Energy band of ternary alloy semiconductors—Calculation by a coherent-potential approximation based on the method of linear combination of bond orbitals

Abstract

A method of calculating the effect of the random distribution of atoms on the energy‐band structure of ternary alloy semiconductors is proposed, where the coherent‐potential approximation based on the method of linear combination of bond orbitals (LCBO) is used. In the case of GaAs_cP_1−c, the nonlinear dependence of the energy upon the alloy composition c at various symmetry points within the first Brillouin zone is calculated. It is found that the effect of disorder is an important factor in explaining the bowing effect of band gaps; In particular, the magnitudes of the direct gap Γ^v₁₅→Γ^c₁, and the indirect gap Γ^v₁₅→X^c₁ agree well with experimental results. The energy‐band structure, including the lifetime broadening of the energy at each Bloch state, is shown for GaAs_0.5P_0.5. Also, the relation between the LCBO parameters and the effect of disorder on various states is qualitatively discussed. The effect of disorder on the p‐like or s‐like states of the valence band increases with increasing the difference between the p‐like or s‐like energy levels, which are represented by the bonding orbitals, of both alloy constituents. The relation between the effect of disorder on the conduction band and the antibonding orbitals is the same as the relation between the effect of disorder at the sites of group‐V atoms and that at the sites of group‐III atoms appears noticeably at the points X^c₁ and X^c₃ of the conduction band and at the points X^v₁ and X^v₃ of the valence band.