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The superb properties of graphene such as high mobility, broad spectral range of optical transparency, high mechanical flexibility, and impermeability to moisture have made it a promising material for transparent conductor (TC) applications. To optimize the properties of graphene-based TCs, an in-depth understanding of the properties of graphene layers on different materials is crucial. In this paper, the electrostatics and charge screening of Bernal-stacked few-layer graphene (FLG) on surface-passivated semiconductors (SC) are investigated. A self-consistent method is developed, which calculates the equilibrium characteristics of the Schottky barrier at the interface and the charge distribution arising from the impurities on FLG and charge transfer from the SC to FLG. The developed model is applied to FLG/Si structures, and the charge distribution and charge screening effects are investigated. It is shown that with proper selection of doping concentration, the barrier height of the FLG/Si structure under study can be reduced by more than 400 mV, which is crucial in improving the contact resistance between FLG and SC. The self-consistent method and the analysis provide a pathway toward high-performance design of FLG-based TCs.