  The upcoming Mu3e experiment will search for the charged lepton flavour
violating decay of a muon at rest into three electrons. The maximal energy of
the electrons is 53 MeV, hence a low material budget is a key performance
requirement for the tracking detector. In this paper we summarize our approach
to meet the requirement of about 0.1 % of a radiation length per pixel detector
layer. This includes the choice of thinned active monolithic pixel sensors in
HV-CMOS technology, ultra-thin flexible printed circuits, and helium gas
cooling.
