Ab initio study of carrier mobility in Bi$_2$O$_2$Se

Technical Summary: Ab initio study of carrier mobility in Bi2O2Se

Problem Statement
Bi2O2Se is an emerging layered semiconductor characterized by excellent air stability and high-performance electronic properties. While experimental studies have demonstrated high electron mobilities in n-type samples and successful fabrication of p-type transistors via Zn doping, a comprehensive theoretical understanding of carrier transport mechanisms remains incomplete. Previous theoretical efforts have relied on approximations such as the Bardeen-Shockley deformation potential theory or the constant relaxation-time approximation within the semiclassical Boltzmann transport equation (BTE). These approaches often neglect the contributions of optical phonons (specifically polar optical phonons) and fail to account for the energy and momentum dependence of carrier relaxation times. Furthermore, while a prior study by the authors addressed electron transport using the self-energy relaxation time approximation (SERTA), a rigorous first-principles investigation of hole mobility and a comparison between approximate and exact BTE solutions for both carrier types in Bi2O2Se were lacking.

Methodology
This work employs parameter-free first-principles calculations to determine electron and hole mobilities in bulk Bi2O2Se. The study utilizes Density Functional Theory (DFT) and Density Functional Perturbation Theory (DFPT) implemented in Quantum ESPRESSO and ABINIT codes. Key methodological features include:

• Iterative BTE Solution: Carrier mobilities are computed by solving the iterative Boltzmann transport equation, which treats electron-phonon and ionized impurity scattering on an equal footing, avoiding the limitations of the SERTA and momentum relaxation time approximation (MRTA).
• Scattering Mechanisms: The calculations explicitly include electron-phonon scattering (accounting for Fröhlich interactions and dynamical quadrupole corrections) and electron-ionized impurity scattering (using a first-principles treatment of band structures and anisotropic dielectric constants).
• Convergence and Corrections: Dynamical quadrupole corrections are included to accurately model electron-phonon interactions in polar materials. The study employs adaptive broadening and linear extrapolation to ensure convergence with respect to k- and q-point grid sizes and energy windows.
• Hall Effect: Hall mobilities are calculated by solving the BTE under a small external magnetic field to facilitate direct comparison with experimental Hall measurements.

Key Results

1. Anisotropic Transport Behavior: The study reveals a unique transport dichotomy in Bi2O2Se: it exhibits three-dimensional (3D) electron transport and two-dimensional (2D) hole transport.
   • Electrons: High mobilities are observed in both in-plane and out-of-plane directions. At 300 K, the intrinsic phonon-limited electron mobilities are calculated to be 447 cm² V⁻¹ s⁻¹ (in-plane) and 227 cm² V⁻¹ s⁻¹ (out-of-plane).
   • Holes: Hole mobility is significant only in the in-plane direction (29 cm² V⁻¹ s⁻¹ at 300 K), while the out-of-plane mobility is nearly zero. This is attributed to a large out-of-plane hole effective mass (13.24 m₀) compared to the in-plane harmonic average (0.31 m₀).
2. Scattering Mechanisms:
   • Electrons: At room temperature, polar optical phonons, specifically the longitudinal optical (LO) mode, dominate electron scattering, contributing approximately 80% of the total scattering rate via the Fröhlich interaction.
   • Holes: The LO phonon mode also accounts for 60% of the hole scattering rate, with longitudinal acoustic (LA) phonons contributing significantly across a broad frequency range.
3. Impact of Approximations: The study demonstrates that while SERTA consistently underestimates in-plane electron mobilities across the entire temperature range, MRTA results agree well with the full iterative BTE solution in the 50–400 K range. However, MRTA underestimates mobility below 50 K.
4. Ionized Impurity Scattering: Due to the exceptionally large static dielectric permittivity of Bi2O2Se (156 in-plane, 83 out-of-plane), Coulomb scattering from ionized impurities is effectively screened. Consequently, electron mobilities remain robust against impurity scattering over a wide concentration range (10¹⁴ to 10¹⁷ cm⁻³) and temperatures above 50 K. At low temperatures (10 K) and high doping (10¹⁷ cm⁻³), total mobilities reach 7.7 × 10⁴ cm² V⁻¹ s⁻¹ (in-plane) and 2.9 × 10⁴ cm² V⁻¹ s⁻¹ (out-of-plane).
5. Hall Mobility: The calculated in-plane electron Hall mobility at 300 K is 517 cm² V⁻¹ s⁻¹, which shows excellent agreement with experimental data (440 cm² V⁻¹ s⁻¹) from low-residual-carrier samples.

Significance and Claims
The authors claim that this work provides a rigorous, parameter-free theoretical benchmark for carrier transport in Bi2O2Se. By utilizing an iterative solution of the BTE with quadrupole corrections, the study clarifies the dominance of Fröhlich interactions in limiting mobility and explains the material's defect tolerance and high low-temperature mobility through its large dielectric constant. The identification of 3D electron and 2D hole transport suggests the feasibility of planar p-n homojunctions in Bi2O2Se for future high-performance transistors. The results offer predictive benchmarks for future theoretical and experimental investigations into Bi2O2Se-based electronic and optoelectronic applications. The paper does not propose new experimental protocols but rather interprets existing experimental trends through a more accurate theoretical lens.