Study of bulk damage of high dose gamma irradiated p-type silicon diodes with various resistivities

The bulk damage of p-type silicon detectors caused by high doses of gamma irradiation has been studied. The study was carried out on three types of n+-in-p silicon diodes with comparable geometries but different initial resistivities. This allowed to determine how different initial parameters of studied samples influence radiation-induced changes in the measured characteristics. The diodes were irradiated by a Cobalt-60 gamma source to total ionizing doses ranging from 0.50 up to 8.28 MGy, and annealed for 80 minutes at 60 °C. The Geant4 toolkit for simulation of the passage of particles through matter was used to simulate the deposited energy homogeneity, to verify the equal distribution of total deposited energies through all the layers of irradiated samples, and to calculate the secondary electron spectra in the irradiation box. The main goal of the study was to characterize the gamma-radiation induced displacement damage by measuring current-voltage characteristics (IV), and the evolution of the full depletion voltage (V FD) with the total ionizing dose, by measuring capacitance-voltage characteristics (CV). It has been observed that the bulk leakage current increases linearly with total ionizing dose, and the damage coefficient depends on the initial resistivity of the silicon diode. The effective doping concentration and therefore V FD significantly decreases with increasing total ionizing dose, before starting to increase again at a specific dose. We assume that this decrease is caused by the effect of acceptor removal. Another noteworthy observation of this study is that the IV and CV measurements of the gamma irradiated diodes do not reveal any annealing effect.


Introduction
Silicon detectors that are used for tracking purposes in large particle accelerator experiments operate in high radiation environments.High particle fluences and ionizing doses introduce defects in the silicon substrate, causing bulk damage, as well as in the SiO 2 insulating layer and the Si-SiO 2 interface, leading to the deterioration of the sensor surface.
The primary cause of bulk damage in the silicon detectors, induced by hadrons or gamma rays with higher energies, is the displacement of the Primary Knock-on Atom (PKA) from its lattice site.The minimum energy required for this process is ≈ 25 eV.Such a single displacement resulting in a pair of a silicon interstitial and a vacancy (Frenkel pair) can be generated by e.g.neutrons or electrons with an energy above 175 eV and 260 keV respectively.For our investigation, silicon samples were irradiated by Cobalt-60 gamma rays.In this case, the displacement damage is caused primarily due to the interaction of Compton electrons with energies of a few hundreds of keV, with the maximum energy of approximately 1 MeV.It is important to note that production of clusters of defects is not possible as the minimum electron energy needed for production of clusters is ≈ 8 MeV and the maximum recoil energy for the Si PKA by Compton electron is only around 140 eV.Consequently, the damage observed in our silicon samples is exclusively attributed to the point defects.
The bulk damage of silicon detectors induced by gamma rays from a Cobalt-60 source was previously studied in detail for n-type bulk [1], revealing an initial drop of the full depletion voltage up to a specific dose of about 2 MGy followed by a subsequent increase of the full depletion voltage up to 9 MGy.This behaviour has been interpreted as a result of the creation of deep acceptor-like defects and donor removal, which lead to a decrease of the initially positive space charge followed by its total compensation at a certain dose, and thereafter to the inversion of the space charge sign.
Given that the vast majority of semiconductor detectors recently developed for experiments to be installed at the High Luminosity LHC use the p-type bulk silicon technology, a detailed study of gamma induced damage of p-type silicon detectors was highly demanded.The first studies performed on p-type silicon samples irradiated by gamma rays up to 3 MGy have shown a clear decrease of the full depletion voltage and effective doping concentration with increasing total ionizing dose [2].
The presented study brought up a goal to study radiation damage of the high resistivity p-type silicon samples irradiated to high total ionizing doses up to 8.28 MGy using a variety of samples with different resistivities.

Sample Characterisation
The study was carried out on three types of n + -in-p float zone silicon diodes with comparable geometries but different initial resistivities.Diodes were produced by three different manufacturers, Centro Nacional de Microelectrónica (CNM), Hamamatsu Photonics (HPK), and Infineon Technologies (IFX).
Initial parameters of the tested samples are listed in table 1.The active volume  of the diode was calculated using known active area , that is an area of the diode bounded by a guard ring, and active thickness  quoted by the manufactureres in diode's specifications.The bulk capacitance of the diode  bulk was estimated as where  denotes the permittivity of Si (1.06•10 12 F/cm).The initial values of full depletion voltage listed in the table 1 were obtained from CV characteristics measured for several unirradiated diodes of each type.The full depletion voltage value allows us to determine the bulk resistivity of the silicon wafer  as where  is the hole mobility.Resistivities  stated in the table 1 correspond to the averaged values calculated using formula 2.2.Initial silicon resistivity  varies for each type of diode but it is similar for HPK and IFX samples.

Irradiation and Geant4 Simulation
The diodes were irradiated by the Cobalt-60 gamma radionuclide source installed at UJP PRAHA a. s. [3] up to the maximum total ionizing dose (TID) of 8.28 MGy.
During the irradiation, diodes were placed in a custom-made charged-particle equilibrium (CPE) box consisting of an outer 1.5mm-thick Pb layer and an inner layer of 1mm-thick Al layer, following the recommendations of ESCC [4].While using the CPE box during the irradiation, the dose enhancement from low-energy scattered radiation is minimised by producing electron equilibrium and a uniform distribution of energy deposited in the individual samples is ensured.In the CPE box, up to 5 silicon diodes were stacked on top of each other.
The dose rate was 160-190 Gy/min in silicon and the dose rate uncertainty was estimated to be less than 5 % within the box.The in-silicon dose rate was calculated from the in-air dose rate measured by a calibrated ionizing chamber under the same conditions as the tested samples.The stated homogeneity of the dose rate field was ensured by using a lead collimator (field homogenizer) in the shape of a truncated cone.The cooling of the samples during irradiation was ensured by using a fan for air ventilation which prevented the temperature from exceeding 35 °C during the entire irradiation.Afterwards, the irradiated samples were immediately stored in a refrigerator at temperatures below -20 °C to prevent any uncontrolled post-irradiation annealing.The passage of Cobalt-60 gamma ray with an average energy of 1.25 MeV through the silicon samples and surrounding materials causes ionization and production of secondary electrons mainly via Compton scattering.The secondary electrons generated in the shielding material (Pb and Al) of the CPE box, that surrounds the silicon samples, are slowed down on their way through the shielding before they reach the inner space of the box and cause displacement damage in the silicon samples.
The Monte Carlo transport code Geant4 was used to simulate the deposited energy homogeneity, to verify the equal distribution of total deposited energy through all the layers of irradiated samples, and to calculate the secondary electron spectra in the CPE box.In the simulation, monoenergetic photons with the energy of 1.25 MeV were emitted isotropically from the source and sent through the lead collimator, as well as through the aluminium and lead layers of the CPE box.The schematic of the irradiation setup geometry implemented in the simulation is shown in figure 1.
The simulation clearly demonstrates that usage of the CPE box for gamma irradiation of studied samples ensures a sufficiently homogeneous distribution of the deposited energy which varies within ± 5 % in the irradiation area.The results of the simulation showed that the maximum energy of the secondary electrons leaving the inner aluminium layer of the CPE box is ≈ 1 MeV.The simulation also demonstrated a reasonably homogeneous distribution of the deposited energy in all the layers of silicon during irradiation in the CPE box.

Experimental Methods and Results
To evaluate the effects of bulk radiation damage induced by gamma rays, all the samples were at first measured before the irradiation to determine their initial parameters.After gamma irradiation, the samples were tested both before and after their annealing for 80 minutes at 60 °C.The measured electrical parameters were the leakage current and bulk capacitance of the diodes as a function of the bias voltage (IV and CV characteristics).
A great care was taken to properly determine the leakage current contributing only to the active volume of the diode by subtracting the parasitic currents contributed by the diode surface.The total current  tot is defined as the sum of the surface current and the bulk leakage current  leak .Only the bulk current flowing through the active volume of the diode, which is bounded by the guard ring, will be noted as the diode leakage current in the following text.The measurement is performed by applying negative bias voltage to the backside of the diode, however the absolute value of bias voltage is used for all discussion in the text of this paper.
The measurements of IV and CV characteristics took place in a controlled environment at the temperature of (20 ± 2) °C and relative humidity () lower than 10 %.In order to be able to compare directly the obtained IV characteristics, the measured bulk leakage currents were normalized to the temperature of +20 °C.

Leakage current
To illustrate the IV characteristics measured on diodes prior to irradiation, figure 2 displays the total and leakage currents of 8 unirradiated HPK diodes.The CNM and IFX diodes that are not shown in this plot exhibited equivalent behavior.The IV characteristics of diodes reveal uniform behavior up to 700 V, the total current is more than 2 times greater than the bulk leakage current.While the saturation of the bulk leakage current at the full depletion voltage  FD is clearly visible, the total currents do not exhibit the same behavior.Instead they increase with the increasing bias voltage  bias .This observation indicates that for the study of bulk damage induced by gamma rays it is very important to separate surface and bulk currents.
Figure 3 shows the IV characteristics of HPK diodes irradiated to various TIDs after their annealing.The CNM and IFX diodes that are not shown in this plot exhibited similar behavior.A general behavior of the leakage current as a function of the bias voltage is equivalent to the IV characteristics of unirradiated diodes -the leakage current is increasing with increasing bias voltage until the full depletion is reached, then it remains constant.An increase of the leakage current of fully depleted irradiated diodes with increasing TID is observed for all 3 types of diodes.A comparison of the bulk leakage current measurements of gamma irradiated n + -in-p diodes performed before and after their annealing indicates that the leakage current remains unchanged with the application of annealing.The IV characteristics measured before annealing are not shown in the plot.The radiation-induced current per active volume of the diode Δ/ is plotted as a function of the TID in figure 4. The quantity Δ is defined as the difference between the leakage current of the fully depleted diode measured after and before its irradiation, measured at 60 V for CNM diodes and at 300 V for HPK and IFX diodes. stands for the volume contributing to the current.The leakage current is normalized to 20 °C and it is measured after the annealing.
In the studied range up to 8 MGy the values of the leakage current obtained for all types of n +in-p silicon diodes show a linear increase with the TID.For the CNM diode, which has the highest bulk resistivity, the change of the leakage current with the delivered TID is faster than for the HPK and IFX diodes, which have much lower resistivities.We can express the relation between Δ/ and TID by the formula where   is the current-related damage coefficient.The obtained values of damage coefficient   for each diode type are listed in table 2.

Conclusions
The bulk damage of high resistivity p-type silicon diodes caused by high doses of gamma irradiation has been studied.The study was carried out on three types of n + -in-p diodes with different initial resistivities but comparable geometries.The diodes were irradiated by a Cobalt-60 gamma source to various TIDs ranging from 0.50 to 8.28 MGy, and annealed for 80 minutes at 60 °C.The main goal of the presented research was to study the gamma radiation-induced displacement damage by analysing obtained current-voltage characteristics and to understand the evolution of the full depletion voltage ( FD ) with TID by measuring capacitance-voltage characteristics of the tested diodes.
It was observed that the bulk leakage current increases linearly with the TID, and the damage coefficient depends on the initial resistivity of the silicon diode.The damage coefficients of the diodes with initial silicon resistivities of ≈ 24, 3.3, and 3.1 kΩ•cm were determined to be 10.20•10 −6 , 6.49•10 −6 , and 6.33•10 −6 A•cm −3 •MGy −1 , respectively.
The effective doping concentration ( eff ), and therefore also the  FD , significantly decreases with the increasing TID, before it starts increasing at a specific TID value.A similar effect was observed in p-type silicon samples irradiated by hadrons [6], where the initial decrease of the full depletion voltage was explained by electrically active boron dopants being deactivated while the sample is irradiated to lower fluences.After being irradiated by hadrons to higher fluences, the samples exhibit a different behavior when affected by other radiation-induced effects.Our study reveals that diodes with higher initial resistivity reach the minimum value of  FD at a lower TID compared to diodes with a lower initial resistivity.
Another important conclusion of this study is that annealing for 80 minutes at 60 °C, typically used for hadron-irradiated silicon sensors, has no effect on the gamma radiation-induced damage in p-type silicon.There are no changes in the full depletion voltage or leakage current values observed after such an annealing.This annealing behavior of gamma-irradiated n + -in-p silicon diodes is quite different from that for hadron-irradiated diodes.The fact that neither the  FD nor the leakage current changes with annealing could originate from predominantly immobile defects.

Figure 1 .
Figure 1.Schematic layout of the irradiation setup geometry used in the Geant4 simulation.

Figure 2 .
Figure 2. Dependence of the bulk leakage current  leak (full circles) and the total reverse current  tot (open circles) of unirradiated HPK diodes on the bias voltage  bias .

Figure 3 .
Figure 3. Bulk leakage current as a function of bias voltage measured for HPK diodes irradiated to various TIDs ranging from 0.5 MGy to 8.28 MGy.All displayed measurements were performed after annealing.

Figure 4 .
Figure 4. Radiation-induced leakage current increase Δ/ as a function of the TID of fully depleted CNM, HPK and IFX diodes.Measured currents are normalized to 20 °C.Diodes are annealed at 60 °C for 80 minutes.

Figure 5 .
Figure 5. CV characteristics of HPK diodes irradiated to various TIDs and measured after annealing at 60 °C for 80 minutes.Data obtained for unirradiated HPK diodes (black lines) is shown for comparison.

Figure 6 .
Figure 6.(a) Dependence of the  FD of irradiated CNM diodes on the delivered TID, measured both before (full marks) and after the standard annealing (open marks).(b) Dependence of the  FD of irradiated HPK and IFX diodes on the delivered TID, measured both before (full marks) and after annealing (open marks).

Table 2 .
The averaged values of the damage coefficient   , initial silicon resistivity  and initial full depletion voltage  FD measured for CNM, HPK, and IFX diodes.The measured values of   indicate that diodes with similar initial resistivities and full depletion voltages (HPK and IFX) show the same level of radiation damage.On the other hand, CNM diodes