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

18 2. Operation and Radiation Damage of Silicon Detectorson the other side. When no external voltage is applied the net current of the charge carriers(electrons and holes) through the junction sums to zero. This is not a consequenceof the absence of carrier ow across the junction but only means that as many carriers ofeach type ow in one direction as in the other. In the presence of an external voltage Vthis however is not the case.The diusion current of a given carrier (e.g. holes) can be divided into two components:diusion generation current and recombination current. The diusion generationcurrent of holes (J genh) ows from n to p side. It arises from pairs generated just on then side of the depleted region by thermal excitation of electrons out of the valence band.When such a hole diuses into the depletion layer it is swept to the p side of the junctionby the strong eld in the junction. Diusion generation current does thus not depend onbias voltage. The recombination current of holes (Jhrec ), on the other hand, ows from thep to the n side of the junction where it recombines with a free electron. This current owsin the direction opposite to the electric eld and thus only holes with a thermal energysucient to surmount the potential barrier contribute to the recombination current. Thenumber of 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 for reverse bias. The total diusion current of holes is a dierence of 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 of the holes equals toJ h = J rech; J genh= J genh(e eV=k BT ; 1) (2.25)The size of the diusion generation current J genhcan be estimated in terms of 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 within a diusion length L h from the boundary of the depletedregion. Thus the ow of the thermally generated holes per unit area into the depletedregion will be of order J genh L hp n0 h.The situation is analogous for the electrons except for inverted directions. But sincealso the charge sign is opposite the total electric current is the sum of the electron and