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

22 2. Operation and Radiation Damage of Silicon Detectorsdierence is due to the increase of generation current, caused by additional traps closeto mid-gap, introduced by irradiation. Generation current is thus the main source of thereverse current in irradiated samples, so one should expect that temperature dependenceof the reverse current is following equation 2.39.The situation is however dierent if the major contribution to the leakage currentis from traps with high concentration but somewhat away from the mid-gap [12]. In thatcase, one of the exponential termsincoshin eq. 2.36 prevails and one obtainsr pair = T ehv eh N CV e ;Eg2k B Te ; 1k B T jE T ; 1 2 (E V +E C )j : (2.40)This could account for a higher energy (1.2 eV [13, 14, 15] compared to E g =1.1 eV)observed in the scaling of reverse current with temperature.2.1.6 N eff from C/V MeasurementsOne can dene the depletion layer capacitance as the ratio of dierential change of chargeper dierential change of applied voltageC(V 0 ) = dQdV j V =V 0: (2.41)In case of a one-sided abrupt junction the capacitance is given byC(V )= Si 0 Sw= rSi 0 e 0 N eff2VS (2.42)where Q = e 0 N eff Sw (S is the sample area) was used together with eq. 2.9. It shows thatfor N eff constant over the detector depth, the graph of 1=C 2 (V ) versus V is a straightline for reverse voltages below full depleted voltaged(1=C 2 (V ))dV=2e 0 Si 0 N eff S 2 (2.43)and a constant value for higher voltages. The position of the kink determines FDV andthe slope determines N eff .A similar set of equations can be used to determine the N eff distribution overthe sample depth from a capacitance versus voltage (C/V) measurement in a case of anon-uniform distribution. Equation 2.43 can be rewritten [8] asd(1=C 2 (V ))dV=2e 0 Si 0 N eff (V )S 2 (2.44)