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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48 3. Ir<strong>radiation</strong> FacilityCR suruRuundepleted regionWCdRddepleted regionwFigure 3.11: A simple model <strong>of</strong> a partially biased diode. Both depleted region and undepletedregion are modelled by a capacitor C and a resistor R connected <strong>in</strong> parallel. Depleted andundepleted regions are connected <strong>in</strong> series with a parallel resistor to account <strong>for</strong> the surfacecurrent.Capacitance <strong>of</strong> the depleted region can be determ<strong>in</strong>ed by equationC d = Si 0 Sw = C 0pV0 (3.9)where w is the depletion depth, C 0 = 35 pF is capacitance <strong>of</strong> fully depleted diode andthe dimensionless parameter V 0 = V=V FD is the fraction <strong>of</strong> full depletion voltage, appliedacross the depleted region. Similarly, capacitance <strong>of</strong> the undepleted region is given byC u = Si 0 SW ; w = C 01 ; p V 0 (3.10)where W is the detector thickness. Correspond<strong>in</strong>g impedances Z = (2C) ;1 <strong>for</strong> a 10kHz measur<strong>in</strong>g signal areZ d 0:5 M p V 0 Z u 0:5 M (1 ; p V 0 ) (3.11)decreas<strong>in</strong>g <strong>in</strong>versely with measur<strong>in</strong>g frequency.Resistance <strong>of</strong> the undepleted bulk R u <strong>for</strong> an <strong>in</strong>verted diode can be determ<strong>in</strong>ed fromthe specic resistance <strong>for</strong> <strong>in</strong>tr<strong>in</strong>sic bulk <strong>in</strong>tr (5 C) 1 Mcm. Us<strong>in</strong>g this value, one canobta<strong>in</strong> the resistance <strong>of</strong> the undepleted region <strong>in</strong> dependence <strong>of</strong> the depletion voltageR u = W ; wS= W S (1 ; p V 0 )=30k (1 ; p V 0 ) : (3.12)The resistance <strong>of</strong> the depleted region can be determ<strong>in</strong>ed from the DC current, ow<strong>in</strong>gtrough the diode 24 . Accord<strong>in</strong>g to eq. 2.38, the reverse current is proportional to the24S<strong>in</strong>ce the reverse current is limited by the resistance <strong>of</strong> depleted region, this is a viable estimate.