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.
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