Doping-Compensated Avalanche Region

• Doping-compensated avalanche regions are semiconductor structures engineered through overlapping donor and acceptor implants to produce a tailored high-field region for optimal performance.
• This design minimizes noise, afterpulsing, and premature breakdown by reducing defect densities and balancing dopant removal under high radiation fluences.
• Applications span APDs, LGADs, and SPADs, enabling enhanced timing, charge gain uniformity, and radiation tolerance in environments like collider experiments and high-speed photon detection.

A doping-compensated avalanche region is a semiconductor device architecture in which the effective doping profile—crucially in the high-field (avalanche) region—is tailored by deliberate co-implantation or diffusion of donor and acceptor species to control electric field magnitude, spatial distribution, and temporal stability, especially under ionizing radiation. This concept arises in a broad class of avalanche photodiodes (APDs), low-gain avalanche diodes (LGADs), single-photon avalanche diodes (SPADs), and related devices, and directly addresses noise, breakdown, detector longevity, and charge gain uniformity.

1. Physical Principles and Motivation

Avalanche regions are defined by local electric fields exceeding the impact ionization threshold, typically achieved through a steep doping gradient. In traditional designs—such as a single, heavy p⁺ (acceptor) implant underneath an n⁺ electrode in silicon—the avalanche field is localized according to the implant profile. However, excessive or poorly controlled doping leads to increased densities of deep-level traps, which elevate afterpulsing probability, enhance dark current, reduce breakdown voltage, and limit device radiation hardness (Stipčević, 2015, Kramberger et al., 2017).

Doping compensation is introduced to mitigate these trade-offs by overlapping donor (n⁺) and acceptor (p⁺) concentrations such that the net doping (N_eff) is given by their difference: $N_\text{eff}(x) = N_\text{A}(x) - N_\text{D}(x)$ This profile achieves a set electric field with lower total defect densities, reduced trap-assisted noise, more robust stability under irradiation, and finer spatial confinement of the avalanche region (Sola et al., 2022, Fondacci et al., 8 May 2025, An et al., 24 Jul 2025).

2. Doping Strategies and Implant Schemes

Compensated avalanche regions can be achieved by several approaches:

• Overlapping p⁺/n⁺ Implants: Both acceptor and donor species are implanted at controlled doses so that their spatial overlap yields the target N_eff (typically ~5×10¹⁶ cm⁻³ for standard LGADs). Precise ratios are tuned so N_eff remains stable under irradiation, provided the removal coefficients for donors and acceptors (c_D and c_A) are similar, as shown by the fluence dependence (Sola et al., 2022, Fondacci et al., 8 May 2025):

  $$N_\text{A}(\Phi) = N_{\text{A},0} e^{-c_\text{A}\Phi}, \quad N_\text{D}(\Phi) = N_{\text{D},0} e^{-c_\text{D}\Phi}$$

  $$N_\text{eff}(\Phi) = N_\text{A}(\Phi) - N_\text{D}(\Phi)$$

• Successive Diffusion: For Si SPADs, successive boron and phosphorus diffusions are used so the near-surface region is compensated (N_B ≈ N_D), shifting the avalanche region deeper into higher-quality crystal and away from defect-rich zones (An et al., 24 Jul 2025).
• Carbon Co-implantation: Addition of carbon slows acceptor removal by passivating mobile radiation-induced defects, further enhancing stability of N_eff after high fluence (Mazza et al., 2022, Fondacci et al., 8 May 2025).
• Peripheral and Edge Compensation: P-spray and P-stop diffusions in peripheries counteract surface inversion from oxide-charge buildup, enforce field control, and prevent premature breakdown at edges (Fernandez-Martinez et al., 2015).

3. Electric Field Engineering and Multiplication Dynamics

Electric field magnitude and spatial profile in the avalanche region are direct consequences of the local net doping and device geometry. The compensated structure enables:

• Localized High-Field Regions: The intended effect is that E(x) surpasses the threshold for impact ionization (typically > 2.5×10⁵ V/cm for Si) only in the well-defined gain region, maximizing charge gain while avoiding field extension into defect-rich or periphery regions.
• Mathematical Models: The effective doping feeds into Poisson’s equation for field calculation, and multiplication gain M is given by

  $$M = \exp\left(\int_{x_0}^{x_1} \alpha(E(x))\,dx\right)$$

  where the ionization coefficient α(E) often follows parameterizations derived from experiment and simulation (Rivera et al., 2022).

• Post-Irradiation Performance: Compensation ensures that changes in both donor and acceptor profiles due to irradiation (modeled as exponential removal with fluence) result in a relatively invariant N_eff, preserving field magnitude and multiplication up to extreme fluences (>10¹⁶ cm⁻²) (Sola et al., 2022, Fondacci et al., 8 May 2025).

4. Device Performance Implications

Noise Suppression and Afterpulsing: Lower total impurity content in compensated regions reduces trap-assisted afterpulsing and dark counts; e.g., afterpulsing probabilities of ≪0.05% have been reported at typical excess voltages (Stipčević, 2015).

Signal-to-Noise Ratio & Gain Stability: Uniformity of multiplication and temporal gain stability are improved, as the net field profile is less sensitive to microscopic fluctuations in individual dopant removal or redistributions. With deep, compensated gain regions, HPK and FBK LGADs achieve charge collection >10 fC and timing resolution of 40 ps even after 2.5×10¹⁵ n_eq/cm² (Mazza et al., 2022).

Breakdown Voltage & Operating Margins: Lowering or balancing initial gain-layer doping increases breakdown voltage, expanding operational headroom and improving post-irradiation operability (Mazza et al., 2022).

Radiation Tolerance: Devices maintain internal gain at fluences far beyond conventional LGADs, supporting 4D timing for future collider experiments (Sola et al., 2022, Fondacci et al., 8 May 2025).

Minimized Leakage Current: Doping-compensated peripheries and deep field localization restrict edge leakage, enabling operation at high reverse bias without premature failure (Fernandez-Martinez et al., 2015).

5. Characterization, Simulation, and Process Control

Experimental Characterization: Capacitance–voltage (C-V) measurements, combined with secondary-ion mass spectrometry (SIMS) and van der Pauw test structures, are used to extract active doping profiles, verify compensation effectiveness, and monitor post-irradiation dynamics (Fondacci et al., 8 May 2025).

TCAD Simulation: Technology CAD models, validated with measured data (C-V, I-V), are key to optimizing implant profiles, predicting fluence-dependent gain and depletion behavior, and conducting breakdown margin analysis (Rivera et al., 2022, Fondacci et al., 8 May 2025).

Removal Coefficient Extraction: Experiment-theory comparison shows, e.g., that donor removal rates (c_D) can be approximately twice those for acceptors (c_A), necessitating compensation ratio adjustments to achieve balanced field retention with fluence (Fondacci et al., 8 May 2025).

6. Application-Specific Architectures and Future Development

Single-Photon Detection and SPADs: Doping-compensated avalanche regions concentrate the electric field in deep, low-defect zones, resulting in SPADs with high PDE (up to 84% at 785 nm), low dark count rates (260 cps at 268 K), and reduced afterpulsing (2.9%) when combined with backside-illumination (An et al., 24 Jul 2025).

Time-of-Flight and Imaging: Compensated avalanche regions with geometric field engineering (e.g., spherically uniform field peaks) yield improved detection homogeneity, lower voltage operation, and compatibility with CMOS processes. The implementation of shallow compensation diffusions further reduces surface-triggered noise (Sieleghem et al., 2021).

Radiation-Hard Tracking: The compensated LGAD paradigm supports precise tracking in ultra-high fluence environments (HL-LHC, FCC-hh), maintaining timing resolution and operational gain as both donor and acceptor profiles are depleted in tandem (Sola et al., 2022, Fondacci et al., 8 May 2025).

AC-LGADs and Spatial Resolution: In position-sensitive LGADs, compensated avalanching confines the multiplication volume and minimizes cross-talk, enabling segmentation down to ~10 µm pitch without incurring breakdown at segment boundaries (Nizam et al., 2023).

Material Extensions: In non-silicon systems (e.g., MoS₂-xOx), chemical substitution or compensation by oxygen defects modulates bandgap, field distribution, and carrier transport, yielding drastically improved avalanche gain and breakdown voltage reduction (from 26.2 V to 12.6 V), with impact on sensing modalities (Cai et al., 12 Sep 2024).

7. Process Optimization and Open Challenges

Ongoing research focuses on:

• Fine-tuning Implant Profiles: Balancing donor/acceptor doses with consideration for non-identical removal coefficients, spatial superposition, and energy dependence to customize the response to operational and irradiation environments (Fondacci et al., 8 May 2025).
• Co-implant Effects and Additives: Carbon, oxygen, and other co-implants are under investigation for their modulatory effect on defect passivation and dopant stability (Mazza et al., 2022).
• Edge Termination and Guard Structures: Advanced edge compensation, such as deep n-type diffusions and field plates, expand the high-field region while preventing premature edge breakdown (Fernandez-Martinez et al., 2015).
• Modeling and Datadriven Optimization: Integration of SIMS measurements, high-resolution profiling, and real-time TCAD-based feedback enables increasingly refined tailoring of avalanche region properties (Rivera et al., 2022, Fondacci et al., 8 May 2025).

In summary, the doping-compensated avalanche region concept—employing engineered net doping through spatially controlled donor and acceptor implantation—enables precise electric field control, minimizes noise and instability, enhances radiation tolerance, and enables high-performance operation across photon counting, timing, and particle tracking applications. These advances are substantiated with in-depth measurements, TCAD simulations, and operational results across a range of platforms and irradiation conditions.