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

2. Operation and Radiation Damage of Silicon Detectors 33In the case of two defects with similar initial concentrations N 0 X A= N 0 X Bor a reactionbetween defects of the same type one obtainsN X (t) =N 0 X1+N 0 X kY 2t(2.60)N Y (t) =N 0 X ; N X (t) =N 0 X(1 ;11+N 0 X kY 2t ) (2.61)describing a second order process. If, however, concentration of one type of interactingdefects is much larger than the concentration of the other (NX 0 A NX 0 B) the dynamicsof the process can again be described by the rst order equation with k Y 1= k Y 2NX 0 A.In the equations, N 0 X is the initial concentrations of defect X and k Y 1and k Y 2arethe reaction constants for the rst and second order processes. From equations 2.55 and2.58 it can be seen that in the rst order reaction, the reaction rate depends linearly ondefect concentration while in the second order case it depends quadratically.2.4.1 Time Evolution of Leakage CurrentTraditionally, measurements of the time development of the leakage current have beentted with an ansatz [46, 19, 14, 20]I(t) =I(0)[A C + X iA i e ;t= i ] (2.62)where A C represents the contribution of defects constant in time, A i contributions ofdecaying defects, i their decay times and t time after irradiation. To remove the eectof sample size and irradiation uence, a more fundamental constant =I (eq. 2.50),V eqwhere V is the sample volume, is usually used. Thus eq. 2.62 can be rewritten in termsof the parameter as(t) = C + X i i e ;t= i : (2.63)Only the contribution of defects constant in time and annealing defects has been determinedin the leakage current, while no reverse annealing was observed. However recentresults [35] as well as results presented in this work are showing also a long term annealingcomponent, that could be described by an eective logarithmic time dependence,described by an ansatz(t) = E e ;t= E ; L ln(t= L ) : (2.64)