Fig. 3

Modeling and bandwidth measurements of graphene resonators. a Thermal circuit model. b False-colored scanning electron microscope image of a trampoline of tether width w = 200 nm and diameter d = 6 µm. Black scale bar is 2 µm. c Normalized frequency-shift responsivity \({R}_{f}^ \ast\) as the amplitude of the heating laser is modulated from 100 Hz to 50 kHz. The total resonance shift was found to be constant for low modulation frequency and reached half its maximum value at BW = 13.8 kHz. A thermal circuit model was used to fit the thermal response time of the trampoline; the fitted curve using Eq. 2 is shown in black. d Real and imaginary amplitude of thermal expansion induced displacement for a trampoline (w = 1.2 μm, d = 6 μm). The black curve is a fit to the thermal circuit model. From this fit, we extract the thermal response time, \({\tau }_{\mathrm{T}} = 2.4\) μs. e Bandwidth vs. tether width for nine different trampolines and three different drumheads. For the drumheads, the tether width is taken to be 1/4 of the drumhead circumference. f Sensitivity vs. bandwidth for nine different trampolines and three different drumheads. The black line is the linear fit, \({\mathrm{BW}} \propto {\eta }\) (R-value of 0.97). All bandwidth values in e and f were inferred from the off-resonant thermomechanical method. Symbol legend and vertical axis is shared between e and f. Circles indicate a trampoline with a 6 µm diameter, turquoise triangles indicate a trampoline with an 8 µm diameter, and magenta triangles indicate a drumhead resonator of either 6 or 8 µm diameter. Source data are provided as a Source Data file