A simple recombination model for the pulse height defect in the passivated ion-implanted Si detectors

The recombination process has an important contribution to the pulse height defect (PHD) value when high carrier concentrations are produced by strongly ionizing fragments at energies high enough to neglect the role of the nuclear stopping. In the following, we try to quantify the recombination process by taking into consideration the exact variation of the specific electronic stopping power along the particle track. We consider two processes which have an important contribution to the variation of the carrier concentration: (I) plasma formed in the ionizing particle wake disappears through extraction by the electric field with time constant tp and (II) recombination of electrons and holes with time constant tr. The rate equation for the carrier concentration (holes and electrons) is given. The rate of the infinitesimal PHD is related to the square term occurring in the rate equation. An analytical integration over the time (0,∞) and over the energy (E0,0) was performed with the approximation S = CAZ2/E of the Bethe-Bloch formula (A,Z - mass and atomic number of the ion and C- a constant). Only one fit parameter occurs and it is connected to the detector characteristics: electric field strength and resistivity. This new formula was successfully confronted with experimental data. A figure is given showing the PHD data from Si detectors of INDRA array, as a function of the energy deposited in Si detectors by Ni, Xe and Ta ions, in comparison with different parametrizations used by Ogihara et all and Kaufman et all. (authors)