The presence of a Localized Surface Plasmon Resonance in doped semiconductor nanostructures opens a new field for plasmonics and metasurfaces. Semiconductor nanostructures can be easily processed, have weak dissipation losses, and the plasmon resonance can be tuned from the mid- to the near-infrared spectral range by changing the dopant concentration (in complement to the constituent material, the size and shape of the nanostructure). We present in this paper an extension of the Green Dyadic Method applied to the case of doped silicon nanostructures of arbitrary shape on a planar silica substrate. The method is used to compute both far- and near-field optical properties, such as the extinction efficiency and the electromagnetic near-field intensity inside and around any doped silicon nanostructure, respectively. This theoretical approach provides an important tool for active dopant characterization in doped semiconductor nanostructures, for near-field imaging of complex nanoantennas produced by electron beam lithography, and for the definition of doped semiconductor-based metasurfaces.