One-dimensional surface states on a striped Ag thin film with stacking fault arrays

One-dimensional (1D) stripe structures with a periodicity of 1.3 nm are formed by the introduction of stacking fault arrays into a Ag thin film. The surface states of such striped Ag thin films are studied using a low-temperature scanning tunneling microscope. Standing waves running along the stripes and characteristic spectral peaks are observed by differential conductance ($dI/dV$) measurements, revealing the presence of 1D states on the surface. Their formation can be attributed to quantum confinement of Ag(111) surface states into a stripe by stacking faults. To quantify the degree of confinement, the effective potential barrier at the stacking fault for Ag(111) surface states is estimated from independent measurements. A single quantum well model with the effective potential barrier can reproduce the main features of $dI/dV$ spectra on stripes, while a Kronig-Penney model fails to do so. Thus the present system should be viewed as decoupled 1D states on individual stripes rather than as anisotropic 2D Bloch states extending over a stripe array. The result is discussed in terms of electron localization into stripes due to strain-induced inhomogeneities and absorption from surface to bulk states.

Figure 1

(a) Topographic STM image of a striped Ag film with a nominal thickness of 22 ML grown on the Si(111)-(4$\times$1)-In surface ($V=2$ V, $I=120$ pA). The lower-right section displays the derivative of the topographic height ($dz/dx$, $z$: topographic height, $x$: the horizontal coordinate). (b) The atomic structural model of the Ag stripes with stacking fault planes.

Figure 2

(a) Topographic STM image of parallel stripes running through a monatomic-height island ($V=0.6$ V, $I=120$ pA). The positions of the monatomic and fractional steps are indicated by solid and dashed lines, respectively. The narrow striped regions are labeled by (A)–(E), among which (B) and (C) are single-unit stripes. (b) $dI/dV$ image on the same area as in (a) showing the periodically modulated signal along the stripes ($V=0.58$ V, $I=120$ pA). (c) Series of $dI/dV$ signals taken along the middle of a stripe (B) with different sample voltages $V$ from 0.38 to 0.68 V. The data are offset along the ordinate for clarity. (d) Energy dispersion of the surface states obtained from the standing-wave observations. Closed circles and crosses are data taken on single-unit stripes and a flat area of a Ag(111) film epitaxially grown on Si(111), respectively. The solid and dashed lines show the fitting results using Eq. (1).

Figure 3

(a) Topographic STM image of the central part of an array of four single-unit stripes ($V=0.5$ V, $I=120$ pA). The dashed lines indicate the locations of fractional steps. The crosses on the dotted line indicated by #1 show the spectral sites for $dI/dV$ measurements. The same measurements were performed at the locations indicated by #2– #5 (the spectral sites are not explicitly shown). The lower panel shows the topographic height $z$ averaged along the longitudinal direction of the stripes. (b) Raw spectra taken on the locations indicated by #1– #5 (crosses) and the averaged spectra for each data set (solid lines). The data are offset along the ordinate for clarity. (c) Averaged spectra taken in the middle of an isolated single-unit stripe.

Figure 4

(a) Topographic STM image of an area including a double-unit stripe at center and single-unit stripes at sides ($V=-2$ V, $I=120$ pA). The crosses on the dotted line indicated by #1 show the spectral site where $dI/dV$ measurements were taken. The same measurements were performed at the locations indicated by #2– #5 (the spectral sites are not explicitly shown). The lower panel shows the topographic height $z$ averaged in the longitudinal direction of the stripes. (b) Raw spectra taken on lines #1– #5 (crosses) and the averaged spectra for individual locations (solid lines). The dashed lines show the fitting results using Eq. (2). The data are offset along the ordinate for clarity. (c) Schematic diagram of the Fabry-Perot resonator model for determining the reflection amplitude $R$ and the phase shift $\phi$ at the fractional step.

Figure 5

(a) Reflection amplitude at the fractional steps $R$ calculated using Eq. (5) based on the effective potential barrier (solid line). The solid circles and the dashed line show the previous experimental result and the tight-binding calculation on $R$, respectively (Ref. 20). (b) Phase shift at the reflection $\phi$ calculated with the same method as in (a). The closed squares show the result of the tight-binding calculation. Inset: Schematic diagram of the potential barrier used in the model calculation.

Figure 6

(a), (b) Schematic diagrams for (a) the single quantum well (SQW) and (b) the Kronig-Penney (KP) models. (c) DOS for the transverse direction calculated for the SQW and KP models. (d) DOS including the longitudinal degree of freedom calculated for the SQW and KP models. Averaged spectra taken on the arrayed and isolated stripes are also shown as open squares and crosses, respectively.