1. Introduction
The tuning of the work function of metal oxide is important in the research on the application field of the electronic devices [1]. The modification of the surface with self assembled monolayer (SAM) has been known as a method to change the work function of the metal oxide substrates [2,3]. One of such metal oxide substrates is tin oxide (SnO_{2}), which has been used for gas sensors, transparent conductors, and catalysts [4]. The (110) surface of SnO_{2} is the thermodynamically most stable face compared to other low index faces of tin dioxide and has been investigated not only experimentally [5-8] but also theoretically the properties of its surface [9-15]. Many researchers studied molecular adsorption and oxygen vacancies of tin dioxide surface theoretically [16,17] to interpret how tin dioxide surfaces sense gases [18] and conduct electric current [19]. In this work, we studied the work function change of the SnO_{2}(110) surface using the density functional theory (DFT) with the cluster model of SnO_{2}(110) where surface was modified by various benzoic acid derivatives.
If SAM is conceptualized as parallel charged sheets, the work function change (ΔΦ) can be expressed by the following equation [20]
(1)
where N is the density of the molecules on the surface; is the component of the dipole moment of SAM normal to the surface; k is the dielectric constant of the dipole layer; and is the permittivity of vacuum. By assuming the chemisorbed SAMs are modeled as two dipole sheets with different dielectric constants, Zehner et al. derived the Equation (2) for work function change (ΔΦ) of the chemisorptions of SAM from a series of arenethiol adsorbates on the gold [20].
(2)
where is the dipole moment of the chemisorbed molecule normal to the surface plane, and, k_{Au−S}, and k_{mono} are the dipole moment of Au-S bond, dielectric constant of Au-S bond, and dielectric constant of monolayer, respectively. They were determined independently according to Zehner et al. [20]. If we apply this equation to the system of SnO_{2} surface modified by benzoic acid molecules, the following equation can be formed
(3)
where is the dipole moment of the modified monolayer component normal to SnO_{2}(110) surface, and and are the dipole moment and the dielectric constant of Sn-OOC bonds, respectively. As there are no existing experimental values of surface density (N) and the work function change (ΔΦ) of the modified SnO_{2}(110) surface with benzoic acid derivatives, it is difficult to evaluate the work function change by these dipole moments from Equation (3) directly. Therefore, we substituted left side of Equation (3) to the right side of Equation (1), then, we derived the following equation
(4)
If we assume the coefficient (k/k_{mono}) of the first term and the whole second term of the right side of Equation (4) are constants, we can expect the linear relationship between and. The main aim of this work is to check the relationship between them by using the first principle method. The results showed that the relation between dipole moment of and was linear.
2. Calculation Method
2.1. Calculation Procedure
DFT calculation was performed with Becke’s hybrid three parameters approach [21,22] and Lee-Yang-Parr exchange-correlation functional (B3LYP), [23] which is implemented in Gaussian03 package program, [24] was used. Basis set for Sn atom was chosen by a relativistic effective core potential (ECP) [25] with double zetta function (LanL2DZ) which treats 1s^{2} to 4p^{6} electrons are frozen and 5s^{2}5p^{2} electrons are explicitly included in the valence. For H, C, O, F and Cl atoms, basis set of 6-31G were used [26]. During the optimization, the atoms of the cluster of Sn_{7}O_{14} were frozen and their geometric positions were the same as crystal geometry [27].
2.2. Calculation Model
The surface of SnO_{2}(110) was modeled as a cluster of Sn_{7}O_{14} embedded in point charges (PCs) according to the model of Melle-Franco and Pacchioni (Figure 1) [28]. In this figure, PCs are illustrated by wire model with +2 and −1 electrons substituted in positions of Sn and O atoms in the bulk geometry of SnO_{2}, respectively [27]. This cluster model corresponds to the stoichiometric surface structure of SnO_{2}(110).
The binding structure of the benzoic derivative YC_{6}H_{4}-COOH (Y: H, F, Cl, CCl_{3}, CF_{3}) on the SnO_{2} surface was modeled and shown in Figure 2.
Calatayud et al. [29] calculated the methanol adsorption on SnO_{2}(110) surface. They modeled the cleavage of the methanol O-H bond and the resulting fragments of H and CH_{3}O were bounded to the bridging oxygen (O_{b}) and 5-fold tin (Sn_{5}) atoms, respectively. According to their model, we modeled the cleavage of benzoic acid COO-H bond and the resulting fragments of H and COO were bound to the same bridging oxygen (O_{b}) as Calatayud et al. model [29] and 5-fold tin (Sn_{5}) atoms to make the system with singlet multiplicity as were shown in Figure 2, respectively.
3. Results and Discussion
Modified surface structures, where the benzoic acid derivatives of Y-C_{6}H_{4}-COOH (Y: H, F, Cl, CCl_{3} and CF_{3})
Figure 1. Structure of the Sn_{7}O_{14} cluster model embedded in a point charge potential. Sn_{5}; 5-fold tin, Sn_{6}; 6-fold tin, O_{b}; bridging oxygen, O_{ip}; in-plane oxygen atoms.
Figure 2. The binding structure of Y-C_{6}H_{4}-COOH after optimization. PCs are not shown for simplicity.
bind to the SnO_{2} surface, were investigated using DFT calculation. As the fragments of the cleavage of benzoic acid derivatives of H and Y-C_{6}H_{4}-COO were modeled to bind to the bridging oxygen (O_{b}) and the 5-fold tin (Sn_{5}) atoms, the bound structures were first optimized to check the adequacy of its binding structure. In the optimization, surface atoms of the Sn_{7}O_{14} cluster were fixed in the calculation. After the successful optimization of the binding structures of Y-C_{6}H_{4}-COO on Sn_{7}O_{14}-H cluster, it was found that the plane of benzene ring was oriented close to normal to the SnO_{2}(110) surface. By using the optimized bound structure, dipole moments perpendicular to the surface of SnO_{2}(110), , were evaluated. The obtained values were shown in Table 1. To investigate the relationship between and shown in Equation (4), we calculated the values of the dipole moment of the modified monolayer component normal to SnO_{2}(110) surface,. According to the model of Zehner et al. [20], corresponds to the dipole moment of Y-C_{6}H_{4}-COO radicals. This component of the dipole moment of Y-C_{6}H_{4}-COO radicals (Y: H, F, Cl, CF_{3}, CCl_{3}) was calculated and the dipole moments along to the normal to the surface were shown in Table 1 as. The relation between the dipole moment of and is shown in Figure 3. It shows that there is a good linear relationship between these two dipole moments. The square of the correlation coefficient is 0.998. The value of the slope is 1.102 and the intercept is −22.1 D. As the slope value is close to 1, we can estimate from Equation (4) that the value of k is almost similar to k_{mono}. On the other hand, the intercept value of −22.1 D corresponds to (k/k_{Sn-OOC}) term in equation 4. If we assume the values of k and k_{Sn-OOC} are also equal, the dipole moment for the Sn-OOC bonds, µ_{Sn-OOC}, can be estimated. The evaluated value of µ_{Sn-OOC} is −22.1 D.
It shows that the contribution of the binding group -COO to the surface dipole moment is constant in the series of Y-C_{6}H_{4}-COO molecules, even though the terminal groups of Y in the Y-C_{6}H_{4}-COO molecules are different. Carrara et al. [30] investigated the surface adsorption of carboxylic acid derivatives on both aluminium and indium-tin oxide surfaces and reported that the contribution of the binding group of -COO to the surface permanent dipole is relevant and +0.7 D and −2.2 D respectively in each series. Zehner et al. obtained the value of 2.3 - 3.8 D for some series of thiols on Au surface [20]. Compared to their values, the evaluated value of −22.1 D seems a little large. However, two Sn-OOC bonds are involved in the linkage in this model. By using the partial charges of Sn and oxygen of the carboxyl group, which were evaluated in this model, Sn-O average dipole moment was roughly estimated 12.11 D by using two Sn-O bonds for all five terminal groups (Y: H, F, Cl, CF_{3}, CCl_{3}). As two Sn-OOC bonds are involved in the linkage at the surface, the estimation of the dipole moment for the Sn-OOC bonds, µ_{Sn-OOC}, value seems to be reasonable.
By using Equation (3), work function change can be estimated. As the value of the surface molecular density N can not be found in the literature, the value of 1.3 × 10^{1}^{4} cm^{−}^{2}, which was measured for nitrobenzoic acid by Langmuir isotherms, [31] was used as a rough estimation value for our cluster Sn_{7}O_{14} model. k_{mono} and k_{Sn-OOC} were chosen as benzoic acid dielectric constant equals to 2.5 [31]. The obtained work function changes are shown
Figure 3. Relationship between the calculated dipole moments of µ_{┴} and µ_{┴,mono}.
Table 1. Calculated dipole moments normal to the SnO_{2}(110) surface.
in Table 1. Calculated values of work function change are large compared to the experimentally observed work function changes obtained by Nüesch et al. [30,31] and Appleyard et al. [32] on ITO and Aluminium surfaces graftification. Further calculation works on different series of metal oxide surfaces and the experimental work on the work function change and the molecular density of chemisorbed SAM should be desired.
4. Conclusion
Density functional calculation on the modified surface of SnO_{2}(110) with benzoic acid derivatives was performed to obtain the information of the surface dipole moment and the work function changed using the cluster model. The result shows the linear relationship between the surface dipole moment and the dipole moment of binding molecule. From this relation, dipole moment of the linkage of the Sn and OOC bonds at the surface was evaluated and the average value of −22.1 D was obtained.
5. Acknowledgements
The authors thank the Research Center for Computational Science, Okazaki, Japan for the use of a computer to perform part of the calculation.
NOTES