Calculated spin-orbit splitting of all diamondlike and zinc-blende semiconductors: Effects of p 1 ∕ 2 local orbitals and chemical trends

By P. Carrier, Suhuai Wei. 2004

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We have calculated the spin-orbit $(\mathrm{SO})$ splitting ${\ensuremath{\Delta}}_{SO}=ϵ({\ensuremath{\Gamma}}_{8v})\ensuremath{-}ϵ({\ensuremath{\Gamma}}_{7v})$ for all diamondlike group IV and zinc-blende group III-V, II-VI, and I-VII semiconductors using the full potential linearized augmented plane wave method within the local density approximation. The $\mathrm{SO}$ coupling is included using the second-variation procedure, including the ${p}_{1∕2}$ local orbitals. The calculated $\mathrm{SO}$ splittings are in very good agreement with available experimental data. The corrections due to the inclusion of the ${p}_{1∕2}$ local orbital are negligible for lighter atoms, but can be as large as $\ensuremath{\sim}250\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ for $6p$ anions. We find that (i) the $\mathrm{SO}$ splittings increase monotonically when anion atomic number increases; (ii) the $\mathrm{SO}$ splittings increase with the cation atomic number when the compound is more covalent such as in most III-V compounds; (iii) the $\mathrm{SO}$ splittings decrease with the cation atomic number when the compound is more ionic, such as in II-VI and the III-nitride compounds; (iv) the common-anion rule, which states that the variation of ${\ensuremath{\Delta}}_{SO}$ is small for common-anion systems, is usually obeyed, especially for ionic systems, but can break down if the compounds contain second-row elements such as $\mathrm{BSb}$; $(\mathrm{v})$ for IB-VII compounds, the ${\ensuremath{\Delta}}_{SO}$ is small and in many cases negative and it does not follow the rules discussed above. These trends are explained in terms of atomic $\mathrm{SO}$ splitting, volume deformation-induced charge renormalization, and cation-anion $p\text{\ensuremath{-}}d$ couplings.

Subfields: Electrical and Electronic Engineering, Inorganic Chemistry, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/74f011de1505d1cd9a3d988304e1bcc139f9417a