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The spectra of terahertz generation from the surface of silicon crystals with different types of conductivity upon excitation by femtosecond laser pulses at different temperatures were experimentally recorded. Comparison of the characteristic spectral features with the energy structure of the impurity levels of silicon makes it possible to identify the type of sample conductivity. A comparison is made with the results obtained at cryogenic temperatures in the case of deposition of gold nanoparticles on the surface of a semiconductor. The spectral features obtained after the deposition of nanoparticles are considered in the model of terahertz re-radiation as a result of their two-phonon absorption.