Study of radiation damage in silicon detectors for high ... - F9
Study of radiation damage in silicon detectors for high ... - F9
Study of radiation damage in silicon detectors for high ... - F9
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2. Operation and Radiation Damage <strong>of</strong> Silicon Detectors 33In the case <strong>of</strong> two defects with similar <strong>in</strong>itial concentrations N 0 X A= N 0 X Bor a reactionbetween defects <strong>of</strong> the same type one obta<strong>in</strong>sN 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)describ<strong>in</strong>g a second order process. If, however, concentration <strong>of</strong> one type <strong>of</strong> <strong>in</strong>teract<strong>in</strong>gdefects is much larger than the concentration <strong>of</strong> the other (NX 0 A NX 0 B) the dynamics<strong>of</strong> the process can aga<strong>in</strong> be described by the rst order equation with k Y 1= k Y 2NX 0 A.In the equations, N 0 X is the <strong>in</strong>itial concentrations <strong>of</strong> defect X and k Y 1and k Y 2arethe reaction constants <strong>for</strong> the rst and second order processes. From equations 2.55 and2.58 it can be seen that <strong>in</strong> the rst order reaction, the reaction rate depends l<strong>in</strong>early ondefect concentration while <strong>in</strong> the second order case it depends quadratically.2.4.1 Time Evolution <strong>of</strong> Leakage CurrentTraditionally, measurements <strong>of</strong> the time development <strong>of</strong> 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 <strong>of</strong> defects constant <strong>in</strong> time, A i contributions <strong>of</strong>decay<strong>in</strong>g defects, i their decay times and t time after ir<strong>radiation</strong>. To remove the eect<strong>of</strong> sample size and ir<strong>radiation</strong> 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 <strong>in</strong> terms<strong>of</strong> the parameter as(t) = C + X i i e ;t= i : (2.63)Only the contribution <strong>of</strong> defects constant <strong>in</strong> time and anneal<strong>in</strong>g defects has been determ<strong>in</strong>ed<strong>in</strong> the leakage current, while no reverse anneal<strong>in</strong>g was observed. However recentresults [35] as well as results presented <strong>in</strong> this work are show<strong>in</strong>g also a long term anneal<strong>in</strong>gcomponent, 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)