Light hole states in a strained quantum dot: Numerical calculation and phenomenological models

Starting from the numerical solution of the 6-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ description of a lattice-mismatched ellipsoidal quantum dot situated inside a nanowire, including a spin Zeeman effect with values appropriate to a dilute magnetic semiconductor, we propose and test phenomenological models of the effect of the built-in strain on the heavy hole, light hole, and exciton states. We test the validity and the limits of a description restricted to a $({\mathrm{\ensuremath{\Gamma}}}₈)$ quadruplet of ground states and we demonstrate the role of the interactions of the light hole state with light hole excited states. We show that the built-in axial strain not only defines the character, heavy hole or light hole, of the ground state, but also mixes significantly the light hole state with the split-off band's states: Even for a spin-orbit energy as large as 1 eV, that mixing induces first-order modifications of properties such as the spin value and anisotropy, the oscillator strength, and the electron-hole exchange, for which we extend the description to the light hole exciton. CdTe/ZnTe quantum dots are mainly used as a test case but the concepts we discuss apply to many heterostructures, from mismatched II-VI and III-V quantum dots and nanowires, to III-V nanostructures submitted to an applied stress, and to silicon nanodevices with even smaller residual strains.