Article pubs.acs.org/JPCC
Reactions of Atomic Hydrogen with the Hydroxide- and AmineFunctionalized Si(100)-2×1 Surfaces: Accurate Modeling of Hydrogen Abstraction Reactions Using Density Functional Theory Glen Allen Ferguson, Raghunath O. Ramabhadran, Christopher Trong-Linh Than, Ranjani Krishnan Paradise, and Krishnan Raghavachari* Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States S Supporting Information *
ABSTRACT: Reactions of atomic hydrogen with the hydroxide- or aminefunctionalized Si(100)-(2×1) surface provide a possible way of fabricating ultrathin layers of silicon oxide or silicon nitride. Modeling such radical reactions with popular density functionals such as B3LYP is known to have significant deficiencies. The M06 class of hybrid meta-density functionals presents a possible route to model these systems accurately. We have evaluated M06 for hydrogen abstraction reactions involving main group elements and compared the results to those from B3LYP and CCSD(T)//MP2 methods. M06 offers excellent efficiency and accuracy with a mean absolute deviation from CCSD(T) for hydrogen abstraction barriers of 1.3 kcal/mol as compared to 3.4 kcal/mol for B3LYP. Having established its accuracy, the M06 functional is subsequently used to understand atomic hydrogen-induced silicon oxide and silicon nitride layer formation, focusing on the dominant pathways for insertion into the silicon lattice’s uppermost layer. For oxygen, our results indicate that atomic hydrogen will preferentially abstract the surface silicon monohydride, subsequently leading to oxygen insertion into the dimer bond. In contrast, the corresponding reactions for nitrogen do not result in selectivity for insertion. structures seen in Figure 1.13,28 The surface hydroxide and amine groups can then be induced to insert into the surface forming an ultrathin layer. As shown in Figure 2, on the Si(100)-2×1 surface, it is possible to insert into either the
I. INTRODUCTION The silicon surface has been a subject of intense scientific interest1−7 stemming from the ubiquitous use of silicon by the microelectronics industry. Also important are the Si/SiO2, Si/ Si3N4, and the newer hafnium oxide-based interfaces8−23 that have been studied due to their use as gate dielectric layers for microelectronics devices. Research on these interfaces is important from two perspectives: after the limits of the current silicon paradigm are reached,24−26 future devices are still likely to be built upon silicon giving both silicon and silicon interfaces continuing technological importance. This future use along with the large body of knowledge for silicon makes it an interesting system for fundamental surface science research. Controlled fabrication of ultrathin layers of silicon oxide or silicon nitride is a starting point for surface functionalization. To form these layers, it is necessary to have very precise control over oxygen or nitrogen layer formation. A well-ordered surface can be expected to have much more stable and reproducible properties than a less-ordered surface. While direct exposure of silicon to atmospheric oxygen rapidly forms an oxide layer,27 controlled oxide layer growth may be possible using different chemistries. A potential first step in controlled oxidation or nitridation is to expose the bare Si(100)-2×1 surface to small amounts of water or ammonia in ultrahigh vacuum. These molecules are known to dissociatively chemisorb on the surface to form the © 2014 American Chemical Society
Figure 1. Si9H12 clusters shown with the dissociation products with water (left) showing a hydroxide5b and a monohydride or with ammonia (right) showing an amine group and a monohydride.5c The color key is gray-blue atoms are silicon, white atoms are hydrogen, red atom is oxygen, and dark blue atom is nitrogen. Terminating hydrogens are omitted for clarity. Received: December 31, 2013 Revised: March 28, 2014 Published: April 2, 2014 8379
dx.doi.org/10.1021/jp4128258 | J. Phys. Chem. C 2014, 118, 8379−8386
The Journal of Physical Chemistry C
Article
for the simplest hydrogen abstraction reaction, that is, the H2 + H· reaction.30a In particular, this problem has been observed with one of the most popular density functionals, B3LYP.30 The origin of the poor barrier heights is attributed to the presence of substantial self-interaction errors (SIE). This problem comes from the improper treatment of electronic exchange (and correlation) in approximate density functionals.30 There have been many attempts to overcome this problem such as the method of Perdew and Zunger31 and an improvement on the Perdew−Zunger self-interaction correction by scaling techniques.32 Recently, new classes of functionals have been developed that attempt to systematically correct the known failings of density functionals including SIE. An example is the M06 class of functionals of Zhao and Truhlar.33−36 These functionals have a wide applicability to many problems and have been shown to decrease the errors from SIE, thus correcting barrier heights in addition to fixing other known deficiencies.37 From among the several density functionals in the M06 suite, we have specifically tested the M06 functional because it is the recommended functional for organometallic and inorganometallic applications.36 In this study, we have compared the hydrogen radical abstraction reaction barrier heights from small molecules containing one heavy atom for the first three rows of groups 14−17 (with the exception of fluorine38) with the density functionals M06, B3LYP (using identical basis sets, see Computational Details) and compare them with reference calculations based on the high level ab initio CCSD(T)/aug-ccpVTZ//MP2/aug-cc-pVQZ level of theory. Herein, our goal is not to perform an exhaustive search of many functionals to get heroically correct results but instead to discover an efficient practical method for obtaining reliable results that can then be applied for more complex surface reactions. With this practical objective in mind, we did not assess the performance of plethora of density funtionals. Instead, once we found that the widely used M06 functional is accurate, we proceeded to employ it for surface applications. While some of the reactions investigated are part of the training set used to parametrize M06, many others are not. We also compared abstractions from some silicon cluster models to represent surfaces to ensure consistency of our results from small molecules to cluster models. After establishing its accuracy (vide infra), the M06 functional was then used to characterize the reactions of atomic hydrogen with the functionalized Si(100)-2×1 surface and to model its subsequent reactivity.
Figure 2. Products of oxygen insertion into the dimer bond (left) and backbond (right). Structures for nitrogen are analogous except for one additional hydrogen on the nitrogen.
silicon−silicon dimer bond or the silicon−silicon backbond. Insertion into the dimer bond is unique and creates the most ordered surface. Insertion into the backbond results in the possibility of more complex processes such as multiple adsorbate insertions on a single dimer and no insertion on other dimers. Such a surface is significantly more disordered. It is therefore more desirable to induce preferential insertion into the dimer bond. A possible way of inducing insertion starting from the structures in Figure 1 is via thermal annealing.13 The results of these experiments show nonselective insertion into the silicon surface to form disordered structures. Therefore, thermal annealing of hydroxylated silicon gives an inhomogeneous surface, which may not be ideal for forming ultrathin oxide layers.13 Another means for forming ultrathin oxide layers is to use chemical control. This was accomplished by Weldon et al.13 exposing the hydroxylated Si(100)-2×1 surface to atomic hydrogen. The atomic hydrogen drives the reaction of the hydroxyl group with the silicon surface by creating radicals on the surface via hydrogen abstraction to create molecular hydrogen. Weldon et al.13 used surface infrared spectroscopy to characterize the atomic hydrogen-exposed surfaces. The results indicate a preference for dimer bond insertion over backbond insertion that yields a more ordered surface. This observation is significant and gives insight as to the possible mechanism. One of the proposed mechanisms was that the atomic hydrogen abstracts a hydrogen atom from the hydroxyl oxygen resulting in an oxygen radical that preferentially inserts into the dimer bond.13 The formation of ultrathin nitrogen layers could potentially occur in a similar fashion. Ammonia is known to react in a manner similar to water on the Si(100)2×1 surface. The resulting amine can then insert into the silicon surface. Previous studies by Widjaja and Musgrave indicate that the mechanism of thermal nitrogen insertion is more complicated than that of oxygen, requiring hydrogen diffusion and desorption to achieve insertion.17,20,27,29 An intriguing hypothesis is that exposure of the aminated surface to atomic hydrogen may also induce preferential insertion, creating a more ordered surface analogous to oxygen. To fully exploit this pathway to ultrathin oxygen or nitrogen layers, it is necessary to fully understand the reaction of atomic hydrogen with the hydroxide, amine, and monohydride silicon and the subsequent chemistry of the resulting radicals. To explore this chemistry, we must have a reliable method for effectively modeling the most significant steps in these reaction paths, the hydrogen abstraction reactions. It is well-known that popular density functionals tend to give very poor results even
II. COMPUTATIONAL DETAILS To maintain computational efficiency and calculate all models at the same level of theory, we have used small cluster models in our study to represent the silicon surface. The Si9H12 model is representative of an excised silicon dimer from the Si(100)2×1 surface and is the smallest unit that accurately reproduces the surface.39 Dangling bonds at excision points were capped with hydrogens in accordance with well-established procedure.39 To avoid unphysical relaxations, the third and fourth layer silicons and hydrogens were constrained.39 The silicon atoms representing such atoms were held rigidly at ideal crystal positions, while the hydrogens were frozen along the ideal crystal directions with a bond length of 1.48 Å. The reaction energetics were determined using two density functionals: the popular B3LYP functional40−43 composed of the B88 electron exchange functional and the Lee−Yang−Parr 8380
dx.doi.org/10.1021/jp4128258 | J. Phys. Chem. C 2014, 118, 8379−8386
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barriers for the entire test set is of 3.4 kcal/mol when compared to CCSD(T)//MP2 values. The errors for the reactions involving chlorine, carbon, nitrogen, and oxygen are particularly large. The maximum deviation, 7.7 kcal/mol, occurs for the H· + H2O → H2 + HO· reaction. The second largest deviation occurs for nitrogen with an error of 6.1 kcal/mol. These results show that, despite all of its successes, B3LYP is clearly not an appropriate functional to use for these reactions, particularly for the oxidation and nitridation reactions considered in our study. The M06 functional performs very well for the reactions in this study. The MAD of 1.3 kcal/mol for the 11 main group hydrogen abstraction reactions is much improved from the MAD of the B3LYP model chemistry using the same basis set. The maximum deviation is now only 2.2 kcal/mol from the reference CCSD(T)//MP2 values. The largest improvement of M06 over B3LYP, almost 6 kcal/mol, occurs for the hydrogen abstraction from oxygen (Table 1, column 9). Furthermore, it is interesting to note that carbon is included in the training set (HTBH3838/04 database)37 used to calibrate the M06 functional, although other reactions not part of the training set are generally found to have an even better performance. The overall errors are excellent as compared to the reference values and significantly improved over B3LYP. Interestingly, with hydrides of As, Se, and Br, B3LYP appears to perform better than M06 (Table 1). With HBr, in terms of the absolute deviation, B3LYP is off from the reference value by 1.4 kcal/mol and M06 by 1.8 kcal/mol. Similarly, with H2Se, B3LYP is off by 1.1 kcal/mol and M06 by 2.0 kcal/mol. However, in both cases, while the absolute deviations seem small, B3LYP actually results in negative barriers (Supporting Information Table SI_1). Finally, in the case of H3AS, the B3LYP H abstraction barrier is within 0.5 kcal/mol with respect to the reference value, whereas the M06 functional results in a 2.0 kcal/mol error. However, even in this case, the M06 geometry appears closer to the MP2 geometry. As can be seen in Supporting Information Figure SI_1, the HHAs angle is significantly different in the case of B3LYP (about 140°) as opposed to the 160°−170° noticed with the M06 functional and the reference geometry (MP2/aug-cc-pVQZ). Overall, in all cases M06 yields consistent results, while B3LYP is deficient in several cases, particularly for O and N. It is plausible that the errors for these systems would be reduced further with larger basis sets, but our goal for this study was to determine the efficacy of the general purpose M06 functional with modest-sized basis sets to be applicable to larger systems. All indications are that M06 gives excellent results that are considerably superior to those of B3LYP for our problem. This aspect is further strengthened by the fact that the inclusion of Grimme’s dispersion corrections does not at all affect the MAD obtained with the M06 functional (Supporting Information Table SI_2 vs Table 1), whereas, with B3LYP, the MAD becomes worse (from 3.4 kcal/mol in Table 1 vs 4.1 kcal/mol in Supporting Information Table SI_2). The following discussion for the atomic hydrogen-induced oxidation and nitridation uses the M06 functional for all calculations, and they do not include dispersion corrections because such corrections with the M06 functional do not affect the reactions considered in this work. B. Surface Reactions. The initial reactions to consider for the formation of ultrathin oxide or nitride layers on silicon are the hydrogen abstraction reactions. When considering the reactions of atomic hydrogen with the hydroxide- or amineterminated silicon surface, the two possible reaction sites are
correlation functional, and the M06 functional of Zhao and Truhlar.34−37 Transition states and minima were verified with analytical second derivative calculations. All cluster geometry optimizations used the standard Pople-style polarized double-ζ 6-31G(d,p) basis set for the top two layers of atoms and the adsorbates, while a smaller 6-31G basis set was used for the lower layer constrained atoms.44 These geometries were then used for single-point energy calculations with the slightly larger triple-ζ 6-311+G(d,p) basis set with diffuse functions on the heavy atoms. Throughout, we have intentionally used these modest-sized basis sets to demonstrate the practical utility of our protocol and for future applicability to larger clusters. To calibrate the density functional methods (M06 and B3LYP), we compared their results on small molecule model systems (vide supra) with those from accurate ab initio methods. In these reference calculations, geometry optimizations of the minima and transition states were performed using second-order Møller−Plesset perturbation theory, MP2, with the large aug-cc-pVQZ basis set.45 The energies of these structures were corrected with single-point energy calculations with the CCSD(T)/aug-cc-pVTZ model chemistry46 (coupledcluster singles and doubles with perturbative triples corrections). Calculations were performed with a development version of the Gaussian suite of programs.47 Finally, to assess the role of dispersion effects, we have also added Grimme’s D3 dispersion correction for M06 and B3LYP functionals as singlepoint energies to the optimized geometries.48−50
III. RESULTS AND DISCUSSION A. Density Functional Comparison. As is easily seen in Table 1, there is a major failure of B3LYP in predicting barrier heights for hydrogen abstraction reactions. The B3LYP activation barriers are underestimated uniformly in most cases, and the mean absolute deviation (MAD) in the activation Table 1. Errors for the Hydrogen Abstraction Barrier of the Reaction of Atomic Hydrogen with Main Group Small Molecules (HnX + H· → H2 + ·XHn−1 with X = C, Si, Ge, N, P, As, O, S, Se, Cl, and Br) for B3LYP and M06 Density Functionals Compared to CCSD(T)//MP2 Calculationsa activation barrier errors, kcal/mol reaction
B3LYP
M06
H· + H4C → H 2 + ·CH3
5.1
0.7
H· + H4Si → H 2 + ·SiH3
3.6
−0.9
H· + H4Ge → H 2 + ·GeH3
2.2
−1.2
H· + H3N → H 2 + ·NH 2
6.1
1.6
H· + H3P → H 2 + ·PH 2
2.3
−1.1
H· + H3As → H 2 + ·AsH 2
0.5
−2.0
H· + H 2O → H 2 + ·OH
7.7
2.2
H· + H 2S → H 2 + ·SH
2.8
−1.1
H· + H 2Se → H 2 + ·SeH
1.1
−2.0
H· + HCl → H 2 + ·Cl
4.2
0.0
H· + HBr → H 2 + ·Br
1.4
−1.8
mean absolute deviation for the errors
3.4
1.3
a
See Computational Details for the basis sets used. Table SI_1 in the Supporting Information contains the absolute barriers, and Table SI_2 contains the barrier errors after including dispersion corrections. 8381
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Figure 3. Initial hydrogen abstraction reactions for the reaction of atomic hydrogen with the hydroxylated or aminated Si(100)-2×1 surface. The silicon monohydride abstraction is shown for the aminated surface only, and analogous reaction exists for the hydroxylated surface. See Figure 1 for the color key. Transition states are indicated by dotted lines that show the breaking and forming of bonds.
the hydrogen on the functional group and the hydrogen on the monohydride silicon of the dimer bond. They will lead to the formation of H2 along with the creation of a radical on the functional group or silicon. While there are other silicon sites that would produce side reactions, they would not lead to insertion products. In this work, we restrict ourselves to explore the pathways leading to oxygen and nitrogen insertion products. Formation of the functional group radical occurs via atomic hydrogen abstraction creating a nitrogen or oxygen radical, Figure 3 and Table 2. The atomic hydrogen interacts with a functional group breaking the hydrogen−oxygen or hydrogen− nitrogen bond and forming molecular hydrogen. The formation of the radical is exothermic relative to the surface plus atomic hydrogen for the nitrogen radical and very slightly endothermic for the oxygen radical, ∼1.7 kcal/mol. The source of the reduced stability in the oxygen radical is due to the stronger nature of the original −O−H bond relative to the −N−H bond. The oxygen radical shows some double-bond character as evidenced by the silicon−oxygen bond distance that decreases from 1.673 Å in the reactant to 1.603 Å in the oxygen radical product. The barrier for the abstraction from the adsorbate is 11.4 kcal/mol for the amine and 12.8 kcal/mol for the hydroxide. The silicon radical is formed when the atomic hydrogen abstracts the hydrogen from the silicon dimer monohydride, Figure 3. Silicon monohydride hydrogen abstraction is exothermic regardless of the adsorbate. The barriers to abstraction are slightly less for nitrogen than oxygen by
