Study of radiation damage in silicon detectors for high ... - F9

2. Operation and Radiation Damage of Silicon Detectors 152.1.2 Inuence of External VoltageFor charged particle detection, the e;h pairs created in the depletion region by a traversingparticle are separated by the electric eld, collected and read out. The charge createdin the neutral, non-depleted region recombines with free carriers and is lost. Increasingthe depth of the space charge region thus increases the collected signal.To obtain maximal signal one would like tohave the whole thickness of the detectordepleted of free carriers. This can be achieved by applying an external voltage V withthe same polarity as the built in potential. In that case V bi in equation 2.7 is replaced byV bi + V . Since usually V V bi , V bi can be omitted and we obtainw(V ) =r2Si 0e 0 N DV : (2.9)The voltage necessary to deplete the full depth of the detector (W ), called the full depletionvoltage (FDV or V FD ), is thus given byV FD = e 0N D W 22 Si 0: (2.10)It can be seen that the relation between V FD and N D depends quadratically on sampledepth. For 300 m thick samples, the conversion constant isV FD =6:95 10 ;11 Vcm 3 N D .For a semiconductor with both electrons and holes as carriers, bulk resistivity isgiven by [8] =1e 0 ( e n + h p)(2.11)where e and h are electron and hole mobilities (1350 and 480 cm 2 /Vs at room temperature,respectively). For a fully ionised shallow-dopant n-type silicon, n N D and p n.Equation 2.11 can thus be simplied to =1e 0 e N D (2.12)relating resistivity and initial donor concentration. For a typical value of = 5 kcm oneobtains N D 9 10 11 cm ;3 .High resistivityn-type material ( >2 kcm), that is usually used for the low dopedn side of silicon tracking detectors, is obtained by donor compensation 7 . This means thatdonor and acceptor concentrations are of the same order of magnitude, and N D has to bereplaced by the dierence of the donor and acceptor concentrationsN D ! N eff = jN D ; N A j : (2.13)7Neutron doping is usually used to obtain high resistivity n-type material [8, 9].