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Surprising stability of neutral interstitial hydrogen in diamond and cubic BN

MetadataDetails
Publication Date2016-01-21
JournalJournal of Physics Condensed Matter
AuthorsJohn L. Lyons, Chris G. Van de Walle
InstitutionsUniversity of California, Santa Barbara
Citations9
AnalysisFull AI Review Included

Technical Documentation & Analysis: Interstitial Hydrogen in Diamond

Section titled “Technical Documentation & Analysis: Interstitial Hydrogen in Diamond”

Reference Paper: Lyons, JL, Van de Walle, CG. (2016). Surprising stability of neutral interstitial hydrogen in diamond and cubic BN. JOURNAL OF PHYSICS-CONDENSED MATTER, 28(6).


This theoretical analysis, highly relevant to MPCVD diamond growth and quantum applications, confirms the unique behavior of interstitial hydrogen ($\text{H}_i$) in diamond. 6CCVD provides the high-purity, custom-engineered Single Crystal Diamond (SCD) required to experimentally validate and leverage these findings.

  • Positive-U Behavior Confirmed: $\text{H}_i$ in diamond exhibits strong positive-U character (U = 2.03 eV), a behavior fundamentally different from the negative-U character observed in most other wide-band-gap semiconductors (e.g., GaN, AlN).
  • Neutral State Stability: The neutral charge state ($\text{H}_i^0$) is predicted to be stable over an exceptionally wide Fermi-level range of 2.03 eV, indicating its persistence across various doping conditions.
  • CVD Relevance: Hydrogen is a common unintentional impurity in Chemical Vapor Deposition (CVD) diamond growth. Understanding its charge state stability is critical for controlling material quality and electronic properties.
  • NV Center Impact: The findings directly impact the formation kinetics and charge state stability of the Nitrogen-Vacancy (NV) center, a key defect for quantum computing, spintronics, and metrology applications.
  • Structural Preference: $\text{H}_i$ strongly prefers the Bond-Centered (BC) configuration, leading to significant lattice relaxation, which is attributed to diamond’s small lattice constant.
  • Computational Accuracy: Calculations utilized state-of-the-art Hybrid Density Functional Theory (HSE) to achieve high accuracy, predicting a band gap (5.35 eV) in close agreement with the experimental value (5.47 eV).

The following hard data points were extracted from the HSE calculations regarding bulk diamond properties and $\text{H}_i$ defect levels.

ParameterValueUnitContext
Calculated Lattice Constant3.54ÅDiamond bulk property (Exp: 3.57 Å)
Calculated Indirect Band Gap5.35eVHSE calculation (Exp: 5.47 eV)
Calculated Direct Band Gap ($\Gamma$)7.06eVHSE calculation (Exp: 7.02 eV)
$\text{H}_i$ Positive-U Value (U)2.03eVDefined as the energy difference between (+/0) and (0/-) transition levels
$\text{H}_i$ Stability Range ($\text{H}_i^0$)2.03eVFermi-level range where the neutral state is most stable
$\text{H}_i$ Transition Level (+/0)1.76eVAbove Valence Band Maximum (VBM)
$\text{H}_i$ Transition Level (0/-)3.79eVAbove Valence Band Maximum (VBM)
$\text{H}_i$ Transition Level (+/-)2.78eVAbove VBM (Used for universal band alignment reference)
$\text{H}_i$ Exchange Splitting ($\text{H}_i^0$)2.52eVCalculated for the neutral charge state
$\text{H}_i$ Metastable Energy (Tetrahedral)1.20eVHigher than the preferred Bond-Centered (BC) configuration

The theoretical results rely on a highly specific computational recipe using advanced Density Functional Theory (DFT). Experimental validation of these defect levels requires diamond materials grown under controlled MPCVD conditions, which 6CCVD specializes in.

  1. Computational Method: Generalized Kohn-Sham scheme utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional.
  2. Supercell Geometry: Defect calculations performed using a 216-atom supercell to minimize spurious defect-defect interactions.
  3. Kinetic Energy Cutoff: A high cutoff of 400 eV was applied to ensure convergence and accuracy.
  4. Brillouin Zone Sampling: A 2x2x2 special k-point mesh was used for sampling the Brillouin zone.
  5. HSE Functional Parameters: The HSE mixing parameter ($\alpha$) was set to 0.25, and the screening length ($\omega^{-1}$) was set to 0.2 Å.
  6. Energy Reference: Formation energies were calculated relative to the energy of one-half the $\text{H}_2$ dimer, a standard reference for hydrogen chemical potential.
  7. Correction: Finite-size supercell corrections were applied to accurately model charged defect states.

The research highlights the critical role of hydrogen impurities in CVD diamond, particularly concerning NV center formation and charge state control. 6CCVD provides the necessary high-purity, custom-engineered diamond substrates to experimentally verify these theoretical predictions and advance quantum device fabrication.

Research Requirement6CCVD Material SolutionTechnical Rationale
Intrinsic Defect StudyHigh Purity Single Crystal Diamond (SCD)Required for fundamental studies of $\text{H}_i$ stability, minimizing interference from other unintentional impurities (e.g., Nitrogen).
NV Center ResearchControlled Nitrogen-Doped SCDEssential for studying the interaction between $\text{H}_i$ and NV centers, as discussed in the paper. 6CCVD offers precise nitrogen incorporation during MPCVD growth.
Electronic ControlBoron-Doped Diamond (BDD) PlatesTo experimentally shift the Fermi level ($\text{E}_F$) across the predicted 2.03 eV stability range of $\text{H}_i^0$, controlled p-type doping is necessary.

6CCVD’s in-house manufacturing capabilities directly address the needs of researchers working on diamond defects and quantum applications:

  • Custom Dimensions: We supply SCD and PCD plates/wafers up to 125mm in diameter, allowing for large-scale experimental arrays or device fabrication.
  • Thickness Control: Precise control over active layer thickness is available, ranging from 0.1 ”m to 500 ”m (SCD/PCD), and substrate thicknesses up to 10 mm.
  • Surface Engineering: For high-fidelity optical and electronic measurements (critical for NV centers), 6CCVD offers ultra-smooth polishing:
    • SCD: Surface roughness $\text{R}_a$ < 1 nm.
    • Inch-size PCD: Surface roughness $\text{R}_a$ < 5 nm.
  • Metalization Services: If subsequent device fabrication requires ohmic contacts or gate structures, 6CCVD provides custom metalization stacks (Au, Pt, Pd, Ti, W, Cu) applied directly to the diamond surface.

6CCVD’s in-house PhD team specializes in the physics and chemistry of MPCVD diamond growth and defect engineering. We offer consultation services to assist researchers in:

  • Material Selection: Choosing the optimal diamond grade (e.g., high-purity SCD vs. controlled-doped BDD) to achieve specific Fermi-level positions necessary to probe the predicted $\text{H}_i$ charge states.
  • Growth Recipe Optimization: Tailoring CVD parameters to minimize or intentionally incorporate hydrogen impurities, crucial for controlling NV center formation kinetics.
  • Surface Termination: Advising on surface preparation (e.g., hydrogen termination, which affects the VBM position) to align with specific experimental requirements derived from theoretical models.

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

View Original Abstract

In virtually all semiconductors and insulators, hydrogen interstitials ([Formula: see text]) act as negative-U centers, implying that hydrogen is never stable in the neutral charge state. Using hybrid density functional calculations, we find a different behavior for [Formula: see text] in diamond and cubic BN. In diamond, [Formula: see text] is a very strong positive-U center, and the [Formula: see text] charge state is stable over a Fermi-level range of more than 2 eV. In cubic BN, a III-V compound similar to diamond, we also find positive-U behavior, though over a much smaller Fermi-level range. These results highlight the unique behavior of [Formula: see text] in these covalent wide-band-gap semiconductors.