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A new numerical finite-difference time-domain (FDTD) model of interfaces with metals and semiconductors is developed. The model uses a higher order impedance boundary condition to simulate the fields in conductive media. The approach has been found to be considerably more accurate than the known models based on the simple Leontovich impedance boundary condition. This is because the new model takes the incidence angle of the incident waves into account, and it is valid for all values of conductivity. The derivation of the method is presented in the two-dimensional (2D) case, and the performance is studied over a wide range of conductivity. The validation of the method is made by comparing with the exact results in a 2D example problem. The proposed method is also compared with some other methods available in the literature.