Breakdown of Ohm's Law by Disorders in Low-Dimensional Transistors

Ohm's law provides a fundamental framework for understanding charge transport in conductors and underpins the concept of electrical scaling that has enabled the continuous advancement of modern CMOS technologies. As transistors are scaled to smaller dimensions, channels inevitably enter low-dimensional regimes to achieve a higher performance. Low-dimensional materials such as atomically thin oxide semiconductors, 2D van der Waals semiconductors, and 1D carbon nanotubes have thus emerged as key candidates for extending Moore's law. Here, we reveal the fundamental distinction between three-dimensional and low-dimensional conductors arising from disorder-induced electron localization, which leads to the breakdown of Ohm's law and lateral linear scaling. We develop a quantitative model that captures the disordered region, a unique characteristic intrinsic to low-dimensional transistors. Furthermore, the disorder-induced localization framework consistently explains experimental observations in atomically thin In₂O₃ field-effect transistors. This work establishes a unified physical picture for understanding and optimizing disorder-driven electronic transport in low-dimensional transistors.