Over the last decade, a number of interesting thermoelectric and terahertz device applications have arisen from research into embedded rare-earth monopnictide particles in III-V semiconductors on (100) oriented substrates. For example, nearly spherical nanoparticles of ErAs embedded in semiconducting materials such as (100) GaAs were found to exhibit ultrafast recombination of electron-hole pairs and to significantly alter their optical properties. Previously, we reported that low (up to 10%) atomic concentrations of Er codeposited with Ga and As produced ordered arrays of ErAs nanorods embedded within GaAs when grown on (411)A GaAs, in contrast to ErAs nanoparticles embedded in (100) GaAs and (411)B GaAs. We have also reported that using the same growth conditions as found in reference 3, we were able to grow embedded ErAs nanorods on (111)A, (211)A, and (311)A GaAs.These are very interesting structures due to their potential anisotropic electrical conductivity and thermal conductivity as one can tailor the growth direction and size of the nanorods by modifying the growth conditions. Additionally, the fact that the semimetallic ErAs nanorods are embedded within the GaAs matrix may provide new methods of contacting semiconductors. We present cross-sectional and plan view transmission electron microscopy (TEM) and high-angle annular dark field scanning transmission electron microscopy (HAADF STEM) results that can elucidate the growth mechanism involved in the formation of these ErAs nanorods. ErAs nanorods form by phase-separating at the growth surface during growth that can be controlled by changing the growth parameters used. Increasing the growth temperature as well as the Er concentration used increases both the size of the nanorods as well as the spacing between them. Nanorod orientation can be altered by growing on different GaAs surfaces. We present results obtained for other high-index growth surfaces such as (111)A GaAs, (211)A GaAs, (311)A GaAs, and (511)A GaAs.4 For example, ErAs nanorods were found to form on (111)A GaAs, (211)A GaAs and (311)A GaAs for a range of Er atomic concentrations and a range of growth temperatures. ErAs nanorods on (111)A GaAs were found to align themselves along the  whereas those on the (211)A and (311)A GaAs surface aligned themselves along the  direction, similar to that observed on (411)A GaAs. We show that the ErAs nanorods and the surrounding GaAs matrix are of high crystalline quality and have a continuous As sublattice across their interface. Growth of GaAs on top of these codeposited ErGaAs layers is free of strain contrast as observed in TEM – allowing for heterostructures to be grown above the codeposited layer.