【Member Papers】Machine learning and first-principles calculations for electronic and transport properties in p-type Cd-doped two-dimensional Ga₂O₃

      Researchers from Hunan University of Science and Engineering, Xiamen University, Hunan University, Jishou University have published a dissertation titled "Machine learning and first-principles calculations for electronic and transport properties in p-type Cd-doped two-dimensional Ga₂O₃" in Journal of Physics D: Applied Physics.

Background

      Two-dimensional β-Ga₂O₃ inherits the ultra-wide bandgap advantages of bulk materials, and meanwhile exhibits dimensional confinement effect and large specific surface area, showing broad application prospects in nanoscale optoelectronic devices. Considerable progress has been achieved on n-type doping of two-dimensional Ga₂O₃, nevertheless, the p-type doping bottleneck severely hinders its device implementation. The valence band maximum features relatively flat orbitals, and acceptor impurities tend to form deep-level acceptor states, making effective hole conduction difficult to realize. Existing theoretical works have screened potential p-type dopants including Mg, Zn and Cd. Among them, Cd doping presents obvious Fermi-level downward shift and low activation energy, but most relevant investigations focus on three-dimensional bulk systems. Two-dimensional Ga₂O₃ is obtained via mechanical exfoliation by breaking Ga-O bonds, its atomic arrangement differs evidently from three-dimensional counterparts, and conclusions for bulk phases cannot be directly extrapolated to 2D cases. At present, systematic quantitative investigations on band engineering, hole transport and thermal transport properties for Cd-doped two-dimensional Ga₂O₃ are insufficient. Besides, the application of machine-learning atomic potentials for thermal-transport simulation of this 2D doped system remains to be verified. Such research gap restricts the design and development of two-dimensional p-type Ga₂O₃ materials.

Abstract

      Addressing the p-type doping bottleneck in 2D Ga₂O₃ remains a crucial challenge for advancing next-generation electronics. In this study, we employ Heyd–Scuseria–Ernzerhof hybrid density functional calculation to reveal that the p-type conductivity of 2D Cd-doped Ga₂O₃ (Cd_GaI) originates from the strongly hybridization between Cd-4d_xy and O-2p states at the valence band maximum (VBM), while retaining a direct bandgap feature. The enhanced VBM band curvature reduces the hole effective mass and yields an ultrahigh hole mobility of ~ 417.68 cm² V⁻¹ s⁻¹, accompanied by a pronounced mobility anisotropy of 34.86. Using the highly efficient neuroevolution potential-based machine learning, the calculated lattice thermal conductivity of Cd_GaI is decreased by ∼30% compared with that of perfect 2D Ga₂O₃. This can be attributed to the increased atomic mass of Cd and enhanced scattering of low-frequency acoustic and optical phonons, both of which shorten the phonon mean free path. Temperature-dependent lattice thermal conductivity follows a power law behavior of ~ T^-1.3 along the x direction, indicating combined three-phonon and four-phonon scattering processes, whereas ~ T^-1.1 along the y direction, where three-phonon scattering dominate. Particularly, Cd_GaI structure with −2% compressive strain exhibits the robust p-type conductivity, direct bandgap, ultra-high hole mobility and anisotropy, underlining its strong potential for optoelectronic device applications.

Highlights

      Hybrid HSE functional calculations reveal that p-type conduction of Cd-doped 2D Ga₂O₃originates from strong hybridization between Cd-4d_xy and O-2p states at VBM with direct bandgap maintained.

      Obtain ultra-high hole mobility of ~ 417.68 cm² V⁻¹s⁻¹ and large mobility anisotropy for unstrained Cd_GaI from deformation potential theory.

      NEP-ML simulations show that lattice thermal conductivity of Cd_GaIis reduced by ~30%, and anisotropic phonon scattering mechanisms along x / y directions are clarified.

      −2% compressive-strained Cd_GaIsimultaneously realizes robust p-type conductivity, direct bandgap, high hole mobility and transport anisotropy for optoelectronic applications.

Conclusion

      Using first-principles and ML NEP methods in conjunction with DP theory, the detailed structural stability, electronic properties, lattice thermal transport, and carrier mobilities of Cd-doped 2D Ga₂O₃ are explored. Our result indicate that the foreign Cd preferentially substitute at the GaI site, especially under the O-rich condition. The thermodynamic and dynamic stabilities of Cd_GaI structure are further corroborated by the MD simulations and phonon dispersion analyses, respectively. Charge analysis demonstrates that the charge density of the VBM is predominantly by the Cd dopant and its neighboring O atoms, while the CBM is mainly distributed around the host Ga atoms and a minor contribution of O. Moreover, charge density difference and Bader charge analysis illustrate pronounced charge depletion around the Cd dopant and the lost electron is about 1.32 e. Comparisons between the ML-NEP predictions and DFT reference values for energy, force, and stress display consistently strong correlations. NEP-based phonon dispersion shows a relatively steep slope within the 0–3 THz range, which gradually becomes flatter at higher frequencies. In the low-frequency regime (below 10 THz), the PDOS along the y direction is higher than that along the x direction, indicating that the thermal conductivity along the x direction is greater than that along the y direction. The Debye temperature of the system is estimated to be about 800 K based on the temperature-dependent behavior of the lattice heat capacity. Notably, our calculations reveal that under ±6% biaxial strain, Cd_GaI retains a robustly direct bandgap character. The bandgap steadily varies from 4.24 eV to 3.51 eV because of the faster upward movement of the VBM relative to the CBM.

      Compared with pristine 2D Ga₂O₃, the lattice thermal conductivities of Cd_GaI configuration are decreased from 22.32 to 14.72 and from 16.53 to 11.35 Wm⁻¹ K⁻¹ along the x and y directions, respectively. This reduction can be attributed to the increased atomic mass upon Cd incorporation and the enhanced scattering of low-frequency phonons by the induced point defect, both of which shorten the phonon mean free path. Spectrally resolved lattice thermal conductivity further demonstrates that low-frequency acoustic phonons make a dominant contribution to the lattice thermal conductivity. The contribution from the acoustic branches to phonon transport is also reduced upon Cd incorporation.

      The lattice thermal conductivity decreases from 14.72 to 5.28 Wm⁻¹ K⁻¹ as temperature increases from 300 to 700 K along x direction (following a ~ T^-1.3 trend), which indicates that both three-phonon and four-phonon scattering processes govern the thermal transport. Along y direction, it decreases from 11.35 to 4.78 Wm⁻¹ K⁻¹ and follows an approximate ~ T^-1.1 dependence, indicating that three-phonon scattering process dominates. Moreover, the decline in lattice thermal conductivity along the y direction is also associated with a reduced contribution of acoustic phonons. Strain-dependent phonon dispersions show that the Cd_GaI structure maintains good dynamic stability under tensile strain, whereas its dynamic stability is reduced under compressive strain. The μ_hx and μ_hy are respectively 417.68 cm² V⁻¹ s⁻¹ and 11.98 cm² V⁻¹ s⁻¹ for unstrained case. As the strain moves from −6% compression to 6% tension, μ_hx increases steadily from 266.72-435.68 cm² V⁻¹ s⁻¹ and declines continuously to 322.45 cm² V⁻¹ s⁻¹ along the x direction, while μ_hy shows a monotonic decrease from 14.43 to 11.66 cm² V⁻¹ s⁻¹ along the y direction. Meanwhile, the anisotropy initially increases from 18.48 to 34.86, then decreases to 27.67. In summary, Cd_GaI under -2% compressive strain shows simultaneously robust P-type conductivity, a direct bandgap, ultra-high hole mobility and strong transport anisotropy, underlining its considerable potential for optoelectronic device applications.

Project Support

      This project was funded by the Natural Science Foundation of Hunan Province (Grant No. 2024JJ7200) and the Fundamental Research Funds for Central Universities (Grant No. 20720240147), Scientific Research Foundation of Hunan Provincial Education Department (Grant No. 25A0590), as well as the Open Fund Project of the Key Laboratory of Computational and Applied New Functional Materials in Hunan Provincial Universities (Grant No. 202507).