  We analyse the interaction of charged Janus particles including screening
effects. The explicit interaction is mapped via a least square method on a
variable number $n$ of systematically generated tensors that reflect the
angular dependence of the potential. For $n = 2$ we show that the interaction
is equivalent to a model previously described by Erdmann, Kr\"oger and Hess
(EKH). Interestingly, this mapping is not able to capture the subtleties of the
interaction for small screening lengths. Rather, a larger number of tensors has
to be used. We find that the characteristics of the Janus type interaction
plays an important role for the aggregation behaviour. We obtained cluster
structures up to the size of $13$ particles for $n = 2$ and $36$ and screening
lengths $\kappa^{-1} = 0.1$ and $1.0$ via Monte Carlo simulations. The
influence of the screening length is analysed and the structures are compared
to results for an electrostatic-type potential and for multipole-expanded
Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. We find that a dipole-like
potential (EKH or dipole DLVO approximation) is not able to sufficiently
reproduce the anisotropy effects of the potential. Instead, a higher order
expansion has to be used to obtain clusters structures that are identical to
experimental results for up to $N = 8$ particles. The resulting minimum-energy
clusters are compared to those of sticky hard sphere systems. Janus particles
with a short-range screened interaction resemble sticky hard sphere clusters
for all considered particle numbers, whereas for long-range screening even very
small clusters are structurally different.
