  Ideal two-dimensional (2D) semiconductors with high mobility comparable to
three-dimensional (3D) Si or GaAs are still lacking, hindering the development
of high-performance 2D devices. Here in this work, using first-principles
calculations and considering all the electron-phonon couplings, we show that
monolayer BX (X = P, As, Sb) with honeycomb lattices have intrinsic
phonon-limited carrier mobility reaching record-high values of 1200-14000
$cm^2V^{-1}s^{-1}$ at room temperature. Despite being polar and the band edges
located at the K point with multiple valleys, these three systems unusually
have small carrier scattering rates. Detailed analysis shows that, both the
intravalley scattering and the intervalley scattering between two equivalent K
points are weak, which can be understood from the large mismatch between the
electron bands and phonon spectrum and suppressed electron-phonon coupling
strength. Furthermore, we reveal the general trend of mobility increase from BP
to BAs and to BSb and conclude that: smaller effective masses, larger sound
velocities, higher optical phonon energies, heavy atomic masses, and
out-of-plane orbitals tend to result in small match between the electron and
phonon bands, small electron-phonon coupling strengths, and thus high mobility.
Our work demonstrates that 2D semiconductors can achieve comparable carrier
mobility to 3D GaAs, thus opening doors to 2D high-performance electronic
devices.
