Terms linear inkin the band structure of wurtzite-type semiconductors

Abstract

Wurtzite has the space-group symmetry P6 3 mc. The absence of inversion symmetry allows linear-k terms in the electronic band structure when the spin-orbit interaction is included. Their existence has been confirmed in a number of experiments, but no microscopic calculations have been published. In the present paper, we discuss the origin of these linear-k terms using group theory and k•p arguments. The various contributions to these terms are identified through band-structure models. We present an ab initio calculation, performed with the linear-muffin-tin-orbital method, of these spin splittings in CdS, CdSe, and ZnO. A renormalization of the valence-band spin-splitting coefficients obtained in the linear-muffin-tin-orbital calculations was found necessary to correct for errors in the relative energies of the uppermost valence bands as compared with the experimental values. We point out that a similar procedure should be used when evaluating masses and other band parameters from calculated local-density-approximation band structures.

Electronic structure and optical properties ofZnX(X=O,S, Se, Te): A density functional study

“…The center of gravity of the A, B, and C states, located at (E g (A) − E g (C))/3 below the topmost A state, remains to be nearly the same as the topmost VB corresponding to the case without the SO coupling. 26,27 Consequently, to compare band structures calculated with and without the SO coupling, one should plot the band structure with Fermi energy at the center of gravity of the A, B, and C states for the former and at the topmost VB for the latter. Hence, when the SO coupling is applied, then the A and B states as well as the bottommost CB move upwards to (E g (A) − E g (C))/3 in energy, whereas the C state moves downwards to (E g (A) − E g (C))2/3 compared to the center of gravity.…”

“…Ref. 21,26,27), without the SO coupling top of the VB of ZnX-w is split into a doublet and a singlet states. In the band structure, Fermi level is located at the topmost one [ Fig.…”

“…the potential U ). Not only the band gap (E g ), but also the crystal-field (CF) and spin-orbit (SO) splitting energies (∆ CF and ∆ SO ), the order of states at the top of the valence band (VB), the location of the Zn-3d band and its width, and the band dispersion are found 21,22,26,27 to be incorrect for ZnO-w by the ab initio full potential (FP) and atomic-sphere-approximation (ASA) lin- ear muffin-tin orbital (LMTO) methods within the pure LDA, 26,27 and by the projector-augmented wave (PAW) method within LDA and GGA. 21,22 These findings were ascribed 21,22 to strong Coulomb correlation effects.…”

Phase stability, electronic structure, and optical properties of indium oxide polytypes

“…Not only the band gap, but also the band dispersion comes out incorrectly and this effect is well pronounced in transition metal oxides (see, e.g., Ref. 55,56,58,[61][62][63][64][65][66] Analysis shows that calculated effective masses for In 2 O 3 -I and -II are almost the same, while those for In 2 O 3 -III are much smaller. Hence, carrier mobility in In 2 O 3 -III is expected to be larger than that in In 2 O 3 -I and -II.…”

“…rigid shift of all the CB states, so that the optical spectra shall also be shifted accordingly. 56,65,66,80 The search of literature shows that among In 2 O 3 -I and -II experimental data is available for the latter in Ref. 48, where reflectivity and transmittance spectra were measured by spectrophotometry at room temperature.…”