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

12 2. Operation and Radiation Damage of Silicon Detectorsstructure, surface damage of the top and bottom plane has a negligible eect 3 and theincrease of the reverse current due to surface damage at the edge of detectors can beeliminated by guard rings.The general equationnp = n 2 i = N C N V e ; Egk B T(2.1)gives in the intrinsic case (n = p = n i ) the density of free carriers in non-depleted puresilicon. Here n and p are concentrations of free electrons and holes, respectively, N C andN V are eective densities of states at the conduction and valence band edges respectivelyN CV =2 2m 3eh k B2Th 2 (2.2)E g =1.12 eV is the band gap, k B the Boltzmann constant, h Planck constant, T temperatureand m eh eective masses of electrons and holes. At room temperature N CV is ofthe order 10 19 /cm 3 and n i around 10 10 /cm 3 . In a 300 m thick diode with an area of 1cm 2 this gives a few times 10 8 of free carriers with uctuations comparable to the signalfrom a minimum ionising particle (3 10 4 pairs). In a reversely biased diode, on the otherhand, free carriers are swept out by the electric eld leaving a space charge region (SCR)depleted of free carriers. 4 Thus to obtain a good signal/noise ratio the active volume hasto be depleted.2.1.1 p ; n JunctionThe number of free electrons and holes in silicon can be changed signicantly by dopingit with donors or acceptors. Donors usually are atoms that have in addition to the fourelectrons, needed for the covalent bond, one electron they donate to the conduction band.Acceptors have one electron missing to form bonding to all neighbours. So to completethe missing bond they accept an electron from the valence band, leaving a hole there.Energies needed for those transitions are comparable to k B T at room temperature andalmost all dopants are ionised. Thus at high enough excess concentration of dopantsof certain type, the number of electrons in the conduction band equals the number ofdonors or the number of holes in the valence band equals the number of acceptors. Therelation n 2 i = np still holds as in pure silicon, while n = p = n i is no longer valid. Ifthe concentration of donors N D exceeds the concentration of acceptors N A (i.e. n > p)3Single large pad reduces the surface of the oxide-bulk contact. Absence of integrated decouplingcapacitors and bias resistors removes eects caused by radiation induced changes in their performances.4In fact a small but permanent carrier generation due to emission and capture processes still remainin the SCR region as will be described later.