Non-uniform strain field in a wurtzite GaN cylinder under compression and the related end friction effect on quantum behavior of valence-bands

Strain has a considerable effect on the band structure where conduction and valence bands are shifted and split apart. As a result, the knowledge of strain distributions is essential for the analysis of the optoelectronic properties of the semiconductors. In this paper, an analytical solution for the non-uniform strain field within a finite, transversely isotropic cylinder of wurtzite GaN under compression with end frictions is derived. The method follows Lekhnitskii's stress function approach to decouple the equations of equilibrium. Numerical results reveal that all of the strain components, including the axial, radial, circumferential and shear strains, are non-uniform in both distribution pattern and magnitude. In addition, by employing the effective-mass Hamiltonian, the effect of strain on the valence-band structure of wurtzite GaN is studied. It is found that strain can induce band splitting and alter the shape of constant energy surfaces of the heavy-hole, light-hole and split-off bands of wurtzite GaN.