Restriction on the gain in collected charge due to carrier avalanche multiplication in heavily irradiated Si strip detectors

Recent experiments on silicon detectors developed by the CERN-RD50 collaboration for very high luminosity colliders showed a significant enhancement of the collected charge $Q_c$ in Si detectors irradiated to the fluence of $10^{15} – 10^{16} \ \rm{n}_{eq}/cm^2$ if the devices were operated at high bias voltage. The enhancement arises from carrier avalanche multiplication in high electric field of the junction. However, calculated and experimental results indicated that a maximum $Q _ $ enhancement is much lower than the signal gain in avalanche photodiodes. The study of the collected charge in Si n-on-p strip detectors described here is focused on the restriction of the internal gain in irradiated Si strip detectors. It is demonstrated that (1) the gain in the collected charge due to avalanche multiplication is strongly restricted by the negative feedback arisen from a space charge limited current (SCLC negative feedback), which is an inherent property of heavily irradiated Si detectors with high concentration of radiation- induced defects; (2) the dependence of the gain on fluence is nonmonotonous due to competition between enhanced carrier trapping at high fluence and avalanche multiplication, which correlates with recent experimental results; (3) SCLC negative feedback makes the internal gain practically insensitive to the design of the detector region with high electric field. The results of this study show that the avalanche multiplication effect can be efficient in improving the radiation performance of Si detectors developed for the sLHC in a limited fluence range, which luckily covers the range expected in the upgraded LHC experiments.