Controlling conductivity by quantum well states in ultrathin Bi(111) films

Epitaxial Bi(111) films were subject to many and partly even controversial studies on the semimetal-semiconductor transition triggered by a robust quantum confinement. The residual conductance was ascribed to conducting surface channels. We investigated ultrathin crystalline Bi films on Si(111) as a function of film thickness $d$ between 20 and 100 bilayers by means of electric transport measurements. Varying temperature and magnetic field, we disentangled two transport channels. One remains indeed metallic at all thicknesses investigated and exhibits a slightly increasing conductance as a function of $d$, whereas the second is activated with a $d^{-1}$ dependence of the activation energy, indicating a quasiharmonic confining potential. Both channels reflect the electronic properties of the entire film and do not allow us to strictly separate surface and bulk states. While there is clearly no bulk conductivity, the activated channel is consistently described as electronic excitation into the partly occupied quantum well states, which are also responsible for the metallic conductance and preferentially located close to both interfaces of the film.

Figure 1

(a),(b) Conductance as a function of temperature for variously thick Bi(111) films. While for (b) the films were prepared on fresh Si(111) substrates, in (a) the Si(111) templates were used for multiple deposition experiments and high-temperature annealing cycles. (c) $G$($T$) curves for 40- and 75-BL-thick films together with fits according to Eq. (1). (d) LEED pattern of a 55-BL-thick Bi film.

Figure 2

Energy gap $E_g$ (a), film conductance $G_1$ (b), and surface conductance $G_0$ (c) as a function of film thickness. The symbols denote measurements done on different Si(111) surfaces. The color coding in (a) and (b) illustrates sets of measurements performed with different Bi films prepared on the same Si substrate.

Figure 3

Magnetotransport results: (a) $G\left(B\right)$ and (b) Hall measurements at 11 K. (c) Electron (${\mu }_n$) and hole mobilities (${\mu }_p$). (d) Electron ($n$) and hole ($p$) carrier concentrations as a function of the film thickness.