An ALICE Silicon Drift Detector should undergo two tests before the assembling procedure.
The former regards the linearity of the potential distribution on the integrated divider. A non-linearity could be due either to a local defect generating high current or to a punch-through current among the cathodes. The selection criterion is a crucial point in order to evaluate the production yield. Indeed, depending on the yield of the first batch an external support at the divider could be adopted in order to relax the acceptance conditions. A non-linearity of the potential distribution generates a systematic error on the position resolution along the drift direction. Furthermore when the distortion on one side exceeds a certain level we lose the electrons generated by the ionising particle. Considering that every detector will be calibrated in order to get rid of the systematic errors, the last limit will be used in the acceptance test. We have done some calculations, (reported on a note concerning the leakage current) and we found that if there is a difference of 0.1V on the voltage drop on the resistor connecting two consecutive cathodes, the electron cloud is shifted dangerously to one of the surfaces.
*When the detector has satisfied the requirements of HV divider uniformity under bias, the other acceptance criterion is that of the anode leakage current since this determines the noise - and therefore efficiency - of the detector readout (the anode capacitance can be ignored since it will always be small compared to the fixed contribution introduced by the readout microcables).
Calculating the overall efficiency of a given channel is complex for drift detectors due to the effect of charge diffusion. This means that, despite the fact that there is no charge loss and therefore the total charge signal remains the same, the cluster size in both the space and time coordinates varies with drift distance such that the effective signal/noise for long drift times is substantially poorer than that for short drift times. Thus a channel which has a higher noise than the limit value we choose can still be fully efficient for MIP signals up to a certain drift time. Furthermore, while one can expect that the noise on neighbouring anodes for a given time bin will not be strongly correlated, the fact that a number of consecutive time samples sampling at 40MHz are used for any given anode means that the effective transfer function of the system is not simply that of the preamplifier/shaper. Finally, geometrical effects such as the average angle of tracks within the detector (non-zero in ALICE) and th e average energy deposition (higher than MIP in ALICE) will also have some impact on the overall efficiency.
While a detailed study of this problem remains to be made, here we attempt to make some reasonable assumptions in order to have a starting point. It has been determined empirically, on the basis of beam test data and simulations [ITS TDR], that the normal single channel noise should be no more than about 250 electrons noise. We therefore choose an upper limit of 300 electrons for the single channel noise above which the efficiency of that channel is considered to be compromised.
The simulated response function of the preamplifier/shaper of the PASCAL chip is expected is very close to RC-CR^2, with a peaking time of 36ns and a noise performance of 150 e- + 22 e-/pF [Rivetti]. The preamplifier input is directly coupled to the anodes, but, since the design allows for at least 500nA of input current before the dynamic range starts to be affected, only the noise implications of the anode leakage current need to be considered.
The following table gives the noise contribution due to anode current calculated using the theoretical response function, and the total noise considering a load capacitance of 2pF.
| Anode current | Anode current noise | Total noise |
| 0nA | 0e- | 194e- |
| 1 | 18 | 195 |
|
| 10 | 56 | 202 |
| 20 | 79 | 209 |
| 50 | 125 | 231 |
| 100 | 177 | 262 |
| 200 | 250 | 316 |
The leakage current due to accumulated radiation dose must also be considered. From the ITS TDR, and treating the ionising dose as minimum-ionising pions, the total fluences are expected to be
| Neutron ionizing fluence | Ionizing fluence | Total fluence |
| Layer 3 | 3.5e11 cm-2 | 5.2e11 cm-2 | 8.7e11 cm-2 |
| Layer 4 | 3.3e11 cm-2 | 2.0e11 cm-2 | 5.2e11 cm-2 |
(assuming that the radiation dose from LHC injector loss incidents does not prove to be significant). Using the standard leakage current dependence on fluence with alpha = 2e-17 A.cm-1 (therefore allowing for annealing), maximum drift distance 35.0 mm, anode pitch 294 um, detector thickness 300 um, this translates into anode leakage currents of 54 nA for layer 3 and 32 nA for layer 4 (at 20 degrees Celsius). Thus, without any "safety factor", using a simulation of the preamplifier/shaper, and with a simplistic treatment of the noise, we obtain an upper limit of approximately 150 nA for full efficiency of a given anode channel. Furthermore, it is to be expected that only anodes which collect leakage current from defective regions of the detectors will have such current levels and therefore the stability of this current with both time and accumulated ionisation damage is not easy to predict. Introducing an arbitrary safety factor, we would therefore suggest that a reasonable upper limit for "good" anodes should be 100nA. In order to achieve good overall tracker performance one should aim for at least 98% overall efficiency for each layer so, allowing for the fact that the complex electronics and challenging construction techniques chosen for the ALICE modules must be conceded at least 1% of inefficiency, the aim for the detector quality is that only 1-2% of the anodes for any given detector (3-6 anodes / half detector) should have a leakage current above 100nA (2% at 150nA probably being acceptable since the efficiency is maintained for shorter drift times whereas 2% at 1uA or higher would probably be unacceptable).
*this paragraph is written by Richard Wheadon ( wheadon@to.infn.it)
