Temperature dependence of reverse annealing in bulk damaged silicon

A recent proposal [1] has suggested a model for the operation of silicon detectors which should give rise to the suppression of reverse annealing after neutron irradiation. The results of an experiment to investigate that model, in which the silicon is cooled during irradiations and annealed at high temperature between irradiations, are presented.


Introduction
The unprecedented levels of radiation expected at the Large Hadron Collider (LHC) will provide a challenging environment for the operation of silicon detectors. Studies of the eects of bulk damage in high-resistivity silicon incurred by neutron irradiations comparable to those expected during the lifetime of the LHC have been performed independently by several experiments [2]. Increased leakage currents and decreased charge collection eciency are observed due to the creation by lattice defects of additional energy levels in the silicon band gap. The other signicant eect is the removal of donor states and creation of acceptor states within the silicon bulk, eventually leading to a conversion of the bulk from n-type to p-type. Of primary concern is the mechanism of reverse annealing of the eective doping concentration, N eff . Once conversion from n-type to p-type has ocurred, the number of acceptor states, and therefore N eff , continues to increase even after the irradiation has ceased. The voltage required to maintain full depletion of the detector therefore increases, possibly to a level sucient to initiate breakdown within the detector. Suppression of the reverse annealing of N eff would therefore signicantly enhance the survivability of silicon detectors at the LHC.

A Model for Reverse Annealing of N ef f
Recent studies [3] h a v e suggested the dependence of N eff on neutron uence, , follows: where N D0 and N A0 are the initial concentrations of donor and acceptor states respectively. The parameter c characterises the rate of donor removal, and b characterises the creation of radiation induced acceptor states. The parameter b can be further expressed as b = b s + b n R(t; T ) where b s refers to the number of stable acceptor states produced, and b n refers to the number of initially neutral defects that subsequently produce acceptor states through reverse annealing. In this simple model, the dependence of N eff on time after irradiation (t) and temperature (T) i s d u e to the function R only, where R = 0 a t t = 0, rising to R 1 when t is very large. R has been shown experimentally to have a strong dependence on temperature. Signicant reverse annealing is observed at room temperature, even after several months of anneal time. Reverse annealing appears to be suppressed at low temperatures (0 C), but resumes quickly should the temperature increase.
A model [1] for the operation of silicon detectors has recently been proposed which w ould suppress reverse annealing without the requirement to maintain the detectors at low temperatures throughout the lifetime of the LHC. The model requires the silicon detectors to be operated at high temperatures; defects generated by bulk damage then diuse to the surface, where they are expected to lose their properties. However, high leakage currents would make this method of operation impractical. A best compromise is to run the silicon detectors at low temperature during LHC operation, and perform a high temperature anneal during breaks in the LHC schedule. This cycle of operation would require small integrated doses (210 12 neutrons cm 2 ) b e t w een subsequent high temperature anneals, in order to limit the number of defects and ensure their diusion to the surface.

Experimental Procedure
In this study, ten silicon diodes (see Table 1) were irradiated unbiased every 48 hours at the ISIS neutron spallation source. Each irradiation, of duration 40 minutes, corresponded to a uence 1 of 410 12 n.cm 2 . There were a total of seven irradiations, corresponding to an integrated uence received by each diode of 2.810 13 n.cm 2 . All diodes were cooled to 7 C prior to each irradiation. Between irradiations, half of the diodes were stored at 7 C, and half were stored at 98 C (hereafter referred to as cooled diodes and heated diodes respectively). After the nal irradiation cycle, all diodes were baked at 80 C for a few days in order to promote any further reverse annealing.
The depletion voltage and leakage current for every diode were determined at key stages throughout the experiment, using a Keithly 487 Picoammeter/Volt Source and Hewlett-Packard 4285A and Wayne Kerr 6425B LCR meters to measure the CV and IV characteristics. Capacitance values were measured at 75kHz and 300kHz, and depletion voltages were extracted by straight line extrapolations on the logC-logV curves. After each irradiation, the cooled diodes were measured immediately, whereas the heated diodes were measured after 44 hours at high temperature. During the 80 C bake, all diodes were remeasured after three hours, three days and six days. Diodes were measured within 3 hours of their removal from the oven. Further measurements were taken while the diodes were stored at room temperature after the end of the 80 C bake.

Results
The variation of depletion voltage with uence for the heated and cooled diodes is listed in Tables 2 and  3 respectively. Both heated and cooled diodes clearly exhibit inversion; heated diodes show accelerated reverse annealing with respect to the cooled diodes. Figures 1 and 2 show the variation of N eff with uence for 300m and 200m thick diodes respectively. Fits to the data using the above expression for N eff are superimposed on the gures; parameter values yielded by the ts are listed in Table 4.
Tables 5 and 6 list the variation of depletion voltage for heated and cooled diodes respectively during baking at 80 C and during subsequent storage at room temperature. The corresponding variation in N eff with time for the 300m and 200m thick diodes is shown in Figures 3 and 4 respectively.
During the 80 bake, diodes that had been heated between irradiations showed no signicant variation in N eff , suggesting that the inter-irradiation heating at 98 C w as sucient for N eff to reach saturation. However reverse annealing was observed for the cooled diodes, with N eff close to saturation after 135 hours. Final averaged values for N eff , measured at room temperature one day after the end of the 80 C bake, were 1.30.110 12 cm 3 (1.20.110 12 cm 3 ) for the 300m heated (cooled) diodes, and 1.30.110 12 cm 3 (1.00.110 12 cm 3 ) for the 200m heated (cooled) diodes.
After the 80 C bake, it was noted that N eff had developed a strong dependence on temperature.
Between 80 C and 20 C, the reduction in N eff was 24% for the 300m heated diodes, 13% for the 300m cooled diodes, 15% for the 200m heated diodes, and negligible for the 200m cooled diodes. N eff increased immediately with increasing temperature, but took about 0.5 days to decrease after the temperature was lowered.
Leakage current w as monitored at all stages following the second neutron dose. Current w as measured through the p-side of the diode, with the p-side guard ring held at the same potential. For the cooled samples, at all stages of the irradiation cycle the current-voltage characteristic reached a plateau at depletion corresponding to a damage constant o f 6 10 17 A.cm 1 , in reasonable agreement (allowing for annealing) with previous measurements. During the subsequent reverse annealing at 80 C the characteristic became peaked close to the depletion voltage, exhibiting a sharp fall in diode current, accompanied by a similar increase in guard current. This behaviour was present at all stages in the baked samples, and appears to depend strongly on the diode geometry and proximity t o the edge of the wafer. Although a plateau was still exhibited when probing the n-side we do not have a sucient understanding of this behaviour to draw quantitative conclusions for the leakage current following high temperature treatment.

Conclusions
All diodes irradiated with neutrons in this experiment exhibited both inversion of the silicon from ntype to p-type, and reverse annealing. The evolution of eective doping concentration with uence was described by N eff = N D0 e c N A0 b. Reverse annealing was accelerated for diodes stored at 98 C between irradiations, compared to those stored at 7 C; the dierence was quantied by parameter b. The measured initial doping concentrations, N D0 and N A0 , w ere consistent with expectations, and with the fact that the 300m and 200m diodes were processed from dierent starting material. The rate of donor removal, characterised by parameter c, w as consistent with previous measurements at ISIS [4].
Diodes that had been irradiated and baked at high temperature were observed to develop a strong dependence of N eff on temperature, in agreement with other recent studies [5]. This suggests that a signicant fraction of the radiation-induced acceptor states generated by reverse annealing at high temperature are not electrically active at room temperature. As a consequence of this eect, the value of parameter b (which describes the rate of radiation-induced acceptor state creation) listed in Table 4 for the diodes heated between irradiations may include a contribution from defects which are electrically inactive at room temperature.
A model [1] had predicted that the diusion of radiation induced defects to the surface during high temperature annealing between irradiations may suppress reverse annealing. A re-evaluation [6] of the model predictions according to the conditions of this experiment provisionally suggest a signicant suppression of N eff . H o w ever no such eect was observed in this experiment.      Table 6: Annealing of Cooled Diodes after last Irradiation. All diodes had been stored at 7 C b e t w een irradiations. Note diode E3 was not annealed at high temperature, but stored throughout at 7 C for comparison.