Structural, electronic, and transport properties of silicane nanoribbons

Silicane ribbons do not suffer from aromatic dependence of the band gap making them a more promising candidate for near-term nanoelectronic application compared to armchair graphene nanoribbons. The structural, electronic, and transport properties of free-standing $s{p}^3$-hybridized armchair- and zigzag-edge silicane nanoribbons have been investigated using ab initio and nonlocal empirical pseudopotential calculations. Under ambient conditions, two-dimensional silicane sheets will spontaneously break into stable one-dimensional ribbons similar to density functional theory studies of graphene ribbons. The calculated low-field electron mobility and ballistic conductance show a strong edge dependence, due to differences in the effective mass and momentum relaxation rates along the two transport directions. The mobility in zigzag-edge ribbons is found to be approximately twenty times higher than in armchair-edge ribbons.

Figure 1

Atomic configurations of (a) 11-aSiNR and (b) 8-zSiNR. All the Si (gold balls) dangling bonds are passivated by H (white balls). Note the H atoms passivate the dangling bonds in alternating pairs at the top and bottom sides of the monolayer (chair-like). The charge carrier transport occurs along the z direction, which is equivalent to [11$\overline{2}$] and [10$\overline{1}$] of bulk Si for aSiNR and zSiNR, respectively.

Figure 2

Atomic configuration of an (a) unrelaxed and a (b) relaxed 4-zSiNR for EPs and DFT calculations, respectively. Buckling heights are denoted by $\Delta y$ for unrelaxed and $\Delta y_1$ (inner Si-Si atoms) and $\Delta y_2$ (edge Si-Si atoms) for relaxed geometry, respectively.

Figure 3

Edge free-energy vs chemical potential for a 7-aSiNR and a 4-zSiNR referenced to the free energy of an infinite 2D silicane sheet (represented as dashed horizontal line at ${\gamma }_{\mathrm{edge}}=0$). The top axes show the pressure, in bar, of H${}_2$ molecule corresponding to the chemical potential at $T=$100, 300, and 600 K, following Refs. 25 and 37.

Figure 4

Electronic band structure of a 4-zSiNR and 7-aSiNR using EPs [(a) and (c)] and DFT [(b) and (d)] with unrelaxed (dotted lines) and fully relaxed (solid lines) geometry. The top of the valence band is arbitrarily set to zero. The insets show in detail the conduction band structure near the CBM, which is set to zero.

Figure 5

(a) Difference between the calculated band gap for ribbons and the band gap for bulk Si, $\Delta E_g$, shown as a function of ribbon width for aSiNRs and zSiNRs. The band gaps from EPs and DFT are represented by solid and open symbols, respectively. The electron effective mass (in unit of the free electron mass, $m_0$) at the CBM along the $+k_z$ is shown as a function ribbon width in (b) for aSiNRs and in (c) for zSiNRs. Solid (open) symbols identify EPs (DFT) results.

Figure 6

1D ballistic conductance (in unit of the quantum conductance $G_0=2e^2/h$) for a 4-zSiNR in (a) and a 7-aSiNR in (b) with the conduction band edge $E_{\text{CBM}}$ set to zero. The ballistic conductance calculated using EPs (DFT) is represented by solid (dotted) lines.

Figure 7

(a) Total electron-phonon momentum relaxation rate accounting for the acoustic and optical emission and absorption processes and (b) density-of-states for a 7-zSiNR (solid lines) and an 11-aSiNR (dashed lines) at the electron line density $n_l=5\times {10}^5$ cm${}^{-1}$ and at $T=300$ K. The conduction band minimum $E_{\text{CBM}}$ is set to zero.

Figure 8

Phonon-limited electron mobility (a) as a function of the line density $n_l$ for 7-zSiNR (square) and 11-aSiNR (circle) at $T=300$ K and (b) as a function of ribbon width for zSiNRs (square) and aSiNRs (circle) at an electron line density $n_l=5\times {10}^5$ cm${}^{-1}$ and $T=300$ K.

Figure 9

(a) Conduction band structure (from $\Gamma$ to $X$, solid lines) and corresponding density of states (overlaid dashed lines) calculated using EPs for zSiNRs with width ranging from a 5-zSiNR to an 8-zSiNR. The second subbands at $\Gamma$ are identified by arrows. Fermi levels at a line density $n_l=5\times {10}^5$ cm${}^{-1}$ and $T=300$ K are represented as a horizontal solid lines. (b) Electron occupation factor $f_0\times (1-f_0)$ at $\Gamma$ for the first (square) and second (circle) subbands as a function of width. (c) Phonon-limited momentum relaxation rate at $\Gamma$ for the first (square) and second (circle) subbands as a function of width. (d) Subband mobility for the first (square) and second (circle) subbands and their summation (open triangle) as a function of width. Keeping in mind that the total phonon-limited electron mobility is mainly controlled by the two lowest-energy subbands, a decrease of the Fermi level with increasing width results in a relatively lower occupation of the first subband, as shown in frame (b). This overshadows the reduced electron-phonon scattering, as shown in (c), which is dominated by a smaller overlap integral. Thus the mobility in the first subband decreases with increasing ribbon width. On the other hand, the energy of the second subband is reduced with increasing ribbon width, as indicated as arrows in (a) due to reduced confinement, resulting in increased subband occupation [shown in (b)] as well as in a reduced overlap integral and scattering rate [shown in (c)]. Thus the mobility in the second subband increases as the ribbon is widened from the 5-zSiNR to the 7-zSiNR. But moving to the 8-zSiNR, what we label “second” subband now replaces the “first” subband due to the band crossing, so that the trend reverses. Note that a degradation of the mobility with reduced confinement has been also discussed in Ref. 38 and this has been attributed to a reduced subband occupation.