Tunable electronic transport properties of silicon-fullerene-linked nanowires: Semiconductor, conducting wire, and tunnel diode

We explore the possibility of controllable tuning of the electronic transport properties of silicon-fullerene-linked nanowires by encapsulating guest atoms into their cages. Our first-principles calculations demonstrate that the guest-free nanowires are semiconductors, and do not conduct electricity. The iodine or sodium doping improves the transport properties, and makes the nanowires metallic. In the junctions of I-doped and Na-doped NWs, the current travels through the boundary by quantum tunneling. More significantly, the junctions have asymmetric $I\text{−}{V}_b$ curves, which could be used as rectifiers. The current-voltage curves are interpreted by band-overlapping models. Tunable electronic transport properties of silicon-fullerene-linked nanowires could find many applications such as field-effect transistors, conducting wires, and tunnel diodes.

Figure 1

(Color online) (a) Model used to study the electronic transport in the junction of an I-doped ${\text{Si}}_{16}$-linked NW and a Na-doped ${\text{Si}}_{16}$-linked NW. Small, medium, large light-gray (green), and large gray (purple) particles represent H, Si, I, and Na atoms, respectively. The electrodes are shaded. The chemical potentials of the left and right electrodes are assumed to be ${\mu }_l$ and ${\mu }_r$, respectively. The bias voltage $V_b$ is defined as $V_b=\left({\mu }_r-{\mu }_l\right)/e$, where $e$ is the electron charge. (b) Cluster model used to optimize the structure near the boundary between the I-doped and Na-doped ${\text{Si}}_{16}$-linked NWs. The horizontal bar represents the distance between the two square atomic rings, $2L\left({\text{I}}_2@{\text{Si}}_{24}{\text{H}}_{16}\right)+2L\left({\text{Na}}_2@{\text{Si}}_{24}{\text{H}}_{16}\right)$, where $L\left({\text{I}}_2@{\text{Si}}_{24}{\text{H}}_{16}\right)$ and $L\left({\text{Na}}_2@{\text{Si}}_{24}{\text{H}}_{16}\right)$ are the unit cell lengths of the ${\text{I}}_2@{\text{Si}}_{24}{\text{H}}_{16}$ NW and the ${\text{Na}}_2@{\text{Si}}_{24}{\text{H}}_{16}$ NW, respectively. (c) Structure of I-doped ${\text{Si}}_{16}$-linked NW $\left({\text{I}}_2@{\text{Si}}_{24}{\text{H}}_{16}\text{NW}\right)$. The horizontal bar represents the length of the unit cell in the wire direction. (d) Structure of I-doped ${\text{Si}}_{20}$-linked NW $\left({\text{I}}_2@{\text{Si}}_{30}{\text{H}}_{20}\text{NW}\right)$. The horizontal bar represents the length of the unit cell in the wire direction.

Figure 2

Partial charge differences of $\text{I}@{\text{Si}}_{16}{\text{H}}_8$ and $\text{Na}@{\text{Si}}_{16}{\text{H}}_8$ cages of the ${\text{I}}_{14}{\text{Na}}_{14}@{\text{Si}}_{340}{\text{H}}_{233}$ cluster. The notation $\text{I}i/\text{Na}i$ indicates the $i\text{th}$ $\text{I}@{\text{Si}}_{16}{\text{H}}_8/\text{Na}@{\text{Si}}_{16}{\text{H}}_8$ cage numbering from the boundary.

Figure 3

(Color online) $I-V_b$ curves for (a) ${\text{Si}}_{16}$-linked NWs and (b) ${\text{Si}}_{20}$-linked NWs. Squares, circles, triangles, and diamonds are results for guest-free NW, I-doped NW, Na-doped NW, and the junction of the I-doped NW and the Na-doped NW, respectively. The currents in the I-Na junctions are magnified five times for clarity.

Figure 4

Band structures of infinite Si-fullerene-linked NWs. (a) guest-free, (b) I-doped, and (c) Na-doped ${\text{Si}}_{16}$-linked NWs. (d) guest-free, (e) I-doped, and (f) Na-doped ${\text{Si}}_{20}$-linked NWs. The energy is measured from the Fermi energy shown by the dashed horizontal line.

Figure 5

(Color) Band-overlapping model for I-doped ${\text{Si}}_{16}$-linked NW. (a) Band structure near the Fermi energy. The energy is measured from the Fermi energy shown by the horizontal short dashed line. The $\alpha$ band is drawn by the dashed line. The red and blue dashed lines are the ${\alpha }_{\Gamma T}$ and ${\alpha }_{TX}$ bands, respectively. The $\beta$ band is drawn by the dash-dotted line. (b) $I\text{−}{V}_b$ curves. The curves obtained by the BO model and NEGF calculation are given in the left. The contributions, $I_{b\left(l\right)b\left(r\right)}$ and $I_{r\left(l\right)r\left(r\right)}$, are given in the right. The $I_{b\left(l\right)b\left(r\right)}$ is shifted upward by $10\mu \text{A}$ for clarity. (c) Transmission curves, band structures of the left electrode, and band structures of the right electrode are given in the left, middle, and right, respectively. The energy is measured from the chemical potential of the left electrode ${\mu }_l$. The chemical potential of the right electrode ${\mu }_r$ is shown by the dashed line. The results of 0.0, 0.1, 0.4, and 0.7 V are given in the upper, upper-middle, lower-middle, and lower rows, respectively. The transmission curves obtained by the BO model and NEGF calculations are shown by the red and black lines, respectively.

Figure 6

(Color) Band-overlapping model for Na-doped ${\text{Si}}_{16}$-linked NW. (a) band structure near the Fermi energy. The energy is measured from the Fermi energy shown by the horizontal short dashed line. The $\gamma$ band is drawn by the dashed line. The green and black dashed lines are the ${\gamma }_{\Gamma B}$ and ${\gamma }_{BX}$ bands, respectively. (b) $I\text{−}{V}_b$ curves. The curves obtained by the BO model and NEGF calculation are given in the left. The contributions, $I_{g\left(l\right)g\left(r\right)}+I_{o\left(l\right)o\left(r\right)}$ and $I_{\left[c\left(l\right),m\left(l\right)\right]\left[g\left(r\right),o\left(r\right)\right]}$, are given in the right. (c) Transmission curves, band structures of the left electrode, and band structures of the right electrode are given in the left, middle, and right, respectively. The energy is measured from the chemical potential of the left electrode ${\mu }_l$. The chemical potential of the right electrode ${\mu }_r$ is shown by the dashed line. The results of 0.25, 0.30, and 0.60 V are given in the upper, middle, and lower rows, respectively. The transmission curves obtained by the BO model and NEGF calculation are shown by the red and black lines, respectively. Note that the 1/5 of $T_{\text{BO}}$ is given at 0.25 and 0.30 V for clarity.

Figure 7

(Color online) Overlapping area of DOSs. The dotted line is the DOS of the left electrode (I-doped ${\text{Si}}_{16}$-linked NW), while the dashed line is the DOS of the right electrode (Na-doped ${\text{Si}}_{16}$-linked NW). (a) $V_b=0.6\text{V}$, (b) 0.3 V, (c) 0.0 V, and (d) $-0.6\text{V}$. Horizontal bars represent the chemical potentials of the left and right electrodes. The energy is measured from $\left({\mu }_l+{\mu }_r\right)/2$.

Figure 8

(Color) Map of PDOSs of $\text{I}@{\text{Si}}_{16}{\text{H}}_8$ and $\text{Na}@{\text{Si}}_{16}{\text{H}}_8$ cages of the junction of I-doped and Na-doped ${\text{Si}}_{16}$-linked NWs at zero bias. PDOSs are depicted in arbitrary unit. The notation $\text{I}i/\text{Na}i$ indicate the $i\text{th}$ $\text{I}@{\text{Si}}_{16}{\text{H}}_8/\text{Na}@{\text{Si}}_{16}{\text{H}}_8$ cage numbering from the boundary. PDOSs at $\text{I}\infty$ and $\text{Na}\infty$ correspond to PDOSs of the infinite I-doped and Na-doped ${\text{Si}}_{16}$-linked NWs, respectively.

Figure 9

(Color) Band-overlapping model for I-doped ${\text{Si}}_{20}$-linked NW. (a) band structure near the Fermi energy. The energy is measured from the Fermi energy shown by the horizontal dashed line. (b) $I\text{−}{V}_b$ curves. The curves obtained by the BO model and NEGF calculation are given in the left. The contributions, $I_{r\left(l\right)r\left(r\right)}$, $I_{b\left(l\right)b\left(r\right)}$ and $I_{g\left(l\right)g\left(r\right)}$, are given in the right. The $I_{b\left(l\right)b\left(r\right)}$ and $I_{r\left(l\right)r\left(r\right)}$ are shifted upward by 10 and $20\mu \text{A}$, respectively, for clarity.

Figure 10

(Color) Band-overlapping model for Na-doped ${\text{Si}}_{20}$-linked NW. (a) band structure near the Fermi energy. The energy is measured from the Fermi energy shown by the horizontal dashed line. The $\sigma$ band is drawn by the dashed line. The green and black dashed lines are the ${\sigma }_{\Gamma B}$ and ${\sigma }_{BX}$ bands, respectively. (b) $I\text{−}{V}_b$ curves. The curves obtained by the BO model and NEGF calculation are given in the left. The contributions, $I_{o\left(l\right)o\left(r\right)}$, $I_{m\left(l\right)g\left(r\right)}$, and $I_{g\left(l\right)g\left(r\right)}$, are given in the right. The $I_{o\left(l\right)o\left(r\right)}$ and $I_{m\left(l\right)g\left(r\right)}$ are shifted upward by $10\mu \text{A}$ for clarity. (c) Transmission curves, band structures of the left electrode, and band structures of the right electrode are given in the left, middle, and right, respectively. The energy is measured from the chemical potential of the left electrode ${\mu }_l$. The chemical potential of the right electrode ${\mu }_r$ is shown by the dashed line. The results of 0.50, 0.65, and 0.80 V are given in the upper, middle, and lower rows, respectively. The transmission curves obtained by the BO model and NEGF calculation are shown by the red and black lines, respectively.