We report on photodetection in deep subwavelength Ge(Sn) nano-islands on Si nano-pillar substrates, in which self-aligned nano-antennas in the Al contact metal are used to enhance light absorption by means of local surface plasmon resonances. The impact of parameters such as substrate doping and device geometry on the measured responsivities are investigated and our experimental results are supported by simulations of the three-dimensional distribution of the electromagnetic fields. Comparatively high optical responsivities of about 0.1 A W-1 are observed as a consequence of the excitation of localized surface plasmons, making our nano-island photodetectors interesting for applications in which size reduction is essential.