Generally Substances with a forbidden band widths Wg < 2eV are considered to be semiconductors while those substances for which Wg > 3eV belong to dielectrics. Now, the question goes like if low band gap semiconductors (Eg
Semiconductors are half conducting half insulating. Their conduction type and conductivity can be varied in a wide range by doping which is the strong property of these class of materials. When intrinsic they contain small concentration of free charge carriers and thereby tend to be insulting while when heavily doped they become metal like with high free carrier concentration.
I would like to invite you to read the chapter of semiconductors in the book: Book Electronic Devices
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At microwave frequencies even high resistivity silicon (very low doped or
compensated) can be considered as a low loss dielectric although
its Wg~1.1 eV.
For more details see e.g. "Dielectric properties of semi-insulating silicon at microwave frequencies" APPLIED PHYSICS LETTERS 107, 082105 (2015)
This is dependent on measurement temperature. The concentration of charge carriers depends on temperature, so in turn the dielectric depends on T for pure and doped semiconductors with shallow dopants (especially ionization energy> 0.025eV, 0.025eV is the thermal energy at 27 C (standards lab conditions).
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