Long-period modulations in the linear chains of Tl atoms on Si(100)

The room-temperature $2\times 1$ structure at the one-monolayer $\mathrm{Tl}∕\mathrm{Si}\left(100\right)2\times 1$ surface has been found to undergo a temperature-induced reversible transition into the ground-state $(6,1)\times (0,6)$ structure through the formation of the intermediate “$c(4\times 7)$” structure. The transition is interpreted as an order-disorder transition due to hopping fluctuation of Tl atoms in the chains. The transition is associated with developing of the long-periodic transverse wandering in the chains of Tl atoms through an interchain interaction.

Figure 1

Top and backside view of the 1-ML $\mathrm{Tl}∕\mathrm{Si}\left(100\right)2\times 1$ structural model. Location of the filled-state (left panel) and empty-state (right panel) STM protrusions is indicated. Tl atoms are shown by dark gray circles, Si atoms by white circles. $2\times 1$ unit cell is outlined.

Figure 2

Filled-state (left column) and empty-state (right column) STM images $(85\times 75{\mathrm{\AA }}^2)$ showing the structural evolution of the Tl monolayer on Si(100) upon cooling the sample. The sample temperature is RT for (a) and (b), $150\mathrm{K}$ for (c) and (d), $30\mathrm{K}$ for (e), $65\mathrm{K}$ for (f). The unit cells are outlined. The dashed lines along two neighboring rows in (d) are to illustrate that they show up as two antiphase transverse waves.

Figure 3

(a) Dual-polarity STM image of the Si(100)-“$c(4\times 7)$” structure. The lower part of the image was acquired with negative sample bias, the upper part with positive sample bias. (b) The profile (solid curve) along the line shown in (a). The envelope line of the line profile is shown by dashed curve. The curve in the low panel represents the line profile after subtracting the envelope. The period of the dashed grid is $a_0=3.84\mathrm{\AA }$, the period of the solid grid is about $7a_0$.

Figure 4

(a) Filled-state and (b) empty-state STM images of the $\mathrm{Tl}∕\mathrm{Si}\left(100\right)$ surface at RT. The “$c(4\times 7)$” structure develops near the surface defects, while defect-free regions preserves the $2\times 1$ structure. Scale of the images is $430\times 430{\mathrm{\AA }}^2$. To improve visualization of the reconstruction on the neighboring terraces, (a) two and (b) three gray scales were used. Thus, the lines in the images correspond to the atomic step edges.

Figure 5

(a) Structural model of the low-temperature 1-ML $\mathrm{Si}\left(100\right)(6,1)\times (0,6)$ phase. Schematic sketches of the (b) filled-state and (c) empty-state STM images superposed with the location of the Tl atoms adopted by the model. STM maxima and depressions are shown bright and dark, respectively.

Figure 6

Variation of the energy per $2\times 1$ unit cell versus displacement of valley-bridge (VB) atom (shaded in the sketches of the model structures) along the axis shown by dotted line in the model structures. Squares and dotted curve show the results of the model calculations for the $2\times 1$ unit cell, circles and solid curve are those for the $4\times 2$ unit cell. In the ground-state $4\times 2$ model structure, Tl atoms in the troughs occupy the off-centered VB sites forming antiphase zigzag chains.

Figure 7

(a) A set of ARPES spectra of the double-domain $\mathrm{Si}\left(001\right)2\times 1\text{−}\mathrm{Tl}$ surface taken along the [110] direction with He $I_{\alpha }$ radiation. The step in emission angles $\left({\theta }_e\right)$ is $2\text{degrees}$ between the neighboring spectra. The peak positions of different surface states assigned are marked with different symbols. Surface Brillouin zone (SBZ) of $2\times 1$ $(1\times 2)$ is indicated with symmetry points in the figure. (b) The band structure as determined from the first-principles total-energy calculations. The black and gray curves correspond to dispersions along $\times 2$ and $\times 1$ periodicities, respectively.