Disclosed herein are IC structures, packages, and device assemblies with III-N transistors that include additional materials, referred to herein as “stressor materials,” which may be selectively provided over portions of polarization materials to locally increase or decrease the strain in the polarization material. Providing a compressive stressor material may decrease the tensile stress imposed by the polarization material on the underlying portion of the III-N semiconductor material, thereby decreasing the two-dimensional electron gas (2DEG) and increasing a threshold voltage of a transistor. On the other hand, providing a tensile stressor material may increase the tensile stress imposed by the polarization material, thereby increasing the 2DEG and decreasing the threshold voltage. Providing suitable stressor materials enables easier and more accurate control of threshold voltage compared to only relying on polarization material recess.