Carrier properties of Bi(111) grown on mica and Si(111)

A comparison is presented between properties of Bi(111) films grown by Stranski-Krastanov epitaxy on Si(111) 7 $\times$ 7 and by van der Waals epitaxy on mica substrates. Thin film morphologies and electronic transport properties of Bi(111) films of variable thickness are investigated for each growth method. Atomic force micrographs for Bi(111) films on mica reveal clearly defined triangular regions consisting of layered steps with height 0.4 nm, corresponding to the Bi(111) bilayer height. Variable-temperature electronic transport measurements show the existence of a quantum confinement-induced energy gap in the film interiors, resulting in a semimetal-to-semiconductor transition. Magnetotransport analysis in a three-carrier model including metallic electrons in surface states and electrons and holes in the films' interiors provides a detailed study of densities, mobilities, and mean-free paths of the three carrier types. Improved electronic transport properties are found in Bi(111) films of higher thickness on mica compared to on Si(111), a likely result of the largely strain-free van der Waals epitaxial growth.

Figure 1

Representative SEM micrograph of a 40 nm Bi(111) film (a) on mica and (b) on Si(111). In (a) red outlines delineate triangular and hexagonal growth patterns, which are not observed in (b). The patterns are consistent with the rhombohedral crystal structure of Bi(111) thin films.

Figure 2

(a) AFM micrograph of a 1 $\mu \mathrm{m}\times 1\mu \mathrm{m}$ area of a 10-nm Bi(111) film on mica, showing layered growth and triangular growth patterns. (b) Height profile ($Z$) vs horizontal distance ($X$) in the length direction of the red box in (a). (c) AFM micrograph of a 1 $\mu \mathrm{m}\times 1\mu \mathrm{m}$ area of a 40-nm Bi(111) film on mica, showing layered growth and triangular growth patterns. (d) Height profile ($Z$) vs horizontal distance ($X$) in the length direction of the red box in (c). (e) AFM micrograph of a 1 $\mu \mathrm{m}\times 1\mu \mathrm{m}$ area of a 10-nm Bi(111) film on Si(111), showing layered growth and triangular growth patterns. (f) Height profile ($Z$) vs horizontal distance ($X$) in the length direction of the red box in (e). (g) AFM micrograph of a 1 $\mu \mathrm{m}\times 1\mu \mathrm{m}$ area of a 40-nm Bi(111) film on Si(111) where no triangular growth patterns or terraces are observed. (h) Schematic of the Bi(111) bilayer structure, with surface atoms in red, and with the ${\mathrm{BL}}_{111}$ spacing, the unit cell, and the trigonal $c$ axis indicated.

Figure 3

Normalized $\rho (T$)/$\rho$(296 K) at $B=0$, vs $T$ for 4.1 K $\le T\le$ 296 K for Bi(111) films (a) on mica with $d=10$, 20, 40, 60, and 1000 nm, and (b) on Si(111) with $d=10$, 20, 40, and 60 nm. A SMSCT is observed at $T=T_C$, with $T_C$ largely independent of substrate.

Figure 4

Left axis, filled symbols: Dependence of $T_C$ on film thickness $d$ for Bi(111) on mica and on Si(111). Green datapoints denote $T_C<4.1\text{K}$ (cfr text). Right axis, open symbols: Dependence of $\mathrm{\Delta }E$ on film thickness $d$ for Bi(111) on mica and on Si(111).

Figure 5

Magnetoresistivity vs $B$ over $-1.4\text{T}<B<1.4\text{T}$ for Bi(111) films, plotted as $(\rho \left(B\right)-\rho (B=0))/\rho (B=0)$, with $d=10$, 20, 40, 60, and 1000 nm on mica and $d=10$, 20, 40, and 60 nm on Si(111), (a) at $T=4.1$ K on mica, (b) at $T=4.1$ K on Si(111), (c) at $T=296$ K on mica, and (d) at $T=296$ K on Si(111). For $d=1000$ nm in (a) the magnetoresistivity scale is scaled by a factor 0.001. Fits to the 3-carrier model are plotted as dashed lines (same color for all $d$).

Figure 6

Hall resistance $R_H\left(B\right)$ vs $B$ over $-1.4\text{T}<B<1.4\text{T}$ for Bi(111) films, with $d=10$, 20, 40, 60, and 1000 nm on mica and $d=10$, 20, 40, and 60 nm on Si(111), (a) at $T=4.1$ K on mica, (b) at $T=4.1$ K on Si(111), (c) at $T=296$ K on mica, and (d) at $T=296$ K on Si(111). Fits to the 3-carrier model are plotted as dashed lines (same color for all $d$).

Figure 7

Carrier densities $n=p$ and mobilities $\mu$ and $\nu$ vs $d$, extracted from 3-carrier model fits to the magnetoresistivity and Hall resistance, for Bi(111) films with $d=10$, 20, 40, and 60 nm on mica and Si(111). (a) $n=p$ at $T=4.1$ K, (b) $n=p$ at $T=296$ K, (c) $\mu$ and $\nu$ at $T=4.1$ K, and (d) $\mu$ and $\nu$ at $T=296$ K.