Effective mass theory for III-V semiconductors on arbitrary (hkl) surfaces

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Abstract
The effects of arbitrary substrate orientation on the electronic and optical properties of III‐V zinc‐blende semiconductors are considered. A unitary transformation matrix is used to rotate the 4×4 Luttinger valence band Hamiltonian, and the Bir‐Pikus strain Hamiltonian from the conventional (001) surface to any arbitrary (hkl) surface of interest. The effects of strain on several electronic and optical properties are examined. It is found that the strain‐induced change in the forbidden gap is largest for the (111) plane and other equivalent planes. Furthermore, the strain is also found to induce both a longitudinal and a transverse piezoelectric field. The longitudinal field reaches a maximum for the (111) surface and its other equivalent planes, while the transverse field reaches a maximum for the (110) surface and its other equivalent planes. The orientation‐dependence of the hole effective masses is also examined; it is found that the (111) surface, and other equivalent planes, exhibits the largest heavy‐hole mass among all possible planes. Finally, this article examines the effects of orientation on the optical transition matrix elements. For incident light with in‐plane polarization vectors, the matrix elements are, in general, anisotropic—with the largest anisotropies predicted for two new surfaces: the (√310) and the (1√30) surface.