Electrically conductive, highly flexible graphene membranes hold great promise for harvesting energy from ambient vibrations. For this study, we built numerous three-dimensional graphene ripples, with each featuring a different amount of compression, and performed molecular dynamics simulations at elevated temperatures. These ripples have a convex cosine shape, then spontaneously invert their curvature to concave. The average time between inversion events increases with compression. We use this to determine how the energy barrier height depends on strain. A typical convex-to-concave curvature inversion process begins when the ripple’s maximum shifts sideways from the normal central position toward the fixed outer edge. The ripple’s maximum does not simply move downward toward its concave position. When the ripple’s maximum moves toward the outer edge, the opposite side of the ripple is pulled inward and downward, and it passes through the fixed outer edge first. The ripple’s maximum then quickly flips to the opposite side via snap-through buckling. This trajectory, along with local bond flexing, significantly lowers the energy barrier for inversion. The large-scale coherent movement of ripple atoms during curvature inversion is unique to two-dimensional materials. We demonstrate how this motion can induce an electrical current in a nearby circuit.
Highly flexible, electrically conductive freestanding graphene membranes hold great promise for vibration-based applications. This study focuses on their integration into mainstream semiconductor manufacturing methods. We designed a two-mask lithography process that creates an array of freestanding graphene-based variable capacitors on 100 mm silicon wafers. The first mask forms long trenches terminated by square wells featuring cone-shaped tips at their centers. The second mask fabricates metal traces from each tip to its contact pad along the trench and a second contact pad opposite the square well. A graphene membrane is then suspended over the square well to form a variable capacitor. The same capacitor structures were also built on 5 mm by 5 mm bare dies containing an integrated circuit underneath. We used atomic force microscopy, optical microscopy, and capacitance measurements in time to characterize the samples.
We present five circuit topologies for low power energy harvesting. The most efficient circuit uses a variable capacitor as the power source, a DC bias voltage to charge the variable capacitor, two transistors for rectification, and two storage capacitors. Varying the capacitance performs work and results in stored charge in the capacitors. We experimentally measure the storage capacitor voltage and current over time. The circuit efficiency nears 50% at a maximum power of 10 nW. Multiple circuit topologies are simulated and yield efficiencies from 15% to 50%.
We present an Ito-Langevin model for freestanding graphene connected to an electrical circuit. The graphene is treated as a Brownian particle in a double-well potential and is adjacent to a fixed electrode to form a variable capacitor. The capacitor is connected in series with a battery and a load resistor. The capacitor and resistor are given separate thermal reservoirs. We have solved the coupled Ito-Langevin equations for a broad range of temperature differences between the two reservoirs. Using ensemble averages, we report the rate of change in energy, heat, and work using stochastic thermodynamics. When the resistor is held at higher temperatures, the efficiency of the heat engine rises linearly with temperature. However, when the graphene is held at higher temperatures, the efficiency instantly rises and then plateaus. Also, twice as much entropy is produced when the resistor is hotter compared to when the graphene is hotter. Unexpectedly, the temperature of the capacitor is found to alter the dissipated power of the resistor.
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