Functionalization of hydrogenated (111) silicon surface with hydrophobic polymer chains

The first stage functionalization of hydrogenated (111) Si surface with methyl-terminated monolayers to form hydrophobic coatings has been studied by accurate ab initio density functional total energy calculations. The first stage adsorption events involving one or two deposited $n$-alkane and $n$-alkyl-silane molecules have been characterized from the geometrical and the energetic points of view; the ground-state adsorption configurations together with the geometrical and the energetic parameters relevant to self-assembling processes have been obtained, such as the polymers tilt angles, the rotation energy barriers, the binding energies, and the electrostatic interactions. The above-mentioned quantities have been related to the stability properties of self-assembled monolayers and have been recognized to affect critically the stability and the uniformity of the hydrophobic film elucidating the reasons why some commonly used polymers behave differently.

Figure 1

Total energy of the supercell containing the hydrogen-terminated Si(111) slab as a function of the energy cutoff for different Monkhorst-Pack $k$-point grids.

Figure 2

Adsorption configuration of the alkyl chain on the (111) Si:H surface. The adhesion geometry is described in terms of the ${\varphi }_1$ and ${\varphi }_2$ angles, formed by the Si-C bond direction with respect to the surface unit vectors ${\mathbf{e}}_1$ and ${\mathbf{e}}_2$, and the $\theta$ angle between the polymer chain projection on the surface and the ${\mathbf{e}}_1$ unit vector (see the text). The configuration angles are changed statically during the constrained first optimization stage.

Figure 3

Total energies for different ${\text{CH}}_3{\text{(CH}}_2{\text{)}}_{17}/\mathrm{H}:\mathrm{Si}$ configurations obtained during the constrained first optimization stage (see the caption of Fig. 2 for the details) by varying either ${\varphi }_1$/${\varphi }_2$ (with $\theta \equiv {\theta }_{\min }=0$) (a) or $\theta$ (with ${\varphi }_1={\varphi }_2=\pi /2$) (b). All the energies are referred to the most stable configuration. Both the static calculations have been performed with the fixed Si-C adhesion bond of $\sim$1.88 Å as discussed in the text.

Figure 4

Fully relaxed configuration of the 18-alkyl chain (a) and the hydroxylated OTS molecule (b) adsorbed on the hydrogenated (111) Si surface. In the insets the (111) plane view is reported for both the configurations.

Figure 5

Charge density map (in ${\text{e}}^{-}$ units) in the (010) plane containing the Si-C adhesion bond (a). Contour plot in the (010) plane of the maximally localized Wannier function centered on the Si-C adhesion bond of the alkyl molecule and the (111) Si surface (b). The MLWFs (in units of $a_0^{-3/2}$) observed along the Si-C bond direction reveal the $\sigma$ bonding features between two $s{p}^3$ hybrids belonging to Si and C.

Figure 6

Adsorption configuration of the alkyl chain on the (111) Si:H surface. The adhesion geometry is described in terms of the ${\varphi }_1$ and ${\varphi }_2$ angles, respectively, formed by the Si-O bond direction ($\mathbf{d}$) and the surface unit vectors ${\mathbf{e}}_1$ and ${\mathbf{e}}_2$, and the $\theta$ angle between the polymer chain projection on the surface and the ${\mathbf{e}}_1$ unit vector (see the text). The configuration angles are changed statically during the constrained first optimization stage.

Figure 7

Total energies for different adsorption configurations of a hydroxylated OTS molecule on the (111) Si:H surface obtained during the constrained first optimization stage (see the caption of Fig. 6 for the details) by varying ${\varphi }_1$ (${\varphi }_2$) with $\theta \equiv {\theta }_{\min }=0$) (a) and ${\varphi }_2=\pi /2$ (${\varphi }_1=\pi /2$) (a) or $\theta$ (with ${\varphi }_2=\pi /2$ and ${\varphi }_1={\varphi }_2+\pi /30$) (b). All the energies are referred to the most stable configuration. Both the static calculations have been performed with Si-O adhesion bond length constrained at its equilibrium value $d_{\mathrm{SiO}}\sim 1.65$Å in a fully relaxed ${\text{CH}}_3{\text{(CH}}_2{\text{)}}_{17}{\text{Si(OH}}_3\text{)}$ molecule.

Figure 8

Charge density map (in ${\text{e}}^{-}$ units) in the (010) plane containing the Si-O adhesion bond (a). Contour plot in the (010) plane of the MLWFs centered on the Si-O adhesion bond between the hydroxylated OTS molecule and the (111) Si surface (b). The MLWFs (in units of $a_0^{-3/2}$) observed along the Si-O bond direction evidences a slight distortion of the $\sigma$ bond between Si and O.

Figure 9

Density maps of the electrostatic potential for the ground-state adsorption configurations in the 18-alkyl (a) and the OTS (b) cases. The density maps have been drawn on meaningful planes parallel to the (111) Si surface, respectively: (a) the midplane between the topmost H atoms of the Si:H surface and the lowermost H atom of the alkyl chain (i.e., the one of the lowermost $-{\text{CH}}_2$ trimer); (b) the midplane between the topmost H atoms of the H:Si surface and the lowermost H atom belonging to the OH groups. The distances from the surface are $0.70$ Å$$ in (a) and $0.73$ Å$$ in (b).

Figure 10

Fully relaxed configurations of two polymers adsorbed at adjacent sites on the hydrogenated (111) Si surface for the 18-alkyl (a) and the hydroxylated OTS (b) cases.

Figure 11

Density maps of the electrostatic potential for the ground-state configurations of two polymers adsorbed at adjacent sites on the hydrogenated (111) Si surface. The density maps for the OTS (a) and the 18-alkyl (b) cases have been drawn on meaningful planes parallel to the (111) Si surface, namely the one that in the OTS case contains the (almost) linear H bond between the OH radicals of the two molecules (a) and the middle plane between the topmost H atoms of the Si surface and the lowermost H atoms belonging to the alkyl chain (b) [almost the same as Fig. 9b].