Crystal-orientation effects on the piezoelectric field and electronic properties of strained wurtzite semiconductors

Crystal orientation effects on the piezoelectric field and electronic properties of strained GaN bulk semiconductors are investigated. Analytical expressions for the band gap, wave function, and momentum matrix element of strained wurtzite GaN using a recently derived block-diagonalized Hamiltonian are shown. We find that the energy separation between the top two valence bands increases with the angle θ between the growth ${(z}^{\prime })$ direction and the c axis. This results in a significant reduction of the effective mass of the top valence band along the transverse ${(k}_x^{\prime })$ direction with increasing angle for both compressively and tensilely strained GaN crystals. Similar results are observed in the valence-band dispersion relations for the quantum-well (QW) structure. The dispersion curves for the QW structure also show a lifting of the Kramers degeneracy due to the piezoelectric field, which causes an asymmetry in the potential. We find that the optical matrix element of the TE polarization between the conduction (C) and heavy hole (HH) bands of the compressively strained GaN for a growth direction with $\theta >~30°$ is about twice as large as that of the (0001) orientation $(\theta =0\mathrm{}°).\mathrm{}$ The piezoelectric polarizations of the compressive and tensile strains are plotted as a function of the growth direction. The crystal orientation at which a maximum polarization occurs is shown as a function of strain. In particular, the GaN crystal along the $\left(101\mathrm{}¯0\right)$ growth direction $(\theta =90\mathrm{}°)$ shows zero normal piezoelectric polarization ${(P}_z^{\prime })$ for the compressive and tensile strains. These results show that crystal orientation dependence of the piezoelectric field and strain significantly affect the electronic transport properties as well as optical interband absorption properties.