Extrinsic Doping in Group IV Hexagonal-Diamond-Type Crystals

At a Glance

Metadata	Details
Publication Date	2020-07-07
Journal	The Journal of Physical Chemistry C
Authors	Michele Amato, Thanayut Kaewmaraya, Alberto Zobelli
Institutions	Centre National de la Recherche Scientifique, Université Paris-Saclay
Citations	9
Analysis	Full AI Review Included

Technical Documentation & Analysis: Extrinsic Doping in Group IV Hexagonal-Diamond Type Crystals

This document analyzes the findings of the research paper “Extrinsic Doping in Group IV Hexagonal-Diamond Type Crystals” (arXiv:2007.04027v1) and translates the theoretical insights into actionable material specifications and sales opportunities for 6CCVD’s advanced MPCVD diamond products.

Executive Summary

This DFT study provides critical theoretical insights into optimizing extrinsic doping in diamond, directly impacting the fabrication of Boron-Doped Diamond (BDD) and the pursuit of stable n-type diamond.

Phase Stability of Dopants: Numerical simulations confirm the relative stability of Group III (p-type) and Group V (n-type) dopants in hexagonal-diamond (2H, Lonsdaleite) versus cubic-diamond (3C) structures (C, Si, Ge hosts).
Enhanced 2H Preference in Carbon: Both n-type and p-type dopants show enhanced stability in 2H-Carbon compared to standard 3C-Diamond, suggesting that the presence of stacking faults (which contain 2H inclusions) drives dopant segregation.
N-Type Doping Pathway: The preference for the 2H phase is significantly more pronounced for n-type impurities (N, P, As). For Phosphorus (P), the concentration ratio $[C^{2H}]/[C^{3C}]$ is calculated to be 1.11 x 10⁹, suggesting 2H inclusions could be critical for achieving stable n-type diamond.
P-Type Optimization (BDD): Boron (B) exhibits a strong preference for the 2H phase ($[C^{2H}]/[C^{3C}]$ of 2.58 x 10⁵), confirming that controlling crystal quality and stacking fault density is paramount for achieving uniform doping in Boron-Doped Diamond (BDD).
Structural Mechanism: Dopant stability is linked to local site symmetry (C_3v in 2H vs. T_d in 3C) and atomic radius mismatch, which dictates the structural relaxation required to accommodate the impurity.
6CCVD Value Proposition: 6CCVD provides the high-purity SCD and custom BDD materials necessary for experimental validation of these theoretical models, offering precise control over doping concentration and crystal structure.

Technical Specifications

The following hard data points, primarily focused on Carbon (C) host crystals, were extracted from the DFT calculations (Tables I and II).

Parameter	Value	Unit	Context
3C Lattice Parameter ($a_{3C}$)	3.56	Å	Cubic Diamond (3C)
2H Lattice Parameter ($a_{2H}$)	2.50	Å	Hexagonal Diamond (2H)
2H c-axis Parameter ($c_{2H}$)	4.16	Å	Hexagonal Diamond (2H)
3C Cohesion Energy ($E_{coh}^{3C}$)	8.67	eV	Per atom, 3C Carbon
2H Cohesion Energy ($E_{coh}^{2H}$)	8.65	eV	Per atom, 2H Carbon
3C Atomic Density ($\rho_{3C}$)	3.53	g/cm³	Cubic Diamond (3C)
2H Atomic Density ($\rho_{2H}$)	3.52	g/cm³	Hexagonal Diamond (2H)
Boron (B) $\Delta E_{form}^{2H-3C}$	-0.32	eV	Preference for 2H-C
Phosphorus (P) $\Delta E_{form}^{2H-3C}$	-0.54	eV	Strong preference for 2H-C
Nitrogen (N) $\Delta E_{form}^{2H-3C}$	-0.14	eV	Preference for 2H-C
B Dopant Concentration Ratio ($[C^{2H}]/[C^{3C}]$)	2.58 x 10⁵	N/A	Equilibrium concentration ratio (2H vs. 3C)
P Dopant Concentration Ratio ($[C^{2H}]/[C^{3C}]$)	1.11 x 10⁹	N/A	Equilibrium concentration ratio (2H vs. 3C)

Key Methodologies

The research utilized advanced ab initio computational techniques to model defect formation and stability in Group IV crystals.

Computational Framework: Spin polarized Density Functional Theory (DFT) calculations were performed primarily under the Local Density Approximation (LDA), utilizing the SIESTA code.
Confirmation Calculations: Additional calculations were performed using the Generalized Gradient Approximation plus U (GGA+U) approach (VASP code) to confirm results for Ge, ensuring accurate representation of the electronic structure.
Geometry Optimization: Ground state geometries were optimized using a conjugate gradient algorithm, enforcing strict convergence criteria:
- Force convergence: 0.01 eV/Å.
- Stress convergence: 0.1 GPa.
Supercell Modeling: Large supercells were employed to simulate the high-doping regime (10¹⁹-10²⁰ cm^-3) and minimize spurious interactions between periodic replicas of impurities:
- 3C Phase: 4 x 4 x 4 supercell (512 atoms).
- 2H Phase: 6 x 6 x 3 supercell (432 atoms).
Defect Energy Calculation: The formation energy ($E_{form}$) of neutral substitutional defects was calculated using the Zhang and Nortrup formalism, referencing the bulk ground state total energy and the energy of the free dopant atoms.
Relative Stability Metric: The relative stability between phases was quantified by the energy difference $\Delta E_{form}^{2H-3C} = E_{form}^{2H} - E_{form}^{3C}$, which removes the dependence on the dopant chemical potential.

6CCVD Solutions & Capabilities

This research highlights the critical role of crystal structure (3C vs. 2H inclusions, i.e., stacking faults) in determining dopant stability and segregation, particularly for Boron and potential n-type dopants. 6CCVD is uniquely positioned to supply the high-quality, customized diamond materials required to experimentally validate and leverage these theoretical findings.

Applicable Materials for Experimental Validation

To replicate or extend this research, engineers and scientists require diamond substrates with precise control over purity, doping, and crystal quality.

Material Requirement	6CCVD Solution	Application Context
P-Type Doping (B)	Heavy Boron-Doped SCD (BDD)	Required for validating B segregation phenomena and optimizing conductivity in high-doping regimes (10¹⁹-10²⁰ cm^-3).
Host Crystal Structure	High-Purity Single Crystal Diamond (SCD)	Provides the ideal 3C host lattice for studying the effects of controlled defects (stacking faults/2H inclusions) on dopant incorporation.
Large Area Applications	Boron-Doped Polycrystalline Diamond (PCD)	Available in large formats (up to 125mm) for scaling up BDD electrochemical or sensor applications where phase coexistence may be leveraged.
N-Type Research	High-Purity SCD Substrates	Essential starting material for experimental attempts to introduce N, P, or As dopants, allowing researchers to isolate the effects predicted for the 2H phase.

Customization Potential & Engineering Services

The paper discusses structural effects relevant to both bulk crystals and nanowires (NWs, 20-100 nm range). 6CCVD’s custom fabrication capabilities support device integration and micro-structuring necessary for advanced research.

Custom Dimensions and Thickness: 6CCVD offers SCD and PCD plates/wafers with custom dimensions up to 125mm (PCD). We provide precise thickness control for both SCD and PCD layers, ranging from 0.1 µm to 500 µm, enabling the fabrication of thin films or thick substrates (up to 10mm).
Surface Preparation: The DFT models assume ideal structures. 6CCVD provides ultra-smooth polishing (Ra < 1nm for SCD, Ra < 5nm for inch-size PCD) to minimize surface effects, ensuring experimental results align closely with bulk theoretical predictions.
Metalization Services: For integrating doped diamond into electronic or opto-electronic devices, 6CCVD offers in-house custom metalization using materials such as Au, Pt, Pd, Ti, W, and Cu, facilitating ohmic contact formation and device prototyping.
Doping Profile Control: Our MPCVD expertise allows for precise control over the doping concentration and profile, enabling researchers to test the predicted stability and segregation trends across various doping levels.

Engineering Support

The theoretical findings suggest that controlling the density of 2H/3C interfaces (stacking faults) is key to optimizing doping uniformity and achieving stable n-type conductivity.

Expert Consultation: 6CCVD’s in-house PhD team specializes in MPCVD growth kinetics and defect engineering. We offer authoritative professional assistance in selecting the optimal material grade and growth parameters (e.g., temperature, pressure, gas ratios) to manage stacking fault density for projects focused on Dopant Segregation and Phase Stability in diamond.
Global Logistics: We ensure reliable global shipping (DDU default, DDP available) to support international research collaborations aiming to validate these critical theoretical models.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Over the last few years, group IV hexagonal-diamond type crystals have\nacquired great attention in semiconductor physics thanks to the appearance of\nnovel and very effective growth methods. However, many questions remain\nunaddressed on their extrinsic doping capability and on how it compares to\nthose of diamond-like structures. This point is here investigated through\nnumerical simulations conducted in the framework of the Density Functional\nTheory (DFT). The comparative analysis for group III and V dopant atoms shows\nthat: i) in diamond-type crystals the bulk sites symmetry ($T_d$) is preserved\nby doping while in hexagonal crystals the impurity site moves towards a higher\n($T_d$) or lower ($C_{3v}$) symmetry configuration dependently on the valence\nof the dopant atoms; ii) for Si and Ge, group III impurities can be more easily\nintroduced in the hexagonal-diamond phase, whose local $C_{3v}$ symmetry better\naccommodates the three-fold coordination of the impurity, while n-type\nimpurities do not reveal any marked phase preference; iii) for C, both n and p\ndopants are more stable in the hexagonal-diamond structure than in the the\ncubic one, but this tendency is much more pronounced for n-type impurities.\n

Tech Support

Original Source

DOI: https://doi.org/10.1021/acs.jpcc.0c03713