Physical justification for the time resolution limit of silicon planar detectors of long-range heavy ions

A model of current outflow from the track plasma of a long-range heavy ion irradiating a silicon $p^+$–$n$–$n^+$ detector is presented. Basing on the model, an analytical description of the process was obtained and its numerical simulation was performed. The results on the coordinate and temporal transformation of the electric field and carrier concentrations $N_{pl}$ in plasma and the current signal shape show good quantitative agreement between the calculation and simulation data. The rise time of the current signal is not limited by the carrier outflow from the plasma and is controlled by the track creation time in few ps, which determines the physical limit of the detector time resolution when registering long-range ions. The signal decay contains two components, a fast polarization component associated with the formation of layers with high electric field near the $p^+$- and $n^+$-contacts, whose duration reduces from 480 to 100 ps as $N_{pl}$ rises from 1 $\cdot$ 10$^{15}$ to 1 $\cdot$ 10$^{17}$ cm$^{-3}$, and a slow relaxation component, caused by the depletion of the electron-hole plasma in track.