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	University of Nova Gorica, Laboratoire d’Analyse et d’Architecture des Systèmes
Citations	3
Analysis	Full AI Review Included

Technical Analysis & Documentation: Defect Engineering in Wide-Bandgap Materials

Reference: Simha, C. et al. Deep Levels and Electron Paramagnetic Resonance Parameters of Substitutional Nitrogen in Silicon from First Principles. Nanomaterials 2023, 13, 2123.

Executive Summary

This documentation analyzes a first-principles investigation into the fundamental physical properties of substitutional nitrogen ($N_{Si}$) defects in silicon, a critical topic relevant to defect engineering in wide-bandgap semiconductors like MPCVD diamond.

Robust Theoretical Model: A comprehensive theoretical picture of $N_{Si}$ in silicon was established using advanced Density Functional Theory (DFT) and $G_0W_0$ many-body correction methods.
Ground State Confirmation: The stable ground state geometry was confirmed to be an off-center configuration ($C_{3v}$ symmetry), contrasting with the higher symmetry on-center configuration ($T_d$).
EPR Signature Validation: Calculated Electron Paramagnetic Resonance (EPR) parameters for the off-center $N_{Si}$ configuration show excellent agreement with the experimentally observed SL5 center, providing a firm theoretical assignment.
Metastability and Reorientation: The Minimum Energy Path (MEP) analysis revealed an energy barrier of 129 meV for defect reorientation between equivalent off-center sites, validating thermal activation observed in EPR stress measurements.
Charge Transition Levels (CTLs): Highly accurate thermodynamic CTLs were computed using the PBE+GW approach, providing reference values for the single donor ($\epsilon(+/0)$ at $E_{VBM}$ + 0.83 eV) and single acceptor ($\epsilon(0/-)$ at $E_{CBM}$ - 0.55 eV) levels.
Relevance to Diamond: The methodologies employed (DFT/GW, EPR parameter calculation, defect stability analysis) are directly transferable to the study and engineering of critical defects in MPCVD diamond, such as Nitrogen-Vacancy (NV) centers.

Technical Specifications

The following hard data points were extracted from the first-principles calculations regarding the $N_{Si}$ defect in silicon:

Parameter	Value	Unit	Context
Silicon Lattice Parameter ($a_{PBE}$)	5.47	Å	DFT input value for pristine Si
N-Si Bond Length (On-Center)	2.05	Å	Tetrahedral ($T_d$) configuration
N-Si Bond Length (Off-Center, Short)	1.86	Å	$C_{3v}$ configuration (3 equivalent bonds)
N-Si Bond Length (Off-Center, Long)	3.15	Å	$C_{3v}$ configuration (1 elongated bond)
Energy Difference (Off-Center vs. On-Center)	81	meV	Off-center configuration is the ground state
Reorientation Energy Barrier	129	meV	Barrier for N atom jump between equivalent off-center sites
Donor CTL ($\epsilon(+/0)$)	0.83	eV	Calculated from Valence Band Maximum ($E_{VBM}$) using PBE+GW
Acceptor CTL ($\epsilon(0/-)$)	0.55	eV	Calculated from Conduction Band Minimum ($E_{CBM}$) using PBE+GW
$g_{iso}$ (Calculated SL5 Center)	2.0062	-	Isotropic $g$ factor for off-center $N_{Si}$
$A_{iso}$ ($^{29}Si_{(111)}$)	-264.1	MHz	Isotropic hyperfine coupling for the Si neighbor along the distortion axis
$A_{iso}$ ($^{14}N$)	32.2	MHz	Isotropic hyperfine coupling for the Nitrogen impurity

Key Methodologies

The theoretical investigation utilized state-of-the-art computational techniques to accurately model defect properties in a semiconductor environment:

Ab Initio Framework: Calculations were primarily performed using the Quantum-ESPRESSO package (DFT) and the ABINIT code ($G_0W_0$) for many-body corrections.
Functional and Pseudopotentials: The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional was employed, coupled with norm-conserving Trouiller-Martins pseudopotentials featuring GIPAW reconstruction.
Supercell Modeling: A 216-atom silicon supercell was used to embed the substitutional nitrogen defect, sampled at the $\Gamma$ point, with compensating background charge included for charged states (+1, -1, -2).
Geometry Optimization: Ionic minimization was performed with a strict convergence threshold on forces set to 0.026 eV/Å.
Energy Path 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: Hyperfine ($A$) and $g$ tensors were computed using the QE-GIPAW module, requiring integration over a dense $3 \times 3 \times 3$ Monkhorst-Pack grid to ensure convergence.
Charge Transition Level (CTL) Calculation: Thermodynamic CTLs were determined using the combined DFT and $G_0W_0$ approach, requiring a high energy cutoff (82 eV) for the dielectric matrix and 2600 bands for the GW exchange-correlation self-energy.

6CCVD Solutions & Capabilities

This research highlights the critical role of precise defect characterization (EPR, deep levels) and theoretical modeling (DFT/GW) in semiconductor physics. 6CCVD leverages analogous expertise in MPCVD diamond to provide materials essential for advancing quantum, electronic, and optical applications.

Applicable Materials for Defect Research

While the paper focuses on $N_{Si}$ in silicon, the principles of substitutional doping and defect creation are paramount in diamond research (e.g., NV centers). 6CCVD provides the foundational materials required for such studies:

Optical Grade Single Crystal Diamond (SCD): Essential for establishing a low-defect baseline. We supply ultra-high purity SCD wafers (Type IIa) with extremely low native nitrogen content, allowing researchers to precisely control the introduction of specific defects.
Controlled Nitrogen-Doped SCD: For applications requiring specific defects (like NV centers), 6CCVD offers SCD with controlled nitrogen incorporation during the MPCVD growth process, enabling targeted defect density engineering.
Boron-Doped Diamond (BDD): For studies requiring p-type conductivity or investigating boron-related deep levels, we offer BDD films and substrates with tunable doping concentrations.

Customization Potential for Advanced Device Fabrication

To replicate or extend this research into diamond-based devices (e.g., DLTS structures, quantum sensors), 6CCVD offers comprehensive customization:

Research Requirement	6CCVD Customization Capability
Unique Dimensions	Plates/wafers available up to 125 mm (PCD) and custom sizes for SCD, ensuring scalability and compatibility with existing fabrication lines.
Precise Thickness Control	SCD and PCD films available from 0.1 µm to 500 µm, and substrates up to 10 mm, critical for optimizing DLTS junction depth or quantum coherence.
Device Contact Integration	In-House Metalization: We provide custom metal stacks (Au, Pt, Pd, Ti, W, Cu) tailored for specific ohmic or Schottky contact requirements, essential for electrical characterization (DLTS).
Surface Quality for Spectroscopy	Ultra-Low Roughness Polishing: Our SCD wafers are polished to $R_a < 1$ nm, minimizing surface defects and ensuring optimal conditions for high-resolution optical and EPR measurements.

Engineering Support

The complexity of defect physics, as demonstrated by the need for PBE+GW calculations and detailed EPR tensor analysis, requires specialized material support.

Defect Physics Expertise: 6CCVD’s in-house PhD team specializes in wide-bandgap semiconductor defect physics, offering consultation on material selection, doping strategies, and post-growth processing (e.g., annealing for NV center creation) for similar Deep Level Transient Spectroscopy (DLTS) and EPR spectroscopy projects.
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For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

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

2002 - Mechanical properties of nitrogen-doped CZ silicon crystals [Crossref]
2008 - Multiplicity of Nitrogen Species in Silicon: The Impact on Vacancy Trapping
2009 - Nitrogen diffusion and interaction with dislocations in single-crystal silicon [Crossref]
1996 - Influence of oxygen and nitrogen on point defect aggregation in silicon single crystals [Crossref]
2004 - Nitrogen interaction with vacancies in silicon [Crossref]
1975 - Nitrogen- implanted silicon. II. Electrical properties [Crossref]
1982 - Deep levels associated with nitrogen in silicon [Crossref]
1985 - Nitrogen-related deep electron traps in float zone silicon [Crossref]
2016 - Permanent annihilation of thermally activated defects which limit the lifetime of float-zone silicon [Crossref]