Characterization of p-stop isolation implants in silicon sensors using MOSFET structures

Technical Summary: Characterization of p-stop isolation implants in silicon sensors using MOSFET structures

Problem Statement
Silicon sensors are critical components for tracking, timing, and calorimetry in high-energy physics experiments, particularly for the High-Luminosity Large Hadron Collider (HL-LHC) upgrades of the ATLAS and CMS experiments. In n-on-p silicon sensors, adjacent n-type electrodes must be electrically isolated to prevent short-circuiting via electron accumulation layers at the Si-SiO2 interface. This isolation is typically achieved using p-stop implants. However, these implants locally modify the electric field distribution and effective doping profiles near the surface, influencing device performance. Ensuring the consistency and quality of these implants during large-scale industrial production requires rigorous, non-destructive diagnostic methods. While dedicated test structures exist, there is a need for techniques that can quantitatively characterize the depth-dependent doping profiles and isolation properties of p-stops without damaging the sensor.

Methodology
The authors propose and validate a methodology using Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) test structures as non-destructive probes for p-stop characterization. These devices replicate the inter-electrode geometry of segmented sensors, where adjacent collection electrodes serve as the source and drain, and a gate is placed over the SiO2 layer between them.

The study utilized circular and elliptical MOSFETs fabricated on two types of p-type silicon wafers (T and H) with varying bulk doping concentrations and p-stop configurations (ranging from no p-stops to one or two p-stops with low or high doping levels). The measurement setup involved applying a backside bias voltage ($V_{back}$) ranging from 0.5 V to -600 V to simulate reverse bias conditions, while sweeping the gate-to-source voltage ($V_{gs}$) to record the source-to-drain current ($I_{sd}$).

The analysis proceeded in two main stages:

1. Parameter Extraction: The threshold voltage ($V_{th}$) and field-dependent electron mobility parameters ($\mu_0$ and $V_{1/2}$) were extracted from the transfer characteristics ($I_{sd}$ vs. $V_{gs}$) using a parameterized mobility model. The threshold voltage was determined via linear extrapolation of the transconductance maximum and refined by fitting the data to the mobility model.
2. Profile Reconstruction: The dependence of $V_{th}$ on $V_{back}$ was utilized to reconstruct the effective doping profile in the inter-electrode region. Using analytical relations derived from depletion theory, the depletion depth ($x$) and doping concentration ($p$) were calculated from the first and second derivatives of the $V_{th}$ vs. $V_{back}$ curve. To mitigate noise amplification inherent in numerical differentiation, a smoothing procedure involving second-order polynomial fits over five data points was applied prior to differentiation.

Key Results

• Threshold Voltage Behavior: The presence of p-stop implants induces a distinct dependence of $V_{th}$ on $V_{back}$. Structures with p-stops exhibit a steep initial increase in $V_{th}$ as $|V_{back}|$ increases, followed by a saturation region once the p-stop implants are fully depleted. In contrast, structures without p-stops show a slow, monotonic change in $V_{th}$ across the bias range.
• Mobility Parameters: The extracted electron mobility ($\mu_0$) increases with $|V_{back}|$ and saturates in structures containing p-stops, reaching higher plateau values for higher doping concentrations. This is attributed to the modification of the transverse electric field and surface scattering by the p-stop implants. The parameter $V_{1/2}$ shows an inverse trend, decreasing with bias before plateauing.
• Doping Profile Reconstruction: The reconstructed doping profiles reveal a characteristic high-concentration peak near the Si-SiO2 interface for p-stop structures, with concentrations approaching $10^{16} \text{ cm}^{-3}$. The concentration decreases rapidly (by more than an order of magnitude) within the first micrometer, consistent with expected Gaussian-like implantation profiles and thermal diffusion. The profiles for structures without p-stops remain constant, matching the bulk doping level of approximately $4 \times 10^{12} \text{ cm}^{-3}$.
• Geometric and Doping Sensitivity: The technique successfully distinguishes between different p-stop geometries (circular vs. elliptical) and doping levels. High-doping p-stops (e.g., on wafer H) demonstrate stronger electric field screening, requiring significantly higher backside voltages to achieve full depletion compared to low-doping variants.

Significance and Claims
The paper presents this work as a proof of concept demonstrating that MOSFET-based test structures can serve as a non-destructive diagnostic tool for monitoring p-stop consistency and inter-electrode isolation properties in silicon detectors. The study claims that the methodology allows for the quantitative reconstruction of depth-dependent doping profiles with sub-micrometer resolution near the surface. By correlating the electrical response (specifically the backside bias dependence of $V_{th}$) with the physical implantation characteristics, the technique provides critical data for simulating sensor performance under diverse operating conditions. The authors conclude that this approach is effective for gauging the quality of isolation implants across different wafer types and geometries, supporting the quality control procedures required for the mass production of sensors for the HL-LHC.