Electronic and Optical Properties of ${\rm a}$- and ${\rm m}$-Plane Wurtzite InGaN–GaN Quantum Wells

Electronic and optical properties of a-(∅=0) and 𝔪-plane(∅-π /6) InGaN-GaN quantum-well (QW) structures are investigated using the multiband effective-mass theory with an arbitrary crystal orientation. These results are compared with those of 𝔠-plane or (0001)-oriented wurtzite InGaN-GaN QWs. We derive explicitly the Hamiltonians with their elements and the interband optical matrix elements with polarization dependence for the 𝔞-, 𝔪-, and 𝔠-planes. The bandgap transition wavelen𝔞 -plane. The average hole effective masses of the topmost valence band along 𝑘'ᵧ for the 𝔞- and 𝔪-planes are significantly lower than that of the 𝔠-plane. Here, the prime indicates physical quantities in a general crystal orientation. In addition, their optical gain and optical matrix element show strong in-plane anisotropy. The optical gain of the 𝑦'-polarization is much larger than that of the 𝓍' -polarization because the optical matrix element for the 𝑦'-polarization is larger than that of the 𝓍'-polarization.