The influence of thicknesses of a ZnO sublayer and a copper catalyst film on the morphology of ZnO nanorods grown by carbothermal synthesis on α-Al2O3(11–20) substrates has been studied. An increase in the Cu catalyst film thickness leads to a growth in the diameters, heights, and surface density of nanorods. As the ZnO sublayer thickness is increased, the average diameter of nanorods also increases, while their lengths and surface density decrease. The effect of elevated temperatures on the thermal decomposition of ultrathin Cu films deposited on α-Al2O3 substrates has been studied. The photoluminescence characteristics of nanorod arrays have been measured at high levels of optical pumping. An increase in the pumping level to 250–280 kW/cm2 leads to superluminescence of the nanorods.