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

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48 3. Irradiation FacilityCR suruRuundepleted regionWCdRddepleted regionwFigure 3.11: A simple model of a partially biased diode. Both depleted region and undepletedregion are modelled by a capacitor C and a resistor R connected in parallel. Depleted andundepleted regions are connected in series with a parallel resistor to account for the surfacecurrent.Capacitance of the depleted region can be determined by equationC d = Si 0 Sw = C 0pV0 (3.9)where w is the depletion depth, C 0 = 35 pF is capacitance of fully depleted diode andthe dimensionless parameter V 0 = V=V FD is the fraction of full depletion voltage, appliedacross the depleted region. Similarly, capacitance of the undepleted region is given byC u = Si 0 SW ; w = C 01 ; p V 0 (3.10)where W is the detector thickness. Corresponding impedances Z = (2C) ;1 for a 10kHz measuring signal areZ d 0:5 M p V 0 Z u 0:5 M (1 ; p V 0 ) (3.11)decreasing inversely with measuring frequency.Resistance of the undepleted bulk R u for an inverted diode can be determined fromthe specic resistance for intrinsic bulk intr (5 C) 1 Mcm. Using this value, one canobtain the resistance of the undepleted region in dependence of the depletion voltageR u = W ; wS= W S (1 ; p V 0 )=30k (1 ; p V 0 ) : (3.12)The resistance of the depleted region can be determined from the DC current, owingtrough the diode 24 . According to eq. 2.38, the reverse current is proportional to the24Since the reverse current is limited by the resistance of depleted region, this is a viable estimate.
3. Irradiation Facility 49width of depleted region w and consequently to p V , i.e. I = A p V . The magnitude ofthe parameter A can be estimated from the conditions at full depletion A = p I FDVFD. Thenthe resistance of the depleted bulk at given depletion voltage is given byR d = V I =VpVA p V = A= V FDI FDpV0(3.13)Using reverse current of I FD 25 A at full depletion voltage 25 of V FD 250 V oneobtainsR d =10M p V 0 : (3.14)One can see that in the described case R d =Z d 20 and Z u =R u 15. Thus thedepleted region can be approximated by a capacitor and the undepleted by a resistor.The signicance of the resistance of the undepleted region is however decreasing withincreasing depletion depth. Thus at half of full depletion depth (V = V FD =4), one alreadyobtains Z d =R u > 15. Thus for large depletion depths the bulk can be described well bya single capacitor and both serial and parallel model should give the same result. Theparallel model however has the advantage that it can take into account changes in thesurface current, presented by the surface resistor. They are hard to predict but can getvery important close to the breakdown where the dierential resistance is small. Since fordetermination of full depletion voltage from the C/V characteristic, we are interested inits shape close to full depletion, the parallel model suits better and was used throughoutthis work.The situation however changes dramatically when the measuring frequency is increased.This is reected in a decrease of impedance of both capacitors and at 1 MHz,Z u has the leading role also in the undepleted region. Then the equivalent circuit can beapproximated by two serial capacitors with a constant sum of capacitances. Thus at 1MHz the measured capacitance is almost independent of applied voltage, as seen in gure3.12. Similar eect is obtained by increasing the temperature. Since resistance of both depletedand undepleted region is approximately proportional 26 to e ;Eg=2k BT , increasing thetemperature by a few 10 C has the same relative eect as the above mentioned increasein frequency.Static resistivities, used in the above estimation, do not describe the system veryaccurately. And although dynamic resistivities are somewhat dierent 27 , the qualitativeconclusions remain the same.25Values of reverse current and full depletion voltage at the minimum after benecial annealing wereused.26For depleted region see eq. 2.38 and for undepleted regions equations 2.11 and 2.1.27A dierence of up to about factor of two was estimated.
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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
Page 15 and 16: 1. Introduction 7Figure 1.2: Schema
Page 17 and 18: 1. Introduction 9R(cm)Z(cm)Figure 1
Page 19 and 20: 2Operation and Radiation Damage of
Page 21 and 22: 2. Operation and Radiation Damage o
Page 43 and 44: 3Irradiation Facility3.1 The Reacto
Page 45 and 46: 3. Irradiation Facility 373.3 Irrad
Page 47 and 48: 3. Irradiation Facility 39Fission p
Page 49 and 50: 3. Irradiation Facility 413.4 Irrad
Page 51 and 52: 3. Irradiation Facility 43Figure 3.
Page 53 and 54: 3. Irradiation Facility 45Figure 3.
Page 55: 3. Irradiation Facility 47the inuen
Page 59 and 60: 3. Irradiation Facility 51The full
Page 61 and 62: 3. Irradiation Facility 53percent.
Page 63 and 64: 4Time Development of DefectsIn this
Page 65 and 66: 4. Time Development ofDefects 57* F
Page 67 and 68: 4. Time Development ofDefects 59val
Page 69 and 70: 4. Time Development ofDefects 61for
Page 71 and 72: 4. Time Development ofDefects 63Fig
Page 87 and 88: 4. Time Development ofDefects 79An
Page 89 and 90: 5Dose Rate Dependence5.1 Motivation
Page 91 and 92: 5. Dose Rate Dependence 83Figure 5.
Page 93 and 94: 5. Dose Rate Dependence 85Figure 5.
Page 95 and 96: 5. Dose Rate Dependence 87could be
Page 97 and 98: 6Inuence of Bias VoltageIt was a ge
Page 99 and 100: 6. Inuence of Bias Voltage 91energy
Page 101 and 102: 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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Izjavljam, da je disertacija rezult
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