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Phonon- and defect-limited electron and hole mobility of diamond and cubic boron nitride - A critical comparison

MetadataDetails
Publication Date2021-08-09
JournalApplied Physics Letters
AuthorsNocona Sanders, Emmanouil Kioupakis
InstitutionsUniversity of Michigan
Citations30
AnalysisFull AI Review Included

Phonon- and Defect-Limited Carrier Mobility in Diamond: A 6CCVD Technical Analysis

Section titled “Phonon- and Defect-Limited Carrier Mobility in Diamond: A 6CCVD Technical Analysis”

This document analyzes the findings of the research paper “Phonon- and defect-limited electron and hole mobility of diamond and cubic boron nitride: a critical comparison” to provide technical insights and specific material solutions offered by 6CCVD for ultra-wide-band-gap (UWBG) semiconductor applications.


  • Intrinsic Mobility Limits Established: First-principles calculations confirm the fundamental upper bounds for carrier mobility in diamond (SCD) and cubic boron nitride (cBN) for high-power, high-frequency electronic devices.
  • Superior Electron Mobility: Phonon-limited electron mobility at 300K is high and comparable in both materials (Diamond: 1790 cm2/Vs; cBN: 1610 cm2/Vs), validating their use in high-performance n-type devices, provided high purity is maintained.
  • Diamond Excels in Hole Transport: Diamond exhibits significantly superior intrinsic hole mobility (1970 cm2/Vs) compared to cBN (80.4 cm2/Vs) at 300K, primarily due to the substantially heavier hole effective mass in cBN.
  • Purity is Paramount: The study confirms that at high doping concentrations, mobility is dominated by neutral impurity scattering, driven by the deep ionization energies of common dopants (<1% ionization for B-doped diamond at 300K).
  • Material Quality Validation: The theoretical results underscore the critical need for ultra-high purity, single-crystal diamond (SCD) to minimize defect scattering and achieve the intrinsic mobility limits required for efficient UWBG electronics.
  • 6CCVD Solution: 6CCVD specializes in producing the high-purity SCD and precisely doped BDD materials necessary to meet these stringent intrinsic performance requirements.

The following table summarizes the key calculated intrinsic parameters and mobility limits for diamond derived from the first-principles analysis (300K, phonon-limited unless otherwise noted).

ParameterValueUnitContext
Calculated Band Gap5.66eVDiamond
Calculated Band Gap6.80eVcBN
Phonon-Limited Electron Mobility (ÎŒe)1790cm2/VsDiamond, 300K
Phonon-Limited Hole Mobility (ÎŒh)1970cm2/VsDiamond, 300K
Phonon-Limited Electron Mobility (ÎŒe)1610cm2/VscBN, 300K
Phonon-Limited Hole Mobility (ÎŒh)80.4cm2/VscBN, 300K
Electron Effective Mass (me,l)1.55meDiamond (CBM → Γ/X)
Heavy Hole Effective Mass (mhh)2.52meDiamond (Γ → K)
Boron Acceptor Ionization Energy (Ed)0.37eVUsed for B-doped Diamond calculation
Phosphorus Donor Ionization Energy (Ed)0.84eVUsed for P-doped Diamond calculation
Dopant Ionization Fraction (300K)< 1%Diamond (due to deep Ed)
Dominant Scattering Mechanism (High Doping)Neutral ImpurityN/ADue to high concentration of non-ionized dopants

The intrinsic carrier mobility limits were determined using advanced atomistic first-principles calculations, combining multiple theoretical frameworks:

  1. Structural Relaxation and DFT: Structural relaxation calculations were performed using Density Functional Theory (DFT) with the local density approximation (LDA) within Quantum ESPRESSO.
  2. Quasiparticle Band Structure (GW): Quasiparticle band structures were calculated using the one-shot G0W0 method within BerkeleyGW to accurately determine band gaps and effective masses, converging eigenvalues to within 2 meV.
  3. Phonon Frequencies (DFPT): Phonon frequencies and dispersions were determined using Density Functional Perturbation Theory (DFPT) on an 8 x 8 x 8 BZ sampling grid.
  4. Electron-Phonon Coupling (EPW): Electron-phonon coupling matrix elements were evaluated using the maximally localized Wannier function method within the Electron-Phonon-Wannier (EPW) code, interpolated to fine BZ sampling meshes (up to 88 x 88 x 88).
  5. Mobility Calculation (BTE): Phonon-limited carrier mobility was evaluated as a function of temperature using the iterative Boltzmann Transport Equation (BTE) method.
  6. Impurity Scattering Models:
    • Ionized Impurities: Modeled using the semi-analytical Brooks-Herring model.
    • Neutral Impurities: Modeled using the Erginsoy model, which proved to be the dominant scattering mechanism at high doping levels.

The research confirms that achieving the theoretical intrinsic mobility limits in diamond requires materials with exceptional purity and precise dopant control. 6CCVD’s MPCVD diamond capabilities are engineered specifically to meet these ultra-high standards for UWBG device fabrication.

Application Requirement (Based on Paper)6CCVD Material SolutionKey Specification Match
Achieving Intrinsic Mobility LimitsOptical Grade Single Crystal Diamond (SCD)Ultra-low nitrogen and defect concentration to minimize neutral impurity scattering. Essential for maximizing the 1790 cm2/Vs electron mobility limit.
High-Performance p-type DevicesBoron-Doped Diamond (BDD) SCDPrecise, controlled boron doping (acceptor density up to 1020 cm-3) to enable p-type conduction while minimizing compensation defects.
Substrate/Heat SpreadingHigh Thermal Conductivity SCD/PCD SubstratesDiamond’s superior thermal conductivity (highest known) is critical for managing heat in high-power devices, as noted in the paper. 6CCVD offers substrates up to 10mm thick.

The complexity of UWBG device fabrication demands highly customized material solutions. 6CCVD provides the necessary engineering flexibility:

  • Custom Dimensions and Thickness: The paper discusses thin films and single crystals. 6CCVD supplies SCD plates from 0.1 ”m up to 500 ”m thickness, and PCD wafers up to 125 mm diameter, allowing researchers to scale from fundamental studies to large-area device prototypes.
  • Surface Quality: To reduce surface scattering effects, 6CCVD guarantees ultra-smooth polishing (Ra < 1 nm for SCD and Ra < 5 nm for inch-size PCD), crucial for high-frequency device interfaces.
  • Integrated Metalization: Device contacts are essential for mobility measurements and device operation. 6CCVD offers in-house custom metalization services, including deposition of Au, Pt, Pd, Ti, W, and Cu stacks, tailored to specific ohmic or Schottky contact requirements.
  • Doping Control: We offer precise control over Boron doping concentration in SCD and PCD films, enabling researchers to systematically study the transition from phonon-limited to neutral impurity-limited transport, as detailed in Figure 7 of the paper.

The paper highlights that discrepancies in experimental mobility values often stem from non-optimal material quality (e.g., grain boundaries, mixed phases, or substrate conductivity).

  • Defect Minimization: 6CCVD’s in-house PhD team specializes in MPCVD growth optimization, ensuring the lowest possible concentration of unintentional defects and compensating impurities, which are shown to severely limit mobility, especially in p-type diamond.
  • UWBG Device Optimization: Our experts can assist researchers and engineers in selecting the optimal SCD grade, doping profile, and surface preparation required to replicate or exceed the intrinsic carrier mobility limits identified in this critical UWBG semiconductor research.

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

View Original Abstract

Diamond and cBN are two of the most promising ultra-wide bandgap semiconductors for applications in high-power high-frequency electronic devices. Despite extensive studies on carrier transport in these materials, there are large discrepancies in their reported carrier mobilities. In this work, we investigate the phonon- and dopant-limited electron and hole mobilities of cBN and diamond with atomistic first-principles calculations in order to understand their fundamental upper bounds to carrier transport. Our results show that although the phonon-limited electron mobilities are comparable between cBN and diamond, the hole mobility is significantly lower in cBN due to its heavier hole effective mass. Moreover, although lattice scattering dominates the mobility at low doping, neutral impurity scattering becomes the dominant scattering mechanism at higher dopant concentrations due to the high dopant ionization energies. Our analysis provides critical insights and reveals the intrinsic upper limits to the carrier mobilities of diamond and cBN as a function of doping and temperature for applications in high-power electronic devices.