Ab initio study of lattice dynamics of group IV semiconductors using pseudohybrid functionals for extended Hubbard interactions

At a Glance

Metadata	Details
Publication Date	2021-09-27
Journal	Physical review. B./Physical review. B
Authors	Wooil Yang, Seung-Hoon Jhi, Sanghoon Lee, Young‐Woo Son
Institutions	Pohang University of Science and Technology
Citations	19
Analysis	Full AI Review Included

Technical Documentation & Analysis: MPCVD Diamond for Advanced Lattice Dynamics

Executive Summary

This technical analysis reviews the ab initio study of Group IV semiconductors (Diamond, Si, Ge) using extended Hubbard functionals (DFT+U+V). The findings validate a highly accurate computational methodology essential for designing next-generation diamond-based devices, directly supporting the material requirements fulfilled by 6CCVD.

Validation of Advanced Modeling: The extended Hubbard functional (DFT+U+V) accurately predicts static and dynamic lattice properties (lattice constants, bulk modulus, phonon dispersion, thermal conductivity) for diamond, surpassing traditional LDA, PBEsol, and HSE functionals.
Superior Thermal Prediction: The DFT+U+V method yields increased phonon velocities and lifetimes, resulting in lattice thermal conductivity (κ) predictions for diamond that align exceptionally well with experimental data.
Critical Role of Intersite Interaction (V): The study confirms that the intersite Hubbard term (V) is crucial for correctly describing covalent bonding and $sp^{3}$ hybridization in diamond, leading to accurate electronic band gaps and structural stability.
Direct Relevance to SCD: The high accuracy achieved in modeling diamond’s intrinsic properties (especially thermal transport and band structure) is vital for engineers utilizing 6CCVD’s Single Crystal Diamond (SCD) in high-power and quantum applications.
Material Specification Confidence: This research provides theoretical confidence for material selection in applications requiring ultra-precise control over diamond’s thermal and electronic characteristics.

Technical Specifications

The following hard data points for Diamond (C) were achieved using the extended Hubbard functional (U+V), demonstrating excellent agreement with experimental values, confirming the accuracy of the methodology for material design.

Parameter	Value (U+V)	Unit	Context / Experimental Value
Optimized Lattice Constant	3.562	Å	Exp: 3.567 Å (0.14% error)
Optimized Bulk Modulus	450	GPa	Exp: 442 GPa (1.8% error)
Indirect Band Gap (E_gⁱ)	5.47	eV	Exp: 5.48 eV
Direct Band Gap ($\Gamma$ point)	7.22	eV	Exp: 7.3 eV
On-site Hubbard Term (U_p)	5.91	eV	For p orbital
Intersite Hubbard Term (V_pp)	2.92	eV	For p-p orbitals (critical for $sp^{3}$ bonding)
Phonon Frequency ($\Gamma_{LO/TO}$)	39.9	THz	Exp: 40.3 THz
Thermal Conductivity (κ)	Larger than LDA/PBEsol	W/m·K	Achieved by larger phonon lifetime and steeper acoustic dispersion.

Key Methodologies

The research employed a sophisticated computational approach combining Density Functional Theory (DFT) with advanced corrections to accurately model the lattice dynamics of Group IV semiconductors.

Functional Selection: DFT calculations were performed using the newly developed ab initio extended Hubbard functional (DFT+U+V), which includes both onsite (U) and intersite (V) Coulomb interactions, determined self-consistently (ACBN0 functional).
Computational Environment: Calculations utilized QUANTUM ESPRESSO with norm-conserving pseudopotentials (NC-PP) from the Pseudo Dojo library.
Self-Consistent Parameter Determination: The Hubbard parameters U and V were calculated self-consistently, with a threshold of 10^-8 Ry for total energy convergence. The intersite cutoff distance was set to include nearest neighbors.
Force Calculation: Lattice dynamics required accurate force calculations, including the Pulay forces derived from the localized-orbital projectors (Löwdin orthonormalized atomic orbitals, LOAO). The derivatives of U and V were found to contribute minimally and were largely neglected.
Lattice Dynamics: Harmonic and cubic anharmonic Interatomic Force Constants (IFCs) were calculated using the frozen-phonon method in a 64-atom supercell.
Thermal Transport Calculation: Lattice thermal conductivity (κ) for Diamond (C) was calculated by the direct solution of the linearized Phonon Boltzmann Transport Equation (BTE), necessary due to the dominance of normal processes over Umklapp scattering in diamond.

6CCVD Solutions & Capabilities

This research validates the theoretical tools necessary for engineering high-performance devices based on the intrinsic properties of diamond, particularly its exceptional thermal and electronic characteristics. 6CCVD provides the physical materials required to realize these designs.

Applicable Materials

To replicate or extend this research into functional devices, engineers require high-purity, low-defect diamond materials.

Optical Grade Single Crystal Diamond (SCD): Essential for applications leveraging diamond’s superior electronic band structure (5.47 eV indirect gap) and highest intrinsic thermal conductivity (κ). 6CCVD provides SCD plates with controlled nitrogen incorporation (Type IIa or Type Ib) to meet specific optical and electronic requirements.
High Thermal Conductivity SCD: The study confirms that diamond’s high κ is due to long phonon lifetimes and steep acoustic dispersion. 6CCVD specializes in producing SCD optimized for thermal management, crucial for high-power electronics and heat spreaders.
Boron-Doped Diamond (BDD): While the paper focuses on intrinsic C, Si, and Ge, BDD (a p-type semiconductor) is often used in electrochemical and electronic applications. 6CCVD offers custom BDD films for extending this research into doped systems.

Customization Potential

The precision required for advanced semiconductor research necessitates highly customized material specifications. 6CCVD’s manufacturing capabilities directly address these needs:

Requirement from Research	6CCVD Customization Capability
Precise Geometry/Integration	Custom Dimensions: Plates and wafers up to 125mm (PCD) and custom SCD sizes.
Controlled Thickness	Thickness Control: SCD and PCD layers from 0.1 µm up to 500 µm, ensuring optimal thermal and electronic performance profiles.
Surface Quality	Polishing: Ultra-low surface roughness (Ra < 1 nm for SCD; Ra < 5 nm for inch-size PCD), critical for minimizing phonon scattering and maximizing device yield.
Device Interfacing	Custom Metalization: In-house deposition of Au, Pt, Pd, Ti, W, and Cu for ohmic contacts, electrodes, or heat sinking layers, facilitating integration into complex systems.

Engineering Support

The successful application of the DFT+U+V methodology relies on accurate material parameters. 6CCVD’s in-house PhD team offers authoritative support:

Material Selection for Thermal Management: Our experts assist in selecting the optimal SCD grade based on required thermal conductivity (κ) and operating temperature, directly leveraging the principles validated in this lattice dynamics study.
Structural Integration Consultation: We provide guidance on material dimensions, crystal orientation, and surface preparation necessary for projects involving high-frequency phonon dynamics or quantum sensing.
Global Logistics: We ensure reliable, global shipping (DDU default, DDP available) of highly sensitive diamond materials, minimizing logistical overhead for international research teams.

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

View Original Abstract

We study the lattice dynamics of group IV semiconductors using fully\nab-initio extended Hubbard functional. The onsite and intersite Hubbard\ninteractions are determined self-consistently with recently developed\npseudohybrid functionals and included in force calculations. We analyze the\nPulay forces by the choice of atomic orbital projectors and the force\ncontribution of the onsite and intersite Hubbard terms. The phonon dispersions,\nGruneisen parameters, and lattice thermal conductivities of diamond, silicon,\nand germanium, which are most-representative covalent-bonding semiconductors,\nare calculated and compared with the results using local, semilocal, and hybrid\nfunctionals. The extended Hubbard functional produces increased phonon\nvelocities and lifetimes, and thus lattice thermal conductivities compared to\nlocal and semilocal functionals, agreeing with experiments very well.\nConsidering that our computational demand is comparable to simple local\nfunctionals, this work thus suggests a way to perform high-throughput\nelectronic and structural calculations with a higher accuracy.\n

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.104.104313