Nanotube Wires on Commensurate InAs Surfaces: Binding Energies, Band Alignments, and Bipolar Doping by the Surfaces

Using first-principles methods, we study the physicochemical properties such as the binding mechanism and band offset for single-wall zigzag nanotubes on InAs. While the tubes maintain their structural and electronic integrity, binding energies as large as 0.4 eV per site are obtained. Except for semiconducting tubes on the polar surfaces, an approximate universal band alignment is also obtained. The exception is due to large surface dipoles. In fact, polar $(111)$ and $(\overline{1}\overline{1}\overline{1})$ surfaces have opposite dipoles that cause autodoping of a $(14,0)$ tube to the $n$ and the $p$ type, respectively, without actual dopant.

Figure 1

Ball-and-stick models of a $(6,0)$ nanotube on (a) $(110)$, (b) $(111)$, and (c) $(\overline{1}\overline{1}\overline{1})$ surfaces of InAs. Only the topmost monolayer of each surface is shown. Dashed lines indicate supercells used in the calculation. (d) The binding configuration between a C-C pair on the nanotube and an In atom on the $(110)$ and $(111)$ surfaces. The bond lengths are given in Å.

Figure 2

Calculated band diagram for noninteracting $(6,0)$, $(10,0)$, and $(17,0)$ nanotubes on InAs(110). Dotted lines indicate $E_F^{\mathrm{gr}}$ (defined in the text), which line up to within $\pm 0.08\mathrm{eV}$. For comparison, InP is also shown (its band alignment with InAs is taken from Ref. 16).

Figure 3

Site-decomposed band structures of a $(6,0)$ nanotube on (a) $(110)$, (b) $(111)$, and (c) $(\overline{1}\overline{1}\overline{1})$ surfaces of InAs in the direction of the tube axis. (d)–(f) Band structures of a $(10,0)$ nanotube. Colors indicate the predominant location of a state, being in the nanotube (blue), at the surface In sites (green), at the surface As sites (red), or their combination. Surface here is defined as the topmost monolayer, thus a single layer for $(110)$ but a bilayer for both $(111)$ and $(\overline{1}\overline{1}\overline{1})$. Horizontal red dashed lines indicate the Fermi level. The energy zero is set at the VBM of bulk InAs.

Figure 4

Conducting channel charge densities for the $p$-type $(14,0)$ on the $(\overline{1}\overline{1}\overline{1})$ surface (left) and the $n$-type $(14,0)$ on the $(111)$ surface (right). They are calculated by integrating from $E_F$ to $E_F+0.1\mathrm{eV}$ [i.e., the shaded area in the middle panels in which projected tube band structures (excluding those of InAs surfaces) are shown]. Energy zero is the Fermi level, $E_F$, and the arrow indicates the shift of the overall tube states of 0.6 eV.