  Electron clouds forming inside the beam vacuum chamber due to photoemission
and secondary emission may limit the accelerator performance. Specifically, the
electron clouds can blow up the vertical emittance of a positron beam, through
a head-tail-type single-bunch instability, if the central electron density
exceeds a certain threshold value, that can be estimated analytically. Using
the codes PyECLOUD and VSim, we carried out detailed simulations of the
electron-cloud build up for the main arcs and the damping ring of the FCC-ee
collider, in order to identify the effective photoemission rate and secondary
emission yield required for achieving and maintaining the design emittance. To
this end, we present the simulated electron density at the centre of the beam
pipe for various bunch spacings, secondary emission yields, and photoemission
parameters, in the damping ring and in the arcs of the collider positron ring.
To gain further insight into the underlying dynamics, the obtained spatial and
energy distributions of the cloud electrons are illustrated as a function of
time. In addition, we compare results obtained for two different secondary
emission models ("Furman-Pivi" and "ECLOUD"), thereby indicating the
uncertainty inherent in this type of study, without any prototype vacuum
chambers yet available. We also point out a few situations where the two
secondary-emission models yield similar density values. Finally, based on our
simulation results for two different design variants, we conclude that the new
parameter baseline of the FCC-ee will facilitate electron-cloud mitigation.
