Removing hysteresis in graphene resonators

In conventional resonators, the displacement of a membrane is reversible. As the applied voltage between the resonator and its underlying electrode increases, the membrane moves toward the electrode, and as the voltage decreases, the membrane moves away. This is an important hallmark of resonators, allowing the tuning of its spring constant.

But some 2D resonators exhibit hysteresis with changing applied voltage, and Lu et al. sought to learn why.

“We have observed that every time the membrane is crumpled — very much like a crumpled sheet of paper — this process is hysteretic,” said author Joel Moser. “The membrane jumps toward the gate discontinuously as the voltage is increased past certain values, and it jumps away from the gate as the voltage is decreased past other values.”

The researchers crumpled graphene membranes to develop folds, creases, and wrinkles, like the ones that may appear with fabrication issues. They measured the mechanical response of the resonators and repeated the same measurements after annealing. At certain voltage ranges, they found hystereses in the static displacement and in the resonant frequencies of the membranes, which disappeared with mild annealing.

This behavior may be because the crumpled membrane locally sticks to itself and becomes unstuck as the voltage increases.

“The electrostatic pulling force may partially uncrumple the membrane, much like the surface of a deflated, crumpled birthday balloon becomes smooth as the balloon is filled with air,” said Moser.

Depending on whether hysteresis is desirable for a specific application, the current work can either help identify its origin or offer a straightforward way to remove it without having to fabricate a new device.

Source: “Hysteretic responses of nanomechanical resonators based on crumpled few-layer graphene,” by Heng Lu, Chen Yang, Ce Zhang, YuBin Zhang, FengNan Chen, Yue Ying, Zhuo-Zhi Zhang, Xiang-Xiang Song, Guang-Wei Deng, Ying Yan, and Joel Moser, Applied Physics Letters (2025). The article can be accessed at https://doi.org/10.1063/5.0241213 .