Temperature effects on the anisotropic mobility of doped phosphorene due to carrier scattering on charged impurities evaluated with energy loss method

We present a comprehensive theoretical investigation into the finite-temperature mobility tensor of monolayer black phosphorus (phosphorene), leveraging the energy loss method (ELM) for charge-carrier scattering on charged impurities. Building upon our previous zero-temperature analysis, we extend the ELM framework to systematically examine temperature effects, impurity placement, dielectric encapsulation, and spatial correlation among charged impurities. Our approach is benchmarked against recent results from the Boltzmann transport equation framework, demonstrating quantitative and qualitative agreement and confirming the ELM as a computationally efficient yet accurate methodology. Our detailed analysis reveals distinct behaviors of mobility and anisotropy in phosphorene with respect to temperature, carrier density, impurity proximity, and dielectric environment. We find that placing impurities closer to the phosphorene channel significantly enhances mobility anisotropy, with increased temperature gradually reducing this effect due to enhanced screening. Notably, encapsulation using high-κ gate dielectrics substantially elevates overall mobility and reduces its temperature dependence, particularly at lower carrier densities, attributed to stronger impurity screening effects. Furthermore, spatial correlation among impurities strongly influences mobility at low temperatures, but its impact diminishes notably with rising temperature, converging toward the behavior observed for uncorrelated impurities. Our analytical approach, expressed in dimensionless variables, explicitly highlights how various physical parameters influence mobility in a general anisotropic two-dimensional (semi-)conductor. This study provides new insights that can guide optimized design and engineering of future phosphorene-based nanoelectronic devices.