Toggling Bistable Atoms via Mechanical Switching of Bond Angle

We reversibly switch the state of a bistable atom by direct mechanical manipulation of bond angle using a dynamic force microscope. Individual buckled dimers at the Si(100) surface are flipped via the formation of a single covalent bond, actuating the smallest conceivable in-plane toggle switch (two atoms) via chemical force alone. The response of a given dimer to a flip event depends critically on both the local and nonlocal environment of the target atom—an important consideration for future atomic scale fabrication strategies.

Figure 1

Toggling silicon dimers. (a) Open circles: Frequency shift ($\Delta f$) measured as a function of tip displacement ($z$) towards the “down” atom of a Si(100) dimer. Open triangles: $\Delta f$-vs-$z$ spectrum acquired during retraction of the tip. The insets show NC-AFM images, and illustrations of the atomic configurations, taken before and after the frequency shift measurement (acquired at the position marked with a cross). The dimer flipping event appears as a sharp jump in the $\Delta f$-vs-$z$ spectrum. (b) A $\Delta f$-vs-$z$ spectrum taken above a “down” atom of one of the phasons created in (a) restores the original symmetry via a second correlated flip event. (Image parameters: tip amplitude, 250 pm; $\Delta f$ $\mathrm{\text{set point}}=-9.1\mathrm{Hz}$)

Figure 2

Manipulating and annihilating phasons. The two “native” phasons highlighted in (a) are moved via controlled dimer flipping until they annihilate via the flip event shown in (j) to produce the region of $c(4\times 2)$ symmetry in (k). In (a)–(g) the upper phason is sequentially moved down the dimer row via a succession of single dimer flip events (generated in each case by a single $\Delta f\mathrm{\text{−}}z$ spectrum taken at the position marked by the cross). (A movie of the induced phason motion is available online [26].)

Figure 3

Measuring the force required to flip a dimer. (a) Open circles (triangles): Variation of the short-range force during tip approach (retraction) at the position marked with a cross in the “before” image. Note that it is not strictly valid to use the Sader-Jarvis algorithm [27] to plot the short-range force beyond the “discontinuity” due to the dimer flip and so we show only one force point (for clarity) beyond this threshold. Also plotted is the negligible variation in dissipation (for this tip [26]). The DFT-calculated spectra (solid lines), while in excellent agreement with experiment for the retraction curves, show that the threshold force at which the flip occurs is critically dependent on tip structure. (b) As for (a) except that the tip restores the original zigzag buckling.

Figure 4

(a) Energy profile associated with the transition from a $c(4\times 2)$ structure (position i) to a phason pair configuration (position iv) for a range of tip-sample separations. As the tip-sample separation is decreased (▿), the barrier for the transition to an intermediate three-in-a-row state (positions ii and iii)—never observed in experimental images—collapses ($\mathbf{▿}$). As the tip retracts, the barrier between the three-in-a-row and $c(4\times 2)$ states decreases dramatically (▾). Introduction of a two-dimer-vacancy (2DV) defect produces the energy band shown as (▴) (offset for clarity) at the closest tip approach. Part of the 2DV computational cell is shown in the inset (see 26 for more detail). (b) Long-range influence of a defect on the barrier for dimer flipping. In the row highlighted with an arrow, dimers appear symmetric while neighboring rows are clearly buckled. Image taken at 77 K; $\delta f=-40\mathrm{Hz}$; $\mathrm{\text{amplitude}}=100\mathrm{pm}$; $V_{\mathrm{gap}}=10\mathrm{mV}$.