Confined states in multiple quantum well structures of ${\mathrm{Si}}_n{\mathrm{Ge}}_n$ nanowire superlattices

Mechanical properties, atomic and energy band structures of bare and hydrogen-passivated ${\mathrm{Si}}_n{\mathrm{Ge}}_n$ nanowire superlattices have been investigated by using first-principles pseudopotential plane-wave method. Undoped, tetrahedral Si and Ge nanowire segments join pseudomorphically and can form superlattice with atomically sharp interface. We found that ${\mathrm{Si}}_n$ nanowires are stiffer than ${\mathrm{Ge}}_n$ nanowires. Hydrogen passivation makes these nanowires and ${\mathrm{Si}}_n{\mathrm{Ge}}_n$ nanowire superlattice even more stiff. Upon heterostructure formation, superlattice electronic states form subbands in momentum space. Band lineups of Si and Ge zones result in multiple quantum wells, where specific states at the band edges and in band continua are confined. The electronic structure of the nanowire superlattice depends on the length and cross section geometry of constituent Si and Ge segments. Since bare Si and Ge nanowires are metallic and the band gaps of hydrogenated ones vary with the diameter, ${\mathrm{Si}}_n{\mathrm{Ge}}_n$ superlattices offer numerous alternatives for multiple quantum well devices with their leads made from the constituent metallic nanowires.

Figure 1

(Color online) Optimized atomic structure of bare and hydrogenated ${\mathrm{Si}}_n{\mathrm{Ge}}_n$ nanowire superlattices for $n=75$ and 114. (a) Top view and (b) side view. Small-gray, large-light, and large-dark balls correspond to the hydrogen, silicon, and germanium atoms, respectively.

Figure 2

(Color online) Interatomic distance distribution of optimized bare and hydrogenated ${\mathrm{Si}}_{2n}$, ${\mathrm{Ge}}_{2n}$, and ${\mathrm{Si}}_n{\mathrm{Ge}}_n$ for $n=75$ up to fourth nearest neighbor. Similar distributions for ${\mathrm{Si}}_{114}{\mathrm{Ge}}_{114}$ and $\mathrm{H}\text{−}{\mathrm{Si}}_{114}{\mathrm{Ge}}_{114}$ are also shown. The Si-H (Ge-H) bond lengths being in the range of $\sim 1.5\mathrm{\AA }$ are not shown.

Figure 3

(Color online) Energy band structures of optimized bare and hydrogenated ${\mathrm{Si}}_{2n}$, ${\mathrm{Ge}}_{2n}$ nanowires, and ${\mathrm{Si}}_n{\mathrm{Ge}}_n$ nanowire superlattices for $n=75$. Zero of energy is taken at the Fermi level. Band gaps are shown by shaded zones. Dashed and dotted lines (minibands) are obtained by folding of ${\mathrm{Si}}_{50}$ (also $\mathrm{H}\text{−}{\mathrm{Si}}_{50}$) and ${\mathrm{Ge}}_{50}$ (also $\mathrm{H}\text{−}{\mathrm{Ge}}_{50}$) bands.

Figure 4

(Color online) Energy band structures of optimized bare and hydrogenated ${\mathrm{Si}}_{2n}$, ${\mathrm{Ge}}_{2n}$ nanowires, and ${\mathrm{Si}}_n{\mathrm{Ge}}_n$ nanowire superlattices for $n=114$. Zero of energy is taken at the Fermi level. Dashed and dotted lines are obtained by folding of ${\mathrm{Si}}_{57}$ (also $\mathrm{H}\text{−}{\mathrm{Si}}_{57}$) and ${\mathrm{Ge}}_{57}$ (also $\mathrm{H}\text{−}{\mathrm{Ge}}_{57}$) bands.

Figure 5

(Color online) Energy band structure of bare and hydrogenated ${\mathrm{Si}}_n{\mathrm{Ge}}_n$ nanowire superlattices for $n=25$, 50, and 57.

Figure 6

(Color online) Schematic description of energy band diagram in the unit cell (on the right and upper side), band structure in the momentum space (on the left side), and isosurface charge density of states of $\mathrm{H}\text{−}{\mathrm{Si}}_{75}{\mathrm{Ge}}_{75}$ NWSL at the band edges.

Figure 7

(Color online) Schematic description of energy band diagram in the unit cell (on the right and upper side), band structure in the momentum space (on the left side), and isosurface charge density of states of $\mathrm{H}\text{−}{\mathrm{Si}}_{114}{\mathrm{Ge}}_{114}$ NWSL at the band edges.