Momentum Matrix Elements of GaN

In the analyses of conventional zincblende (ZB) semiconductors, we frequently assume a parabolic band for the conduction bands, and the 6 x 6 Luttinger-Kohn Hamiltonians are used to describe the upper valence bands [1,2], In treating the valence bands together with the conduction bands on an equal footing, as when estimating the momentum matrix elements, we often make use of the 8 x 8 Kane Hamiltonian [3], However, the form of the Hamiltonians reflects the crystal symmetry, and Kane Hamiltonians are constructed under the condition of cubic symmetry. For wurtzite (WZ) materials, therefore, we must consider hexagonal symmetry in the effective Hamiltonian. Let us consider the 8 x 8 k.p Hamiltonian for WZ structure [4,5], 

We take the following basis functions in the order shown  

Here H cc and H w are different in their physical meaning from the Hamiltonians H .(k) and Hv(k) defined in Datareview A6.1, though they have the same form as each other. If the interaction H is also treated within the second-order perturbation, then the block-diagonalised 2x2 and 6x6 matrices are in agreement with 2x2 and 6x6 Hamiltonians, H ,(k) and Hv(k), respectively. 

Note that the momentum matrix elements, P ( and P , are different from each other in WZ structure due to the anisotropy between the directions parallel and perpendicular to the c-axis. P2 and P2i can be analytically derived from the WZ 8x8 Hamiltonian as follows  

WUvIv 111 g (U1U 111 g Uvllvlv Ulv vlCvliUll vllvvllVv llldddCd (HUll Ulv 2 UUvvUvll (U1U ill Uiv Aj Iky piOilV) 

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A6.4 Luttinger and Bir-Pikus parameters of GaN and AIN A6.5 Electron and hole effective masses of GaN and AIN A6.6 Deformation potentials of GaN and AIN A6.7 Momentum matrix elements of GaN A6.8 Subband structures of GaN/AlGaN quantum wells A6.9 Optical gain of bulk GaN and GaN/AlGaN quantum wells... 

A6.7 Momentum matrix elements of GaN B MOMENTUM MATRIX ELEMENTS... 

Kageshima and Shiraishi directly calculated the momentum matrix elements from the wave functions at the T point, with the ultrasoft pseudo-potential method including a core-repair term [14], Their result shows that the momentum matrix elements of ZB and WZ GaN are almost the same and about 40% smaller than that of ZB GaAs. This trend is consistent with the result of Suzuki et al although the absolute values are about 30% smaller. Experimentally, the momentum matrix element was indirectly deduced from a fit to photoluminescence (PL) spectra and optical absorption by Im et al [15], Fanciulli et al measured the g-value by electron spin resonance (ESR) and indirectly determined it with the k.p model [16], The agreement between theoretical and experimental results is fairly good. 

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