Low Gain Avalanche Diodes (LGADs)

• LGADs are silicon-based detectors featuring a thin, highly doped p⁺ gain layer that enables moderate avalanche gain.
• They deliver exceptional timing resolution (~20–30 ps) through controlled internal amplification, ensuring robust performance under high radiation.
• Advanced LGAD variants like DJ-LGADs, AC-LGADs, and TI-LGADs improve segmentation and maintain radiation hardness for high-precision tracking and imaging.

Low Gain Avalanche Diodes (LGADs) are silicon-based detectors that integrate a thin, highly doped p⁺ “gain layer” beneath the n⁺ electrode of a planar diode structure. When reverse biased, electrons generated by radiation passing through the bulk drift into the gain region, where the high electric field induces impact ionization, yielding controlled internal signal amplification. LGADs are designed for moderate multiplication factors (typically $G\approx5$–$100$), enabling high time resolution (as low as $\sim$20–30 ps) and robust signal-to-noise for minimum ionizing particle (MIP) detection, X-ray imaging, and other fast-precision applications in high-radiation environments.

1. Device Structure and Gain Mechanism

LGADs are built as n⁺–p⁺–p⁻ diode structures. The critical element is the p⁺ gain layer, which is typically realized by boron (or gallium) implantation with active concentrations $N_A\approx10^{16}$–$10^{18}$ cm⁻³, positioned $\sim$0.5–2 μm beneath the n⁺ electrode (Pellegrini et al., 2015, Sola et al., 2022). The p⁺ region creates a localized internal electric field peak $E\gg2\times10^5$ V/cm over a thin width $d_g$, where electrons undergo impact ionization with a coefficient $\alpha(E,T)=A(T)E\,\exp(-B/E)$. The accumulated avalanche gain is given by: $$G(V) = \exp\left(\int_{x_1}^{x_2}\alpha_n[E(x)]dx\right)$$ where $100$0–$100$1 delimit the high-field domain.

Sensor thicknesses typically range from 20–150 μm. The gain layer is engineered such that, upon reverse bias, the field aligns for controlled, moderate avalanche, leaving most of the substrate at lower drift fields. Under irradiation, the active acceptor concentration is reduced exponentially: $100$2 with $100$3 the acceptor-removal constant (Rivera et al., 2023, Wu et al., 2022). LGAD designs using both epitaxial and Si-on-Si substrates have been optimized for depleting the full thickness at modest voltages, achieving high breakdown margins (Grieco et al., 2022).

2. Internal Gain Physics and Suppression Mechanisms

Avalanche multiplication in LGADs is fundamentally governed by the field-dependent ionization coefficients. Electrons traversing the high-field gain region acquire sufficient energy to induce secondary electron-hole pair production; the total gain is highly sensitive to local $100$4 and temperature $100$5 (Pellegrini et al., 2015, Currás et al., 2021). The gain–voltage characteristic is exponential: $100$6 where $100$7 is set by implantation dose and $100$8 is the gain-layer depletion voltage.

A notable operational effect is “gain suppression” under high-density charge deposition: for concentrated carrier clouds, the space charge screens the intrinsic high field, reducing the effective multiplication. The modified gain is well described by: $100$9 where $\sim$0 is local carrier density and $\sim$1 a characteristic threshold ($\sim$2 e/cm³ for 50 μm LGADs). Experiments using IR lasers and rotated β-source beams confirmed that spatial charge density directly modulates gain, with $\sim$325% suppression at %%%%20$d_g$21%%%%MIP and 50% at 30$\sim$6MIP densities (Currás et al., 2021). This phenomenon must be considered for non-MIP signal sources or high-rate collider environments.

3. Radiation Hardness and Acceptor Removal

Performance degradation in LGADs under irradiation arises primarily from acceptor removal in the gain layer (Rivera et al., 2023, Wu et al., 2022, Lange et al., 2017). The exponential decay parameter, measured for standard boron layers, is $\sim$7–$\sim$8 cm² for neutrons and $\sim$9–$N_A\approx10^{16}$0 cm² for protons, with proton damage approximately 2.5$N_A\approx10^{16}$1 more effective at deactivating acceptors. After $N_A\approx10^{16}$2 n$N_A\approx10^{16}$3/cm², gain typically falls to $N_A\approx10^{16}$4–$N_A\approx10^{16}$5, and the time resolution degrades from $N_A\approx10^{16}$630 ps to $N_A\approx10^{16}$7–$N_A\approx10^{16}$8 ps unless mitigated by increased bias voltage or optimized electronics.

Mitigation strategies include carbon co-implantation (halve $N_A\approx10^{16}$9), deeper and more concentrated gain-layer profiles, and compensated gain-layer architectures where p⁺ and n⁺ implants are tuned such that $10^{18}$0 remains nominal despite individual dopant removal (Sola et al., 2022, Wu et al., 2022). Such approaches extend LGAD applicability to fluences well beyond $10^{18}$1 n$10^{18}$2/cm², essential for future 4D trackers (Cartiglia et al., 2019).

Radiation studies with gammas ($10^{18}$3Co, up to 2.2 MGy) show modest acceptor removal but rapid surface leakage increase, tied to oxide and interface trap buildup, necessitating robust passivation and edge termination designs for multi-MGy environments (Hoeferkamp et al., 2021).

4. LGAD Variants, Segmentation, and Granularity

High-precision spatial and timing resolution is achieved in LGADs via segmentation. However, standard millimeter-scale pixel LGADs require junction-termination extensions, which introduce “dead” regions between pixels (Ayyoub et al., 2021). Advanced variants address this:

• Deep Junction LGADs (DJ-LGADs): The gain region is buried several microns below the segmented electrodes, enabling segmentation down to 20 μm pitch with uniform gain and eliminating surface JTE dead zones (Ayyoub et al., 2021).
• AC-LGADs (Resistive AC-Coupled LGADs): A resistive n⁺ layer beneath a dielectric allows capacitive coupling to fine metal pads ($10^{18}$4200 μm). Charge sharing among neighboring pixels enables position resolution well below the pitch ($10^{18}$510 μm), suitable for imaging and 4D tracking. Timing jitter remains competitive ($10^{18}$620–30 ps) (Giacomini et al., 2019, Molnar et al., 25 Apr 2025).
• Trench Isolated LGADs (TI-LGADs): Dielectric trenches isolate each pixel or strip, yielding true inter-pixel isolation and little cross-talk (Molnar et al., 25 Apr 2025).
• Strip LGADs: Extended-length (19 mm) strips with widths down to 0.3 mm achieve $10^{18}$737 ps timing resolution and sub-mm position encoding along the strip, providing reduced electronics density and cost (Sun et al., 2024).

5. Timing and Signal Performance

LGADs achieve time resolutions as low as 26.5 ps for 50 μm Micron LGADs at $10^{18}$8 °C and 200 V (Moriya et al., 2023). Time resolution $10^{18}$9 is a function of gain and noise: $\sim$0 with $\sim$1 ps, $\sim$2 ps for 45 μm devices (Lange et al., 2017). Jitter scales inversely with $\sim$3, and Landau fluctuations can be minimized with thin substrates. After moderate irradiation, time resolution remains below 40 ps for both Si-on-Si and epi LGADs at bias voltages up to 700 V (Grieco et al., 2022). For thicker LGADs ($\sim$4150 μm), time resolution degrades due to longer drift paths ($\sim$5900 ps at optimal bias) (Molnar et al., 25 Apr 2025).

Spectroscopic and fast-timing applications have been demonstrated for X-rays, gammas, and highly-ionizing protons (Giacomini et al., 2024, Mazza et al., 2023). Signal-to-noise and energy resolution are optimized at moderate gain ($\sim$6–$\sim$7), reaching $\sim$86–12% at 30 keV X-rays, and time resolutions below 100 ps for thin devices (Mazza et al., 2023).

6. Advanced Materials and Ultra-Thin LGADs

Simulations and preliminary fabrication of LGADs in 4H–SiC and diamond suggest substantial improvements in radiation hardness and timing relative to standard silicon (Kalani et al., 23 Jan 2026). 4H–SiC LGADs, with superior breakdown fields ($\sim$9) and faster carrier velocities, retain high gain and sub-25 ps time resolution up to $E\gg2\times10^5$0 n$E\gg2\times10^5$1/cm² in ultra-thin ($E\gg2\times10^5$2m) devices, outperforming Si and C for next-generation high-fluence operation.

Thin LGADs (25–50 μm) are key for sustaining gain at fluences $E\gg2\times10^5$3 n$E\gg2\times10^5$4/cm², as they minimize trapping and support “bulk multiplication” when the original gain layer is removed; trench isolation can preserve 100% fill factor for fine segmentation (Cartiglia et al., 2019).

7. Practical Considerations and Applications

Optimization of LGAD designs balances gain profile, substrate resistivity, guard-ring layout, breakdown voltage, and passivation for application-specific constraints: timing layers (ATLAS HGTD, CMS ETL), 4D tracking, high-rate X-ray imaging/spectroscopy, TOF-PET, and high-flux radiotherapy monitors (Braun et al., 2024, Farook et al., 11 Mar 2025, Pellegrini et al., 2015).

The field continues evolving toward radiation-hard compensated gain layers, advanced segmentation technologies, and new materials (SiC), with validated device models (TCAD, WF2) guiding next-generation collider, medical, and photonics detector developments.