To study the track structure of light ions, a measuring device has been developed at the Legnaro National Laboratory of INFN, which can be used to investigate separately the penumbra region of particle tracks and the trackcore region, which is a few nanometres in diameter. The device is based on single-electron counting techniques by means of a gas detector; it simulates a 'nanometre-sized' biological volume of about 20 nm in diameter that can be moved with respect to a narrow particle beam to measure the ionizationcluster-size distributions caused within the target volume by the passage of single primary particles, as a function of the impact parameter. To investigate the ionization-cluster-size formation caused by primary particles of medical interest when they penetrate through or pass by the target volume at a specified impact parameter, measurements and Monte Carlo simulations were performed for 20 MeV protons, 16 MeV deuterons, 48 MeV 6 Li-ions, 26.7 MeV 7 Li-ions and 96 MeV 12 C-ions. The detailed analysis of the resulting distributions showed that in the track-core region their shape is mainly determined by the mean free ionization path length of the primary particles, whereas in the penumbra region the shape of the distributions is almost independent of the impact parameter, and also of the particle type and velocity.