Anisotropic electronic conduction in metal nanofilms grown on a one-dimensional surface superstructure

We performed in situ conductivity measurements by multiple microscopic probes of Ag nanofilms grown on a periodic array of indium atomic wires on Si(111). Within the investigated thickness range the transport properties differ markedly from the bulk case. The ratio between the in-plane conductivity along and perpendicular to the In wires is 1.4 for the 3 monolayer (0.7 nm) thick Ag film and approaches unity with increasing film thickness. The observed anisotropy at the initial stage of the film growth is far larger than expected from the quasi-one-dimensional quantum well electronic structure of the films and ascribed to the carrier scattering at the film/vacuum and film/substrate interfaces. Our findings show that an ordered monolayer inserted at the interface enables drastic changes of the transport behavior of the whole metal nanofilm.

Figure 1

(a) Measurement geometry of the square-4PP method. (b) Current-voltage curves of 6 ML thick Ag(111) films grown on Si(111)7$\times$7. (c)–(f) Those of (c) 3 ML, (d) 6 ML, (e) 16 ML, and (f) 26 ML thick Ag films grown on Si(111)4$\times$1-In. Blue and red data were taken with probe configurations $V_{12}/I_{43}$ and $V_{14}/I_{23}$, respectively.

Figure 2

(a) ${\sigma }_x$ and ${\sigma }_y$ 2D conductivity values for Ag films of different thickness on the Si(111)4$\times$1-In and Si(111)7$\times$7 substrates. The 2D conductivity values $\sigma$, estimated from the bulk Ag crystal (black continuous line) or measured by the van der Pawl method [23], are shown for comparison. (b) Ag thickness dependence of the anisotropic ration ${\sigma }_y/{\sigma }_x$. Values estimated from different models are also indicated.

Figure 3

Gray-scale band mapping and Fermi surface of the 6 ML thick Ag films. (a), (b) Gray-scale $E_{\text{B}}$-$k_{x,y}$ diagram for the Ag film on Si(111)4$\times$1-In along the (a) [$\overline{1}\overline{1}2$] ($\perp$ In chain) axes and (b) [$1\overline{1}0$] ($\parallel$ In chain) axes. Calculated band structures at near the Fermi level are described as solid curves. (c) Fermi surfaces of the freestanding Ag(111) calculated by the tight-binding model. (d) In-plane photoemission intensity map at the Fermi level for the 6 ML thick Ag film on Si(111)4$\times$1-In [29]. The left half of the simplified model for the experimental Fermi surface is drawn by dashed lines on the intensity map. The Ag(111)1$\times$1 surface Brillouin zone and the Si(111)4$\times$1 zone boundary are shown in the figure.

Figure 4

(a) The relation between the film thickness and the 2D resistivity of Ag/Si(111)4$\times$1-In. Calculations by C-S formalism are added by a blue dashed curve and a red dotted curve. A green solid curve represents the function of $d^{-1}$ adjusted to match with the experimental points of the thick films. (b) Temperature dependence of the 2D resistivity of Ag/Si(111)4$\times$1-In at “0 ML” [Si(111)4$\times$1-In bare substrate], 3 ML, and 6 ML of Ag films.

Figure 5

Schematic image of the film morphology in Ag films prepared on Si(111)4$\times$1-In. The upper critical thickness of Ag/Si(111)4$\times$1-In is 3 ML at which percolated highly anisotropic islands are formed without stacking fault planes. The stripe structure based on the stacking-fault model appears at 6 ML. The initial stage of film growth mentioned above is reported in Ref. [8]. The thickness dependence of film morphology at more than 6 ML is estimated from the results of film conductivity shown in Fig. 4.