Mobility Anisotropy in Black Phosphorus MOSFETs With HfO₂; Gate Dielectrics

Precise measurements of the mobility anisotropy along high-symmetry crystal axes in black phosphorus (BP) MOSFETs are reported. Locally back-gated BP MOSFETs with 13-nm HfO₂ dielectric and channel length ranging from 0.3 to 0.7 μm are fabricated. A single BP flake of a uniform thickness is exfoliated and etched along armchair (AC) and zigzag (ZZ) crystal axes, and the orientations are confirmed using optical and transmission electron microscopy analyses. The hole and electron mobilities along each direction are extracted using the transfer length method. The AC-to-ZZ hole mobility ratio is found to increase from 1.4 (1.5) to 2.0 (2.9) as the sheet concentration increased from 5.1× 10¹¹ to 1.9× 10¹² cm^-2 at room temperature (77 K). The room-temperature electron mobility anisotropy is found to be similar to that for holes with an AC-to-ZZ mobility ratio increasing from 1.4 to 2.1 from 5.1× 10¹¹ to 1.9× 10¹² cm^-2 though electrons showed only a very weak temperature dependence. A Boltzmann transport model is used to explain the concentration- and temperature-dependent mobility anisotropies which can be well described using a charge center scattering model.