Film Thickness of Pb Islands on the Si(111) Surface

We analyze topographic scanning force microscopy images together with Kelvin probe images obtained on Pb islands and on the wetting layer on Si(111) for variable annealing times. Within the wetting layer we observe negatively charged Si-rich areas. We show evidence that these Si-rich areas result from islands that have disappeared by coarsening. We argue that the islands are located on Si-rich areas inside the wetting layer such that the $\mathrm{Pb}/\mathrm{Si}$ interface of the islands is in line with the top of the wetting layer rather than with its interface to the substrate. We propose that the Pb island heights are one atomic layer smaller than previously believed. For the quantum size effect bilayer oscillations of the work function observed in this system, we conclude that for film thicknesses below 9 atomic layers large values of the work function correspond to even numbers of monolayers instead of odd ones. The atomically precise island height is important to understand ultrafast “explosive” island growth in this system.

Figure 1

(a) The quantum size effect leads to a bilayer oscillation of the work function with atomic-scale film thickness in Pb on Si. Top and bottom horizontal axes represent two different models leading to two different phases of the oscillation [2]. (b) SFM topographic image obtained after long annealing time, 6 h 50 min, ($F=50\mathrm{nA}$) and (c) corresponding KPFM image. $f_0=283\mathrm{kHz}$, $\mathrm{\Delta }f=-37\mathrm{Hz}$, $A=15\mathrm{nm}$. (d) Growth of Pb on Si(111) where the island is inserted in the wetting layer. (e) Growth of Pb on the wetting layer. (f) Growth of Pb islands on Si-rich areas inside the wetting layer. This scheme is supported by our measurements.

Figure 2

(a) and (d): SFM topographic image obtained after warming up for 20 min ($F=27\mathrm{nA}$) and for 1 h 30 min ($F=50\mathrm{nA}$). (b),(c),(e), and (f): corresponding Kelvin microscopy image using two different color scales. Images (b) and (e) show quantum size effects on the islands. Images (c) and (f) focus on the wetting layer. For (a) $f_0=280\mathrm{kHz}$, $\mathrm{\Delta }f=-20\mathrm{Hz}$, $A=10\mathrm{nm}$, $c_L=50$ N/m. For (d) $f_0=283\mathrm{kHz}$, $\mathrm{\Delta }f=-27\mathrm{Hz}$, $A=15\mathrm{nm}$. (g) The root mean square roughness (blue squares) and the autocorrelation length (red rhombs) plotted as a function of annealing time. Both the root mean square roughness and the autocorrelation length increase as a function of annealing time.

Figure 3

(a) SFM topographic image obtained during warming up the sample starting from 115 K after 5 h 30 min ($F=50\mathrm{nA}$) (b) Corresponding KPFM image where the color scale was chosen to focus on the wetting layer. Two islands have been marked by circles in (a) and (b). An island marked with 1 has an outer rim of greater height. (c) A subsequent topographic SFM image to (a) acquired after 11 h 30 min and (d) the corresponding KPFM image. The same positions as in (a) and (b) have been marked by circles. One island has decayed, another has become significantly smaller. At both positions a larger Kelvin voltage is observed. A shadow has been added artificially to (a) and (c) to highlight atomic steps. Acquisition time 3 h. (e) Line profile extracted at the position of the black line in part (d) and a line profile taken at the same position from the image acquired between (b) and (d). The line profiles show a local maximum of contrast at the position where the island has disappeared. $f_0=283\mathrm{kHz}$, $A=15\mathrm{nm}$ (a) $\mathrm{\Delta }f=-33\mathrm{Hz}$, (b) $\mathrm{\Delta }f=-34\mathrm{Hz}$.