General Remarks on the Band Structures of Group III Nitrides

In order to solve these problems, it is very important and useful to clarify band structures of group-III nitrides and their QW structures and also to obtain their band structure parameters. In this Datareview, definitions of band structure parameters and available data on them for GaN and AIN are given. The data are mainly about theoretical results with first-principles band structure calculations within the local density functional approximation (LDA). They are compared with currently available experimental results. Note that the LDA calculation grossly underestimates a bandgap and that it gives almost zero bandgap for InN. Such a calculation is unlikely to yield reliable parameters for InN, especially effective masses. Therefore, the band structure parameters of InN are not given in this Datareview. 

In the analyses of conventional ZB semiconductors, we frequently assume a symmetric parabolic band for the conduction band state, and the Luttinger-Kohn Hamiltonian is used to describe the valence band states. In general, the effective Hamiltonian is derived from a k.p perturbation theory or from the theory of invariants developed by Pikus and Bir. In the latter theory, the operator form of the effective Hamiltonian can easily be constructed from symmetry consideration alone. Within this framework, the lowest two conduction bands and the upper six valence bands are described to the second order of k. The invariant forms of the Hamiltonians are written as follows [26,27]  

Here are Luttinger parameters, and me is an electron effective mass, av, b, d and ac are Bir-Pikus deformation potentials. As0 is a spin-orbit splitting energy. L and a denote orbital and spin angular momentum operators, respectively. [Lf, LJ is defined as [Lf, LJ = (LjLj + LjLj)/2. The summation of i,j runs through x, y, z. 

For WZ compounds, we must consider hexagonal symmetry in the effective Hamiltonian. The Luttinger-Kohn Hamiltonian is constructed under the condition of cubic symmetry and the form reflects cubic crystal symmetry. Thus, in the analysis of WZ nitrides, we must use a k-dependent parabolic band for the conduction band state and Bir-Pikus Hamiltonians for the valence band states. The Hamiltonians for the upper six valence bands and the lowest two conduction bands are given by [28] 

Here Ai are inverse mass parameters in WZ structure, corresponding to Luttinger parameters in ZB structure, me11 and me1 are k-dependent electron effective masses. D , aic and a2c are Bir-Pikus deformation potentials. Ai and 3A2,3 correspond to the crystal-field and spin-orbit splitting energies, respectively. The definition of several operators is given as L+ = (U iLy)/V2, a+ = (ax iay)/2, 

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A6.1 General remarks on the band structures of group III nitrides... 

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