First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-01-10 |
| Journal | Reports on Progress in Physics |
| Authors | Samuel Poncé, Wenbin Li, Sven Reichardt, Feliciano Giustino |
| Citations | 277 |
| Analysis | Full AI Review Included |
6CCVD Technical Documentation: Ab Initio Analysis of Charge Carrier Mobility in Advanced Semiconductors
Section titled â6CCVD Technical Documentation: Ab Initio Analysis of Charge Carrier Mobility in Advanced SemiconductorsâThis documentation analyzes the key findings of the research review, âFirst-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials,â connecting advanced theoretical requirements to 6CCVDâs state-of-the-art MPCVD diamond material solutions.
Executive Summary
Section titled âExecutive SummaryâThis review validates the critical role of first-principles (ab initio) methods in predicting intrinsic charge carrier transport properties for advanced semiconductors. The findings underscore the superior performance potential of high-purity diamond, a core 6CCVD specialization.
- Validation of Diamond: Ab initio Boltzmann Transport Equation (BTE) calculations confirm that diamond possesses extremely high intrinsic electron and hole mobilities (up to 4,500 cm2/Vs), positioning it as the leading wide-bandgap material for high-power/high-frequency electronics.
- Mobility Bottleneck Identified: Unlike many III-V materials where polar optical phonons dominate scattering, diamondâs intrinsic mobility at room temperature is primarily limited by acoustic phonon scattering, validating its robust thermal characteristics.
- Requirement for Purity: Achieving the predicted intrinsic mobilities necessitates minimizing extrinsic scattering sources (impurities and defects), demanding ultra-high-purity Single Crystal Diamond (SCD) materials.
- Methodological Complexity: Accurate calculation of transport coefficients requires highly complex theoretical approaches (DFPT for EPI, GW corrections, iterative BTE solutions) and relies on highly converged results from ultra-dense Brillouin zone grids.
- Material Selection Criticality: The predictive accuracy of transport models hinges directly on the precision of the input material parameters (e.g., band structure, effective mass), emphasizing the need for defect-controlled, high-quality crystalline substrates.
Technical Specifications
Section titled âTechnical SpecificationsâThe table below summarizes key performance indicators (KPIs) extracted for diamond and relevant competing wide-bandgap materials discussed using first-principles calculations.
| Parameter | Value (Electron Mobility) | Value (Hole Mobility) | Unit | Context |
|---|---|---|---|---|
| Diamond Intrinsic Mobility (Calculated) | 1,800 - 4,500 | 1,830 - 3,800 | cm2/Vs | Room Temperature (300 K) |
| Silicon Intrinsic Mobility (Calculated) | ~1,366 | ~658 | cm2/Vs | Room Temperature (300 K) |
| Wurtzite GaN Mobility (Calculated) | 457 - 905 | 18 - 44 | cm2/Vs | Room Temperature (300 K) |
| GaAs Intrinsic Mobility (Calculated) | 7,050 - 8,900 | 459 - 658 | cm2/Vs | Room Temperature (300 K) |
| Diamond Bandgap (Indirect) | 5.55 | eV | Fundamental Property | Highest wide-bandgap reviewed |
| Dominant Scattering (Diamond, 300 K) | Acoustic Phonons | Acoustic Phonons | N/A | High-energy optical phonons become significant only at T > 300 K |
| Minimum SCD Polishing Requirement | Ra < 1 | nm | Surface Roughness | Essential for low-loss interfaces and 2D material studies (MoS2, Silicene) |
Key Methodologies
Section titled âKey MethodologiesâThe advanced ab initio modeling techniques reviewed demand input materials of exceptionally high structural and electronic quality. Replicating or advancing this research requires stringent material control aligned with the following computational methodology steps:
- Transport Equation Selection: Utilization of the Boltzmann Transport Equation (BTE) solved iteratively, or the Kubo formalism, to describe time-independent (DC) or AC transport, respectively.
- Electronic Structure Foundation: Electronic band structures must be derived from Density Functional Theory (DFT) inputs, typically requiring subsequent many-body corrections (e.g., GW perturbation theory or Hybrid Functionals) to accurately describe wide bandgaps (like 5.55 eV in diamond).
- Scattering Rate Derivation: Electron-Phonon Interaction (EPI) matrix elements must be computed ab initio using Density Functional Perturbation Theory (DFPT) to ensure non-empirical accuracy.
- Brillouin Zone Integration: Mobility calculations are highly sensitive to the integration accuracy, necessitating the use of ultra-dense k-point and q-point grids (e.g., 4003) facilitated by techniques like Maximally Localized Wannier Function (MLWF) interpolation.
- Relativistic Inclusion: Spin-Orbit Coupling (SOC) must be included, particularly for accurate calculation of hole mobility (e.g., SCD hole mobility is strongly underestimated if SOC is neglected).
- Mechanisms Included: Full inclusion of key scattering mechanisms: acoustic-deformation potential, polar optical phonon (Fröhlich coupling, critical for polar materials like GaN or InSe), and piezoelectric scattering (critical for non-centrosymmetric materials).
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & Capabilitiesâ6CCVD provides the specialized MPCVD diamond substrates and engineering services necessary to validate the predictive power of ab initio transport models and realize next-generation high-mobility devices.
Applicable Materials for High Intrinsic Mobility Research
Section titled âApplicable Materials for High Intrinsic Mobility ResearchâThe core challenge identified in the research review is ensuring that the experimental mobility approaches the high intrinsic, phonon-limited theoretical values. This requires the suppression of scattering from defects and impurities.
| Material Requirement (Based on Review) | 6CCVD Solution | Technical Justification & Application |
|---|---|---|
| Ultra-High Purity Substrates | Single Crystal Diamond (SCD): Electronic Grade, Nitrogen-Free. | SCD minimizes extrinsic scattering (impurities, defects), allowing research to isolate and measure the intrinsic acoustic phonon-limited mobility predicted in Section 4.1.2. |
| Large-Area Diamond Plates | Polycrystalline Diamond (PCD) wafers up to 125mm diameter. | Supports scaling R&D findings (e.g., on GaN/SiC alternatives) from small research samples to commercially viable high-power device architectures. |
| Electrochemical/Doping Studies | Boron-Doped Diamond (BDD). | Enables targeted studies on carrier transport dependence on doping concentration and defect screening effects, addressing parameters like $n_{h}$ and $n_{i}$ discussed in Sections 2 and 4.1.1. |
Customization Potential for Advanced Engineering
Section titled âCustomization Potential for Advanced EngineeringâThe precise nature of ab initio modeling demands exact physical realization of simulated structures. 6CCVDâs capabilities directly address these engineering needs:
| Service Category | 6CCVD Capability | Research Relevance |
|---|---|---|
| Dimensional Control | Plates/Wafers up to 125mm (PCD); Thicknesses 0.1”m - 500”m (SCD/PCD). | Enables production of custom-geometry diamond devices and epitaxial growth substrates for materials like GaN and Ga2O3. |
| Surface Quality | Ultra-low roughness polishing: Ra < 1nm (SCD); Ra < 5nm (Inch-size PCD). | Critical for interfaces in 2D material studies (Graphene, MoS2) and for minimizing interface roughness scattering in high-electron-mobility devices. |
| Device Integration | In-house custom metalization (Au, Pt, Pd, Ti, W, Cu). | Essential for creating precise Hall measurement contacts (Fig. 3) and fabricating low-resistance Ohmic contacts required for validating mobility and conductivity tensors $\sigma_{\alpha\beta}$. |
| Substrate Form Factor | Precision laser cutting and shaping services. | Supports complex device geometries and integration with cooling/packaging solutions for high-power electronics where diamondâs superior thermal properties are leveraged. |
Engineering Support
Section titled âEngineering SupportâThe successful realization of predicted intrinsic mobilities depends on meticulous material selection and quality control. 6CCVDâs in-house PhD-level engineering team provides comprehensive support in:
- Material Specification: Assisting researchers in selecting the optimal SCD or PCD grade to minimize background impurity scattering, ensuring experimental results align closely with the intrinsic, phonon-limited transport calculations (BTE/Kubo).
- Interface Optimization: Providing consultation on surface preparation and metalization schemes compatible with specific wide-bandgap and 2D materials (e.g., GaN, MoS2) to achieve predictive device performance in high-power and spintronics applications.
- Global Logistics: Offering reliable Global DDU shipping (with DDP available upon request) to ensure researchers worldwide receive highly controlled diamond materials promptly and reliably.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
One of the fundamental properties of semiconductors is their ability to support highly tunable electric currents in the presence of electric fields or carrier concentration gradients. These properties are described by transport coefficients such as electron and hole mobilities. Over the last decades, our understanding of carrier mobilities has largely been shaped by experimental investigations and empirical models. Recently, advances in electronic structure methods for real materials have made it possible to study these properties with predictive accuracy and without resorting to empirical parameters. These new developments are unlocking exciting new opportunities, from exploring carrier transport in quantum matter to in silico designing new semiconductors with tailored transport properties. In this article, we review the most recent developments in the area of ab initio calculations of carrier mobilities of semiconductors. Our aim is threefold: to make this rapidly-growing research area accessible to a broad community of condensed-matter theorists and materials scientists; to identify key challenges that need to be addressed in order to increase the predictive power of these methods; and to identify new opportunities for increasing the impact of these computational methods on the science and technology of advanced materials. The review is organized in three parts. In the first part, we offer a brief historical overview of approaches to the calculation of carrier mobilities, and we establish the conceptual framework underlying modern ab initio approaches. We summarize the Boltzmann theory of carrier transport and we discuss its scope of applicability, merits, and limitations in the broader context of many-body Greenâs function approaches. We discuss recent implementations of the Boltzmann formalism within the context of density functional theory and many-body perturbation theory calculations, placing an emphasis on the key computational challenges and suggested solutions. In the second part of the article, we review applications of these methods to materials of current interest, from three-dimensional semiconductors to layered and two-dimensional materials. In particular, we discuss in detail recent investigations of classic materials such as silicon, diamond, gallium arsenide, gallium nitride, gallium oxide, and lead halide perovskites as well as low-dimensional semiconductors such as graphene, silicene, phosphorene, molybdenum disulfide, and indium selenide. We also review recent efforts toward high-throughput calculations of carrier transport. In the last part, we identify important classes of materials for which an ab initio study of carrier mobilities is warranted. We discuss the extension of the methodology to study topological quantum matter and materials for spintronics and we comment on the possibility of incorporating Berry-phase effects and many-body correlations beyond the standard Boltzmann formalism.