The alternating-direction implicit finite-difference time-domain (ADI-FDTD) method is a promising unconditionally stable scheme that may improve the computational efficiency. However, no general dispersive media were considered in the ADI-FDTD community. The dispersive property, in fact, is important for semiconductor device design at radio-frequency. In this paper, the ADI-FDTD method is applied to complex structures such as on-chip spiral inductor with honeycomb oxide trench, buried layer removal, and radial patterned ground shield. The proposed formula is applicable to linearly dispersive and lossy media. Using this approach, the overall accuracy has been obtained with little computational overhead