Confinement of electrons in size-modulated silicon nanowires

Based on first-principles calculations we showed that superlattices of periodically repeated junctions of hydrogen-saturated silicon nanowire segments having different lengths and diameters form multiple quantum-well structures. The band gap of the superlattice is modulated in real space as its diameter does and results in a band gap in momentum space which is different from constituent nanowires. Specific electronic states can be confined in either narrow or wide regions of superlattice. The type of the band lineup and hence the offsets of valence and conduction bands depend on the orientation of the superlattice as well as on the diameters of the constituent segments. Effects of the SiH vacancy and substitutional impurities on the electronic and magnetic properties have been investigated by carrying out spin-polarized calculations. Substitutional impurities with localized states near band edges can make modulation doping possible. Stability of the superlattice structure was examined by ab initio molecular-dynamics calculations at high temperatures.

Figure 1

(Color online) Energy-band structure of the superlattice, ${\text{Si}}_{138}{\text{H}}_{42}$, formed from periodically repeated junctions consisting of one unit cell of SiNW with $D_1\sim 11\text{Å}$ and two unit cell of SiNW with $D_2\sim 7\text{Å}$ formed along [111] direction. Here the diameter $D$ is defined as the largest distance between two Si atoms in the same cross-sectional plane. Isosurface charge densities of specific bands and their planarly averaged distribution along the superlattice axis together with their confinement in percentages are also shown. Large and small balls indicate Si and H atoms. Zero of energy is set at the Fermi level shown by dash-dotted line.

Figure 2

(Color online) Band structures of infinite and periodic ${\text{Si}}_{45}{\text{H}}_{20}$, ${\text{Si}}_{25}{\text{H}}_4$, and ${\text{Si}}_{21}{\text{H}}_{12}$ nanowires, which constitute ${\text{Si}}_{157}{\text{H}}_{64}$ structure. The front and side view of these relevant structures are shown on the top of the band-structure plots. Numerals as subscripts of Si and H indicate the number of Si and H atoms in the unit cell. Energy-band gaps are shaded.

Figure 3

(Color online) (a) Electronic structure and isosurface charge densities of selected states for pristine ${\text{Si}}_{157}{\text{H}}_{64}$ and defected ${\text{Si}}_{156}{\text{H}}_{63}$ (with one Si-H on the surface removed) nanowire superlattices. Arrows pointing at the same isosurface charge-density plot indicates that those states are not affected by the formation of the defect and have nearly the same charge-density profile. Fermi level, represented by dashed-dotted (red) line, was shifted to the valence-band edge and set to zero. Solid (blue) and dashed (green) lines in the right-hand side box represent the majority- and minority-spin bands, respectively. (b) The distribution of interatomic distances of relaxed superlattice. The arrows indicate the ideal bulk first-, second-, and third-nearest-neighbor distances.

Figure 4

(Color online) (a) Energy per unit cell of ${\text{Si}}_{157}{\text{H}}_{64}$ superlattice as its temperature is increased from 500 to 1400 K (green/light) and kept constant at 1300 K (red/dark). Trajectories of atoms at the surface of (b) wide and (c) narrow parts and at the center of (d) wide and (e) narrow parts of the superlattice, projected on a plane perpendicular to the wire axis, as the system is kept at 1300 K.

Figure 5

(Color online) Atomic and electronic structure and charge-density isosurfaces of ${\text{Si}}_{157}{\text{H}}_{64}$ substitutional doped by B and P atoms [namely, ${\text{Si}}_{156}\text{P}\left(\text{B}\right){\text{H}}_{64}$]. Top panel presents a view of the superlattice structure, where the doped site is represented by large red (dark) ball. Arrows between the bands of the undoped (pristine) superlattice and the bands of the B- and P-doped superlattices indicate the states, which preserved their character even after doping. The charge-density isosurfaces of specific states are linked to the corresponding bands by arrows. Fermi level, represented by dashed-dotted (red) line, was shifted to the valence-band edge and set to zero. Solid (blue) and dashed (green) lines represent the majority- and minority-spin states, respectively. Small panel at the left-hand side presents the charge-density isosurface plot of B-Si bonds.