How dopants limit the ultrahigh thermal conductivity of boron arsenide: a first principles study

The study addresses how substitutional group IV dopants (C, Si, Ge) and their charge states limit the ultrahigh lattice thermal conductivity of cubic boron arsenide (BAs), a material of interest for power electronics due to its exceptionally high κ (~1300 W·m⁻¹·K⁻¹ at room temperature) and predicted high carrier mobilities. While intrinsic anharmonic phonon scattering and native defects are known to affect κ, a comprehensive assessment of extrinsic dopants’ impact was lacking. The research aims to quantify κ reduction as a function of dopant species, site (B or As), concentration, and charge state, and to understand the roles of mass versus bond perturbations and of compensation (Fermi-level pinning) during doping. The work is significant for enabling doped BAs devices that retain superior heat dissipation, informing dopant selection and process conditions to minimize thermal performance loss.

Prior experiments and first-principles studies established ultrahigh κ in BAs consistent with theory, attributable to features such as high bond stiffness, large As/B mass ratio, a wide acoustic–optic gap, narrow optic bandwidth, acoustic branch bunching, and weak four-phonon scattering. Predictions also suggest high room-temperature electron and hole mobilities (>1000 cm²·V⁻¹·s⁻¹). Earlier works examined intrinsic defects (antisites, vacancies) and their κ suppression, and investigated thermodynamic stability and ionization of neutral and charged dopants in BAs, highlighting group IV species (C, Si, Ge) due to their periodic-table positions. Recent studies indicated BAs is highly p-dopable and that unintentional C and Si impurities (from precursors) may influence conductivity, motivating a systematic evaluation of extrinsic dopants’ phonon scattering and κ impact.

• Transport framework: The lattice thermal conductivity was computed by solving the linearized phonon Boltzmann Transport Equation (BTE) with the full iterative solution using almaBTE, treating three-phonon processes beyond SMRTA (included in the collision operator) and four-phonon and defect scattering within SMRTA.
• Scattering processes: Total phonon relaxation rates combine three-phonon, four-phonon, isotope, and phonon-defect scattering via Matthiessen’s rule. Four-phonon rates were interpolated from prior first-principles results.
• Defect scattering theory: Substitutional dopants introduce on-site mass perturbations (V_M) and bond/force-constant perturbations (V_K). Phonon-defect scattering was treated to all orders using a T-matrix formalism with the retarded Green’s function of the pristine crystal, yielding mode-resolved scattering rates. The dilute-defect limit (≲0.1% of B or As sites) and random distribution were assumed; multiple-defect interference and frequency renormalization were neglected.
• First-principles calculations: DFT (VASP, PAW, PBE) provided harmonic force constants for pristine and defected 5×5×5 supercells (250 atoms). Bond perturbations were constructed from IFC2 differences with locality enforced via real-space cutoffs (pair cutoff ~0.6 nm; neighbor list cutoff ~0.8 nm) and acoustic sum-rule projection. For neutral defects exhibiting metallic character, VASP smearing parameters (ISMEAR=1, SIGMA=0.2) were used. Charged states were modeled by adding/removing one electron for As/B substitutions with a compensating uniform background.
• Brillouin-zone sampling: A 28×28×28 mesh was used for transport; Green’s functions on a 16×16×16 grid.
• Dopant species and charge states: Group IV dopants C, Si, Ge substituting on As or B sites were considered in neutral and singly charged states, guided by lowest formation energies (Si_As, Ge_As, C_As, Si_B, Ge_B, C_B; charged cases e.g., Si_B⁻, Ge_B⁻, C_B⁻).
• Descriptor for bond scattering: A descriptor D_def,κ was defined as the sum over phonon-defect scattering rates due to V_K only within 4–8 THz (the dominant κ-contribution window) at one defect per unit cell, to compare neutral vs charged impurities’ bond-scattering strengths.
• Compensation modeling: Donor compensation beyond Fermi-level pinning was modeled using formation energy crossings and ionization energies from first principles (literature values). Charge neutrality p−n=N_A⁻−N_D⁺ was enforced with parabolic-band DOS and effective masses (m*≈0.56 for holes, ≈0.4 for electrons). Growth temperature T_growth=1163 K set fixed acceptor/donor fractions (via formation-energy differences), then acceptor ionization fractions were evaluated at 300 K. κ vs impurity concentration curves included contributions from charged and neutral acceptors and compensating donors.
• Growth conditions: As-rich and B-rich cases were considered using reported Fermi-level pinning values for C, Si, Ge; transport temperature was 300 K.

• Neutral vs charged impurities: A general trend is identified whereby neutral impurities scatter phonons more strongly than charged, approximately isoelectronic, counterparts. This arises because ionized states more closely match the host’s electronic occupation, reducing bond perturbations.
• Mass vs bond perturbations: In BAs (large As/B mass ratio), acoustic modes are dominated by As motion; thus mass defects on As sites strongly scatter acoustic phonons, whereas mass defects on B sites can be comparatively weak. However, bond (force-constant) perturbations can dominate when mass variance is small (e.g., Ge_As, C_B) or complement mass effects (e.g., Si_B).
• Dopant-specific κ impacts at 300 K: • Ge_As and C_B exhibit exceptionally weak phonon scattering; BAs maintains κ > ~1000 W·m⁻¹·K⁻¹ even at high densities for these defects. • Strongest κ suppression arises from C_As and Ge_B; a 50% κ reduction to ~600 W·m⁻¹·K⁻¹ occurs at ~10¹⁹ cm⁻³. Si_As closely follows due to large mass variance despite relatively weak bond perturbation. • Si_B shows significant κ reduction driven by strong bond perturbations in the 4–8 THz range, despite weak low-frequency mass scattering.
• Compensation effects: • Ge doping: At low concentrations, Ge_As (neutral/acceptor) reduces κ only slightly; beyond Fermi-level pinning, formation of compensating Ge donors (e.g., Ge_As⁻/donor states) accelerates κ reduction relative to the uncompensated case. • C doping: Since C⁻ scatters weakly compared with C⁰/C⁺ on the relevant sites, inclusion of compensation yields κ curves that lie above the uncompensated C_As case, especially for B-rich growth. • For As-rich growth typical of current synthesis, Ge doping allows p-type levels approaching ~10¹⁹ cm⁻³ with comparatively small κ reduction up to the compensation threshold; beyond that, κ drops faster.
• Carrier concentrations: Maximum free hole densities (As-rich growth) are estimated as ~2×10¹⁸ cm⁻³ (Si), ~1×10¹⁸ cm⁻³ (Ge), and ~1.5×10¹⁷ cm⁻³ (C), the lower C value stemming from its larger acceptor ionization energy (0.09 eV vs 0.03 eV for Si/Ge).
• Absolute κ levels: Even at high dopant densities across C, Si, Ge, BAs retains κ > ~600 W·m⁻¹·K⁻¹, far exceeding common semiconductors (e.g., Si ~140 W·m⁻¹·K⁻¹, GaAs ~45 W·m⁻¹·K⁻¹).
• Practical implication: Measuring κ vs dopant concentration can reveal the onset of donor compensation via characteristic changes in slope relative to charged-acceptor-only expectations.

The results directly address the central question of how group IV dopants limit BAs’s ultrahigh thermal conductivity and which dopant/site/charge configurations best preserve κ while enabling doping. The general finding that charged impurities (isoelectronic with the substituted host) scatter phonons more weakly than neutrals explains why dopant charge state and activation are critical for κ retention. Site dependence and the large As/B mass ratio clarify why As-site substitutions (with large mass variance) can strongly scatter, unless bond perturbations are minimal (e.g., Ge_As). The compensation analysis links growth thermodynamics (Fermi-level pinning) to thermal transport: beyond pinning, donor formation alters the defect population and scattering landscape, producing experimentally observable κ signatures. Practically, Ge_As and C_B substitutions allow high κ even at substantial concentrations, suggesting routes to dope BAs (notably p-type with Si_As or Ge_As) while minimizing thermal penalties. The ability to maintain κ well above that of conventional semiconductors supports BAs’s promise as a self-cooling functional material. Moreover, κ measurements can serve as a diagnostic for compensation doping, informing process optimization.

First-principles BTE–T-matrix calculations show that in BAs neutral group IV impurities generally scatter phonons more strongly than charged ones, due to larger bond perturbations. Ge_As and C_B are exceptionally weak phonon scatterers, enabling κ ≳ 1000 W·m⁻¹·K⁻¹ even at high dopant densities, whereas C_As, Ge_B, and Si_As produce the largest κ reductions. Si and Ge can achieve relatively high hole densities (~10¹⁸ cm⁻³) while maintaining high κ, making them attractive p-type dopants. Donor compensation beyond Fermi-level pinning produces distinct κ vs concentration behaviors (accelerated drop for Ge, mitigation for C), offering an experimental handle to detect compensation. Overall, BAs can retain κ > ~600 W·m⁻¹·K⁻¹ under significant doping, underscoring its potential in high-power electronics. Future work should identify viable n-type dopants (given large formation/ionization energies for C_As donors) and further investigate the generality of weaker phonon scattering by isoelectronic charged impurities across materials.

• The compensation analysis relies on formation energies, ionization energies, and effective masses from prior ab initio studies; uncertainties in these inputs and in actual growth conditions (As-rich vs B-rich) affect quantitative predictions.
• Parabolic-band approximations for DOS and fixed effective masses were used; nonparabolicity and full band structures could modify carrier and ionization estimates.
• Four-phonon scattering rates were interpolated from previous calculations rather than recomputed for the exact settings used; residual inconsistencies may remain.
• The defect treatment assumes dilute, randomly distributed, non-interacting impurities; clustering, multiple-defect interference, or higher concentrations could alter scattering and κ.
• Frequency renormalization and long-range effects from defects were neglected at the considered concentrations.
• Some affiliations and experimental corroborations are not provided within this text; empirical validation of compensation-induced κ signatures remains for future work.