In this paper we report experimental results on the fabrication and characterization of vertical Ge gate-all-around p-channel TFETs, utilizing GeSn as a channel material. Through two sample series, the potential and challenges of implementing the low-band gap material GeSn are reviewed. It is verified that I_ON can be effectively enhanced by increasing the Sn-content in the G eSn-channel, due to increasing tunneling probabilities. Further it is found that when limited to a 10 nm δ-layer,Ge_0.96Sn_0.04 is most beneficial for I_ON when positioned inside the channel as opposed to in the source, with a maximum of I_ON = 180 μA/μm at V_DS= -2 V and V_G = -4 V. Enhanced leakage currents (I_OFF), which also degrades the subthreshold swing (SS), is a consequence of a smaller band gap and enhanced defect densities, and represent key challenges with implementing GeSn.