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

30 2. Operation and Radiation Damage of Silicon Detectorsdefect complexes. It is well proven by experiments that deep level acceptor-like statesare generated during irradiation. According to equations 2.10 and 2.13 the full depletionvoltage is proportional to jN eff j. It means that, for an initially n type bulk, at low uencesFDV is decreasing with uence until the inversion point is reached and then it starts toincrease with uence. Thus at high total uences full depletion voltage may grow toohigh for a normal operation of the device. This increase of depletion voltage is the mainproblem for operation of silicon detectors in a high radiation environment.The uence dependence of the initially present shallow level dopants is however notwell understood yet. Dierent models have been proposed to explain experimental results.R. Wunstorf et al. [29] reports on measurements of removal of both initial shallowdonors and acceptors, together with deep level acceptor creation. Development of theeective dopant concentration with uence can thus be parametrised asN eff () = N 0 De ;c D ; N 0 Ae ;c A ; g (2.51)Donor removal constant has been determined to be c D 2:5 10 ;13 cm 2 and acceptorremoval constant c A 1:98 10 ;13 cm 2 .F. Lemeilleur [30] however reports linear dependence of the inversion uence oninitial dopant concentration with inv = (18 0:6cm) N eff (0). At the same time uencedependence of N eff is parametrised bywith c D 2:5 10 ;14 cm 2 and g 1:1 10 ;2 cm 2 .N eff () = N 0 De ;c D ; N 0 A ; g (2.52)H. Feick [20] assumes low level of compensation of his initial material (N 0 A N O D )and is thus not sensitive to changes in concentration of initial acceptors. Exponentialdependence of the donor concentration on uence is reported with removal rate equal toc D =(2:4 1:4) 10 ;13 cm 2 , but with only about a third of initial donors being subjectto the removal. Reduced donor removal was also reported in [50].Watts [31] used numerical modelling of deep acceptor creation to generate N effversus neutron uence for p and n type diodes. No initial dopant removal was used inthe calculations and good agreement with the data is reported. It is thus claimed that noinitial dopant removal is required to successfully explain the uence dependence of N eff .Similarly, compensation of initial donors by deep acceptors instead of donor removal isalso suggested by [32].Due to lack of information about initial donor and acceptor concentration, lowcompensation 15 has been assumed throughout this work. Initial donor concentration is15Assuming low compensation N 0 A N 0 D , and with initial donor concentration N 0 D < 4 1011 cm ;3 ,initial acceptor concentration can be neglected.