Quasi-One-Dimensional Quantized States in an Epitaxial Ag Film on a One-Dimensional Surface Superstructure

The in-plane energy dispersion of quantized states in an ultrathin Ag film formed on the one-dimensional (1D) surface superstructure $\mathrm{Si}(111)\mathrm{\text{−}}(4\times 1)\mathrm{\text{−}}\mathrm{In}$ shows clear 1D anisotropy instead of the isotropic two-dimensional free-electron-like behavior expected for an isolated metal film. The present photoemission results demonstrate that an atomic layer at the film-substrate interface can regulate the dimensionality of electron motion in quantum films.

Figure 1

(a) Normal-emission ARPES spectra of Ag films with various thickness on $\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$ (open circles) and $\mathrm{Si}(111)\mathrm{\text{−}}(4\times 1)\mathrm{\text{−}}\mathrm{In}$ (solid diamonds) surfaces. The peak positions of the Ag(111) surface state (SS) and quantized states are assigned. (b) The $sp$-band dispersion for Ag films along the surface normal direction ($\Gamma -L$ line). The solid circles are the experimental points taken from Ag films on $\mathrm{Si}(111)\mathrm{\text{−}}(4\times 1)\mathrm{\text{−}}\mathrm{In}$. The solid curve is a least-squares fit based on the two-band nearly free-electron model. (c) Change of the phase shift at the film-substrate interface ${\varphi }_{\mathrm{sub}}$ for the Ag films on $\mathrm{Si}(111)\mathrm{\text{−}}(4\times 1)\mathrm{\text{−}}\mathrm{In}$ (solid diamonds) and on $\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$ (open circles) as a function of the binding energy.

Figure 2

(Upper) Photoemission intensity maps at $E_F$ of Ag quantum films prepared on (a) $\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$ and (b) $\mathrm{Si}(111)\mathrm{\text{−}}(4\times 1)\mathrm{\text{−}}\mathrm{In}$ surfaces. Schematic drawing of Fermi surfaces of subbands of 2D quantum-well states and quasi-1D state are depicted left and right, respectively. (Lower) ARPES spectra for a 26-ML-thick Ag(111) film on $\mathrm{Si}(111)\mathrm{\text{−}}(4\times 1)\mathrm{\text{−}}\mathrm{In}$ taken along the (c) $[1\overline{1}0]$ and (d) $[\overline{1}\overline{1}2]$ axes of the Si substrate.

Figure 3

The gray-scale $E_B-k_{x,y}$ diagram for the 26-ML-thick Ag(111) film on a $\mathrm{Si}(111)\mathrm{\text{−}}(4\times 1)\mathrm{\text{−}}\mathrm{In}$ surface along the (a) $\mathrm{Si}(111)\mathrm{\text{−}}(4\times 1)\mathrm{\text{−}}\mathrm{In}$$[1\overline{1}0]$ ($\parallel$ In chain) and (b) $[\overline{1}\overline{1}2]$ ($\perp$ In chain) axes of the Si substrate taken from the ARPES scans shown in Fig. 2. The relation between the ARPES scan direction (arrow) and the surface Brillouin zone (SBZ) of Ag(111) is schematically indicated in the figure. The dashed lines are the parabolic fits of the dispersion curves for subbands, and the fitted in-plane effective mass $m_{\parallel }^{*}/m_e$ is indicated.

Figure 4

(a) Cross sectional structure model for the Ag(111) film on $\mathrm{Si}(111)\mathrm{\text{−}}(4\times 1)\mathrm{\text{−}}\mathrm{In}$ [16]. Locations of the stacking faults are indicated by arrows. Different alphabets are assigned for Ag atoms at different sites and a unit cell is indicated. (b) Schematic diagram describing discretization of the wave vector along the surface normal ($z$ direction, $\Gamma \mathrm{\text{−}}\mathrm{L}$ direction) in an isotropic 2D film. The $\Gamma \mathrm{\text{−}}\mathrm{L}$ line of bulk 3D Ag metal is projected to the $\overline{\Gamma }$ point ($k_{2\mathrm{D}}^{x,y}=0$) of the 2D Ag film. (c) Discretization of the wave vector perpendicular to the In chain ($x$ direction, $\overline{\Gamma }-\overline{M}$ direction). The binding energy of each subband at the $\overline{\Gamma }$ point for quasi-1D (q-1D) is smaller than that of the isotropic 2D film.