11074
J. Phys. Chem. B 1999, 103, 11074-11077
Initial Stage of the Catalyzed Growth of SiO2 Films on Si(001): An ab Initio Study Yasuharu Okamoto Fundamental Research Laboratories, NEC Corporation, Tsukuba, Ibaraki 305-8501, Japan ReceiVed: April 26, 1999; In Final Form: October 12, 1999
Ab initio molecular orbital calculations were performed to simulate the elemental processes of the initial stage of the layer-controlled SiO2 growth on Si(001). The calculations produced good agreement with experimental results in terms of both adsorption and activation energy when no catalyst was present. On the other hand, when there was a catalyst, the calculations reproduced the general catalysis observed in the experiment, but the effects of the catalyst (i.e., the downward shift of the activation energy and the growth temperature compared to those of the noncatalyzed reaction) were somewhat underestimated in the calculations as compared with the experimental results.
Introduction The understanding of catalysis is increasingly important in various fields of research. For example, enzymes that serve as catalysts are indispensable for most biochemical reactions.1 The key reactions of ozone depletion over the Antarctic continent proceed with the polar stratospheric clouds acting as a catalyst.2 The formation of dioxins in municipal waste incinerators is catalyzed by the surface of flyash containing CuCl2.3 However, although most chemicals are produced by using catalysts in the chemical industry, the use of catalysts in the crystal growth process has been rare.4 Recently, Klaus et al. succeeded in the layer-controlled growth of SiO2 thin films at room temperature by using pyridine as catalyst.5 Without a catalyst, the growth has been done above 600 K.6,7 The total reaction SiCl4 + 2H2O f SiO2 + 4HCl performed by Klaus et al. was composed of two catalyzed sequential half-reactions5-7
Si-OH* + SiCl4 f SiO-Si-Cl3* + HCl
(a)
S-Cl* + H2O f Si-OH* + HCl
(b)
where an asterisk designates the surface species. These two reactions are used to grow SiO2 film in an (a)(b)(a)(b)... binary sequence. Layer-controlled growth such as Klaus’ scheme may be promising for the fabrication of the ultrathin gate oxide films (about 15 Å in SiO2 thickness) that will be needed for the MOS transistors at the beginning of the next century. It may also be promising for the growth of other oxides such as Al2O3.8 The investigation of the elementary process of these catalyzed halfreactions by using ab initio calculations will deepen the fundamental understanding of catalysis and might provide a guide to further improvement of the growth process. Moreover, if we can obtain rate constants which are comparable with experimental values by ab initio calculations, computed rate constants could be used as input parameters in process simulations of crystal growth. In this report, as a first step toward the understanding of the above complicated surface reactions, ab initio molecular orbital calculations were performed to examine model reactions that simulate the initial stage of two half-reactions of layer-controlled
SiO2 growth with and without the presence of a catalyst. The calculated adsorption energy of the molecular precursor of SiCl4 on a hydroxy (-OH)-terminated silicon surface and the activation energy of the rate-determining step without a catalyst agreed well with experimental results.9,10 However, while the activation energy of the rate-determining step with a catalyst qualitatively explained experimental results, the effect of a catalyst is still somewhat underestimated in the present calculations.5 Computational Method I used the second-order Mo¨ller-Plesset perturbation theory (MP2). The MP2 method includes the electron correlation effect which is necessary for an accurate evaluation of the electronic energy.11 Also, the method can properly treat weak interactions between molecules, such as the hydrogen bond and the van der Waals (vdW) interaction. I found that inclusion of the vdW interaction is essential to evaluate the experimentally observed molecular precursor of the SiCl4 molecule on a silica surface.9 Although methods based on the density-functional theory (DFT) also include the electron correlation effect, and the hybrid-DFT12 especially gave results as reliable as those of the MP2 for the reaction of a H2O molecule on a diamond surface,13 methods based on the DFT were not suitable for the present study since DFT cannot properly incorporate the vdW interaction. My preliminary calculations using the hybrid-DFT (B3LYP functional12,14,15) did not give the molecular precursor of SiCl4 on the OH-terminated silicon surface. The Si(001) surface was simulated using a cluster model of Si9H12. In this cluster model, unphysical dangling bonds of the Si atoms (except for the surface Si atom) are terminated by a hydrogen atom. Since the semiinfinite system of the Si surface was represented by a cluster model, my calculations corresponded to a low-coverage situation. Although the above cluster model is small and the effect of the adjacent Si dimer and the steric effect from the neighbor adsorbed molecule are ignored, the local nature of chemical reaction will give some worthy information to understand the complicated catalyzed reactions. The 6-31G(d′) basis set was used for the Si cluster (Si9H12) and the 6-31G(d′,p′) basis set was used for the surface species -OH and -Cl and the molecules of SiCl4, H2O, and HCl. The stable molecular structures and the transition states (TSs) were
10.1021/jp991353r CCC: $18.00 © 1999 American Chemical Society Published on Web 12/01/1999
Growth of SiO2 Films on Si(001)
J. Phys. Chem. B, Vol. 103, No. 50, 1999 11075
TABLE 1: Comparison of the Energy (∆E in kcal/mol) and Length (R(N-H) in Å) of the Hydrogen Bond C5H5N-H2O NH3-H2O
∆E
R(N-H)
7.44 7.36
1.95 1.98
Figure 1. Reaction scheme considered in the calculations.
also calculated using these basis sets. The optimized structures of reactant, precursor, and product were determined by gradient techniques. The optimized structure of the transition state (TS) was determined by the following conventional procedure: first, the TS geometry of a reaction was estimated based on chemical intuition; second, the force constants for the estimated geometry were calculated; third, the estimated TS geometry was relaxed by using a Berny algorithm16 with the calculated force constants. If the initially estimated TS geometry is good, this procedure finds a TS. The vibrational frequencies needed to evaluate the zero-point energies (ZPEs) and Gibbs free energies are calculated at the Hartree-Fock (HF) level of theory with these basis sets and a scale factor (0.8929). (Calculation of the vibrational frequencies at the MP2 level would require too much computational time.) It is well-known that the reaction and activation energies are usually more sensitive to the incompleteness of the employed basis set than the molecular structures.11 Thus, to improve the accuracy of the computed energies, one-shot MP2 energy calculations at the above optimized molecular geometries (the stable molecular structures and TSs) were done with much larger triple-ζ level basis sets: the 6-311G(d,p) set for the Si9 H12 cluster and the 6-311++G(2d,2p) set for the above surface species and molecules. All the calculations in this report were done using the GAUSSIAN94 program17 on the NEC-SX4 supercomputing system. Although Klaus et al. used pyridine (C5H5N) as a catalyst,5 I used ammonia to reduce the required computing time. The interaction between C5H5N and H2O molecules was compared with that between NH3 and H2O (Table 1). Both the energy and length of the hydrogen bond (N-H) are similar in the NH3H2O and C5H5N-H2O systems. Although the substitution NH3 for C5H5N will give a different transition geometries and reaction barriers compared to their experiment5, I expect the present calculation will give some important information for the mechanism of the catalyzed reactions since the primary effect of the catalyst is based on the hydrogen bond (N-H). Actually, Tripp and Hair used N(C2H5)3 for amine-promoted chemical attachment of chlorosilanes to silica.4 Thus, the aromatic nature of pyridine may be not so much important. Results and Discussion The initial stage of SiO2 growth examined in this report is given in Figure 1. An H2O molecule reacts with a monochloride Si(001) surface, which leads to a surface structure with a hydroxyl group (OH) at one end of the Si dimer and a Cl on the other end (reaction A in Figure 1). A further reaction of an H2O molecule with the surface changes the remaining Cl atom
Figure 2. Optimized structure of the reaction A TS in the presence of a catalyst.
Figure 3. Optimized structures of the reaction B molecular precursor (left) and TS in the presence of a catalyst (right).
into a hydroxy group and forms an oxygen layer (reaction A′). Next, a SiCl4 molecule reacts with the OH-terminated surface and forms a Si layer (reaction B). Reactions A and B, respectively, correspond to the first layer-controlled growth of the oxygen and silicon layers. I began my examination of the elementary processes of the initial stage of SiO2 growth by calculating the stable structures of the reactants, the TSs (with and without the presence of the catalyst), and the products of reactions A and B. Here, the reactants corresponded to isolated Si clusters and molecules (H2O for reaction A and SiCl4 for reaction B). In the experiment, the activation energy of the rate-determining step (reaction B in these calculations) corresponds to the energy difference between the TS and molecular precursor of SiCl4 on the OHterminated silicon surface.5-7 Thus, I also tried to determine the molecular precursors and found it for reaction B, but not for reaction A. The optimized molecular structure of the TS (in the presence of catalyst) of reaction A, and the structures of molecular precursor and the TS (in the presence of catalyst) of reaction B, are shown in Figures 2 and 3, respectively. The bond length of the four-center TS are listed in Table 2, and the reaction energy and activation energy with and without the presence of a catalyst of reactions A and B (with the ZPEs included) are listed in Table 3. The calculated adsorption energy is 6.1 kcal/ mol (with the ZPEs included), which agrees with the experimental values (5.4 kcal/mol) obtained by Tripp and Hair.9 Moreover, Hair and Hertl measured the activation energy of noncatalyzed SiCl4 deposition on the silica surface,10 and the calculated activation energy (23.1 kcal/mol) also agrees well with their experimental value (22.0 kcal/mol). This agreement
11076 J. Phys. Chem. B, Vol. 103, No. 50, 1999
Okamoto
TABLE 2: Comparison of the Geometries of the Four-Center Transition State of Reactions A and B in the Presence of a Catalyst (in Å) Calculated by the MP2 Methoda R(O-H)
R(Si-Cl)
R(H-Cl)
R(Si-O) R(N-H)
reaction A 1.02 (1.00) 2.93 (2.62) 1.96 (1.94) 1.80 (1.86) reaction B 1.09 (1.11) 2.79 (2.70) 1.67 (1.60) 1.78 (1.79)
2.10 2.38
a The numbers in parentheses show the geometries of the transition state without a catalyst.
TABLE 3: Comparison of the Reaction Energy (ER), the Adsorption Energy of the Molecular Precursor (Eads), and the Activation Energy (∆EA) with and without a Catalyst, of Reactions A and B Calculated by the MP2 Method Including the ZPEs (in kcal/mol)a ERb
Eads
reaction A -2.64c reaction B 19.25 6.1 (5.49)
∆EA (noncatalyzed)
∆EA (catalyzed)
17.8 23.1 (22.010)
10.8 17.5 (11.4 ( 1.15)
a The numbers in parentheses show experimental values. b The reaction energy is defined as the energy difference between the reactant and the product. c A minus sign means the reaction is endothermic.
TABLE 4: Reaction Energy (in kcal/mol) of Several Reactions Calculated at the MP2/6-311++G(d,p) Level of Theory
b
reaction
reaction energya
SiCl4 + H2O f Si(OH)Cl3 + HCl SiHCl3 + H2O f Si(OH)HCl2 + HCl SiH2Cl2 + H2O f Si(OH)H2Cl + HCl SiH3Cl + H2O f Si(OH)H3 + HCl
5.14 3.11 1.67 -1.52b
a Zero-point vibrational energy is included in the reaction energy. A minus sign means the reaction is endothermic.
with experimental results confirmed that the present calculations explain fairly well the initial stage of sequential half-reactions when a catalyst is not used. Reaction A is endothermic and reaction B is exothermic (Table 3). This result is seemingly inconsistent with a simple reaction energy evaluation of subtracting bonds broken from bonds formed, which yield the same heat of reaction in both reactions. I found that the heat of reaction of the substitution -OH for -Cl bonded to Si significantly depends on the number of Cl atoms bonded to Si atom. This was checked by calculating the reaction energy of SiClnH4-n + H2O f SiCln-1H4-n(OH) + HCl (n ) 4, 3, 2, 1). Table 4 shows that these reactions become less exothermic as the number of Cl atoms decreases, which is consistent with the relationship observed between reaction A and B in Table 3. Since the activation energy of reaction B is higher (irrespective of whether a catalyst is used), the rate-determining step of the whole reaction process is reaction B, which is consistent with experimental observation.5 Klaus et al. experimentally determined the activation energy (11.4 ( 1.1 kcal/mol) and the reaction preexponential (3.1 × 1013(1.1 s-1) of a catalyzed halfreaction of silicon-layer growth.5 They also found this halfreaction is 4 times slower than the half-reaction of the oxygenlayer growth.5 Assuming that the reaction preexponential of the oxygen-layer growth is the same as that of the silicon-layer growth, the difference in the activation energy between the two catalyzed half-reactions is about 0.83 kcal/mol. In comparison, the difference of the calculated activation energies between the catalyzed reactions A and B is too large (6.7 kcal/mol from Table 3). This suggests that there was a molecular precursor which could not be found in the present calculation in reaction A as was the case in reaction B. The
Figure 4. Calculated rate constants of reaction B. Solid and dotted lines show catalyzed and noncatalyzed reactions, respectively. The dotted arrows indicate the growth temperature of noncatalyzed reaction, which corresponds to the growth temperature of 333 K for the catalyzed reaction.
calculated activation energy of the catalyzed reaction B shows a substantial downward shift (5.6 kcal/mol) compared to the noncatalyzed reaction B. Thus, the present calculation qualitatively explains the effect of the catalyst on the layer-controlled SiO2 growth. However, the computed downward shift is somewhat smaller than the experimentally observed value (9.511.7 kcal/mol),5,10 which might be due to the inadequate treatment of cluster model and the substitution NH3 for C5H5N. As shown in Table 3, the downward shift of the activation energy brought about by adding the catalyst in reaction A is larger than that in reaction B, and it corresponds to the shorter N-H distance (i.e., a stronger hydrogen bond) in the former reaction (Table 2). I then examined the rate constant of reaction B, which is the rate-determining step of the layer-controlled SiO2 growth. According to the transition-state theory (TST),18 the rate constant k(T) is given by
(
k(T) ) kbT exp -
∆G kbT
)
(1)
Here, T is temperature, and kb and h are Boltzman’s and Planck’s constants, respectively. The Gibbs energy change is defined as ∆G ) G(TS) - G(adduct). I calculated the Gibbs free energy as follows:
G ) E0 + ET,vib - TSvib
(2)
where E0 is total energy (electronic plus nuclear repulsion energies), ET,vib is a thermal correction to energy from vibration, and Svib is the vibrational entropy. Although modern ab initio molecular orbital programs can routinely calculate the translational and rotational contributions to thermal energy and to entropy, inclusion of these contributions in the calculation seems irrelevant in this study because they correspond to the overall translation and rotation of the whole cluster system. Thus, I ignored these contributions when evaluating the Gibbs free energy. I also ignored the tunneling effect, since this effect is not important in the temperature range of interest (300-600 K).19 The calculated rate constants with and without the presence of a catalyst are shown in Figure 4. Figure 4 indicates that the primary effect of the catalyst is due to the change of the preexponential factor (kbT/h) exp(∆Svib/ kb). ∆G and -T∆Svib of catalyzed and noncatalyzed reactions are shown in Figure 5. This suggests that the catalyzed reaction gains the vibrational entropy due to a hydrogen bond N-H (Figure 3), which leads to increase in the preexponential factor.
Growth of SiO2 Films on Si(001)
J. Phys. Chem. B, Vol. 103, No. 50, 1999 11077 calculation showed good agreement with experiments in terms of both adsorption and activation energy when a catalyst was not present. On the other hand, when there was a catalyst, the calculations generally describe the catalysis, but the effects of the catalyst (i.e., the downward shift of the activation energy and the growth temperature) are still somewhat underestimated in the calculations compared to the experimental results. References and Notes
Figure 5. Calculated Gibbs energy change (∆G), and change of -T∆Svib (in kcal/mol).
The downward shift of growth temperature due to the addition of a catalyst was also examined. I found that the rate constant of the catalyzed reaction B at 333 K corresponds to that at about 490 K without a catalyst for the same reaction (the dotted arrows in Figure 4). This calculated downward shift of growth temperature (157 K) is about one-half of the experimentally observed value (600 K f 300 K), since the calculation seems to overestimate the reaction barrier in the presence of a catalyst by about 6 kcal/mol compared to the experiment (Table 3).5 Thus, further elaboration of the cluster model will be necessary for a quantitative evaluation of the catalysis on layer-controlled SiO2 growth, but this is beyond the scope of the present study. Summary Through ab initio molecular orbital calculations, I examined the initial stage of the sequential half-reactions of layercontrolled SiO2 growth on Si(001). The MP2 method was more suitable for this study than methods based on DFT because the MP2 method can properly include the vdW interactions, which is essential to evaluate the molecular precursor of SiCl4 on a silicon surface terminated by the hydroxy group. The MP2
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