Role of Quantum and Surface-State Effects in the Bulk Fermi-Level Position of Ultrathin Bi Films

We performed high-resolution photon-energy and polarization-dependent ARPES measurements on ultrathin Bi(111) films [6–180 bilayers (BL), 2.5–70 nm thick] formed on Si(111). In addition to the extensively studied surface states (SSs), the edge of the bulk valence band was clearly measured by using $S$-polarized light. We found direct evidence that this valence band edge, which forms a hole pocket in the bulk Bi crystal, does not cross the Fermi level for the 180 BL thick film. This is consistent with the predicted semimetal-to-semiconductor transition due to the quantum-size effect [V.B. Sandomirskii, Sov. Phys. JETP 25, 101 (1967)]. However, it became metallic again when the film thickness was decreased (below 30 BL). A plausible explanation for this phenomenon is the modification of the charge neutrality condition due to the size effect of the SSs.

Figure 1

Band dispersion of the 180 (a), 30 (b), 10 (c), and 6 (d) BL thick ultrathin Bi(111) films measured along the $\overline{\mathrm{\Gamma }}-\overline{M}$ direction, respectively. The data were taken with $P$ polarization at $h\nu =15\mathrm{eV}$. SS and QWS correspond to surface and quantum-well states, respectively.

Figure 2

(a) Band dispersion of the 180 BL thick Bi(111) film along the $\overline{\mathrm{\Gamma }}-\overline{M}$ direction taken with $S$-polarized photons at $h\nu =15\mathrm{eV}$. (b) Close-up of the region indicated by the dotted rectangle in (a). (c),(d) Same as (b) but taken at $h\nu =18\mathrm{eV}$ (c), and 8 eV (d), respectively. (e) Normal-emission ARPES spectra showing the bulk edge (BE) for the 180 BL thick Bi(111) film taken at different photon energies and polarizations. The last spectrum is that for the metallic surface states (SSs) taken at the solid line in (d). (f) Experimental geometry of the polarization-dependent ARPES. (g) Initial-state electronic orbital excited by polarized light at normal emission. The spatial symmetry of the $p$ orbitals was oriented with respect to the mirror plane, and the orbitals were selectively excited with each polarization ($S$ or $P$). The mirror plane including the direction of incidence and emission was defined along the $x$ axis, as shown by the bold lines. (h) Calculated band dispersion of a 20 BL thick freestanding Bi(111) slab. (i),(j) The orbital components of the bands shown in (h) for the in-plane $p_x$ and $p_y$ orbitals (i), and the out-of-plane $p_z$ orbital (j), respectively.

Figure 3

(a)–(d) Band dispersion of the 180 (a), 30 (b), 10 (c), and 6 BL (d) thick ultrathin Bi(111) films near the $\overline{\mathrm{\Gamma }}$ point taken with $P$-polarized photons at $h\nu =9.5\mathrm{eV}$, respectively. (e)–(h) Same as (a)–(d) but taken with $S$-polarized photons at $h\nu =9.5\mathrm{eV}$. The red dotted lines in (e) and (h) indicate the approximate positions of the bulk edge (BE).

Figure 4

Thickness dependence of the Fermi surface composed of the surface states (SSs) for the 180 (a), 30 (b), 10 (c), and 6 BL (d) thick Bi(111) films, respectively. The size of each pocket shows slight thickness dependence due to the side effect and induces change in the bulk Fermi level position.