Ab initio study of lattice dynamics of group IV semiconductors using pseudohybrid functionals for extended Hubbard interactions
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-09-27 |
| Journal | Physical review. B./Physical review. B |
| Authors | Wooil Yang, Seung-Hoon Jhi, Sanghoon Lee, YoungâWoo Son |
| Institutions | Pohang University of Science and Technology |
| Citations | 19 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis study introduces the application of a fully ab initio extended Hubbard functional (DFT + U + V) to accurately model the lattice dynamics and electronic structure of Group IV semiconductors (C, Si, Ge).
- Core Value Proposition: The extended Hubbard functional achieves predictive accuracy comparable to high-level methods (e.g., GW, HSE hybrid functionals) but maintains a computational demand similar to simple local functionals (LDA/PBE).
- Methodology: Onsite (U) and intersite (V) Hubbard interactions are determined self-consistently using a pseudohybrid approach (ACBN0), eliminating empirical parameter fitting.
- Structural Accuracy: Calculated equilibrium lattice constants and bulk moduli show excellent agreement with experimental measurements (within 0.2% and 3% error, respectively).
- Dynamic Accuracy: The functional accurately predicts phonon band structures, mode GrĂŒneisen parameters, and phonon lifetimes, correctly capturing the effects of covalent bonding via the intersite V term.
- Thermal Performance: The calculated lattice thermal conductivities (kappa) for C, Si, and Ge are significantly improved compared to LDA/PBEsol results, matching experimental values very well due to increased phonon velocities and lifetimes.
- Engineering Impact: This approach suggests a viable path for performing high-throughput electronic and structural calculations with significantly higher accuracy than traditional DFT methods.
Technical Specifications
Section titled âTechnical SpecificationsâThe following table summarizes key calculated and experimental parameters for the Group IV semiconductors using the extended Hubbard functional (U + V).
| Parameter | Material | Calculated Value (U + V) | Experimental Value | Unit | Context |
|---|---|---|---|---|---|
| Lattice Constant | C | 3.562 | 3.567 | Angstrom | Optimized structure |
| Lattice Constant | Si | 5.434 | 5.431 | Angstrom | Optimized structure |
| Lattice Constant | Ge | 5.662 | 5.658 | Angstrom | Optimized structure |
| Bulk Modulus | C | 450 | 442 | GPa | Structural stiffness |
| Bulk Modulus | Si | 95 | 96-99.4 | GPa | Structural stiffness |
| Bulk Modulus | Ge | 72 | 75-75.8 | GPa | Structural stiffness |
| Indirect Band Gap (Eig) | Si | 1.23 | 1.12 | eV | Electronic structure |
| Direct Band Gap (Edg) | C | 7.22 | 7.3 | eV | Electronic structure |
| On-site U (p orbital) | C | 5.91 | N/A | eV | Self-consistent Hubbard term |
| Intersite V (p-p orbital) | C | 2.92 | N/A | eV | Extended Hubbard term |
| Phonon Frequency (LO/TO) | C | 39.9 | 40.3 | THz | Gamma point frequency |
| Phonon Frequency (LO/TO) | Si | 15.6 | 15.5 | THz | Gamma point frequency |
| Thermal Conductivity (kappa) | C | ~2000 | ~2300 | W/mK | Calculated at 100 K (Linearized BTE) |
Key Methodologies
Section titled âKey MethodologiesâThe computational study utilized a specialized DFT framework incorporating self-consistent Hubbard parameters to model lattice dynamics accurately.
- Functional Choice: Density Functional Theory (DFT) calculations were performed using the extended Hubbard functional (DFT + U + V), based on the Agapito-Curtarolo-Buongiorno Nardelli (ACBN0) pseudohybrid method.
- Parameter Determination: The onsite (U) and intersite (V) Hubbard parameters were calculated self-consistently using Hartree-Fock (HF) formalism, ensuring they are ab initio (non-empirical).
- Software and Pseudopotentials: Calculations utilized the QUANTUM ESPRESSO package and norm-conserving pseudopotentials (NC-PP) from the Pseudo Dojo library.
- Convergence Settings: A kinetic energy cutoff of 100 Ry was used. The self-consistency threshold for total energy and Hubbard interactions was set to 10-8 Ry. The intersite V cutoff included only nearest neighbors.
- Force Calculation Basis: Forces were calculated using orthogonalized atomic wave functions (Löwdin orthonormalized atomic orbitals, LOAO) as projectors. This choice was critical for correctly handling the Pulay forces arising from the localized orbital basis, which are essential for accurate lattice dynamics.
- Interatomic Force Constants (IFCs): Harmonic (second-order) and cubic anharmonic (third-order) IFCs were calculated using the frozen-phonon method on a 64-atom supercell.
- Thermal Transport Modeling: Lattice thermal conductivity was calculated using the Phonon Boltzmann Transport Equation (BTE).
- For Si and Ge, the Relaxation Time Approximation (RTA) was employed.
- For C (Diamond), the direct solution of the linearized BTE was used due to the dominance of normal scattering processes.
Commercial Applications
Section titled âCommercial ApplicationsâThe ability to accurately and efficiently model the structural, electronic, and thermal properties of semiconductors is crucial for several high-performance engineering sectors.
- High-Power Electronics and RF Devices:
- Accurate modeling of Diamond (C) thermal conductivity (kappa) is essential for designing high-efficiency heat spreaders and substrates in GaN and SiC power modules.
- Improved prediction of phonon lifetimes leads to better thermal management solutions for high-frequency applications.
- Semiconductor Manufacturing (CMOS/FinFET):
- Precise calculation of lattice constants and bulk moduli for Si and Ge allows for accurate simulation of strain engineering effects, which are vital for boosting carrier mobility in advanced transistor architectures.
- Materials Discovery and Optimization:
- The computational efficiency of the U + V functional enables high-throughput screening of new Group IV alloys (e.g., SiGe) and heterostructures, accelerating the discovery of materials with tailored band gaps and thermal properties.
- Optoelectronics and Infrared Technology:
- Accurate band gap and structural modeling of Ge is critical for its use in integrated silicon photonics, especially for infrared detectors and light sources.
- Thermal Expansion Control:
- Accurate calculation of mode GrĂŒneisen parameters (especially the negative values in Si and Ge acoustic modes) provides the necessary input for predicting and controlling thermal expansion in composite materials and micro-electromechanical systems (MEMS).
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