258 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 49, NO. 1, FEBRUARY 2002 Optimization of Electric Field Distribution by Free Carrier Injection in Silicon Detectors Operated at Low Temperatures E. Verbitskaya, M. Abreu, V. Bartsch, W. Bell, P. Berglund, J. Bol, W. de Boer, K. Borer, S. Buontempo, L. Casagrande, S. Chapuy, V. Cindro, N. D’Ambrosio, C. Da Viá, S. R. H. Devine, B. Dezillie, A. Dierlamn, Z. Dimcovski, V. Eremin, A. Esposito, V. Granata, E. Grigoriev, F. Hauler, S. Janos, L. Jungermann, I. Konorov, Z. Li, C. Lourenço, M. Mikuz, T. O. Niinikoski, V. O’Shea, S. Pagano, V. G. Palmieri, S. Paul, P. Rato Mendes, G. Ruggiero, L. Schmitt, K. Smith, P. Sousa, and M. Zavrtanik Abstract—We present a study of the modeling of the electric field distribution, which is controlled by injection and trapping of nonequilibrium carriers, in Si detectors irradiated by high neutron fluences. An analytical calculation of the electric field distribution in detectors irradiated by neutrons up to fluences of 1 10 to 5 10 cm shows the possibility of reducing the full depletion voltage at low temperatures via hole injection. For this calculation, we use the detector operating parameters and equivalent neutron fluences expected for Large Hadron Collider experiments. The re- sults of the calculation are in good qualitative agreement with pub- lished experimental data, lending strong support for the model and Manuscript received November 6, 2000; revised November 15, 2001. This work was supported in part by the Russian Academy of Sciences under Contract GR 01.9.30 005437 and in part by the U.S. Department of Energy under Contract DE-AC02-98CH10886. E. Verbitskaya and V. Eremin are with Ioffe Physico-Technical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia (e-mail: elena.verbitskaya@pop.ioffe.rssi.ru). M. Abreu, P. Rato Mendes, and P. Sousa are with LIP Algavre, University Algavre, Portugal, P-1000 Lisbon, Portugal. V. Bartsch, W. Bell, S. R. H. Devine, V. O’Shea, and K. Smith are with the Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, U.K. P. Berglund is with Low Temperature Laboratory, Helsinki University of Technology, FI-02150 Espoo, Finland. J. Bol, W. de Boer, A. Dierlamn, E. Grigoriev, F. Hauler, and L. Jungermann are with IEKP University of Karlsruhe, D-76128 Karlsruhe, Germany. K. Borer and S. Janos are with LHEP, University of Bern, CH-3012 Bern, Switzerland. S. Buontempo and N. D’Ambrosio are with I.N.F.N. Sezione di Napoli, I-80126 Napoli, Italy. L. Casagrande, C. Lourenço, T. O. Niinikoski, and V. G. Palmieri are with CERN, CH-1211 Geneva, Switzerland. S. Chapuy and Z. Dimcovski are with the Department de Radiologie, Univer- sité de Geneve, CH-1211 Geneva, Switzerland. V. Cindro, M. Mikuz, and M. Zavrtanik are with the Experimental Particle Physics Department, Joˇ zef Stefan Institute, SI-1001 Ljubljana, Slovenia. C. Da Viá is with Brunel University, Uxbridge, Middlesex UB8 3PH, U.K. B. Dezillie was with Brookhaven National Laboratory, Upton, NY 11973-5000 USA. She is now with CERN, CH-1211 Geneva, Switzerland. A. Esposito, I. Konorov, S. Paul, and L. Schmitt are with Physik Dep. E18, Technische Universität München, D-85748 Garching, Germany. V. Granata is with Brunel University, Uxbridge, Middlesex UB8 3PH, U.K., and with CERN, CH-1211 Geneva, Switzerland. Z. Li is with Brookhaven National Laboratory, Upton, NY 11973-5000 USA. S. Pagano is with I.N.F.N. Sezione di Napoli, I-80126 Napoli, Italy, and with the Istituto di Cibernetica del CNR, Italy. G. Ruggiero is with the Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, U.K., and with CERN, CH-1211 Geneva, Switzerland. Publisher Item Identifier S 0018-9499(02)01832-4. for an earlier proposal of electric field manipulation by free carrier injection. Index Terms—Cryogenic detectors, electric field, injection, radi- ation-induced defects, silicon. I. INTRODUCTION O NE OF the main problems of Si detector applications for high-energy physics (HEP) experiments is associated with detector degradation under irradiation. Numerous investi- gations of this process (see, e.g., [1]) have shown that the degra- dation is caused by the introduction of high concentrations of radiation-induced defects that act as trapping centers with deep energy levels. The main degradation effect is the observed in- crease of the full depletion voltage ( ) with radiation fluence ( ) at a nearly constant rate after space-charge sign inversion (SCSI). Attempts have been made to improve the radiation hard- ness of the silicon material—for example, using oxygen enrich- ment or epitaxial growth of the material [2], [3]. However, en- couraging results were obtained only for detectors irradiated by -rays and charged particles , whereas no such positive effect was revealed for neutron irradiation [2], [4]–[6]. An alternative way to maintain the radiation tolerance may be through the proper choice of the detector mode of operation. It was shown in [7] and [8] that operation at cryogenic tem- peratures of detectors irradiated to high neutron fluences (up to 10 cm ) results in the recovery of the charge collection ef- ficiency (CCE). This CCE recovery, or “Lazarus effect,” studied by the CERN RD39 collaboration, is most pronounced at 140 K. The extent of the CCE recovery depends on both the de- tector bias voltage and the irradiation fluence. Unfortunately, for detectors operating at reverse bias voltages, this positive effect is not stable and the CCE starts to degrade with time [8], [9]. The observed degradation is related to the freezing-out of car- rier detrapping since the accumulation of trapped charge leads to screening of the electric field in the detector space-charge region (SCR). This accumulation of trapped carriers and elec- tric field screening, referred to as the “polarization effect,” was considered in detail in [10] for detectors irradiated by neutrons. One way found to overcome this polarization effect consists of operating the detector with forward bias voltage [8], [9]. The 0018-9499/02$17.00 © 2002 IEEE