid in our understanding of its
geometry. We find that the covering factor of the circumnuclear material is
correlated with NH, and as such the most heavily obscured AGN are in fact also
the most geometrically buried. We come to these conclusions from the result
that f_scatt decreases as NH increases and from the prevalence of the torus
model with the smallest opening angle as best fit model in the fits to the most
obscured AGN. We find that a significant fraction of sources (~ 20%) in the
CDFS are likely to be buried in material with close to 4 pi coverage having
been best fit by the torus model with a 0\degree opening angle. Furthermore, we
find 41 CTAGN in the CDFS using the new torus models, 29 of which we report
here for the first time. We bin our sample by z in order to investigate the
evolution of f_CT. Once we have accounted for biases and incompleteness we find
a significant increase in the intrinsic f_CT, normalised to LX= 10^43.5 erg/s,
from \approx 20% in the local universe to \approx 40% at z=1-4.
