A New Approach to Enhancing Radiation Hardness in Advanced Nuclear Radiation Detectors Subjected to Fast Neutrons

Abstract

Low-Gain Avalanche Diodes (LGADs) are critical sensors for the ATLAS and CMS timing detectors at the High Luminosity Large Hadron Collider (HL-LHC), offering enhanced timing resolution with gain factors of 20 to 50. However, their radiation tolerance is hindered by the Acceptor Removal Phenomenon (ARP), which deactivates boron in the gain layer, reducing gain below the threshold for accurate timing. This study investigates the radiation hardness of thin, carbon-doped LGAD sensors developed by Brookhaven National Laboratory (BNL) to address ARP-induced limitations. Active dopant profiles in the gain layer, junction, and bulk were measured using a Spreading Resistance Probe (SRP) profilometer, and the effects of annealing and neutron irradiation at fluences of 3 × 10¹⁴, 1 × 10¹⁵, and 3 × 10¹⁵ neq/cm² (1 MeV equivalent) were analyzed. Low carbon dose rates showed minimal improvement due to enhanced deactivation, while higher doses improved radiation hardness, demonstrating a non-linear dose–response relationship. These findings highlight the potential of optimizing gain layers with high carbon doses and low-diffusion boron to extend LGAD lifetimes in high-radiation environments. Future research will refine carbon implantation strategies and explore alternative approaches to further enhance the radiation hardness of LGADs.

1. Introduction

Fast timing detectors are poised to play a pivotal role in the forthcoming upgrades of the ATLAS and CMS experiments at the High Luminosity Large Hadron Collider (HL-LHC). The response time of LGADs is determined by the rapid drift of charge carriers in the thin active layer (~50 µm). Most of the signal arises from multiplied holes moving toward the sensor’s back, with saturated drift velocities enabling electrons to drift in ~500 ps and holes in ~700 ps, resulting in a total drift time of ~1 ns. This ensures excellent timing performance critical for HL-LHC experiments, enabling a timing resolution of <35 ps for unirradiated sensors, increasing to <50 ps under high particle fluences. The fast timing and radiation hardness features of Low-Gain Avalanche Diodes (LGADs) ensure their suitability for precise timing applications in particle physics. However, their performance degradation under high particle fluences presents a significant challenge for their use in future high-energy physics (HEP) experiments like CMS and ATLAS. In these experiments, LGADs will face extreme radiation conditions, with fluences reaching up to 10¹⁵ neq/cm² and doses of several MGy. These conditions lead to a reduction in gain and timing resolution, primarily due to the Acceptor Removal Phenomenon (ARP), which deactivates boron dopants in the gain layer, rendering the gain insufficient for accurate timing resolution. Numerous irradiation campaigns have demonstrated a strong correlation between gain reduction and hadron fluence.

To mitigate ARP effects, two approaches have been explored: (1) replacing boron implants with gallium, which is less prone to complex formation with silicon, and (2) introducing carbon into the gain layer. The latter method enhances radiation hardness by forming Si-C complexes, which trap interstitial silicon and prevent boron deactivation in the gain region. Carbon-doped LGADs exhibit at least twice the radiation resistance compared to non-doped sensors, with minimal impact on performance before irradiation due to carbon’s lack of electrical activity. Importantly, carbon doping does not alter the electric field configuration or carrier drift velocities in the gain layer, ensuring that the fast response time of the sensors, driven by carrier drift in the thin active layer, remains unaffected. Another critical factor in LGAD radiation tolerance is leakage current. In unirradiated devices, the leakage current scales with the gain factor. After irradiation, as gain diminishes, the leakage current stabilizes to levels comparable to those of thicker non-LGAD sensors. To extend detector lifespan, ongoing R&D focuses on optimizing the gain layer using carbon doping and low-diffusion boron implants. Continued efforts in LGAD development aim to address these challenges and improve their performance in high-radiation environments [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15].

To maintain optimal instrument performance, a robust detector development strategy is not just recommended but essential. Neutron interactions with silicon nuclei involve both elastic and inelastic processes. In elastic collisions, the kinetic energy of the incident neutron is shared between the recoiling silicon nucleus and the neutron, governed by two-body kinematics. The recoiling silicon nucleus, being a charged particle, can be detected. Based on elastic collision dynamics, up to 13% of the neutron’s incident energy can be transferred to the silicon nucleus. In contrast, inelastic collisions occur when the resulting nucleus differs structurally or energetically from the target nucleus before the reaction. These interactions can result in the excitation or fragmentation of the silicon nucleus, altering its internal state or composition. Understanding these processes is critical for optimizing detector performance under high neutron fluence environments, as they directly impact the material’s radiation tolerance and detection capabilities [3,4,10,16,17,18,19,20,21,22,23].

This chapter summarizes the key features of the carbon-doped LGAD devices under investigation and presents findings from recent R&D efforts aimed at developing advanced LGAD technologies. The focus is on their static performance and radiation hardness, evaluated through standardized and reliable methodologies. The results include insights into static characterizations, the microstructural mechanisms underlying performance degradation, and the dopant deactivation processes observed in carbon-doped LGADs. These experiments were conducted at multiple facilities, including the Microelectronic Systems Laboratory at the University of Trento, CERN, CNR-IMM, and Brookhaven National Laboratory (BNL).

2. Devices Under Test

LGAD detectors, known for their exceptional radiation hardness and fast timing capabilities, are considered essential technology for the 4D trackers required in the HL-LHC runs. These detectors can theoretically be achieved by modifying the doping levels of an Avalanche Photodiode (APD) or incorporating an internal gain mechanism into a PIN silicon photodetector. Internal amplification factors typically range between 5 and 100, which is sufficient to compensate for the low number of signal electrons generated by Minimum Ionizing Particles (MIPs) within a thin active volume. To ensure optimal experimental performance, the gain and bias voltage of the detector under irradiation must be carefully calibrated and stabilized, while mitigating electrical and environmental factors that degrade the device’s time resolution. With a thickness of approximately 50 µm and a pad area of 1.3 × 1.3 mm², LGADs are a proven and promising choice for applications requiring both fast timing precision and radiation hardness. Figure 1 illustrates the schematic of an LGAD structure, based on an n+/p/p−/p+ detector configuration. Designed to operate in a linear mode, this sensor provides an adjustable proportional response to deposited energy. The internal gain, achieved through the impact ionization technique, enhances the detection of low-energy particles and X-rays with an improved signal-to-noise ratio (SNR). Thin LGADs offer a wide spectral range, improved collection efficiency, and heightened sensitivity. These detectors exhibit comparable performance before and after irradiation, lower incremental power consumption, and reduced ionization-induced damage in the oxide layer for n-on-p structures. By contrast, PIN diodes in n-on-p configurations have a lower SNR, higher power consumption, and increased ionization damage. As depicted in Figure 1, the n-type electrode typically extends about 1 µm into the bulk, with a peak doping concentration in the order of 10¹⁹ cm⁻³. In comparison, the p-type gain layer penetrates approximately 4 µm into the bulk, with a peak doping concentration of around 10¹⁶ cm⁻³ [1,2,3,4,5,6,7,8,9,10,18].

In the experiments described in this research, one of the standard configurations manufactured by BNL was used as the object of study. This work leveraged specific fabrication technologies developed at BNL for the detection of Minimum Ionizing Particles (MIPs). The sensors feature a p-type epitaxial layer that is 50 µm thick, with a doping concentration of approximately 5 × 10¹³ cm⁻³. The developed sensors include single-pad LGADs with dimensions of 1 × 1 mm², 2 × 2 mm², and 3 × 3 mm², all utilizing identical terminal structures. Additionally, arrays of pads with these dimensions were produced, aligning with future research objectives. For reference, groups of standard diodes of the same dimensions, but without gain, were also included in the study. To ensure the quality of the fabrication process, standard test structures were incorporated to assess batch quality and reproducibility across different production batches. Figure 2 illustrates a selection of these fabricated sensors.

3. Neutron Irradiation at JSI

The LGADs were subjected to unbiased irradiation at fluences ranging from 4 × 10¹⁴ neq/cm² to 4 × 10¹⁵ neq/cm² at the Jožef Stefan Institute (JSI) TRIGA research reactor in Ljubljana. This reactor has been successfully utilized for decades in the development of radiation-hard sensors. The neutron energy and flux were precisely characterized, and the fluence was expressed in terms of 1 MeV equivalent neutrons per cm² (neq/cm²) using the Non-Ionizing Energy Loss (NIEL) scaling factor. After irradiation, the devices underwent annealing for 80 min at 60 °C. To prevent further annealing, the devices were subsequently stored at −20 °C in cold storage [3].

4. Study of Static Characteristics

Static characterization is a widely used method for qualifying semiconductor devices and multilayered structures. It involves I–V and C–V measurements performed inside a probe station in the absence of external particles, allowing for comprehensive testing and characterization of electronic devices while providing valuable information about the detector type. Additionally, deviations in these plots often reveal faults that occur during the production process. For fast timing detectors, the gain layer properties can be analyzed by examining full depletion voltages and their exponential behaviors. Electrical measurements, such as I–V and C–V characteristics, offer insights into critical device properties, including breakdown voltage (VBD), full depletion voltage (VFD), gain layer voltage (VGL), leakage current (Id), capacitance (C), transition region, and thickness. These properties can be directly derived from I–V and C–V results or indirectly deduced using information obtained from C–V tests and the following formula (Equation (1)):

$${\mathrm{N}}_{\mathrm{c}}\left(\mathrm{x}\right)=-{\displaystyle \frac{{\mathrm{C}\left(\mathrm{V}\right)}^3}{{\mathsf{ϵ}}_{\mathrm{S}\mathrm{i}}·\mathrm{q}·{\mathrm{A}}^2·\frac{\mathrm{d}\mathrm{C}\left(\mathrm{V}\right)}{\mathrm{d}\mathrm{V}}}}\mathrm{d}={\displaystyle \frac{{\mathsf{ϵ}}_{\mathrm{S}\mathrm{i}}·\mathrm{A}}{\mathrm{C}\left(\mathrm{V}\right)}}$$

(1)

In this context, N_c(x), d, A, ϵ_Si, and q represent the gain layer doping concentration as a function of device thickness (x), depletion depth at voltage (V), junction area, silicon’s dielectric constant, and the elementary electrical charge, respectively. It is important to note that, due to the presence of a shallow multiplication layer, this method primarily allows for the study of the deepest regions of the doping concentration profile. Given the substrate’s extremely thin thickness compared to the pad dimensions, the objective is to derive an accurate 1-D profile while minimizing edge effects. A probe station, which includes an optical microscope and a chuck, is used to apply a bias voltage to the Device Under Test (DUT) via tungsten–rhenium needle connections held at zero voltage. This setup enables precise I–V and C–V measurements. Figure 3 illustrates a schematic overview of the I–V and C–V setup, highlighting the concepts based on a probe station [1,2,3,4,5,6,7,8,9,10,18].

Measurements for this campaign were conducted on a variety of sensors, culminating in a comprehensive comparison of unirradiated and irradiated carbon-doped sensors to evaluate the performance across different batches fabricated by BNL. Two measurement setups, based at the University of Trento (UniTN) and CERN, were utilized to characterize fast timing detectors under development for this purpose, as illustrated in Figure 4. These tests provided critical data for extracting key parameters such as the breakdown voltage and doping profile of the devices. Figure 5 shows an example connection from a relevant campaign. In the setup, the pad is represented by the central circle, while the ground connection is made to one of the rectangular contacts at the edges. A vacuum system secures the sensors in place during measurements, which are controlled using LabVIEW software (version 20.1.0f1). To prevent sensor damage due to high currents during breakdown, the maximum applied voltage, the number of increment steps, and the compliance current were carefully preset.

A wide range of sensors was studied in this research, and the comprehensive results are presented in the following sections. The figures summarize the performance of all single-pad sensors that were measured, highlighting the near-identical characteristics of sensors of the same type. These evaluations were conducted at room temperature, focusing on the measured leakage currents (Id) of various prototypes, which allowed for precise differentiation between the detectors under test. The characteristics of LGADs and PIN diodes were also compared. Under reverse polarization, a standard detector follows the Shockley diode equation, reaching a temperature-dependent plateau value that remains stable until the breakdown voltage (VBD) is reached. In contrast, LGADs exhibit an exponential behavior beyond a specific voltage due to the implanted gain layer. Additionally, the perimeter designs of LGADs significantly influence their I–V characteristics. For instance, the breakdown voltage (VBD) of a BNL LGAD was measured to be approximately −400 V.

The gain layer depletion voltage (VGL) and saturation capacitance (VFD) of the BNL sensors were determined from the C–V characteristics measured on the same prototypes (Figure 6). Additionally, from the measured C–V, the doping profile distribution of the gain region was extracted according to Formula (1) (Figure 7). In the LGADs, capacitance showed a pronounced reduction at a few tens of volts, which was proportional to the active doping concentration, the square of the gain implant width, and the gain implant depth. This reduction point determines VGL. Conversely, VFD was identified as the voltage at which the capacitance stabilized, with the VFD-VGL difference corresponding to the bulk depletion voltage (Vbulk) of the device. These results enabled an evaluation of the uniformity of gain dopants across sensors by comparing VGL values. For the BNL sensors, the gain layer doping concentration was approximately 1 × 10¹⁶ cm⁻³, with VGL and VFD ranging from 15 to 18 V and 18 to 28 V, respectively, as the reverse bias voltages. The figures present full depletion voltage regions for the devices prior to irradiation, clearly distinguishing LGADs from standard diodes without gain.

The data reveal that capacitance is higher at low applied voltage values because the gain layer remains undepleted within these bias ranges. In the C–V graph, a distinct “foot” is observed at higher bias voltages, where capacitance values rapidly decline. This occurs as the depletion zone extends into the less-doped epitaxial layer shortly after the complete depletion of the multiplication layer. In the extrapolated graphs, higher voltage values of the “foot” indicate a higher dose of the implanted gain layer in the BNL sensors. The graphs suggest that a portion of the boron does not contribute to the formation of the electric field or the multiplication mechanism, assuming a symmetric distribution of the doping concentration relative to the peak. This transition also reflects the high quality of the oxide and its surface. The gain layer depletion voltage VGL determines the overall boron implantation dose, making its measurement critical. To achieve greater precision, finer voltage steps were employed for parameter extraction. All BNL sensors exhibited reasonable homogeneity in their C–V characteristics, underscoring the consistency of their fabrication.

5. Profile Deactivation Analysis of Carbon-Doped BNL-LGADs

In this section, the microstructural mechanisms contributing to the degradation of BNL-LGADs are investigated to better understand the effects of neutron irradiation at varied fluences on device performance. The study followed these key steps:

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Sample implantation to create the p+/epi junction;

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Annealing to activate the junction;

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Irradiation to evaluate whether degradation is caused by p++ deactivation, using a Spreading Resistance Probe (SRP) profilometer to assess the active dopant profiles in the gain layer (p+/p− or p+/n− junction).

Table 1. Implantation condition.

Item	Qty	Species	Dose Rate (cm−2)	Energy (keV)	Angle (°)	Description
1	4	Boron (B)	3 × 1012	343	7	p+/epi junction
2	1	Carbon (12C)	3 × 1012	400	7	Co-implantation 1
3	1	Carbon (12C)	3 × 1013	400	7	Co-implantation 2
4	1	Carbon (12C)	9 × 1012	400	7	Co-implantation 3
5	1	Boron (B)	Setup Charge	343	---	Calibration setup
6	1	Carbon (12C)	Setup Charge	400	---	Calibration setup
7	4	---	---	---	---	Mounting charge

summarizes the implantation conditions, including dose rates and energies. Boron implantation was used as the baseline, followed by co-implantations of boron and carbon at three different carbon dose rates.

The deactivation study of BNL-LGADs was conducted using a qualified SSM150 Spreading Resistance Probe (SRP) system. This investigation focused on comparing the active regions of carbon-doped LGADs with conventional LGADs, rather than analyzing entire devices.

Figure 8 illustrates the schematic representation of the Spreading Resistance Profiling technique. A small voltage of 5 mV was applied between two metallic probes to measure charge carrier distributions as a function of depth. Depth information was obtained by progressively stepping the probes along the beveled surface of the sample. During the measurements, a resistance profile was generated, which was then computed and converted into resistivity and carrier concentration using calibration curves, mobility parameters for monocrystalline silicon, and specific algorithms that account for sampling volume effects in ultra-shallow profiles.

Figure 9 shows the experimental calibration curves used to quantify the measured data. Reference samples with the same crystallographic orientation and known resistivity were precisely diamond-ground and analyzed for this purpose. The Thurber plot, which incorporates charge carrier mobility in monocrystalline silicon, was employed in subsequent stages. After multilayer analysis calculations, which correct for field effects from underlying layers, the final carrier concentration distributions were extrapolated.

The probes used in these measurements must meet stringent requirements to optimize both noise reduction and sensitivity. This necessitates the use of low-penetration, non-rectifying probes with suitable I–V characteristics, particularly for structures with thicknesses of 100 nm or less. Furthermore, proper sample preparation is essential for accurate profile analysis. During diamond grinding, the silicon surface must be carefully protected, and the bevel edge must be a distinct, sharp line. The primary objective is to achieve a smooth surface finish that minimizes measurement noise and provides a well-defined bevel edge, enabling accurate identification of the profile’s starting point. To achieve this, a high-quality diamond compound is applied to a slowly rotating frosted glass plate during the grinding process.

The sensors were independently irradiated at the Jožef Stefan Institute (JSI) TRIGA research reactor in Ljubljana, which has a long history of contributing to sensor radiation hardness advancements. The dedicated information is provided in Section 3.

6. Outcomes of the Study on Carbon-Doped BNL Detectors

This section presents the results of the carbon-doped BNL sensor investigation in two parts: first, the deactivation analysis of the detectors, and second, the main findings from the C–V characterizations of the same devices. For the deactivation analysis, the as-grown epitaxial layer was examined in ion-implanted and neutron-irradiated samples. Figure 10 illustrates the carrier concentration and resistivity profiles of the grown wafer as a function of depth, based on SRP analysis, revealing the pre-irradiation active profiles. The presence of a depletion layer approximately 45 µm before the p-type substrate indicates that the grown material is n-type. In the flattest portion of the grown region, the carrier concentration is slightly below 10¹⁴/cm³, while the resistivity averages around 60 Ω·cm.

Prior to neutron irradiation and during the co-implantation process of B and C ions, the electrical activation of implanted B ions (reference) was studied on this substrate. Figure 11 provides a comprehensive overview of the initial results obtained in the SRP laboratory. This pre-irradiation measurement examines the junction using the active profiles derived from Spreading Resistance Profiling (SRP). The figure displays the pre-irradiation active profiles evaluated through SRP analysis, showing a p− substrate doping concentration of less than 10¹⁴ cm⁻³ (p− < 10¹⁴ cm⁻³) with a thickness of approximately 45 µm. Boron appears to be fully activated following annealing, as evidenced by the formation of a p+pp− junction. While this is not the actual junction, it provides insight into the boron deactivation process. During implantation, significant deactivation of boron occurs, with the epitaxial layer plateau representing a micron in depth. After annealing, activation occurs, and the junction forms.

The results also indicate that carbon has minimal impact on the deactivation mechanism, showing only minor deactivation at the highest carbon dose. However, carbon cannot be detected via the spreading method, as SRP analysis reveals only active profiles, not chemical profiles. Notably, observing deactivation prior to irradiation offers valuable insights.

The as-implanted doping profiles (dashed lines) reveal significant deactivation within the first micron of the epitaxial layer, primarily due to extensive damage to the silicon crystalline structure. Since the total implanted dose and implantation energy are closely tied to this process, the reference boron (B) profile highlights the shallowest damaged region. A long deactivation tail is also observed, where the presence of carbon (C) ions appears to mitigate deeper deactivation as the implanted dose increases. Following furnace annealing, these deactivation effects are fully resolved, and the electrical activation of the introduced boron dopants is restored. The deactivated epitaxial level is completely recovered, with an electrical junction forming at approximately 1 µm depth. With a measurement uncertainty of less than 10%, the charge carrier concentration distributions are consistent in both shape and active dopant fraction. Only the highest carbon dose shows a slightly reduced activation efficiency.

The second set of measurements focused on the deactivation of previously analyzed materials after neutron irradiation. Carrier profiles, grouped by neutron-equivalent dose, are shown in Figure 11. It was anticipated that irradiated particles would affect the boron (B) profiles in terms of electrical activation, potentially benefiting from B-C interactions. However, the peak levels of the B distributions remained relatively constant following irradiation at low and medium neutron doses. The results are presented in Figure 12, Figure 13 and Figure 14, corresponding to the deactivation processes in the boron gain region, the p+/p− junction, and the sensor bulk, respectively.

An exception was observed with co-implantation at the lowest carbon (C) dose, where significant deactivation occurred at the peak. The case with the highest neutron dose, however, exhibited distinctly different behavior. Across all doping conditions, a detrimental effect on both the electrical activation and the profile shape of the implanted B ions was observed. Additionally, neutron irradiation revealed an unexpected phenomenon: the electrical junction lost its characteristic reverse cusp shape. Charge carrier distributions indicated a highly depleted region, suggesting the epitaxial level had vanished, at least within the first few microns of depth.

Further investigations were conducted to clarify these results. To explore greater depths, two samples irradiated at the lowest neutron dose were examined with lower resolution. As shown in Figure 14, the charge carrier profiles of the epitaxial layers were studied. In comparison to the as-grown sample, both irradiation processes led to complete dopant deactivation, extending down to the substrate.

The first plot corresponds to the reference sample, which contains boron (B) and is subjected to varying doses of neutron irradiation. From dose rates A to C, deactivation progressively increases. At the lowest dose, the profile remains relatively active. However, as the total particle dose increases, so does the deactivation. The lowest carbon (C) dose, which is comparable to the B dose rate, shows minimal effect and is therefore not a beneficial dose rate. In contrast, the intermediate carbon dose appears advantageous for enhancing the radiation hardness of the device. At the maximum dose rate, significant deactivation is observed, indicating a non-linear relationship in the opposite direction.

The global analysis highlights that, as neutron irradiation dose rates increase, deactivation becomes more pronounced in scenarios without carbon. It can be inferred that carbon remains positioned similarly to boron within the structure. In general, low carbon doses offer no benefit, as they lead to greater deactivation. However, higher carbon doses, particularly at intermediate levels, show favorable effects, improving radiation hardness.

Figure 14 demonstrates that neutron irradiation significantly impacts the p+/p− junction, resulting in its disappearance in most cases. Ultimately, carbon was shown to enhance the radiation hardness of LGADs by capturing silicon interstitials that would otherwise deactivate boron in the multiplication region. Additionally, since carbon is electrically inactive, it does not affect sensor performance prior to irradiation.

7. Conclusions

The high-radiation environment of the HL-LHC presents unparalleled challenges for detector performance, far surpassing the intensity encountered in space. As CERN prepares for higher particle fluxes, Low-Gain Avalanche Diodes (LGADs) with approximately 50 µm thicknesses emerge as a pivotal technology for their exceptional timing precision and radiation hardness, making them indispensable for the ATLAS and CMS experiments. However, maintaining LGAD performance, particularly the integrity of the internal gain layer, demands extensive evaluation under these extreme conditions.

This study investigated the radiation hardness of carbon-doped BNL LGADs, focusing on the deactivation mechanisms caused by neutron irradiation. Comprehensive analyses of C–V characteristics, active dopant profiles, and deactivation processes revealed that carbon implantation plays a critical role in mitigating radiation-induced damage. Intermediate carbon doses were found to significantly enhance radiation hardness, reducing the deactivation of boron in the gain layer by capturing silicon interstitials. In contrast, higher carbon doses resulted in non-linear deactivation effects, while lower doses offered limited benefits. Additionally, complete substrate deactivation at depths of approximately 10 µm indicated the presence of complex degradation mechanisms extending beyond the gain layer.

These findings underscore the importance of optimizing carbon implantation strategies to achieve durable LGAD performance in high-radiation environments. By fine-tuning implantation parameters and leveraging the advantages of carbon doping, LGAD technology can be further developed to meet the stringent demands of next-generation particle physics experiments at the HL-LHC.