Anisotropic carrier transport in layered semiconductors is a fundamental aspect that distinguishes these materials from conventional isotropic semiconductors. The directional dependence of electronic properties arises from the structural asymmetry in layered crystals, where in-plane and out-of-plane bonding exhibit significant differences. This anisotropy manifests in carrier mobility, effective mass, and scattering mechanisms, influencing the performance of electronic and optoelectronic devices.

Layered semiconductors such as molybdenum disulfide (MoS2) and black phosphorus (BP) exhibit strong anisotropy due to their crystal structure. In MoS2, a transition metal dichalcogenide, the hexagonal lattice within the plane results in isotropic transport parallel to the layers. However, carrier movement perpendicular to the layers is hindered by weak van der Waals interactions. Black phosphorus, with its puckered orthorhombic structure, shows even more pronounced anisotropy. The armchair and zigzag directions within the plane exhibit different carrier transport properties due to variations in atomic arrangement and bond angles.

The directional dependence of carrier mobility is a key metric for understanding anisotropic transport. In black phosphorus, experimental studies have reported hole mobility values ranging from approximately 1,000 cm²/Vs along the armchair direction to around 600 cm²/Vs along the zigzag direction at room temperature. Electron mobility follows a similar trend but with lower absolute values. For MoS2, in-plane mobility typically falls between 10 and 200 cm²/Vs depending on defect density and dielectric environment, while out-of-plane mobility is orders of magnitude lower due to the high barrier for interlayer hopping.

Hall effect measurements in anisotropic systems require careful interpretation. The standard Hall effect assumes isotropic conductivity, but in layered materials, the resistivity tensor must account for directional differences. The Hall coefficient and carrier concentration are derived from a tensor analysis rather than a scalar approach. For example, in BP, the Hall voltage depends on the orientation of the current flow relative to the crystallographic axes. Measurements along different directions yield distinct mobility values, reflecting the anisotropic nature of the material.

Scattering mechanisms also exhibit directional dependence. In isotropic materials like silicon, phonon scattering and impurity scattering are uniformly distributed. In contrast, anisotropic materials have direction-specific phonon modes and defect interactions. For instance, in MoS2, longitudinal acoustic phonons dominate scattering in the in-plane direction, while interlayer phonons affect out-of-plane transport. Black phosphorus shows anisotropic acoustic phonon coupling, with stronger scattering along the zigzag direction compared to the armchair direction.

Temperature-dependent studies further highlight anisotropy. Carrier mobility in isotropic semiconductors typically follows a power-law dependence on temperature due to uniform phonon scattering. In anisotropic materials, the temperature dependence varies with direction. For BP, mobility along the armchair direction decreases more rapidly with increasing temperature than along the zigzag direction, indicating stronger electron-phonon coupling in the former.

Comparison with isotropic semiconductors reveals fundamental differences. Silicon and gallium arsenide exhibit nearly identical transport properties regardless of crystal orientation. In contrast, layered semiconductors require explicit consideration of directionality in device design. For example, field-effect transistors made from BP perform optimally when the channel is aligned with the high-mobility armchair direction. Misalignment can lead to significant performance degradation.

The effective mass tensor is another critical factor. In isotropic materials, effective mass is a scalar quantity. In anisotropic materials, it becomes a tensor with different components along principal axes. For electrons in BP, the effective mass is approximately 0.08m₀ in the armchair direction and 0.15m₀ in the zigzag direction, where m₀ is the free electron mass. This difference directly impacts carrier velocity and device speed.

Anisotropic transport also affects quantum phenomena. In isotropic materials, quantum confinement effects are symmetric. In layered semiconductors, confinement varies with direction. For example, quantum wells in MoS2 exhibit different energy level spacings for in-plane and out-of-plane confinement due to the anisotropic effective mass.

Practical implications of anisotropic transport include the need for orientation control during material integration. Misaligned layers can lead to unpredictable device behavior. Techniques such as angle-resolved Raman spectroscopy and polarized photoluminescence are used to determine crystal orientation before device fabrication.

The study of anisotropic carrier transport provides insights into fundamental material properties and guides the design of next-generation electronic devices. Understanding directional dependence enables optimization of performance metrics such as speed, power efficiency, and noise characteristics. Future research may explore engineered anisotropy through strain or heterostructuring to achieve tailored transport properties.

In summary, anisotropic carrier transport in layered semiconductors is a complex phenomenon governed by crystal structure, scattering mechanisms, and directional dependencies. Hall measurements must account for tensor properties, and comparisons with isotropic materials highlight the unique challenges and opportunities presented by these systems. The continued investigation of anisotropic transport will drive advancements in semiconductor technology.