Charge Collection and Electrical Characterization of Neutron Irradiated Silicon Pad Detectors for the CMS High Granularity Calorimeter

The replacement of the existing endcap calorimeter in the Compact Muon Solenoid (CMS) detector for the high-luminosity LHC (HL-LHC), scheduled for 2027, will be a high granularity calorimeter. It will provide detailed position, energy, and timing information on electromagnetic and hadronic showers in the immense pileup of the HL-LHC. The High Granularity Calorimeter (HGCAL) will use 120-, 200-, and 300-$\mu\textrm{m}$ thick silicon (Si) pad sensors as the main active material and will sustain 1-MeV neutron equivalent fluences up to about $10^{16}~\textrm{n}_\textrm{eq}\textrm{cm}^{-2}$. In order to address the performance degradation of the Si detectors caused by the intense radiation environment, irradiation campaigns of test diode samples from 8-inch and 6-inch wafers were performed in two reactors. Characterization of the electrical and charge collection properties after irradiation involved both bulk polarities for the three sensor thicknesses. Since the Si sensors will be operated at -30 $^\circ$C to reduce increasing bulk leakage current with fluence, the charge collection investigation of 30 irradiated samples was carried out with the infrared-TCT setup at -30 $^\circ$C. TCAD simulation results at the lower fluences are in close agreement with the experimental results and provide predictions of sensor performance for the fluence regions not covered by the experimental study. All investigated sensors display 60$\%$ or higher charge collection efficiency at their respective highest lifetime fluences when operated at 800 V, and display above 90$\%$ at the lowest fluence, at 600 V. The collected charge close to the fluence of $10^{16}~\textrm{n}_\textrm{eq}\textrm{cm}^{-2}$ exceeds 1 fC at voltages beyond 800 V.


Introduction
Silicon (Si)-based high granularity technology was chosen for replacement of the existing CMS experiment's endcap calorimeter for the era of the high-luminosity Large Hadron Collider (HL-LHC) [1]. The HL-LHC is expected to increase the instantaneous luminosity of LHC by at least a factor of five and deliver an estimated integrated luminosity of 3,000-4,000 fb −1 in 10 years of operation 1 , resulting in maximum integrated doses in excess of 1.5 MGy and neutron fluences of about 1.0 × 10 16 n eq cm −2 that the CMS endcap calorimeters must sustain [2].
The High Granularity Calorimeter (HGCAL) aims to perform 3D-position, energy and time measurements in the endcap region (1.5 ≤ |η| ≤ 3.2). The electromagnetic calorimeter (CE-E) consists of 28 layers of silicon sensors, with Cu, Cu/W, and Pb absorbers. Similar silicon sensor technology is utilized in the high-radiation region of the hadronic calorimeter (CE-H) for the 8 front layers interleaved with steel absorber plates, while the following 14 layers combine silicon sensors, with plastic scintillator readout by silicon photomultipliers (SiPM) in the higher-and lower-η regions, respectively. The approximately 27,000 hexagonal 8-inch silicon modules 2 represent about 6M channels and an area of 600 m 2 . The hexagonal shape of the sensors maximizes the usable area of the circular wafers while remaining tileable. The main properties of the silicon detector channels, along with their expected fluences for the HGCAL, are given in Table 1. The detectors must operate in a high-radiation environment for a decade, while maintaining sufficient signal-tonoise performance for minimum-ionizing particle (MIP) detection. Clean MIP detection in each sensor cell is required to achieve acceptable inter-cell calibration accuracy. Macroscopic radiation damage in the silicon bulk manifests as increase in leakage current, space charge, and trapping of the drifting charge, all of which are detrimental to the performance of a silicon detector [3,4].
The increase of leakage current with fluence will be mitigated by operating the silicon sensors at -30 • C (243 K). In response to the trapping of the drifting charge, thinner sensors will be used at the higher-η (smaller radius) regions of the endcaps, along with high voltage operation (≥ 600 V for heavily-irradiated sensors) and readout at segmented n + electrodes collecting electrons (n-on-p sensors) in all regions. In this study, we discuss experimental and simulation results from the test diodes diced from the full sensor wafers.
The studies of the detector response, which used a sub-nanosecond IR-laser, provide information on 1 https://home.cern/resources/faqs/high-luminosity-lhc 2 The prototyping was done with sensors originating from 6-inch wafers, while 8-inch wafers were chosen to reduce the total number of modules needed for the HGCAL. Table 1: Hexagonal Si sensor cells (DC-coupled planar diodes without biasing structure) in CE-E and CE-H all-silicon layers, showing the properties of different sensor types and the expected 1-MeV equivalent neutron fluence for each type after an estimated integrated luminosity of 3,000-4,000 fb −1 . The upper fluence limits are the current estimates for the highest levels that may be reached, which are somewhat larger than in [2].
The lowest lifetime fluences at the outer radii of each region are roughly equal to the highest fluence of the next region, while in the case of 300-µm thick sensors, it is about 1 × 10 14 n eq cm −2 .
Active thickness [ the carrier transport and electric field distribution in the sensor bulk, which are the input parameters for the long-term prediction of the detector's charge collection efficiency (CCE) with increasing fluence. By complementing observed CCE with leakage current and capacitance measurements, an extensive picture of the macroscopic effects from the microscopic radiation-induced defects in the silicon bulk is obtained that continue to refine guidelines for detector design and operation.
In a previous study [5] with deep-diffused float-zone (dd-FZ) and epitaxial test diodes at -20 • C, the 300-µm-thick n-types were found to collect significantly more charge than the p-type sensors at a fluence of 5 × 10 14 n eq cm −2 , while negligible differences in charge collection between the two sensor types were observed for thinner sensors at their respective expected maximum fluences. Additionally, epitaxial 100-µm active thickness diodes were reported to display substantially better charge collection performance compared to the 120-µm dd-FZ diodes at the fluence of 1.0 × 10 16 n eq cm −2 . The following results complete the study introduced in [6] and address the processes leading to the observations described above. The study involved 30 irradiated test diode samples diced from 8-inch (shallow diffused-FZ and epitaxial) and 6-inch (standard and deep diffused-FZ) wafers.
The experimental results were reproduced with Technology Computer-Aided Design (TCAD) simulations that allow reconstruction of the potential and electric field distributions as well as the charge and current response of the irradiated test diodes within the validated fluence range of the defect model for neutrons [7,8]. In the light of an earlier charge collection study at extreme fluences [9], the investigation of 200-and 300-µm-thick n-on-p sensors is extended beyond their respective maximum lifetime fluences up to about 1 × 10 16 n eq cm −2 . The CCE evolution of the two sensor thicknesses is presented.
The radiation hardness results presented here cover only the bulk properties of the silicon sensor. Investigations of surface properties for the functionality of a multi-channel detector −such as of accumulation of Si/SiO 2 interface charge density with fluence, charge sharing, and inter-electrode capacitances and resistances− are presently ongoing.
The paper is arranged in following order: Section 2 introduces the samples and target fluences involved in the neutron irradiation campaign. Measurement and simulation setups are presented in Section 3. In Section 4, characterization results of irradiated pad sensors are presented by first extracting effective fluences (Φ eff ) from the leakage curret volume density. Next, measured and simulated charge collection results are presented, followed by full depletion voltages (V fd ) extracted from the capacitance-voltage data. Finally, the results are discussed and summarised in Sections 5 and 6.

Samples and target fluences
The irradiation campaigns were carried out in reactors in two facilities, Rhode Island Nuclear Science Since the deep diffusion process used by HPK for reducing the active thickness to 300, 200, and 120 µm, while maintaining the physical thickness to 320 µm, was only applied to the 6-inch wafers, the 8-inch 200and 300-µm-thick sensors have the same physical and active thickness. Three distinct diffusion processes were applied to produce the heavily-doped backplane blocking contact: in 6-inch wafers standard-diffusion ('std-FZ') to produce 300-µm active thickness sensors and deep-diffusion ('dd-FZ') for 200-and 120-µm active thickness, while the 8-inch wafers applied shallow-diffusion ('shd-FZ') for 300-and 200-µm-thick sensors. The only 8-inch wafer sensor in the study with a nominal active thickness of 120 µm was produced by growing epitaxial silicon on a lower resistivity substrate, resulting in a total physical thickness of 300 µm [2]. While the substrate material of both 6-and 8-inch wafers is float-zone Si, the 8-inch wafers have roughly an-order-of-magnitude lower oxygen concentration in the bulk relative to the 6-inch wafers. All the samples in the irradiation campaign are listed in Table 2. The samples are identified in Section 4 by e.g. 'shd-FZ − LO − 300P' that refers to a 300-µm-active thickness float-zone n-on-p type sensor with shallow diffused backplane implant and low oxygen bulk concentration (all varieties are presented in Table 2).
The 16 samples irradiated at the RINSC reactor were exposed at all six fluence levels shown in Table 2.
The facility's dosimetry is based on the activation data of ultrapure foils of several different elements. Neutron flux spectrum of the reactor is extracted by using the known cross section of these elements to interact with neutrons as a function of energy. This measured neutron flux spectrum is then convoluted with the damage function for silicon [10] and integrated to obtain the 1-MeV neutron equivalent flux of φ = (4.0 ± 0.8) × The 14 samples irradiated at the MNRC reactor were exposed to the four highest fluences listed in Table 2.
The first fluence was measured to be 7.37 × 10 14 n eq cm -2 using the fast sulfur activation method. The errors associated with this method are counting uncertainty in measuring the activation of 32 P (< 0.5%), and the small non-uniformity in the flux along the length of the samples which contributes at most 5%.
Since higher fluences would have made the sulfur samples too radioactive, the other three fluences were estimated based on the dosimetry results from the first irradiation. The reactor power levels were increased linearly to reach the higher fluences, resulting in a maximum uncertainty of 5% associated with the sample position, with additional 5% uncertainty associated with the normal power fluctuations in the reactor. When the uncertainties were assumed to be independent, the maximum dosimetry uncertainty expected for the three higher power irradiations was at most 7%.
The dosimetry-determined fluences from both irradiation facilities, along with the target fluences and the leakage current extracted effective fluences, are further discussed in Section 4.1.
After irradiation, the samples were shipped in thermally isolated containers packed with cold gel to Texas Tech University (TTU) to avoid annealing of the radiation induced defects, and were then kept at -40 • C at all times between the measurements.   The test diode is connected to the measurement circuit by a vacuum chuck from its backplane, which also provides fixed position, and by probe needles on the segmented front surface for the diode region and guardring, respectively. A Peltier cooler below the stainless-steel chuck provides cooling while the heat from the Peltier is removed by a closed circuit liquid cooling system. The sample temperature and the humidity inside the cooling box are monitored by a thermocouple and a Vaisala DSS70A dew point meter, respectively.

CV/IV-probestation
Since full depletion voltage (V fd ) has negligible sensitivity to measurement temperature in the studied Trange, the CV -measurements were carried out below +5 • C to suppress leakage current to ≤ 1 mA during Vramping for low power dissipation. Due to high sensitivity of leakage current to the measurement temperature, the temperature during IV -measurements was fixed as closely as possible to +5 • C.

TCT-setup
The infrared-Transient Current Technique (IR-TCT) setup constructed at TTU for the measurement campaign is based on a Particulars commercial system 5  The IR-TCT setup produces well-defined and stable transient signals that can be closely reproduced by simulation, as shown in Figure 3 (simulation parameters are introduced in Section 3.3). The IR-laser mimics a MIP by penetrating the entire thickness of the silicon sensors, thus providing straightforward means for a CCE investigation. A wire-bond connection minimizing the signal path between the sensor and the SMA cable was found to be essential in minimizing signal undershoot and reflections.
The setup utilizes four Peltier coolers to achieve -30 • C sample temperature. As in the CV /IV -setup, to avoid any condensation, N 2 flow was supplied to the sample during cooling. The temperature and humidity monitoring are accomplished by a four-wire resistance temperature detector (RTD) circuit and a Vaisala DSS70A dew point meter, respectively, thus ensuring that all measurements were carried out above dew point temperature.

Simulation setup and parameters
All simulations in this paper were carried out using the Synopsys Sentaurus TM6 finite-element TCAD software framework. The simulations applied Neumann boundary conditions as well as Dirichlet boundary conditions for carrier densities and AC potential at Ohmic contacts that were used to excite the system.
For the simulation of the evolution of electrical properties and charge collection with fluence, the two dimensional structures presented in Figure 4 were applied. The sensor width was set to wide enough to fully contain the generated charge carrier clouds within the structure during the transient simulation, when the laser illumination was performed at the center of the front surface (x = 100, y = 0 in Figure 4a). The simulation was focused at the center part of the test diodes. Due to the large surface areas of the real diodes, any contribution from the edges to the local electric fields at the center were considered negligible, and no edge regions were included in the modeled structures.
The parameters extracted from CV /IV -and TCT-measurements before irradiation (bulk doping, active thickness, charge carrier trapping times, and backplane doping profiles for deep-diffused diodes) were used as an input to reproduce the devices as closely as possible by simulation. Doping profiles of all modeled diodes are presented in Figure 4b.
All modeled sensors were DC-coupled (with no oxide layer between the collecting electrode and Si bulk) as the real devices. High potential was provided from the backplane contact, while the front surface electrode at zero potential was used for charge collection in transient simulations.
As in the experimental setup, an IR-laser of 1.06 µm wavelength and sufficient penetration depth to model a MIP was applied to generate charge carriers in the detector. The laser spot diameter was set to 11 µm and the pulse length to 0.45 ns to match the values used in the IR-TCT setup. The laser intensity was tuned to produce MIP equivalent collected charge (22 ke − in 300 µm of silicon), while generating low enough e-h pair density (about 1100 µm −2 ) to avoid any space charge density current effects that might modify sensor properties during the transient simulation. The bias-T circuit was modeled by including a high-resistance bias circuit and a charge-collection circuit with 50 Ω termination to the DC-and AC-parts of the simulation, respectively.
In heavily-irradiated silicon sensors (between 10 14 to 10 16 n eq cm −2 ), carrier trapping is the main factor reducing the collected charge. To model this in simulation, a neutron defect model [7], validated from 1 × 10 14 n eq cm −2 up to 1 × 10 15 n eq cm −2 and presented in Table 3, was applied. The neutron defect model  was chosen over other models for higher fluences (e.g. [11]) because, at the moment, it is the only model that has been shown to closely reproduce the experimentally observed evolution with fluence of leakage current, full depletion voltage, and double-peak electric field distribution in the Si bulk, as well as charge collection efficiency. Although the model still reproduces expected leakage current well beyond the 1 × 10 15 n eq cm −2 limit over which it has been validated, the effective bulk doping (N eff ) increase with fluence becomes exaggerated, leading to high enough electric fields to generate e-h avalanche that in turn leads to CCE values not in line with experimental observations. All charge collection simulations were carried out at matching temperature (T = 243 K) to the measurements.

Leakage currents and effective fluences
The leakage current (I leak ) measurements of the irradiated samples were carried out at +5 • C up to a voltage of 1.1 kV. The I leak of fully depleted diodes, monitored by CV -measurements and discussed further in Section 4.3, was then used to determine the leakage current volume densities. For the active volumes, the diode area (A) information shown in Figures 1 and 2 was used in combination with active thicknesses (d) extracted from measured geometrical capacitances (C geom = 0 s A/d, where 0 and s are the vacuum permittivity and the relative permittivity of silicon, respectively [12]).
Since current-related damage rate α has been shown to be strictly proportional to the 1-MeV neutron equivalent fluence as well as being independent of the silicon material, it is defined by [13] where ∆I leak is the change in the leakage current due to irradiation, V is the active volume of either por n-type detector, and Φ eff is the 1-MeV neutron equivalent effective fluence. By using Eq. 1, the ∆I leak /V extracted Φ eff was determined by using α(293 K) = 4.0 × 10 −17 A/cm, a value established in previous studies [13,14]. To scale the +5 • C measured leakage currents to room temperature, a method described in [15] was applied. Several diodes were measured, and the final Φ eff was determined as the mean value for all the samples corresponding to a given target fluence at a respective irradiation facility, as shown in Table 2.
The results, along with the fluences determined by the dosimetry of the two irradiation facilities, are presented in Table 4. When Φ dosi values and α(293 K) are inserted into Eq. 1, the resulting expected mean respectively, displaying agreement within uncertainty between data sets.
All the measurements in this and the following sections were taken after about 10 min at 60 • C, which is identical to the approach described in a previous Si sensor radiation hardness study for HGCAL [5]. Additionally, after all samples had been TCT-and CV -characterized, five samples exposed to four different

Extracting CCE from IR-TCT data
To extract the CCE of the irradiated diodes, the IR-laser induced transient currents were first recorded at -30 • C for both the irradiated and non-irradiated-reference samples. This was done to compensate for the observed temperature dependence of the transient-signal amplitudes. The reference and the corresponding irradiated sample were always diced from the same Si wafer to minimize any effect from possible processing differences between the wafers.
Transient currents of the reference diodes were recorded for reverse bias voltages from about 50 V above V fd up to 500 V. The laser spot was focused at the center of the laser window (see Figures 1 and 2) and the light intensity was set as low as possible, while not compromising the stability of the transient signal, to avoid  28 irradiated samples were included in the CCE study. The investigated voltages for the irradiated samples ranged from 400 V to 1 kV and the same analysis methods described above for reference diodes were applied.
The charge collection efficiency was then determined as a ratio CCE = Q coll (irradiated)/Q coll (reference). The RTD-monitored mean temperature throughout all measurements was T = (-30.10±0.13) • C. The CCE results were also converted to the collected charge by considering a MIP-induced charge deposition of 73 e − /µm in silicon [16]. Both are presented in the following section.

300-µm-thick sensors
In Figure 5, the measured results for 300-µm thick diodes also include comparison with TCAD simulated CCE. All expected lifetime fluences for 300-µm thick sensors at HGCAL, from 1 × 10 14 n eq cm −2 to about (5 − 6) × 10 14 n eq cm −2 [2], are within the validated range of the neutron defect model. The simulation closely reproduces both voltage (with input fluences within uncertainty of Φ eff , as shown in Table 5) and Table 5: Sensor identification, IV -extracted effective fluences (Φ eff ) and simulation input fluences (Φ TCAD ) for the CCE results in Figure 5a. Bulk material is indicated as 'shd-' and 'std-FZ' for shallow-and standarddiffused float zone, respectively. High ('HO') and low ('LO') oxygen bulk concentrations correspond to samples diced from 6-and 8-inch wafers, respectively.

200-µm-thick sensors
The The CCE of 200P sensors does better by about 11% and 25% at 800 V and 1 kV, respectively, compared to at 600 V, close to the maximum expected fluence (Φ max ) to which the 200-µm thick sensors will be exposed.
When extrapolated, the simulated CCE for the 200N sensor is consistent with the measured data points for the three voltages in Figure 6b. About 9% and 12% gains in CCE from increasing the voltage to 800 V and 1 kV, respectively, are observed at the fluence of (1.5 ± 0.3) × 10 15 n eq cm −2 .

120-µm-thick sensors
Since the 120-µm-thick sensors will have to operate in a neutron fluence range from about 2.5×10 15 n eq cm −2 to 1 × 10 16 n eq cm −2 , which is well beyond the validated fluence limit of the TCAD neutron defect model, all the curves in Figure 7 are fits to data points.
In Figure 7a, the results from the 8-inch epitaxial 120P sample at the fluence of about 3.5 × 10 15 n eq cm −2 display higher CCE values than the three lower-fluence data sets from the dd-FZ samples. This could be an indication of charge multiplication produced by high electric fields resulting from radiation induced increase in effective bulk doping (N eff ) and needs to be investigated in future studies.
In Figure 7b, the CCEs of both polarity sensors benefit about 20% and 40% due to increased operating voltage from 600 V to 800 V and 1 kV, respectively, at the highest fluence. Both polarities display similar CCE performance at the highest fluences.

Charge collection summary
The measured CCE results for the three sensor thicknesses for the full expected fluence range are shown in Figures 8a, 9a, and 10a, while separating for the operating voltages of 600 V, 800 V, and 1 kV, respectively.
At fluences around Φ max CCE ≥ 60% and over 70% are observed at 800 V and 1 kV, respectively, for all measured sensors, while the same level of CCE performance at corresponding fluences is only seen for 300N sensors operated at 600 V, as marked in Figure 8a. Close to lower lifetime fluence limits expected at the outer radii of each sensor thickness (1 × 10 14 n eq cm −2 for 300 µm, 5 × 10 14 n eq cm −2 for 200 µm and 2.5 × 10 15 n eq cm −2 for 120 µm), operating at 600 V provides high CCE performance.
The corresponding MIP-induced charge deposition results in Figures 8b, 9b, and 10b indicate that the 120-µm-thick sensors close to the fluence of 10 16 n eq cm −2 are able to collect about 3.6 at 600 V, 5.4 at 800 V, and 7.3 ke − at 1 kV of the 9 ke − generated in the silicon bulk.

Charge collection of 300P and 200P sensors at extreme fluences
The CCE results of the six n-on-p samples at neutron fluences up to 10 16 n eq cm −2 are presented in Figure 11. Both the linear voltage dependence and the absolute values of CCE of the two highest fluence 300P sensors in Figure 11a are closely in line with the results of an earlier charge collection study of 300-µm sensors at extreme neutron fluences [9]. Displayed in Figures 11b and 11c, the fluence evolution of the charge collection in 300P sensors can be estimated by second-order polynomial and logarithmic fits below and above the fluence of 1.3 × 10 15 n eq cm −2 , respectively. This agrees with the behavior described in ref. [17] where at higher fluences radiation-induced increase in effective bulk doping generates high enough electric fields to trigger charge multiplication that compensates charge carrier trapping and slows down the degradation of charge collection.
Additionally, the advantageous CCE performance of the 200P sensor in the range (1.5−3.5)×10 15 n eq cm −2 (about 20%, 30%, and 36% higher at 3.5×10 15 n eq cm −2 compared to 300P for 600 V, 800 V, and 1 kV, respectively) diminishes almost completely at the highest fluence in Figure 11b. This is also observed throughout the voltage range of Figure 11a. Similar convergence between sensor thicknesses around 1 × 10 16 n eq cm −2 was reported in an earlier study [18]. The highest fluence CCE and Q coll values in Figures 11b and 11c are presented in Table 6. The results display some differences in Q coll between sensors with high (HO) and low (LO) bulk oxygen content. To investigate further the similar CCE performance of the 200P and 300P sensors at highest neutron fluence, the following relations were considered. The CCE of an irradiated sensor is formulated as a product of two terms, geometrical factor (CCE GF ) and trapping factor (CCE t ) [19,20] where W is the depletion depth, d the active thickness of the sensor, τ t the trapping time constant for electrons or holes, and t dr the carrier drift time in the depletion region. To solve for W from the CCE data would first require to determine τ t . This would demand a short-range charge injection (e.g. red laser), where only one type of charge carriers generate the transient signal. However, when it is considered that the investigated samples were exposed to equal fluence (leading to identical τ t ), the CCE results were acquired at equal bias voltage V , and that the observed carrier drift times were close to equal (mean t dr of the 200P and the two   Figures 11b and 11c, respectively, at the fluence of (9.3 ± 1.1) × 10 15 n eq cm −2 and for 600 and 800 V. 300P diodes at the highest fluence in Figure 11b was 3.7 ± 0.2 ns), leads to the relationship (3) Figure 12 shows the depletion-depth ratios when the CCE(V ) results from Figure 11a  sensors the result indicates that the charge is collected from equal depth in both sensors within uncertainty.
However, the ratio is significantly smaller between low and high oxygen concentration 200P and 300P sensors, respectively. This could suggest a beneficial influence of the higher oxygen concentration on the build-up of negative space [14,21] at extreme fluence, leading to longer depletion depth at given voltage. Trapping times have not been observed to be significantly influenced by the oxygen content after hadron irradiation [15].
Thus, Eq. 3 is expected to be also applicable for comparison between LO and HO sensors.

Full depletion voltages
The fluence evolution of full depletion voltage (V fd ) is presented in Figure 13 with measured and simulated results of 300-and 200-µm-thick diodes in Figures 13a and 13b, respectively, and measured results of 120µm-thick diodes in Figure 13c. The simulated results in the lower-fluence region were produced by applying the neutron defect model using as an input the leakage current extracted Φ eff from Table 4, and frequencies in the range of the measured CV (O(10 4 Hz)). The simulated V fd was extracted both from CV -curve and from the voltage where electric field had extended throughout the active thickness of the sensor. The frequency was tuned until the two results were in agreement.
V fd was defined as the crossing point of the two linear fits made on the dynamic and static regions of the reciprocal capacitance curve, as demonstrated in Figures 14 and 15. Measurements were carried out at frequencies from 20 to 50 kHz, and to take into account the increasing frequency dependence [22,23] of V fd with fluence, the two verifying methods utilized were the aforementioned simulations up to 1×10 15 n eq cm −2 for both sensor polarities and analytical method using parametrized effective bulk doping for n-on-p sensors [17,24]. To reach analytical V fd (Φ eff ), the fluence evolution of effective bulk doping was considered as where g eff is the acceptor creation coefficient with a standard value of 0.02 cm −1 and saturated value of 0.01 cm −1 at high fluences [17,25]. N A (0) and N A (Φ eff ) are the acceptor concentrations before and after irradiation, respectively, and c = 3 × 10 −14 cm 2 [24] is a constant that depends on the initial acceptor concentration and on the type of irradiation. V fd (Φ eff ) is then given by the relation [12] V  Figure 13c, respectively. Additionally, the fluence evolution of V fd above 1×10 15 n eq cm −2 in Figure 13c is logarithmic, with a fit value of (0.33 ± 0.11) ln(x) − (11 ± 4), as opposed to the linear behavior below 1 × 10 15 n eq cm −2 seen in Figure 13a. These observations support the saturating behavior of the acceptor creation mechanism at high fluences, as described in ref. [17].
Also visible in Figure 13a is the effect of SCSI, discussed in Section 4.2.2, in the n-type doped silicon substrate, which results in the decrease of V fd (300N) from 200 V before irradiation to about 40 V at about 1 × 10 14 n eq cm −2 . Thus, the combined information from measured and simulated data suggests that 300N sensors operated at 600 V are fully depleted below the fluence of 5 × 10 14 n eq cm −2 , while the corresponding fluence limit for 300P sensors is below 3 × 10 14 n eq cm −2 . Furthermore, the results indicate that operating at 800 V extends the fluence region where the 300P sensor is still fully depleted at about 4 × 10 14 n eq cm −2 . Figure 13b shows that both polarities of 200-µm-thick sensors are fully depleted at 800 V below a fluence of about 1.5 × 10 15 n eq cm −2 and below about 1 × 10 15 n eq cm −2 at 600 V. At about 3.5 × 10 15 n eq cm −2 , the 120P epitaxial diode is still reaching full depletion at 600 V in Figure 13c.

Discussion
1. The 300N std-FZ(HO) sensor displays better CCE performance to 300P shd-FZ(LO) for a given operating voltage above about 4 × 10 14 n eq cm −2 due to SCSI, which enables it to be fully depleted at significantly lower voltages than the 300P sensor (the 300N sensor is fully depleted at 600 V up to the fluence of about 5 × 10 14 n eq cm −2 , while the 300P sensor is not fully depleted at 800 V above the fluence of about 4 × 10 14 n eq cm −2 ). At the fluence of about 6 × 10 14 n eq cm −2 ∆CCE of (17 ± 2)% in favor of the 300N sensor is observed at 600 and 800 V, and 12% at 1 kV. Similar CCE behavior was observed in the earlier studies [2,5].
2. No clear difference was observed in the CCE performance of 120-µm-thick dd-FZ(HO) diodes between the sensor polarities at the highest fluence, which is also in agreement with the earlier observations [2,5]. One of the main advantages of the n-on-p sensor at fluences above 1 × 10 15 n eq cm −2 is the superposition of the weighting field and the electric field maxima on the segmented side of the planar sensor, while in the p-on-n sensor after SCSI, these are located on the opposite sides of a planar sensor. In strip and pixel sensors used in tracking and vertexing detectors, the effect of the weighting field is optimized by sensor geometry, which favors electron contribution to the signal collected at the n + electrode [9,26], while in the large area pad detectors, the benefit from the weighting field (simply the inverse of the sensor thickness 1/d [27]) is minimal, leading to negligible differences in CCE performances between sensor types at high fluences.
3. The slowing down of the degradation of charge collection of 300P-sensors at fluences above 1 × 10 15 n eq cm −2 in Figures 11b and 11c can be interpreted as a result of charge multiplication (CM) that compensates charge carrier trapping [17]. Since CM is a function of electric field, it's effect is expected to be more pronounced in thinner sensors that have higher electric fields for a given bias voltage during charge collection. Thus, higher influence of CM could explain the previously reported [5] better charge collection performance of epitaxial 100-µm active thickness diodes relative to the 120-µm dd-FZ diodes at the fluence of 1.0 × 10 16 n eq cm −2 .
4. TCAD simulation tuning with input from CV /IV -measurements before irradiation and IR-TCT parameters resulted in closely reproduced transient signal shapes that minimize error sources for modeling of radiation damage in silicon. Further study will need to be conducted to develop a neutron defect  model that is able to reproduce all properties of irradiated silicon sensors observed in this and previous studies in the fluence range of (0.1 − 1) × 10 16 n eq cm −2 .

Summary
After neutron irradiation campaigns at RINSC and MNRC, the electrical characterization of 12 and 18 irradiated samples diced from 8-inch and 6-inch wafers, respectively, was completed and the most probable effective fluences were extracted from the leakage currents above V fd . The results of the CCE study of test diodes at -30 • C and for operating voltages of 600, 800, and 1000 V, along with the results of the electrical properties, indicate the following: • For 300-µm-thick sensors: -TCAD simulation verifies and complements the CCE results from the IR-TCT measurements.
-CCEs of both sensor polarities gain about 10% due to increased operating voltage from 600 V to 800 V at highest expected fluences, resulting in CCEs of about 76% and 60% for the 300N and 300P sensors, respectively. Corresponding gains at 1 kV are 16% and 22%, respectively.
At the lowest lifetime fluence, a CCE of about 96% was observed for both sensor types. The 300N sensor displays better CCE performance compared to the 300P above the fluence of about 4 × 10 14 n eq cm −2 due to SCSI.
-In the fluence range 1 × 10 14 − 1 × 10 16 n eq cm −2 evidence of CM, that slows down the degradation of charge collection performance by compensating charge carrier trapping, was observed at fluences above 1 × 10 15 n eq cm −2 .
• For 200-µm-thick sensors: -The CCE of the 200P increases by about 11% and 25% from operating at 800 V and 1 kV, respectively, instead of 600 V, at the fluence of about 2.5 × 10 15 n eq cm −2 , resulting in CCEs of about 63% and 77%, respectively. At the lowest fluence, a CCE of about 91% is expected from simulation for both sensor types. Furthermore, the CCE performance of 200P sensor displays 16% and 35% improvement from increasing the operating voltage from 600 V to 800 V and 1 kV, respectively, at the fluence of about 3.5 × 10 15 n eq cm −2 , resulting in CCEs of about 60% and 77%, respectively.
-Combined measured, simulated and analytically calculated V fd results suggest that the 200Psensor is not fully depleted at 800 V beyond the fluence of about 1.3 × 10 15 n eq cm −2 , while it can be operated at 600 V fully depleted below the fluence of 1 × 10 15 n eq cm −2 .
• For 120-µm-thick sensors: -The collected charges from a MIP-induced charge deposition close to the fluence of 10 16 n eq cm −2 show values of 0.58 at 600 V, 0.87 at 800 V, and 1.17 fC at 1 kV operating voltage. Thus, the sensors require more than 800 V biasing to collect at least 1 fC from a single-MIP-charge-injection at highest lifetime fluences.
-The CCE performance of both polarity sensors improves by 20% and 40% due to increasing the operating from 600 V to 800 V and 1 kV, respectively, at the fluence of about 9.3×10 15 n eq cm −2 .
At lowest investigated fluences, both sensor types display essentially non-degraded CCE performance.
-Similar CCE performance was observed between sensor types at the highest fluence due to minimal benefit from the weighting field to electron collection in n-on-p pad sensors.
-Combined measured and analytically calculated V fd results suggest that 120P-sensors are not fully depleted at 800 V above the fluence of about 6 × 10 15 n eq cm −2 , while both polarity sensors are fully depleted at 600 V below the lifetime fluence of about 3.5×10 15 n eq cm −2 . Fluence evolution of V fd above 1 × 10 15 n eq cm −2 is logarithmic and shows evidence of the saturation of acceptor creation mechanism above 5 × 10 15 n eq cm −2 .
• CCE analysis suggests that the similar charge collection performance between 200P(LO) and 300P(LO) sensors at the fluence of about (9.3±1.1)×10 15 n eq cm −2 results from close-to-equal depletion regions.
Higher Q coll in 300P(HO) relative to 200P/300P(LO) at equal fluence could be evidence of small benefit to radiation hardness from higher oxygen content in the sensor bulk at extreme neutron fluences.