Electronic structure of 3d transition elements in β-Si₃N₄

Abstract

Impurity levels due to the presence of 3d transition elements (M) in β-Si₃N₄, the net impurity charge, and the chemical bonds around the impurity atom are all examined by the use of first-principles molecular-orbital calculations for atomic clusters consisting of 13 atoms. The structure of the valence band obtained from calculations on a (Si₃N₁₀)^18- cluster is in good agreement with the experimental X-ray photoelectron emission spectra as well as the Si L X-ray emission spectra of bulk Si₃N₄. M-3d levels are located in a gap between occupied and unoccupied bands of Si₃N₄. The energy of M-3d levels decreases and the occupation number increases with rising atomic number. The net charge is between + 2·1 and + 1·6, depending on the atomic number of M when the formal charge is M⁴⁺. The net charge increment from M²⁺ to M⁴⁺ is about 0·5 for V, Cr and Mn, and it is smaller in the other elements. When formal charges higher than M⁴⁺ are assumed, viz, for V⁵⁺ Cr⁶⁺ and Mn⁷⁺, the net impurity charge turns out to be not significantly different from that obtained for M⁴⁺. This means that N, rather than M, is oxidized when the oxidation number of M is higher than 4+. The overlap population between M and N is far below zero for Ca²⁺, and it increases with rising atomic number. It is between 0·0 and 0·2 for elements between Ti and Ni when the formal charge is M⁴⁺ The overlap population is smaller for M²⁺. The value is negative except for Zn²⁺. The variation of the overlap population is determined by the balance of two terms, i.e. (i) anti-bonding between M core electrons and N-2s/2p valence electrons, and (ii) bonding and anti-bonding between M-3d/4s, 4p valence electrons and N-2s/2p valence electrons. The overlap population may be correlated to the solid solubility and the magnitude of solution effects for 3d transition elements in β-Si₃N₄. The results may be useful as guiding principles for additive selection and alloying design of new Si₃N₄ transition-element systems.