  We use an $sp^3d^5s^* $ tight-binding model to investigate the electronic and
optical properties of realistic site-controlled (111)-oriented InGaAs/GaAs
quantum dots. Special attention is paid to the impact of random alloy
fluctuations on key factors that determine the fine-structure splitting in
these systems. Using a pure InAs/GaAs quantum dot as a reference system, we
show that the combination of spin-orbit coupling and biaxial strain effects can
lead to sizeable spin-splitting effects in these systems. Then, a realistic
alloyed InGaAs/GaAs quantum dot with 25\% InAs content is studied. Our analysis
reveals that the impact of random alloy fluctuations on the electronic and
optical properties of (111)-oriented InGaAs/GaAs quantum dots reduces strongly
as the lateral size of the dot increases and approaches realistic sizes. For
instance the optical matrix element shows an almost vanishing anisotropy in the
(111)-growth plane. Furthermore, conduction and valence band mixing effects in
the system under consideration are strongly reduced compared to standard
(100)-oriented InGaAs/GaAs systems. All these factors strongly indicate a
reduced fine structure splitting in site-controlled (111)-oriented InGaAs/GaAs
quantum dots. Thus, we conclude that quantum dots with realistic (50-80~nm)
base length represent promising candidates for polarization entangled photon
generation, consistent with recent experimental data.
