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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18 2. Operation and Radiation Damage <strong>of</strong> Silicon Detectorson the other side. When no external voltage is applied the net current <strong>of</strong> the charge carriers(electrons and holes) through the junction sums to zero. This is not a consequence<strong>of</strong> the absence <strong>of</strong> carrier ow across the junction but only means that as many carriers <strong>of</strong>each type ow <strong>in</strong> one direction as <strong>in</strong> the other. In the presence <strong>of</strong> an external voltage Vthis however is not the case.The diusion current <strong>of</strong> a given carrier (e.g. holes) can be divided <strong>in</strong>to two components:diusion generation current and recomb<strong>in</strong>ation current. The diusion generationcurrent <strong>of</strong> holes (J genh) ows from n to p side. It arises from pairs generated just on then side <strong>of</strong> the depleted region by thermal excitation <strong>of</strong> electrons out <strong>of</strong> the valence band.When such a hole diuses <strong>in</strong>to the depletion layer it is swept to the p side <strong>of</strong> the junctionby the strong eld <strong>in</strong> the junction. Diusion generation current does thus not depend onbias voltage. The recomb<strong>in</strong>ation current <strong>of</strong> holes (Jhrec ), on the other hand, ows from thep to the n side <strong>of</strong> the junction where it recomb<strong>in</strong>es with a free electron. This current ows<strong>in</strong> the direction opposite to the electric eld and thus only holes with a thermal energysucient to surmount the potential barrier contribute to the recomb<strong>in</strong>ation current. Thenumber <strong>of</strong> such holes is proportional to e ;e 0V=k B T , thusJ rech / e e 0(;V bi +V )=k B T (2.23)where V < 0 <strong>for</strong> reverse bias. The total diusion current <strong>of</strong> holes is a dierence <strong>of</strong> bothcomponents J h = Jhrec ; J genh. From the condition that there is no net current when noexternal voltage is applied follows Jhrecgen(V = 0) = Jhand taken together with 2.23 itgivesJ rech= J genhe eV=k BT : (2.24)Thus the total current <strong>of</strong> the holes equals toJ h = J rech; J genh= J genh(e eV=k BT ; 1) (2.25)The size <strong>of</strong> the diusion generation current J genhcan be estimated <strong>in</strong> terms <strong>of</strong> diusionlengths and carrier lifetimes. Holes are generated by thermal generation at a rate p n0 hper unit volume, where p n0 is the equilibrium hole density on the n side and h the holelifetime. They stand a considerable chance to enter the depleted region and to be sweptto the n side if generated with<strong>in</strong> a diusion length L h from the boundary <strong>of</strong> the depletedregion. Thus the ow <strong>of</strong> the thermally generated holes per unit area <strong>in</strong>to the depletedregion will be <strong>of</strong> order J genh L hp n0 h.The situation is analogous <strong>for</strong> the electrons except <strong>for</strong> <strong>in</strong>verted directions. But s<strong>in</strong>cealso the charge sign is opposite the total electric current is the sum <strong>of</strong> the electron and