Atomic Structure Affects the Directional Dependence of Friction

Friction between two objects can be understood by the making, stretching, and breaking of thousands of atomic-scale asperities. We have probed single atoms in a nonisotropic surface [the H-terminated Si(100) surface] with a lateral force microscope operating in noncontact mode. We show that these forces are measurably different, depending upon the direction. Experimentally, these differences are observable in both the line profiles and the maximum stiffnesses. Density functional theory calculations show a concerted motion of the whole Si dimer during the tip-sample interaction. These results demonstrate that on an asperity-by-asperity basis, the surface atomic structure plays a strong role in the directional dependence of friction.

Figure 1

(a) A schematic of the experimental setup. By cutting the Si wafer on the $\{011\}$ planes, the (011) crystallographic direction can be aligned with the tip oscillation. By moving from one terrace to another, data can be acquired with the tip oscillating either parallel or perpendicular to the Si dimers. (b) Constant-height $I_t$ data at a lateral oscillation amplitude of 50 pm. (c) Same as (b) but with an amplitude of 300 pm. (d) $\Delta f$ data over two terraces, with the step edge highlighted with a dashed line. A bias of 1.5 V was applied. Above the black line, $I$ is used to control the tip height (set point of 4 nA). Below it, the feedback is switched off. The tip oscillation in all subfigures is indicated by double-headed arrows. Images are taken with a scan angle of 45°. White scale bars represent 500 pm.

Figure 2

(a) $\Delta f$ data taken over two terraces (step edge is highlighted by a dashed line). Scan angle 45°, oscillation amplitude 100 pm, bias voltage 1.5 V, set point 3.4 nA. The white scale bar represents 500 pm. Line profiles were taken along the solid lines shown in (a). The direction of the tip oscillation is shown as a white arrow. (b) Convoluted force gradient for the line profile on the upper left terrace, corresponding to the tip oscillation perpendicular to the Si dimers. From the top down: Data are black dots, and the Fourier fit is a solid line; deconvolved force gradient from the Fourier fit; lateral force as evaluated from the data (solid line) and calculated from density functional theory (black points); structural model. (c) As in (b) for the lower-right terrace.

Figure 3

(a)–(c) Relaxed atomic positions corresponding to motion parallel to the Si dimer, indicated by the dark arrow in (a), for various positions over a Si dimer as indicated by the vertical dashed lines in (g). (d)–(f) Motion perpendicular to the dimer, indicated by the dark arrow in (d), with positions indicated by the dashed lines in (h). (e),(f) At the same tip position but rotated to show the dimer displacement. (g),(h) Shown is the vertical displacement of the Si atoms of the dimer below the tip.