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Silicon nitride (Si₃N₄) possesses excellent mechanical properties and high thermal conductivity, which is an important feature in many applications. However, achieving the theoretically high thermal conductivity of Si₃N₄ in practice is challenging. In this study, we adopted a first-principles calculation method to assess the effects of doping β-Si₃N₄ and γ-Si₃N₄ with carbon and oxygen atoms. Applying geometric structure optimization combined with calculation of the electronic phonon properties generated a stable doped structure. The results revealed that carbon and oxygen doping have little effect on the Si₃N₄ unit cell size, but that oxygen doping increases the unit cell volume. Energy band structure and state density calculation results showed that carbon doping reduces the nitride band gap width, whereas oxygen doping results in an n-type Si₃N₄ semiconductor. The findings from this study are significant in establishing a basis for targeted increase of the thermal conductivity of Si₃N₄.