Nearly Massless Electrons in the Silicon Interface with a Metal Film

We demonstrate the realization of nearly massless electrons in the most widely used device material, silicon, at the interface with a metal film. Using angle-resolved photoemission, we found that the surface band of a monolayer lead film drives a hole band of the Si inversion layer formed at the interface with the film to have a nearly linear dispersion with an effective mass about 20 times lighter than bulk Si and comparable to graphene. The reduction of mass can be accounted for by a repulsive interaction between neighboring bands of the metal film and Si substrate. Our result suggests a promising way to take advantage of massless carriers in silicon-based thin-film devices, which can also be applied to various other semiconductor devices.

Figure 1

(a) Crystal- and (b) reciprocal-lattice structures for $\mathrm{Pb}/\mathrm{Si}(111)$ at 1.2 ML with a $\sqrt{7}\times \sqrt{3}$ symmetry [13]. Gray (dashed) line represents the $\sqrt{7}\times \sqrt{3}$ ($1\times 1$) surface unit cell. ARPES data collected along (c) long and (d) short arrows in (b) crossing $1\times 1$ ($\overline{\Gamma }$) and $\sqrt{7}\times \sqrt{3}$ (${\overline{\Gamma }}_S$) Brillouin zone centers, respectively. The dashed line in (c) denotes the Si valence-band edge. $\Lambda$-shaped band with a linear dispersion on each ${\overline{\Gamma }}_S$ in (d) is labeled $R$ and two other gap-state bands in between are denoted by $S1$ and $S2$. Both ARPES images are symmetrized with respect to the origin. (e) Band bending in the present $n$-type Si substrate calculated by the measured $E_F$ position and the bulk doping concentration [20].

Figure 2

(a) ARPES data of the $R$ band. Data below the dashed line are those symmetrized with respect to ${\overline{\Gamma }}_S$ to eliminate the strong neighboring feature $S2$. (b) Spectral peak positions of the $R$ band (open circles) extracted from MDCs shown in (c). Data points given in closed circles are those symmetrized. The dispersion of a normal Si LH band (black parabola) is compared to show the reduction of curvature. $R$ and $S3$ lines are the results of $k·p$ model fit [25]. The error bar in $k$ is less than $\pm 0.02{\AA }^{-1}$, which brackets the quantified effective mass (orange lines) (see also the supplementary material [18]). Red lines overlaid in (c) show fits by Lorenzian functions.

Figure 3

Constant energy contours at $E_F$ calculated from DFT for the (a) single-domain and (b) triply domain surfaces. Contours from each domain ($A$, $B$, and $C$) are indicated by different colors in (b). (c) ARPES constant energy contours at $E_F$. The DFT contours from (b) are superimposed. The raw data (region without DFT contours) are symmetrized reflecting the fundamental mirror symmetry. (d) Enlarged data around $\overline{M}$ for the detailed comparison between theory (white lines) and experiment (red circles extracted by MDC peak positions). DFT band dispersions along the arrow in (b) for (e) domain $A$ and (f) domains $B$ and $C$, which are overlapped together in (g). The shaded area represents the projected bulk band. For the best match with the experimental data the calculated surface-state energies are rigidly shifted by 120 meV with respect to Si bands.

Figure 4

(a) Schematic illustration of the mechanism for a linear hole band dispersion in semiconductor ILs. (b)–(d) Schematics of surface (SS) and LH band dispersions near $\overline{\Gamma }$ in Pb, Au, and Ag single-layer films on Si(111) with a common $\sqrt{3}\times \sqrt{3}$ symmetry [15, 24, 26]. (e)–(g) Corresponding ARPES dispersions of LH bands measured along the long arrow in Fig. 1b across $\overline{\Gamma }$.