First-Principles Calculations of P-B Co-Doped Cluster N-Type Diamond

At a Glance

Metadata	Details
Publication Date	2024-05-16
Journal	Crystals
Authors	Huaqing Lan, Sheng Yang, Wen Yang, Maoyun Di, Hongxing Wang
Institutions	Taiyuan University of Science and Technology, Xi’an Jiaotong University
Citations	2
Analysis	Full AI Review Included

Technical Documentation & Analysis: P-B Co-Doped N-Type Diamond

Executive Summary

This computational study validates a critical pathway toward realizing stable, high-performance n-type diamond semiconductors, a key bottleneck for high-power electronics.

N-Type Challenge Solved: First-principles calculations confirm that Phosphorus (P) doping alone is highly unstable (Formation Energy: 7.493 eV) and induces severe lattice distortion, rendering it unsuitable for n-type devices.
P-B Co-Doping Success: The introduction of Boron (B) as a compensatory dopant significantly enhances the solubility of P and mitigates lattice distortion, crucial for structural stability.
Cluster Formation: P-B co-doped impurities exhibit a strong tendency to form stable cluster configurations (e.g., P-B-P, P-P-B), which are structurally preferred over individual substitutional doping.
Shallow Donor Levels: Optimized P-B cluster structures achieve remarkably low ionization energies, with the lowest calculated value at 1.52 eV (P-B-P configuration). This confirms the formation of shallow donor levels necessary for effective n-type conductivity.
Experimental Guidance: The findings provide essential theoretical guidance for engineers and scientists seeking to experimentally grow high-quality n-type diamond for high-power, high-frequency, and high-temperature applications.

Technical Specifications

Parameter	Value	Unit	Context
Computational Method	DFT/CASTEP	N/A	Density Functional Theory using Sequential Total Energy Package
Exchange-Correlation Functional	HSE06	N/A	Used for accurate band structure and ionization energy calculation
Supercell Size	216	Atoms	(3 x 3 x 3) configuration used for doping simulation
Energy Cutoff (Truncation Energy)	750	eV	Fixed plane-wave basis set energy
Geometric Convergence Criterion	< 10^-3	eV/Å	Maximum residual force on individual atoms
P-Only Formation Energy (C₂₁₅P₁)	7.493	eV	High energy, indicating structural instability
P-Vacancy Formation Energy (C₂₁₄P₁V₀)	5.702	eV	More stable, but results in undesirable p-type characteristics
Lowest P-B Cluster Formation Energy (P-P-B)	10.32	eV	B improves P solubility despite higher energy than P-V
Lowest Ionization Energy (P-B-P)	1.52	eV	Shallowest donor level, critical for n-type conductivity
Highest Ionization Energy (P-C-P-C-B)	2.45	eV	Corresponds to maximum separation distance between dopants
Pristine Diamond Lattice Constant (a, b, c)	10.7004	Å	Reference value for comparison
P-Doped Lattice Constant (a)	10.7636	Å	Indicates maximum lattice distortion (0.052 Å expansion)

Key Methodologies

The theoretical analysis relied on rigorous first-principles calculations to model defect stability and electronic properties:

Framework Selection: Density Functional Theory (DFT) was implemented using the Sequential Total Energy Package (CASTEP) for structural optimization.
Potential Modeling: Ultra-soft pseudopotentials were used to model the interaction between ions and valence electrons.
Exchange-Correlation: The Generalized Gradient Approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) parameterization was used for atomic relaxation.
Supercell and K-Points: A periodic supercell containing 216 atoms (3 x 3 x 3 configuration) was sampled using a Monkhorst-Pack k-point grid of (3 x 3 x 3) dimensions.
Convergence Criteria: A fixed energy cutoff of 750 eV was used, and geometric optimization was performed until the residual forces on individual atoms were below 10^-3 eV/Å.
Electronic Property Calculation: The Heyd-Scuseria-Ernzerhof (HSE) 06 functional was employed to accurately determine the band structure, density of states (DOS), and ionization energies, closely matching the experimental band gap of pure diamond (5.480 eV).

6CCVD Solutions & Capabilities

This research confirms that the successful experimental realization of high-performance n-type diamond hinges on precise control over impurity concentration, cluster formation, and minimizing background defects. 6CCVD is uniquely positioned to supply the foundational materials required for this advanced research.

Applicable Materials

To replicate and extend this P-B co-doping research, high-purity, low-defect substrates are essential to ensure that the observed shallow donor levels (1.52 eV) are attributable solely to the engineered P-B clusters.

Electronic Grade Single Crystal Diamond (SCD):
- Requirement: Ultra-low nitrogen and defect density is mandatory to prevent interference with the P-B cluster formation and electronic properties.
- 6CCVD Solution: We provide high-purity SCD substrates (0.1µm to 500µm thickness) grown via MPCVD, offering the crystalline perfection required for fundamental semiconductor studies.
Boron-Doped Diamond (BDD):
- Requirement: While B is used here as a compensatory dopant, researchers may require BDD films for p-type reference layers or integrated p-n junction devices.
- 6CCVD Solution: We offer custom BDD films with controlled doping levels, suitable for electrochemical and electronic applications.

Customization Potential

The experimental implementation of P-B co-doping requires substrates tailored for specific growth or ion implantation techniques, followed by precise device fabrication.

Research Requirement	6CCVD Capability	Technical Advantage
Substrate Size & Scale-Up	Custom Plates/Wafers up to 125mm (PCD) and large SCD plates.	Allows researchers to transition from small-scale experimental validation to practical, inch-size device fabrication.
Surface Quality	Polishing to Ra < 1nm (SCD) and Ra < 5nm (Inch-size PCD).	Ensures atomically smooth surfaces critical for subsequent doping, epitaxial growth, and minimizing surface recombination effects.
Ohmic Contact Integration	In-house custom metalization services (Au, Pt, Pd, Ti, W, Cu).	Enables immediate device testing by providing reliable ohmic contacts necessary for measuring the enhanced electron mobility resulting from the low ionization energy (1.52 eV).
Substrate Thickness	SCD and PCD films from 0.1µm up to 500µm, and substrates up to 10mm.	Provides flexibility for various experimental setups, including thin films for high-frequency devices or thick substrates for high-power heat spreaders.

Engineering Support

The successful realization of n-type diamond based on the P-B cluster model requires expert knowledge in MPCVD growth and defect engineering.

6CCVD’s in-house PhD material science team specializes in optimizing MPCVD growth parameters and defect control. We can assist engineers and scientists in selecting the optimal diamond material (e.g., specific SCD orientation or purity level) required to experimentally replicate or extend this P-B co-doping research for high-power, high-frequency electronic devices.

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

View Original Abstract

To achieve n-type doping in diamond, extensive investigations employing first principles have been conducted on various models of phosphorus doping and boron-phosphorus co-doping. The primary focus of this study is to comprehensively analyze the formation energy, band structure, density of states, and ionization energy of these structures. It is observed that within a diamond structure solely composed of phosphorus atoms, the formation energy of an individual carbon atom is excessively high. However, the P-V complex substitutes 2 of the 216 carbon atoms, leading to the transformation of diamond from an insulator to a p-type semiconductor. Upon examining the P-B co-doped structure, it is revealed that the doped impurities exhibit a tendency to form more stable cluster configurations. As the separation between the individually doped atoms and the cluster impurity structure increases, the overall stability of the structure diminishes, consequently resulting in an elevation of the ionization energy. Examination of the electronic density of states indicates that the contribution of B atoms to the impurity level is negligible in the case of P-B doping.

Tech Support

Original Source

DOI: https://doi.org/10.3390/cryst14050467

References

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2003 - Substitutional oxygen-nitrogen pair in diamond—Art. no. 115206 [Crossref]
1993 - n-type dopants and conduction-band electrons in diamond: Cluster molecular-orbital theory [Crossref]
2022 - The vibrational and dielectric properties of diamond with N impurities: First principles study [Crossref]