Theoretical investigation of silicon nanowires: Methodology, geometry, surface modification, and electrical conductivity using a multiscale approach

The structural and electronic properties of hydrogenated silicon nanowires (SiNWs) oriented in ⟨100⟩, ⟨110⟩, ⟨111⟩, and ⟨112⟩ directions are investigated systematically using a multiscale approach: geometry optimization is done by a semiempirical method and electronic band structure is calculated by density-functional theory with Gaussian basis set. The calculated band gaps agree very well with the available experimental data. We propose that the multiscale approach is an accurate and effective way for calculating the structural and electronic properties of SiNWs with diameter up to $3\mathrm{nm}$. Besides, we found that surface modification of the SiNWs using the hydroxyl and fluoro groups can strongly reduce the band gap by as much as $1\mathrm{eV}$, and more interestingly, alter the gap nature. On the contrary, the ⟨110⟩ SiNWs exhibiting different patterns at the cross section do not show significant difference in their band gaps $(<0.09\mathrm{eV})$, indicating that the electronic structures of SiNWs are much more sensitive to surface modification than the change of cross section. Moreover, SiNWs of different orientations exhibit different degrees of band gap reduction upon surface modification, in which the ⟨110⟩ SiNW demonstrates the highest sensitivity. The result indicates that SiNWs oriented in ⟨110⟩ direction are the better candidate for sensor application. On the contrary, the ⟨111⟩ SiNW is found to be very tight to structural change with diameter and the most reluctant to surface modification, showing that it is structurally stable and rather inert. In addition, from the $I\text{−}V$ curves of the SiNWs with surfaces modified with hydroxyl groups, which are calculated by the nonequilibrium Green’s function theory, we found that the electrical conductivity of the SiNWs is highly chemical sensitive. Besides, the phenomenon of negative differential resistance is observed in the $I\text{−}V$ curves.

Figure 1

(Color online) (a) The cross sections of the ⟨100⟩, ⟨110⟩, ⟨111⟩, and ⟨112⟩ SiNWs. Yellow (gray) and white balls represent Si and H atoms, respectively. (b) The side view of the ⟨110⟩ SiNWs with symmetric dihydride and canted dihydride on the (100) surfaces. $d=1.439\mathrm{\AA }$ and $d^{\prime }=1.853\mathrm{\AA }$ are the distances between two closest neighboring hydrogen atoms in symmetric and canted dihydride, respectively.

Figure 2

(a) Variation of band gaps as a function of SiNW diameters. Solid and open symbols indicate direct and indirect gaps, respectively. The straight line indicates the experimental band gap of bulk silicon. (b) The band structures of the ⟨100⟩, ⟨110⟩, ⟨111⟩, and ⟨112⟩ SiNWs. The band structure is calculated using the primitive repeating unit for each SiNW. The mean diameters of these SiNWs are 3.06, 2.77, 2.98, and $3.21\mathrm{nm}$, respectively. The arrows indicate the band gap for each SiNW. The lines connecting the points are guides for the eyes.

Figure 3

(Color online) (a) The cross sections of the -F substituted ⟨110⟩ SiNWs and the -OH substituted ⟨112⟩ SiNWs. Yellow (gray), white, red (dark gray), and green (black) balls represent Si, H, O, and F atoms, respectively. (b) The HOMO-LUMO molecular orbital (MO) plots for the hydrogenated and substituted ⟨112⟩ SiNWs. Isodensity value for all MO plots is 0.02. All atoms are shown in white color for clearance.

Figure 4

The HOMO-LUMO energy diagram for the hydrogenated and substituted ⟨100⟩, ⟨110⟩, ⟨111⟩, and ⟨112⟩ SiNWs.

Figure 5

Variation of band gaps as a function of percentage of substitutions. Solid and open symbols indicate direct and indirect gaps, respectively.

Figure 6

(Color online) The cross sections of the 13 ⟨110⟩ SiNWs with different patterns. Yellow (gray) and white balls are Si and H atoms, respectively. Blue (dark gray) balls are Si atoms that highlight the extra facets grown on the surfaces of the SiNWs.

Figure 7

(Color online) (a) The cross sections of the hydrogenated and substituted ⟨110⟩ SiNWs. Yellow (gray), white, and red (dark gray) balls represent Si, H, and O atoms, respectively. (b) A two-probe system contains three components: the left electrode (L), the central scattering region, and the right electrode (R). The system adopts Li (001) metal as electrodes (left panel) and SiNW itself as electrodes (right panel). (c) $I\text{−}V$ curves of the hydrogenated SiNW calculated by the two different systems: [line (i)] Li (001) metal as electrodes and [line (ii)] SiNW as electrodes. The dotted lines are drawn for completing the $I\text{−}V$ curves. (d) $I\text{−}V$ curves for SiNWs with different surface modifications: [line (i)] hydrogenated SiNW, [line (ii)] partly -OH substituted SiNW, and [line (iii)] fully -OH substituted SiNW. The inset shows the $I\text{−}V$ curves from $2\text{to}3\mathrm{V}$ for vision.