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 6x6 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 3x3 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. (C) 2000 American Institute of Physics. [S0021-8979(00)05101-X].