Characterization of thin carbonated LGADs after irradiation up to 2.5· 1015 n1 Mev eq./cm2

EXFLU1 is a new batch of radiation-resistant silicon sensors manufactured at Fondazione Bruno Kessler (FBK, Italy). The EXFLU1 sensors utilize thin substrates that remain operable even after extensive irradiation. They incorporate Low-Gain Avalanche Diode (LGAD) technology, enabling internal multiplication of charge carriers to boost the small signal produced by a particle crossing their thin active thicknesses, ranging from 15 to 45 μ m. To address current challenges related to acceptor removal, the EXFLU1 production incorporates improved defect engineering techniques. This includes the so called carbonated LGADs, where carbon doping is implanted alongside boron in the gain layer. This contribution focuses on evaluating the performances of thin sensors with carbonated gain layer from the EXFLU1 production, before and after irradiation up to 2.5· 1015 n1 Mev eq./cm2. The conducted tests involve static and transient characterizations, including I-V and C-V measurements, as well as laser and β-source tests. This work aims to present the state of the art in LGAD sensor technology with a carbonated gain layer and shows the characterization of the most radiation-resistant LGAD sensors produced to date.


Introduction
In recent years, Low-Gain Avalanche Diodes (LGADs) have gained prominence as timing sensors in high-energy physics experiments.The standard LGAD structure consists of an n-in-p design: a  type bulk with a thin  + gain layer beneath the  ++ electrode as illustrated in figure 1 [1].LGADs operate on the principle of controlled avalanche multiplication, a distinctive process where a locally high electric field   ∼ 300 kV/cm within the sensor triggers charge multiplication.This high electric field is contained within a so called gain layer: a thin, highly-doped layer near the sensor's surface.When charge carriers produced by particle interactions with the sensor bulk enter this region during their drift to the collecting electrode, they experience a strong electric field, leading to an avalanche multiplication effect.This significantly enhances the sensor's signal while maintaining low noise levels, thus enabling the operation of thin LGADs ( ≲ 55 μm) for precise timing measurements.
EXFLU1 is a new batch of thin LGAD sensors manufactured at Fondazione Bruno Kessler (FBK, Italy).This work is centered on the most advanced design of the carbonated gain layer included in the EXFLU1 production, aiming to validate its suitability for the production of LGAD sensors capable of delivering robust 4D tracking performance at fluences as high as Φ ≃ 3 • 10 15 n 1 Mev eq./cm 2 .The results also indicate the potential for additional optimization of the doping density and thickness to further enhance radiation resistance.-1 -

Effects of radiation on LGADs
A brief overview of the radiation effects on LGAD sensors is given before detailing the characteristics and test results of EXFLU1 devices.
As with any silicon sensor, radiation damage from charged particles and neutrons manifests as defects in the silicon crystal throughout the whole sensor bulk.These defects behave as acceptor-like energy levels and they lead to a reduction in collected charge efficiency due to trapping effects, an increase in dark current, and, more broadly, a distortion of the electric field profile within the bulk.Additionally, radiation damage leads to an increase in the effective doping density, denoted as  eff .Since the depletion voltage  FD for a sensor with a thickness  is given by operating the irradiated sensor at a higher reverse bias and lower temperature becomes necessary to achieve depletion throughout the entire bulk while keeping the thermal current low.In the formula  ≃ 1.602 • 10 −19 C is the elementary charge and  ≃ 11.7 0 is the permittivity of silicon.It has been observed that radiation damage weakens the charge multiplication mechanism typical of LGAD sensors [2].This phenomenon has been extensively studied in -in- LGADs ( bulk,  + gain layer, and  ++ collecting electrode) and is explained as a radiation-induced transformation of electrically active dopant atoms into neutral defect complexes, a mechanism referred to as acceptor removal [3].The removal by irradiation has been measured using different initial acceptor densities,  A (0).The effective doping concentration is exponentially dependent on the irradiation fluence Φ: Here,  A represents the acceptor removal coefficient, which depends on the initial concentration.A higher initial concentration  A (0) results in slower acceptor removal (lower  A ), reducing the probability of experiencing removal under irradiation.
The challenge towards a radiation resistant LGAD design has been effectively addressed through a long R&D process, including the implementation of carbon enrichment in the gain layer [2].FBK has developed two distinct processes for activating the gain layer enriched with carbon: CBL, where thermal activation with low thermal load follows both carbon and boron implantation, and CHBL, where an additional thermal activation step with high diffusion is introduced between the carbon and boron implantations [4].Past measurements indicate that CBL implants have superior effectiveness in mitigating the acceptor removal effect [2].
In general, the decrease in multiplication can be mitigated by increasing the external bias.However, when sensors are exposed to a high energy particle beam while their bulk electric field exceeds   ≳ 11 V/μm, a rare and destructive event can occur.Current understanding suggests that in such events an excessive amount of charge is generated within the sensor and this supposedly leads to a destructively large and sudden current flow which renders the sensor irreversibly inoperable.This phenomenon is referred to as Single Event Burnout (SEB), and it poses a limitation on freely increasing the bias voltage to restore the gain of irradiated sensors.Recent results on thin LGADs, however, show that the threshold electric field for SEB is higher for thinner sensors and reaches   ≳ 15 V/μm for 15 μm thick LGADs [5].

Characteristics of EXFLU1 devices under test
The key characteristics of the sensors featured in this contribution, part of the EXFLU1 production, are summarized in table 1.The active thicknesses span from 15 μm for wafer 18 to 45 μm for wafer 1, which aligns with the standard for LGADs for timing applications.The EXFLU1 sensors' thin active volume facilitates depletion even under severe irradiation.These sensors also incorporate FBK's state-of-the-art carbon-enriched gain layer.The geometry of the wafer and the device under test are illustrated in figure 2. The test structure consists of two identical pads: one with the gain layer implant (LGAD) and the other without, essentially a standard PIN diode.This configuration enables the study of gain and minimizes most systematic errors.The samples underwent neutron irradiation at the research reactor center of the Jožef Stefan Institute in Ljubljana, Slovenia, at fluence points of 4 • 10 14 , 8 • 10 14 , 1.5 • 10 15 , and 2.5 • 10 15 n 1 Mev eq./cm 2 .The samples were annealed for 80 minutes at 60 • C before the measurements.

Sensor characterization
Sensor characterization involves both static and transient measurements.The static measurements examine the operational points of the sensor by assessing the inverse current  and sensor capacitance  as a function of the applied reverse bias .These tests evaluate the overall quality of the production and allow for the determination of the gain layer depletion voltage  GL and bulk depletion voltage  FD .
-3 -Monitoring the degradation of these values as a function of irradiation serves as a metric for assessing the radiation resistance of the sensors.These measurements are conducted using a probe station (figure 3, top), with the sensor placed on a temperature-controlled chuck, and electrical connection made via needles contacting metal pads on the sensor surface.
The transient characterization (setup in figure 3, bottom) investigates the sensor response, i.e. the signal it generates, when exposed to a stimulus, simulating conditions similar to when it is struck by a particle.A short-pulse infrared laser ( = 1064 nm), focused tightly within the optical window of the sensor, releases energy and consequently charges throughout the sensor thickness.Although this process is more uniform and controllable, it is not too dissimilar from the interaction with a passing particle.
Recording the statistical properties of the signal produced by a sensor when exposed to a -source can also offer insights into its performance.The conditions of this test closely resemble the final operation of the sensor, as in a high-energy physics experiment.-4 - The capacitance measurements were conducted at  = 20 • C and at a frequency between 1 − 2 kHz, determined from a preliminary measurement of the capacity versus frequency (C-f) for each sensor [4].Plotting  −2 () facilitates a more straightforward interpretation of the measurement due to the sharper features of its curve.These curves are shown in figure 6 The gain layer depletion voltage  GL is determined by identifying the voltage point at which the capacitance value starts to rapidly decrease, corresponding to an increase in  −2 (), indicating the onset of rapid depletion in the low-doped sensor bulk.The chosen algorithm for extracting  GL involves intersecting two linear fits of the curve, as depicted in figure 5. Since  GL ∝   , the relation in equation (1.2) also holds for  GL .The resulting  GL (Φ) curves, one per wafer (see table 1), are fitted using an exponential function and the acceptor removal coefficient values are extracted: (2.1)

I-V and C-V measurements
These values are the lowest measured so far for comparable LGAD devices, as shown in figure 7. -5 -  -6 -

Transient laser stimulation
The transient current technique (TCT) involves directing pulsed laser beams onto the optical window of the sensor, while maintaining the entire setup at a cooled temperature of  ≃ −13 • C. The laser intensity is tuned to achieve an amount of released charge in the sensor approximately 4-5 times greater than the most probable value (MPV) of the charge produced by a minimum ionizing particle (MIP) in the same sensor [6].This specific intensity ensures an enhanced signal for improved measurements while avoiding excessively high charge release, which could potentially lead to screening effects.The LGAD-PIN test device is installed in a custom readout PCB, its signal is then amplified by a 40 dB, 2 GHz Cividec amplifier working in current mode, and is recorded and measured by a Lecroy WaveRunner 8000HD oscilloscope, triggered by the laser pulse signal.Since the signal area is proportional to the collected charge [4], by varying the bias voltage  on the sensor and measuring the effective signal area  eff , computed as  eff =  signal −  baseline , the sensor's gain  can be determined:  () =  eff, LGAD ()/ eff, avg, PIN .Given the small signal area for the PIN sensor, an average value  eff, avg, PIN is utilized to enhance precision, as no dependence of the signal on the bias voltage was observed for this device.In figure 8, the gain of irradiated 30 μm W5 LGAD sensors is depicted.The curve illustrates that the charged produced by the sensor irradiated at Φ = 1.5 • 10 15 n 1 Mev eq./cm 2 is more than enough to allow time measurements in current dedicated ASICs ( > 5 fC [7]), while avoiding the Single Event Burnout (SEB) limit for the bulk electric field, which is   ≳ 14 V/μm for this sensor thickness [5].The most heavily irradiated sensor, exposed to Φ = 2.5 • 10 15 n 1 Mev eq./cm 2 , has remarkably retained some multiplication power, reaching a gain of  ∼ 10 before the SEB threshold for   .

𝜷-source measurements
The charge released by the interaction between a charged particle and the sensor is less predictable and less uniform than the one in a laser test [8].A 45 μm W1 LGAD sensor from the EXFLU1 production, cooled to −25 • C, is exposed to a Strontium-90 source emitting electrons with an energy up to   ≃ 2.2 MeV.These particles traverse the entire sensor thickness, and generate a trigger signal in a subsequent detector.Upon triggering, the LGAD signal is recorded by the oscilloscope, Pre-irradiated 4 × 10 14 n eq /cm 2 8 × 10 14 n eq /cm 2  1.5 × 10 15 n eq /cm 2 2.5 × 10 15 n eq /cm 2 Q = 5fC SEB danger and its area is calculated and presented in a histogram (figure 9, left).After applying background removal, the distribution is fitted with a convolution of a Landau and Gaussian distribution (figure 9, right).Of particular interest is the MPV of the Landau and its variations in relation to bias voltage and fluence.In figure 10, the MPV of the signal area, obtained from the beta setup, is presented as a function of the bias voltage for two 45 μm W1 LGAD sensors: one non-irradiated and the other exposed to Φ = 1.5 • 10 15 n 1 Mev eq./cm 2 .Notably, the heavily irradiated sensor displays robust performance, as evidenced by the distinct peak in the signal area distribution compared to the background noise, as shown in figure 11.

Conclusions
This contribution explores the performance after irradiation of thin carbonated LGAD sensors in the FBK EXFLU1 production.The characterization confirms the effectiveness of carbon enrichment in the gain layer implant with CBL activation, successfully mitigating acceptor removal effects.The observed acceptor removal coefficients for all wafers hover around the notably low value of   ≃ 1.36 • 10 −16 cm 2 .
Transient characterization reveals that the technology under examination in this study produces well-performing sensors with an excellent signal-to-noise ratio for fluences as high as Φ ≃ 1.5 • 10 15 n 1 MeV eq./cm 2 and retaining some multiplication power even after the highest fluence investigated of Φ ≃ 2.5 • 10 15 n 1 MeV eq./cm 2 .
-9 -Ongoing investigations into the timing performance of these devices via a beam test will complement the overall positive outlook of this production.
Furthermore, it's worth noting that the performances highlighted in this work are primarily specific to the 30 and 45 μm thick LGADs, each with a single gain layer dopant concentration.Past experience suggests that future sensor productions could benefit from further optimization of these characteristics, potentially leading to enhanced radiation resistance.

Figure 3 .
Figure 3. MPI TS200-SE probe station for static characterization (top) and Particulars Transient Current Technique setup (bottom).

Figure 4
Figure 4 shows I-V curves for thin carbonated LGADs from the EXFLU1 production at  = −20 • C. Trends indicate a shift in breakdown voltage to higher values with increasing fluences, suggesting potential degradation in the multiplication mechanism due to radiation damage.

Figure 8 .Figure 9 .
Figure 8. Characterization of the gain of the irradiated 30 μm W5 LGADs measured with TCT, presented in terms of the charge generated by the sensor from the passage of a MIP.

Table 1 .
Characteristics of thin carbonated LGAD wafers in the EXFLU1 production.Dopant  + dose in the gain layer is expressed as a factor of a standard concentration.
Comparison of acceptor removal coefficients in this article with past measurements.