Deep Levels and Electron Paramagnetic Resonance Parameters of Substitutional Nitrogen in Silicon from First Principles

At a Glance

Metadata	Details
Publication Date	2023-07-21
Journal	Nanomaterials
Authors	Chloé Simha, Gabriela Herrero-Saboya, Luigi Giacomazzi, Layla Martin‐Samos, Anne Hémeryck
Institutions	National Research Council, University of Nova Gorica
Citations	3
Analysis	Full AI Review Included

Executive Summary

This study provides a definitive theoretical characterization of substitutional nitrogen (N_Si) in silicon, resolving long-standing ambiguities regarding its structure and spectroscopic signatures (SL5 EPR center and DLTS levels).

Ground State Confirmation: The ground state of neutral N_Si is confirmed to be an off-center configuration with C_3v symmetry, rather than the high-symmetry on-center (T_d) site.
EPR Validation (SL5 Center): Calculated Electron Paramagnetic Resonance (EPR) parameters (g-tensor and hyperfine A-tensors) for the off-center N_Si configuration show excellent agreement with the experimentally observed SL5 center signature.
Metastability Model: The Potential Energy Surface (PES) was mapped, confirming the existence of a shallow, metastable on-center minimum (T_d). The energy barrier for reorientation between equivalent off-center sites is calculated at 129 meV, consistent with experimental thermal activation estimates (0.11 ± 0.02 eV).
Reference Deep Levels: Highly accurate thermodynamic Charge Transition Levels (CTLs) were computed using the DFT + GW method, providing reference values for the single donor (0/+) and single acceptor (0/-) states.
DLTS Reassignment: The calculated CTLs (Donor: E_VBM + 0.83 eV; Acceptor: E_CBM - 0.55 eV) suggest that previous DLTS assignments (e.g., E_CBM - 0.31 eV and E_CBM - 0.08 eV) to N_Si were likely incorrect.

Technical Specifications

Parameter	Value	Unit	Context
N_Si Ground State Symmetry	C_3v	-	Off-center configuration
N_Si Metastable State Symmetry	T_d	-	On-center configuration
Energy Difference (Off-center vs. On-center)	81	meV	Off-center configuration is lower in energy
Reorientation Energy Barrier	129	meV	Barrier for N atom jump between equivalent off-center sites (via on-center T_d state)
Experimental Reorientation Barrier	0.11 ± 0.02	eV	Inferred from EPR stress measurements (T > 35 K)
N-Si Bond Length (Off-center)	1.86	Angstrom	Three equivalent short bonds
N-Si Bond Length (Off-center)	3.15	Angstrom	One elongated bond (along distortion axis)
N-Si Bond Length (On-center)	2.05	Angstrom	Four equivalent bonds
CTL Donor Level (0/+)	E_VBM + 0.83	eV	Calculated using PBE + GW approach
CTL Acceptor Level (0/-)	E_CBM - 0.55	eV	Calculated using PBE + GW approach
g-tensor Isovalue (g_iso)	2.0062	-	Calculated for off-center N_Si (SL5 center)
Hyperfine A_iso (²⁹Si)	-264.1	MHz	Calculated for Si atom along the distortion axis (off-center)
Hyperfine A_iso (¹⁴N)	32.2	MHz	Calculated for Nitrogen impurity (off-center)

Key Methodologies

The investigation relied on advanced ab initio calculations combining Density Functional Theory (DFT) and Many-Body Perturbation Theory (GW).

DFT Setup: Calculations were performed using the Quantum-ESPRESSO package, employing the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional.
Supercell and Basis: A 216-atom silicon supercell was used, sampled at the Gamma (Γ) point for geometry optimization. A plane wave basis set with a kinetic energy cutoff of 84 Ry was employed.
Potential Energy Surface (PES) Mapping: The Minimum Energy Path (MEP) between the on-center and off-center configurations was explored using the climbing-NEB (Nudged Elastic Band) method.
EPR Parameter Calculation: Electron Paramagnetic Resonance (EPR) parameters (g-tensor and hyperfine A-tensors) were computed using the GIPAW (Gauge-Including Projector Augmented Wave) module within Quantum-ESPRESSO. A 3 x 3 x 3 Monkhorst-Pack grid was used for k-point integration to ensure convergence.
Charge Transition Level (CTL) Calculation: Thermodynamic CTLs were determined using the combined DFT and GW (G₀W₀) approach, implemented in the ABINIT code, to accurately account for band gap corrections and self-interaction errors.
GW Convergence: The GW calculations utilized the Godby-Needs plasmon-pole model, requiring 2600 bands and an energy cutoff of 30 eV for the exchange-correlation self-energy.

Commercial Applications

The precise understanding of the N_Si defect is crucial for industries relying on nitrogen-doped silicon, particularly for controlling material properties and defect engineering.

Advanced Silicon Crystal Growth: Nitrogen is intentionally introduced in Czochralski (CZ) and Float Zone (FZ) silicon to suppress the diffusion of self-interstitials and restrain the formation of voids, leading to higher quality wafers for microelectronics.
Power Electronics and Devices: Accurate CTLs (E_VBM + 0.83 eV and E_CBM - 0.55 eV) provide essential data for modeling carrier recombination and lifetime control in silicon power devices (e.g., high-voltage diodes, IGBTs), where deep levels dictate device performance and efficiency.
Mechanical Strength Enhancement: Nitrogen doping is used to enhance the mechanical strength of silicon wafers, reducing warpage and dislocation formation during high-temperature processing steps.
Defect Engineering: The robust correlation between the calculated off-center N_Si structure and the SL5 EPR signal provides a reliable reference point for identifying and characterizing other complex nitrogen-related defects (e.g., nitrogen-vacancy complexes) that impact device functionality.
Photovoltaic Manufacturing: Controlling nitrogen defects is relevant for mitigating bulk lifetime degradation kinetics in silicon solar cells, contributing to improved long-term efficiency and stability.

View Original Abstract

Nitrogen is commonly implanted in silicon to suppress the diffusion of self-interstitials and the formation of voids through the creation of nitrogen-vacancy complexes and nitrogen-nitrogen pairs. Yet, identifying a specific N-related defect via spectroscopic means has proven to be non-trivial. Activation energies obtained from deep-level transient spectroscopy are often assigned to a subset of possible defects that include non-equivalent atomic structures, such as the substitutional nitrogen and the nitrogen-vacancy complex. Paramagnetic N-related defects were the object of several electron paramagnetic spectroscopy investigations which assigned the so-called SL5 signal to the presence of substitutional nitrogen (NSi). Nevertheless, its behaviour at finite temperatures has been imprecisely linked to the metastability of the NSi center. In this work, we build upon the robust identification of the SL5 signature and we establish a theoretical picture of the substitutional nitrogen. Through an understanding of its symmetry-breaking mechanism, we provide a model of its fundamental physical properties (e.g., its energy landscape) based on ab initio calculations. Moreover by including more refined density functional theory-based approaches, we calculate EPR parameters (↔g and ↔A tensors), elucidating the debate on the metastability of NSi. Finally, by computing thermodynamic charge transition levels within the GW method, we present reference values for the donor and acceptor levels of NSi.

Tech Support

Original Source

DOI: https://doi.org/10.3390/nano13142123

References

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