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

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32 2. Operation and Radiation Damage of Silicon DetectorsNeffΣgi Φeqfastbeneficialannealingreverse annealinggYΦ eqslowplateaudays at R.T.g CΦeqyears at R.T.time (lin scale)time (log scale)Figure 2.8: Schematic plot of time development of N eff . All three phases are shown withintroduction rates for responsible defects. Note that reverse annealing is shown in the logarithmictime scale. Defects stable in time Electrically active defects that change to non-active ones(annealing) Electrically non-active defects that change to active ones (reverse annealing)The change of a defect can be either due to dissociation or combination of a defect complex.In case of the dissociation X ! Y the reaction can be described as a rst order processwith the general solution; dN Ydt= dN Xdt= ;k Y 1N X (2.55)N X (t) =N 0 Xe ;kY 1 t (2.56)N Y (t) =N 0 X(1 ; e ;kY 1 t ) : (2.57)When the new complex is due to a reaction of two defects X A + X Bdescribed by! Y it can be; dN Ydtwith the solution (N 0 X A>N 0 X B)= dN X Adt= dN X Bdt= ;k Y 2N XA N XB (2.58)N Y (t) =N 0 X B1 ; e ;kY 2 t(N 0 X A;N 0 X B)1 ; (N 0 X B=N 0 X A)e ;kY 2 t(N 0 X A;N 0 X B) : (2.59)
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)
Page 1: UNIVERSITY OF LJUBLJANAFACULTY OF M
Page 5: Najprej gre moja zahvala delovnima
Page 8 and 9: PovzetekSevalne poskodbe v siliciju
Page 10 and 11: 3.5 Measurement Setup, Methods and
Page 13 and 14: 1IntroductionSilicon detectors play
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Page 17 and 18: 1. Introduction 9R(cm)Z(cm)Figure 1
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5. Dose Rate Dependence 83Figure 5.
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5. Dose Rate Dependence 85Figure 5.
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5. Dose Rate Dependence 87could be
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6Inuence of Bias VoltageIt was a ge
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6. Inuence of Bias Voltage 91energy
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6. Inuence of Bias Voltage 93Figure
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6. Inuence of Bias Voltage 99that t
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6. Inuence of Bias Voltage 101(abou
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6. Inuence of Bias Voltage 103Figur
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7Comparison with Other GroupsWhile
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7. Comparison with Other Groups 107
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8ConclusionsA systematic study of r
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8. Conclusions 111Implications for
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9Povzetek doktorskega dela9.1 UvodS
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9. Povzetek doktorskega dela 115Ski
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9. Povzetek doktorskega dela 117sre
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9. Povzetek doktorskega dela 1199.2
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9. Povzetek doktorskega dela 121Sli
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9. Povzetek doktorskega dela 123Ce
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9. Povzetek doktorskega dela 127Cep
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9. Povzetek doktorskega dela 129Mer
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9. Povzetek doktorskega dela 131Sam
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9. Povzetek doktorskega dela 1379.6
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10Appendix: List of Symbols and Abb
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10. Appendix: List of Symbols and A
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References[1] J. Straver et al., Nu
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[27] A.M. Ougang et al.: Dierential
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[57] M. Huhtinen et al, HU-SEFT-R-1
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