Current-dependent periodicities of Si(553)-Au

We investigate quasi-one-dimensional atomic chains on Si(553)-Au with a scanning tunneling microscope (STM). The observed periodicity at the Si step edge can be altered by the STM and depends on the magnitude of the tunneling current. In a recent report this reversible structural transition was attributed to transient doping with a characteristic time scale of a few milliseconds [S. Polei et al., Phys. Rev. Lett. 111, 156801 (2013)]. Here we explore the evolution of the STM topography as a function of the magnitude of the tunneling current for a wide temperature range. Based on a decomposition of topographic line profiles and a detailed Fourier analysis we conclude that all observed current-dependent STM topographies can be explained by a time-averaged linear combination of two fluctuating step-edge structures. These data also reveal the precise relative alignment of the characteristic STM features for both phases along the step edges. A simple diagram is developed, presenting the relative contribution of these phases to the STM topography as a function of tunneling current and temperature. Time- and current-dependent measurements of fluctuations in the tunneling current reveal two different transition regimes that are related to two specific current injection locations within the surface unit cell. A method based on spatially resolved $I$($z$) curves is presented that enables a quantitative analysis of contributing phases.

Figure 1

STM topography ($U_{\mathrm{gap}}=1$ V) of Si(553)-Au taken at 60 K and different tunneling currents. (a) At $I$ = 2 pA bright protrusions on the step-edge chains form a 1$\times$3 periodicity. (b) same sample area at $I$ = 2 nA. On the step edges a 1$\times$2 periodicity is observed.

Figure 2

STM topography ($U_{\mathrm{gap}}$ = +1 V, $T$ = 60 K) of a single Si step edge. (a) 3 pA: 1$\times$3 periodicity, (b) 10 pA: 1$\times$6 periodicity, and (c) 2.1 nA: 1$\times$2 periodicity. (d)–(f) Corresponding line profiles at locations indicated by the black arrows on the right side of the topography images. The red dashed curve in (e) corresponds to a linear combination of the 1$\times$3 and 1$\times$2 line profiles in (d) and (f) with α = 0.55 [see Eq. (1)]. This shows that the 1$\times$6 structure is a (time-averaged) linear combination of the two other phases. In (d) a line profile at 78 K and $I$ = 10 pA is added (dashed gray line) to illustrate that at 60 K and 3 pA the topography already contains an admixture of the 1$\times$2 phase. The blue arrows refer to data in Fig. 3.

Figure 3

(a) and (b) Line profiles of the step edge (black) and of the Au chain (blue) extracted from the STM images shown in Figs. 2 and 2, respectively. The line profiles were taken along the directions indicated by the black and blue arrows in Figs. 2 and 2. Red lines represent parabolic fits used to determine the positions of the peak maxima. In (a) the line profiles of the step edge and the Au chain both exhibit a 1$\times$2 periodicity. The maxima are aligned in phase, whereas in (b) a clear displacement between dominant maxima of step edge and the Au chain is evident. An average offset of ${\mathrm{b}}_{\mathrm{mean}}$ = 0.17 nm is found. (c) Schematic structure of the underlying Si lattice of the step edge on Si(553) to illustrate the distance between atoms directly at the step edge and atoms one row behind: ${\mathrm{b}}_{\mathrm{model}}$ = 0.19 nm.

Figure 4

Simple phase diagram of the 1 × 3 ↔ 1 × 2 transition: normalized ratio $r$ of the Fourier coefficients $a_{1\times 2}$ and $a_{1\times 3}$ for different tunneling currents and temperatures (circles). Larger values of $r$ (i.e., the periodicity is increasingly dominated by 1 × 2 order) are found for increasing current or decreasing temperature. Colored dashed lines are guides to the eye. The current limits in our experiments are indicated by vertical dotted lines. A typical Fourier spectrum for 60 K and ∼100 pA is displayed in the inset, where peaks corresponding to different periodicities are indicated. For 7 and 13 K $r$ is found to be constant because for low temperatures the system is always excited to the 1 × 2 phase, even at the lowest currents.

Figure 5

(a) Typical $I$($z$) curves ($U_{\mathrm{gap}}$ = 1.3 V, $T$ = 57 K) measured over a bright 1 × 3 protrusion (black; position $x_1$) and in between (red; position $x_2$), respectively. The dotted line is a guide to the eye representing a purely exponential behavior. Inset: topography ($U_{\mathrm{gap}}$ = 1.3 V, $I$ = 10 pA, $T$ = 60 K) of a single Si step edge showing a 1 × 3 periodicity and the locations of $x_1$ and $x_2$. Fluctuations on top of bright 1 × 3 protrusions can be seen as dark horizontal stripes. (b) The relative standard deviation of the tunneling current as a function of the mean current measured on positions $x_1$ and $x_2$. The curves represent an average over ∼200 measurements. The peaks in the relative standard deviation reveal the typical currents where the 1 × 3 ↔ 1 × 2 structural fluctuations occur and show that at these currents differ for the two locations $x_1$ and $x_2$.

Figure 6

Tip displacement $z$($I$) as a function of tunneling current for positions $A$ and $B$ (black and green curves, right $y$ axis) as indicated in the bottom of the inset. The data are calculated from measured $I$($z$) curves and represent an average over equivalent locations along the chain. The locations are chosen such that all contributions from the 1 × 2 phase cancel out in the difference $A$−$B$ (gray dots, left $y$ axis; see Appendix pp1 for a detailed description). The values of $A$−$B$ are proportional to the fraction of the 1 × 3 contribution. A double-exponential fit of $A$−$B$ matches the data, reflecting the saturation behavior of the phase transition induced by transient doping at increasing current. Two exponential functions are necessary, one for each location with pronounced fluctuations (cf. Fig. 4). Within the scaling error indicated by red dashed lines the absolute amount of 1 × 3 can be read from the red axis (for a description see text). Inset (top): scheme of inequivalent locations ($A$ and $B$) relative to 1 × 3. Inset (bottom): 1 × 3 topography measured at 3 pA and simultaneously recorded with the $I$($z$) curves. Red and black circles indicate positions $A$ and $B$, respectively.