(Color online) (a) 6 nm × 6 nm filled-state STM image of freestanding graphene, taken with a tip bias of 0.1 V at a setpoint current of 1.0 nA. (b) Cross-sectional schematic of the Z(V) and Z(I) measurements performed on suspended graphene using feedback-on electronics. (c) Tip height versus bias voltage curves for three different tunneling current setpoints. Inset shows the measured tunneling currents were constant. (d) Tip height versus tunneling current curves for six different constant bias voltages. Inset confirms the measured current agreed with the setpoint as it was varied.
(a) To-scale diagram illustrating the iterative method-of-images technique described in the text to approximate the tip–sample system and calculate the attractive force. (b) Theoretical sphere-plane forces as a function of the sphere potential for multiple sphere radii a and sphere-plane separations d. (c) Experimental tip height versus bias voltage curves at three different current setpoints for graphene on copper (used to determine how d changes with V). (d) Final corrected Fc (V) curves, letting d begin at 0.5 nm and changing with V, and with a = 20 nm.
(a) Same Z(V) data as in Fig. 1(c) , but offset to agree with the Z(I) results in Fig. 1(d) . The inset shows the 3.0 V curve used to set the final heights relative to one another. (b) Force exerted on graphene by the tip as a function of height, deduced from the data shown in (a). Each curve roughly follows the same path. (c) and (d) Schematic diagrams illustrating the entropic rubber band model, to which freestanding graphene is compared. The same change in temperature occurs in both, resulting in a larger displacement for the smaller weight and a smaller displacement for a larger weight (for the same amount of work, W, done).
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