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In the presence of structural disorders, carrier conduction via localized hopping sites emerges in two-dimensional systems and results in a unique thermopower characteristic with T1/3 dependence. The disorders induced potential differences of hopping sites leading to energy variations along current-carrying paths. A systematic thermoelectric study is presently required in comprehending the statistical effects. Therefore, we proposed a statistical model of the Seebeck coefficient on the basis of percolation theory and hopping mechanisms. With this model, the carrier density and temperature dependences can be practically predicted. Key parameters can be extracted by calibration to molybdenum disulfide and black phosphorus experiments, providing a deeper insight into device physics. Moreover, a Mott-like analytical model is developed to investigate the parametric dependence. The thermopower deviations from the noninteracting Mott picture at high and low temperatures are analyzed. Finally, the temperature dependence on the thermoelectric figure of merit is evaluated in a variable range hopping regime. Our model is essential for a reliable prediction of the disorder induced statistical effects on thermoelectric behaviors, which guides both device optimization and material engineering. [ABSTRACT FROM AUTHOR]

A surface potential based compact model for two-dimensional field effect transistors (2D-FETs) is proposed to incorporate the structural disorders induced transition behaviors among variable range hopping (VRH), nearest neighbor hopping (NNH), and band-like transport in most 2D materials. These functions coupled with effective transport energy and multiple trapping and releasing theory enable our developed model to predict the temperature and carrier density dependent current characteristics. Its validity is confirmed by the experimental results such as the metal insulator transition (MIT) in transition metal dichalcogenides and VRH-NNH transition in black phosphorus nanoribbon. Based on this model, the band-tail effects on the crossover gate voltage of MIT behavior are quantitatively investigated. It is found that the transition behavior is closely related to the distribution of the band-tail states. Furthermore, this model is implemented in Verilog-A for circuit-level prediction and evaluation of 2D-FETs to provide deeper insight into the relationship between material properties, device physics, and circuit performances. [ABSTRACT FROM AUTHOR]