  Halo model is a physically intuitive method for modelling the non-linear
power spectrum, especially for the alternatives to the standard $\Lambda$CDM
models. In this paper, we exam the Sheth-Tormen barrier formula adopted in the
previous \texttt{CHAM} method \citep{2018MNRAS.476L..65H}. As an example, we
model the ellipsoidal collapse of top-hat dark matter haloes in $f(R)$ gravity.
A good agreement between Sheth-Tormen formula and our result is achieved. The
relative difference in the ellipsoidal collapse barrier is less than or equal
to $1.6\%$. Furthermore, we verify that, for F4 and F5 cases of Hu-Sawicki
$f(R)$ gravity, the screening mechanism do not play a crucial role in the
non-linear power spectrum modelling up to $k\sim1[h/{\rm Mpc}]$. We compare two
versions of modified gravity modelling, namely with/without screening. We find
that by treating the effective Newton constant as constant number ($G_{\rm
eff}=4/3G_N$) is acceptable. The scale dependence of the gravitational coupling
is sub-relevant. The resulting spectra in F4 and F5, are in $0.1\%$ agreement
with the previous \texttt{CHAM} results. The published code is accelerated
significantly. Finally, we compare our halo model prediction with N-body
simulation. We find that the general spectrum profile agree, qualitatively.
However, via the halo model approach, there exists a systematic
under-estimation of the matter power spectrum in the co-moving wavenumber range
between $0.3 h/{\rm Mpc}$ and $3 h/{\rm Mpc}$. These scales are overlapping
with the transition scales from two halo term dominated regimes to those of one
halo term dominated.
