We study the current-driven perpendicular magnetization switching in Ta/CoFeB(wedge)/[TaOx or MgO/TaOx] devices with a lateral structural asymmetry introduced by a varying CoFeB thickness. In these devices, an in-plane current can generate a field-like torque and its corresponding effective magnetic field (H-z(FL)) is out-of-plane, which can deterministically switch perpendicular magnetization at zero magnetic field. Experimental results indicate that the method used for breaking lateral structural symmetry greatly affects the resulting field-like torque, and that the gradient of perpendicular anisotropy, resulting from the CoFeB thickness variation, is not by itself sufficient to give rise to the current-induced H-z(FL). Analysis of the oxidation gradient at the CoFeB/TaOx interface indicates that the oxidation gradient may play a more important role than the gradient of magnetic anisotropy for the generation of H-z(FL). For practical applications, the demonstration of perpendicular magnetization switching in Ta/CoFeB(wedge)/MgO/TaOx devices potentially allows for using MgO-based magnetic tunnel junctions for readout in three-terminal memory devices without the need for external magnetic fields. (C) 2014 AIP Publishing LLC.