Comparison of zinc-blende and wurtzite GaN semiconductors with spontaneous polarization and piezoelectric field effects

The electronic properties of (001)-, (111)-oriented zinc-blende and (0001)-oriented wurtzite crystals are investigated theoretically, where the spontaneous polarization and piezoelectric (PZ) field effects are taken into account. We show that the Luttinger–Kohn 6×6 Hamiltonians for the valence bands of the zinc-blende crystals written in the wurtzite bases for (001) and (111) crystal orientations and the Hamiltonian for the (0001)-orientation of wurtzite crystals can all be block diagonalized to two 3×3 Hamiltonians, which have analytical solutions for eigenvalues and eigenvectors. We then derive analytical expressions for the strain dependent band-edge effective masses and interband optical matrix elements of zinc-blende and wurtzite GaN crystals and compare their numerical results as well as valence band structures. Although the compressively strained zinc-blende quantum wells in materials such as GaAs- and ZnSe-based systems show reduced threshold carrier densities due to the lower in-plane effective mass, we find that for GaN the reduction of the effective mass with the biaxial compressive strain is not significant in both zinc-blende and wurtzite structures. An alternative method is the application of a uniaxial strain to reduce the in-plane effective masses in both structures. It is also found that the valence band structures and the overlap integral of the electron and hole wave functions of GaN/AlGaN quantum-well structures are affected significantly by the PZ field for (111) zinc-blende structures and by both the spontaneous polarization and PZ fields for (0001) wurtzite structures.