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-fied 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.During the three last decades, a huge amount of work has been devoted to the understanding of the plasmonic properties of complex metallic nanostructures, either individually or as the elementary brick of a metamaterial. This interest was also driven by potential applications in sensing devices [1], nanophotonic devices [2], photocatalysis [3], and field-enhanced spectroscopies [4,5,6,7]. However, the use of metals such as gold or silver is still an issue due to a poor compatibility with the semiconductor processing technology, and to strong dissipation losses at optical and infrared frequencies.Recently, a new category of plasmonic materials emerged, with the study of Localized Surface Plasmon Resonance (LSPR) in heavily doped semiconductor nanostructures and metamaterials [8,9,10,11]. Compared to metals, the imaginary part of the dielectric constant in the visible and infrared range is low for most semiconductors, leading to weak losses. As for metals, the LSPR frequency is tunable by the constituent material, the size and shape of the nanostructure, and its dielectric environment. However, the active dopant concentration, thus the free carrier (electrons or holes) concentration, allows to finely tune the LSPR frequency [8,10]. Notably, the lower order of magnitude of carrier density in degenerate semiconductors with respect to noble metals has an attractive consequence: even a minor modification of the * Corresponding author