Novel Electronic Structure of Inhomogeneous Quantum Wires on a Si Surface

A one-dimensional system of $\mathrm{S}\mathrm{i}(111)\mathrm{\text{−}}(5\times 2)\mathrm{\text{−}}\mathrm{A}\mathrm{u}$ is explored using scanning tunneling microscopy and spectroscopy. The chain of Si adatoms called bright protrusions (BP’s) is found to be semiconducting with an evanescent state in the gap, which originates from adjoining metallic BP-free segments. A quantitative analysis shows that the evanescent state decays in inverse-Gaussian form, leading to an appearance of a parabolic BP chain, and scales to its chain length. Spatial decay of the state suggests a quadratic band bending and the existence of a Schottky-like potential barrier at the interface driven by charge transfer.

Figure 1

(a) A $7.5\times 10.5{\mathrm{n}\mathrm{m}}^2$ STM image of typical $\mathrm{S}\mathrm{i}(111)\mathrm{\text{−}}(5\times 2)\mathrm{\text{−}}\mathrm{A}\mathrm{u}$ at ${\mathrm{V}}_{\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}}=+0.8\mathrm{V}$ and $i_t=0.05\mathrm{n}\mathrm{A}$, and (b) bias-dependent STM images of a 8 BP long, $4a_0$ spaced chain and a $6a_0$ BP-free segment (arrow). The bracket in (b) denotes a local unit cell of a BP chain, with a BP and a pair of less bright “ears.” (c) Vertically aligned line cross sections of the chain at corresponding biases are shown, with a parabolic fit to a $+0.3\mathrm{e}\mathrm{V}$ case. A small deviation of the fourth BP from the right side is due to a defect on the lower row.

Figure 2

(a) A diagram of a parabolic envelope of the tip trajectory under a constant current mode. Each plate with one large and two small balls represents a local unit cell depicted in Fig. 1b. (b) A log-log plot of normalization constant $a_L$ vs length $L$ of BP chains. The inset displays $z$ positions of BP’s in each chain as a function of $x^2$, with $x$ and $z$ as defined in (a). The number next to each fit is the length of the BP chain in units of $4a_0$.

Figure 3

A STM image of a chain with 5 BP’s and their corresponding normalized $dI/dV$ spectra at the site of each BP (lower 5 curves), and at a BP-free segment (top curve), taken at $V_{\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}}=-1.5\mathrm{V}$ and $i_t=1.0\mathrm{n}\mathrm{A}$. Long ticks on the $y$ axis denotes $(dI/dV)/(I/\mathrm{V})=0$. The inset is a plot of $z$ positions of 5 BP’s in the chain (×), in comparison with the log of the peak intensities at states $B$ (▽) and $C$ (○). $Z$ positions of state $B$ and $C$ were rigidly shifted for the best fit. $\alpha$, $\beta$, and $\gamma$ denote locations within local unit cells, running parallel to Au rows.