  We present the results from an X-ray spectral analysis of active galactic
nuclei (AGN) in the Chandra Deep Field-South, AEGIS-XD and Chandra-COSMOS
surveys, focussing on the identification and characterisation of the most
heavily obscured, Compton thick (CT, $N_{H}>10^{24} cm^{-2}$) sources. Our
sample is comprised of 3184 X-ray selected extragalactic sources, which has a
high rate of redshift completeness (97.6 %), and includes improved photometric
redshifts over previous studies. We use spectral models designed for heavily
obscured AGN which self consistently include all major spectral signatures of
heavy absorption. We identify CT sources not selected through our spectral
fitting method using X-ray colours, validate our spectral fitting method
through simulations, and take considerations for the constraints on $N_{H}$
given the low count nature of many of our sources. After these considerations
we identify a total of 100 CT AGN with best-fit $N_{H}>10^{24} cm^{-2}$ and
$N_{H}$ constrained to be above $10^{23.5} cm^{-2}$ at 90% confidence. These
sources cover an intrinsic $L_{X}$ range of $10^{42}-3x10^{45}$ ergs s$^{-1}$
and a redshift range of z=0.1-4. This sample will enable characterisation of
these heavily obscured AGN across cosmic time and to ascertain their
cosmological significance. Furthermore, by using the torus models to test
different covering factor scenarios, and by investigating the inclusion of the
soft scattered emission, we find evidence that the covering factor of the
obscuring material decreases with $L_{X}$ for all redshifts, consistent with
the receding torus model, and that this factor increases with redshift,
consistent with an increase in the obscured fraction towards higher redshifts.
We make $N_{H}$, $\Gamma$ (with uncertainties), observed X-ray fluxes and
intrinsic $L_{X}$ for all sources analysed in this work publicly available in
an online catalogue.
