An electronic device including a breakdown layer having variable thickness. The device includes a variable resistance material positioned between two electrodes. A breakdown layer is interposed between the variable resistance material and one of the electrodes. The breakdown layer has a non-uniform thickness, which serves to bias the breakdown event toward the thinner portions of the breakdown layer. As a result, the placement, size, and number of ruptures in the breakdown layer are more consistent over a series or array of devices. The variable resistance material may be a phase-change material. The variable-thickness breakdown layer may be formed through a diffusion process by introducing a gas containing a resistivity-enhancing species to the environment of segmented variable resistance devices during fabrication. The resistivity-enhancing element penetrates the outer perimeter of the variable resistance material and diffuses toward the interior of the device. The resistivity-enhancing species increases the resistance of the interface between the variable resistance material and the electrode by interacting with the variable resistance material and/or electrode to form a resistive interfacial material. Based on the diffusional nature of the process, the concentration of the resistivity-enhancing species decreases toward the center of the device and as a result, the breakdown layer is thinner toward the center of the device.