Analysis of the Sn chain length fluctuations on Si(100)$2\times 1$: An extraction of microscopic parameters

Tin chains grown on the Si(100)$2\times 1$ surface were studied by scanning tunneling microscopy. Real time measurements were used for recording chain length fluctuations in a temperature range from 310 to 350 K. The recorded data were analyzed by means of a statistical model containing both interfering processes observed at a chain termination—random attachment and detachment of metal atoms. Rates of the both processes were calculated from lifetimes of two different chain terminations (monomer or dimer) by means of derived formulas. The activation energies for the detachment and frequency prefactors were calculated from dependence of the corresponding time constants on temperature in an Arrhenius plot. A similar approach was used for characterization of binding Sn atoms on $C$-type defects which represent preferential adsorption sites.

Figure 1

(a)–(f) Shortening of the tin chain nucleated at a $C$-type defect (empty state images—$U_s=-2\text{V}, I_{}=0.3\text{nA}$—of area $7.5\text{nm}\times 7.5\text{nm}$ taken at room temperature with coverage 0.1 ML). The six representative images were picked from a larger record of a fluctuating chain in order to demonstrate monotonically decreasing chain length. Line profiles of the chains marked by the white arrows are shown below the set of images. Buckling of dimers in the chain when terminated by a single atom can be recognized. Additional faint traces of the chains visible on the images are caused by doubling the very tip.

Figure 2

An example of a line scanning measurement ($U_s=-2\text{V}, I_{}=0.3\text{nA}$) of a Sn chain at 326 K. The white ticks are added to guide the eye and help to recognize the segments sections of different lengths. Where it was possible the lengths of the chain were added in the lower section of the image. The lower end of the chain is anchored by a $C$-type defect.

Figure 3

A probability $P_0\left(t\right)$ that the termination of the chain will not change (via detachment or attachment) in a time interval $(0;t)$ obtained from experimental data for odd terminations fitted by the corresponding function (2).

Figure 4

Temperature dependence of time constants for (a) odd and (b) even terminations of tin chains on various scanning conditions. The temperature axis is in a reciprocal scale.

Figure 5

Sequence of STM images taken at 350 K. $U_s=-2\text{V}, I_{}=0.3\text{nA}$. An arrow marks the position of a $C$-type defect.

Figure 6

Temperature dependence of the time constants for adatom detachment from a $C$-type defect. The temperature axis is in a reciprocal scale.