Research Article Archive Versions 2 Vol 2 (1) : 19020103 2019
Nitridation-Etch of Silicon Oxide in Fluorocarbon/Nitrogen Plasma: A Computational Study
: 2019 - 02 - 21
: 2019 - 03 - 22
4135 89 0
Abstract & Keywords
Abstract: The continually increasing number of silicon oxide (SiO2) and nitride (Si3N4) layers in 3D-NAND offers both motivations and challenges for developing all-in-one plasma etch solutions for etching SiO2 and Si3N4 at a selectivity near unity while maintaining a high etch rate. This is essential for a simultaneous etch landing of all holes that differ in their respective SiO2 and Si3N4 layer numbers and dummy SiO2 thickness, and for a quick wafer turnover. Surface modification may be employed to make the SiO2 and Si3N4 layers closer in composition, either by converting Si3N4 to oxynitride (SiOxNy) [J. Micro. Manuf.1 , 20180102 (2018)], or by converting SiO2 to SiOxNy, presented in this paper. We computationally demonstrate the feasibility of a nitridation-etch process for SiO2 in fluorocarbon/nitrogen-based plasma with molecular dynamics (MD) and quantum chemistry (QC) simulations. First, the nitridation via ion implantation is observed with MD, which replaces surface oxygen by nitrogen. Second, the reactions involving oxygen and silicon volatilization are energetically favorable per QC calculations. Finally, both MD and QC simulations indicate a synergy between fluorine and nitrogen etchants by enhancing each other’s reactivity with the SiO2 surface. These atomistic surface reaction mechanisms will offer insight for the development of robust engineering solutions for 3D-NAND fabrication.
Keywords: 3D-NAND; oxide; nitride; oxynitride; plasma etch; molecular dynamics; quantum chemistry
1.   Introduction
The growing demand for solid-state memory devices has generated significant interest in process technology development for 3D-NAND fabrication along with challenges that need to be overcome. Particularly, plasma etch engineers are faced with the task of etching high-aspect-ratio contact (HARC) holes through up to ~100 layers of stacked ONON layers (i.e. silicon oxide, SiO2, and silicon nitride, Si3N4) as well as dummy SiO2 of varied thickness within the same structure, landing all holes simultaneously. To this end, the development of a plasma etch process that etches both SiO2 and Si3N4 with a high etch rate and a near unity selectivity is highly desirable. One strategy is to make SiO2 and Si3N4 etch fronts closer in composition via surface modification, illustrated by our previous simulation work on the feasibility of Si3N4 oxidation-etch1 , where the Si3N4 surface oxidation to silicon oxynitride (SiOxNy) was explored. The indicated role of oxygen (O2) addition to the feed gas in attaining closer etch rates for Si3N4 was also experimentally reported2 ,3,4.
Another approach of surface modification is to convert the SiO2 surface to SiOxNy via plasma nitridation. For the SiO2 plasma nitridation per se, there have been extensive studies. N2 feed was the most commonly used5 ,6,7,8,9, while N2O5 and NH310 were also reported as well as He/N2 mixed gas11. Multiple plasma sources, including inductively-coupled plasma (ICP)9, helical resonator plasma5, and electron-cyclotron resonance (ECR) plasma7, were investigated. In terms of the nitrogen penetration in the oxynitride product with remote He/N2 plasma, Hattangady et al. found via XPS and SIMS characterizations that the implanted nitrogen was confined to the immediate vicinity of the surface 11. Moreover, the extent of nitridation also depends on the substrate temperature based on the findings by Kobayashi et al.: a more complete nitridation to Si3N4 was observed at 25 oC than at 700 oC in their experiment using N2 plasma generated by electron impact6. Plasma nitridation can also alter the surface stress of the silicon oxide film, and particularly Itakura et al. demonstrated that the compressive surface stress formed by thin oxide on Si(100) was relaxed8. Simulation studies of SiO2 nitridation in pulsed inductively coupled N2 plasma using a coupled plasma equipment-surface model show that N atoms and N2+ ions are the primary species that contribute to the nitridation9.
The etching behavior of silicon oxynitride was also investigated, where the oxynitride was mostly prepared via plasma-enhanced chemical vapor deposition (PECVD). Cavallari and Gualandris found that the oxynitride shows a significantly higher etch rate than does the thermal oxide in a CF4/O2-based plasma, as well as a correlation between the etch rate to the nitrogen inside the layer12. Focusing on plasmas based on CF4/CHF3/CO, Ueno et al.13 established a negative correlation between the SiOxNy etch rate and the amount of carbon deposition, with the highest SiO2/SiOxNy selectivity afforded by the CHF3 + CO plasma generating a more carbon-rich deposition. Moreover, they also observed that the etch rate of the low-N-percantage SiO1.4N0.4 to be higher than SiO2 for CF4 plasma and CHF3 plasma. In addition to the nitrogen implantation effects, studies using downstream plasma reactors reveal the nitric oxide (NO) molecule as an additional contributor to the etching reaction. For instance, Kastenmeier et al. investigated the Si3N4 etch rate enhancement by N2 addition to CF4/O2 plasma and identified the NO species formed in the plasma to be a key contributor through assisting in the Si-N cleavage14. The same enhancement by N2 addition to CF4/O2 plasma for polycrystalline silicon etch was also observed, occurring via NO assisting in Si-O cleavage and exposing the open Si bond to be easily attacked by incoming fluorine species15.
While the studies above mentioned provide valuable insights into the feasibility of an enhanced nitridation-etch of SiO2, such evidence is mostly indirect: firstly because of the difference between the PECVD SiOxNy and the plasma nitridation SiOxNy, and secondly because of the nitrogen implantation effect not explicitly accounted for by downstream studies. Thus, in this paper we provide a theoretical understanding of the SiO2 nitridation-etch via molecular dynamics and quantum chemistry simulations, in order to acquire a better knowledge of the atomistic mechanisms. We evaluate the effectiveness of the nitrogen implantation into the SiO2 substrate as well as its mechanism. We also investigate the energetics of the key reactions in the etching reactions of SiO2 by fluorine and nitrogen, the most important etchants produced by a fluorocarbon/nitrogen-based plasma. Furthermore, we also highlight the synergy between nitrogen and fluorine in delivering a high SiO2 etch rate. This simulation work will offer insight for future experimental and theoretical studies aimed at developing high-performance non-selective SiO2/Si3N4 etch processes in 3D-NAND all-in-one etching applications and beyond.
2.   Methodologies
Molecular dynamics simulations were performed with LAMMPS16 incorporated in MedeA®17 with the ReaxFF reactive force field for C/H/O/N/S/F/Si parametrized in Ref18 . The subsrate slab was prepared with O-terminated {001} surface of α-quartz, and consists of 108 Si atoms and 240 O atoms, around 16 Å in thickness (along Z). The supercell lattice constant along Z is 50 Å to create sufficient vacuum area. The bottom Si and O layers were fixed during the simulation, and the next 3 layers of Si and O were thermalized with a Langevin thermostat at 300 K. The rest of the system was allowed to freely propagate with the microcanonical ensemble (NVE). The time step was chosen as 0.05 fs. The substrate was equilibrated with the canonical ensemble (NVT) at 300 K for 5 ps before the ion bombardment. Two sets of bombardment simulations, N only bombardments and alternating N/F bombardments, were performed. For N only bombardments, one N atom is launched every 5 ps at 25 eV after randomly placing it above the surfacewith random ion angles at most ± 10o from the -Z direction (40 N atoms launched in total, 220 ps total simulation time). For the alternating N/F bombardment, the same set-up was used, except that the launching sequence is N-F-N-F… rather than N-N-N-N … (40 N atoms plus 40 F atoms launched in total, 420 ps total simulation time). All volatlized products were regularly removed from the system. Statistics were performed over 10 repeated simulation runs. The Pearson correlation coefficient, defined as \({\rho }_{XY}=\frac{\mathrm{c}\mathrm{o}\mathrm{v}\left(X,Y\right)}{{\sigma }_{X}{\sigma }_{Y}}\), was calculated to determine the correlation between the volatility of N and that of O. Here X and Y are the amount of N and O removals, respectively, while, \(\mathrm{c}\mathrm{o}\mathrm{v}\left(X,Y\right)\) is the sample covariance, and \({\sigma }_{X}\) and \({\sigma }_{Y}\) are the sample standard deviations; positive (negative) \({\rho }_{XY}\) values indicate positive (negative) linearities.
The quantum chemsitry calculations were performed with the Gaussian 1619 package using B3LYP/6-31++G(d,p)20 ,21,22,23,24. A molecular cluster containing 4 Si atoms and 10 O atoms was used to simulate the reaction energetics. The structures were verified as local minima and transition states from harmonic frequency calculations25. The transition states were located using the STQN method26 ,27.
3.   Results and Discussion
3.1. Molecular dynamics (MD) simulations of ion bombarding on the SiO2 surface
We begin this section by examining the post-bombardment substrate structures (Figure 1), in order to identify the major chemical reactions and etch products. For both sets of bombardment simulations, i.e. the alternating N/F bombardments (40 N’s and 40 F’s) and the N only (40 N’s) bombardments, the formation of Si-N bonds is observed. Also common to both sets of simulations is the formation of N-O bonds, which leads to the volatilization of O from the substrate as NOx species. Together, the implantation of N atoms via Si-N formation combined with the O volatilization as NOx results in the substitution of O atoms in the SiO2 substrate by N atoms, thus forming an oxynitride-like surface (Figure 1 (b)). Furthermore, the addition of F to the bombardment leads to Si-F bond formation, which is essential for the ultimate volatilization of Si as SiFx (Figure 1 (a)). Finally, the impinging N atoms can also bond with N atoms that are already on the surface. This generates volatile N2 molecules, creating a pathway for N self-scavenging. At the steady state, the outflux of N via self-scavenging as N2 plus O abstraction as NOx, must equal its influx as impinging N ions, consequently maintaining the surface concentration of N (as well as other elements) at a quasi-static level.
The steady-state concentrations of various elements, however, also depends on the composition of impinging species. As illustrated in Figure 2, the average numbers of N atoms in the final structure are different for the alternating N / F bombardments and the N-only bombardments. The addition of F results in a visibly lower (7.7 atom counts) average N content compared to that from N-only bombardments (12.1 atom counts). This is likely due to the passivating role of F for under-coordinated Si atoms on the surface, by forming Si-F bonds. With the under-coordinated surface Si terminated with F, its recombination with surface N atoms is inhibited, leaving N more volatile. This inhibition is further warranted by the higher Si-F bond energy than those of both Si-O and Si-N bonds, making the substitution of Si-F by Si-O / Si-N energetically unfavorable. The higher volatility of O given the addition of F, similarly to that of N, is evidenced by the increase in the average numbers of O removed from the surface during the bombardments (from ~13.5 atom counts to 18.0 atom counts), with the number of impinging N atoms being 40 for both the N / F bombardments and N bombardments.

Figure 1.   Representative final substrate structures after the bombardments with (a) alternating N / F atoms and with (b) N atoms only. The colors representing different elements: Si – yellow, O – red, N – dark blue, F – green. The key product functional groups are shown as balls and sticks, while the rest of the sytem are shown as sticks.

Figure 2.   The average atom counts for implanted N atoms in the final substrate structure (blue), removed O atoms from the substrate during the bombardment (orange), and implanted F atoms in the final substrate (gray, for alternating N / F bombardments only). The error bars represent the sample standard deviations. 10 simulation runs were averaged.
To further demonstrate the correlation between the N and O volatility, Figure 3 shows the scatter plots for the number of N atoms in the final substrate structure and the number of O atoms volatilized from the surface. The data points for alternating N/F bombardments, N only bombardments, and their combination, are given in Figures (a), (b), and (c), respectively. Despite the relatively small sample size, the consistently negative Pearson correlation coefficients nonetheless reveal a positive correlation between N and O volatility. This is consistent with the observation of NO species as one of the O etch products (Figure 1), which also suggests the simultaneous O and N removal in the form of NOx as an underlying mechanism.

Figure 3.   Scatter plots for the number of N atoms in the final structure versus the number of O atoms removed from the surface for (a) alternating N / F bombardments, (b) N bombardments, and (c) combined plot for alternating N / F bombardments and N bombardments. The Pearson correlation coefficients for each plot are -0.599 (alternating N / F bombardments), -0.536 (N bombardments), and -0.726 (combined plot).
To summarize this section, the MD simulations have revealed that the N treatment of the SiO2 through ion bombarding partially replaces the O atoms by N atoms, forming an oxynitride-like surface. This is effected by the Si-N bond formation combined with O volatilization as NOx molecules. Moreover, the F addition to the ion bombardments leads to a higher removal rate for O; however the F additionalso reduces the extent of N implantation via surface Si passivation as Si-F. In fact, the presence of F simultaneously makes both O and N more volatile, in addition to its crucial role of volatilizing Si, showing synergistic effects and trade-offs between impinging ions of different elements.
3.2.   Quantum chemistry (QC) simulations
With a phenomenological understanding of surface reactions offered by the MD simulations, we now examine their underlying energetics using QC calculations in order to derive fundamental mechanistic insights. These static energetics calculations with QC not only yield the equilibrium structures of reaction intermediates and transition states, but also offer electronic structure information absent from MD simulations. Therefore, it is beneficial to cross-compare the MD and QC results for a better understanding of the etch mechanisms.

Figure 4.   The reaction energetics for the surface dangling *Si-O attacked by N leading to NO abstraction. The most stable spin states are presented for each geometry. The potential energy sum for isoalted *Si-O (doublet) and N atom (quartet) is chosen as reference.

Figure 5.   Geometries and potential energies of various possible configurations of surface adsorbed NO. The potential energy sum for isolated *Si-O (doublet) and N atom (quartet) is chosen as reference, consistently with Figure 4. The singlet *Si-O-N structure is unstable, which upon geometry optimization spontaneously re-organizes into singlet *Si-N-O. All 3 other structures are confirmed as local minima by the absence of imaginary vibrational frequencies. For an isolated doublet NO molecule in vacuum, the Mulliken spin densities on N and O are 0.719 e and 0.281 e, respectively.
With the surface under continuous ion bombardment, the surface becomes amorphous, with many dangling bonds or under-coordinated atoms present. Examination of the surface structures in Figure 1, for instance, shows the abundance of -O dangling bonds (mostly *Si-O groups). The presence of these dangling bonds or under-coordinated atoms provides active sites for forming new chemical bonds with incoming species from the plasma, which eventually results in volatile product formation. Thus, the surface reactions and substrate volatilization in a plasma etch system are ion-enhanced, allowing for significantly lower process temperatures than plasma-less dry etch (which relies totally on the thermal fluctuations to overcome the activation energy barriers).
Given this, we may justifiably start with the model structure (Figure 4) for the surface *Si-O dangling bond (apparently the most abundant form of dangling bonds according to Figure 1). The most stable electronic state for the *Si-O group is a spin doublet, with 1 unpaired electron. After the attack by an incoming N (quintet) radical, a triplet *Si-O-N intermediate is formed, at a ΔE of -3.360 eV. Evidently, the N-O bond formation is energetically highly favorable. Subsequently, the triplet *Si-O-N undergoes a rotation of the NO adsorbate, breaking the Si-O bond and forming the Si-N bond instead, which slightly lowers the potential energy by another 0.263 eV. Eventually, the triplet *Si-N-O group releases the NO adsorbate in its doublet state, and an under-coordinated Si (bonded to 3 O atoms, also a doublet) is exposed. The NO elimination requires a potential energy increase by 1.857 eV, which can be readily afforded by the incoming ion bombardment in the nearby area and its associated local heating. Overall, the reactions from the initial N attack leading up to the desorption of NO has a favorable ΔE of -1.766 eV.
We now take another look at the adsorbed-NO intermediates, to further unravel the intricacies of the various possible configurations, both structural and electronic. Firstly, for both the *Si-O-N and the *Si-N-O structures, the triplet is lower in energy than the singlet (Figure 5). Second, for both the singlet and the triplet, the *Si-O-N structure is higher in energy than the *Si-N-O structure. Specifically, for singlet *Si-O-N, the structure is not a true local minimum, which upon geometry optimization spontaneously relaxes into the *Si-N-O singlet local minimum, at a ΔE of about -1.2 eV. This unstable singlet *Si-O-N structure may also undergo a spin flip to generate the triplet *Si-O-N structure, with about 1.3 eV decrease in potential energy. Finally, to comment on what structures may be involved during the N attack on O, we assume that the electronic and nuclear degrees of freedom are decoupled and that the incoming N and the surface *Si-O are both in their electronic ground state. In this case, the electronic state for a system of *Si-O and N atom approaching each other will opt for the lower-energy triplet as the groups gradually approach each other. This yields the *Si-O-N triplet structure as shown in Figure 4.
Following the NO desorption, the created 3-coordinated *Si group (doublet) becomes an excellent open site for F atom attack, forming Si-F bond (Figure 6) at a significant 6.687 eV potential energy drop. Then a second F atom approaches and becomes physisorbed, which again has a favorable ΔE of -0.409 eV. Subsequently, the Si-O-to-Si-F substitution reaction takes place via a transition state with a 0.105 eV activation energy, forming another Si-F bond and lowering the potential energy further by 1.537 eV. Further Si-O-to-Si-F substitutions ultimately leads to the formation of the SiF4 molecule as a major Si etch product. We also notice that each Si-O-to-Si-F substitution creates an additional *Si-O, which in essence is the reactant for N attack in Figure 4, thus completing a full circle of reactions driving the plasma-assisted SiO2 etching.
We summarize the QC findings in comparison with the MD results. Both QC and MD predict the N-O bond formation and NO desorption. The overall downhill energetics (Figure 4) for O volatilization as NO via N attack thus serves as the fundamental mechanism behind the O abstraction by N as well as the positive correlation between N and O volatility (Figures 2 and 3). Moreover, QC findings also indicate that F and N play synergistic roles, just as earlier shown with MD. Specifically, the F attack on Si apparently assists in the N attack on O by generating additional surface *Si-O dangling bonds other than by ion bombardment, creating more active sites for N-O formation than would otherwise be available (Figure 6). This eventually leads to the observed greater volatility of both N and O when F is added to the bombardment (Figure 2). Finally, QC calculations also suggest that, vice versa, N attack on O in turn also assists in F attack on Si, facilitated by the creation of under-coordinated surface *Si following the volatilization of the NO adsorbate (Figure 4).

Figure 6.   The reaction energetics for the surface 3-coordinated *Si undergoing 2 sequential F attacks leading to the formation of 2 Si-F bonds. The most stable spin states are presented for each geometry. The potential energy sum for *Si-O (doublet) and N atom (quartet) is chosen as reference, consitently with Figures 4 and 5. The atom movements are marked with arrows for the transition state structure involving the second F attack via a subsitution pathway. The formation of another surface dangling *Si-O at the end of the 2 F attacks is high-lighted.
4.   Conclusion
We have investigated the nitridation-etch of silicon oxide in a fluorocarbon/nitrogen-based plasma with atomistic simulations. Ion bombardment simulations with molecular dynamics (MD) and static energetics calculations with quantum chemistry (QC) have been employed. The simulations indicate a surface conversion from oxide to oxynitride enabled by the implantation of sheath-accelerated ions. During the coversion, Si-N bonds replace Si-O bonds and O atoms are volatilized as NO molecules, whereby generating a surface that is closer in composition to the nitride surface. We have also shown that the crucial reaction steps for oxygen and silicon abstraction are energetically favorable. In addition, our presented data reveal a synergy between fluorine and nitrogen etchants, where fluorine and nitrogen mutually enhances each other’s reactivity via creating additional surface active sites. These microscopic mechanistic insights indicate the potential value of utilizing a fluorocarbon/nitrogen-containing plasma to efficiently etch silicon oxide layers at a similar rate to the nitride layers in 3D-NAND applications and beyond.
The authors would like to thank to Aelan Mosden, Peter Biolsi and Alexander Oscilowski from TEL Technology Center, America, LLC for their continuous support and moral encouragement.
1 Yu-Hao Tsai, Du Zhang, and Mingmei Wang, “Silicon Nitride Etch via Oxidation Reaction in Fluorocarbon/Oxygen Plasma: A First-Principle Study”, J. Micro. Manuf.1 , 20180102 (2018).
2 Y. Yoriike, and M. Shibagaki, “A New Chemical Dry Etching,” Jpn. J. Appl. Phys. 15 , 13 (1976).
3 F. H. M. Sanders, J. Dieleman, H. J. B. Peters, and J. A. M. Sanders, “Selective Isotropic Dry Etching of Si3N4 over SiO2,” J. Electrochem. Soc.129 , 2559-2561 (1982).
4 H. K. Lee, K. S. Chung, and J. S. Yu, “Selective Etching of Thick Si3N4, SiO2 and Si by Using CF4/O2 and C2F6 gases with or without O2 or Ar addition,” J. Korean Phys. Soc.54 , 1816 (2009).
5 S. R. Kaluri, and D. W. Hess, “Nitrogen incorporation in thin oxides by constant current N2O plasma anodization of silicon and N2 plasma nitridation of silicon oxides,” Appl. Phys. Lett.69 , 1053 (1996).
6 H. Kobayashi, T. Mizokuro, Y. Nakato, Y. Yoneda, and Y. Todokoro, “Nitridation of silicon oxide layers by nitrogen plasma generated by low energy electron impact,” Appl. Phys. Lett.71 , 1978 (1997)
7 T. Seino, T. Matsuura, and J. Murota, “Atomic-order nitridation of SiO2 by nitrogen plasma”, Surf. Interface Anal.34 , 451-455 (2002).
8 A. N. Itakura, M. Shimoda, and M. Kitajima, “Surface stress relaxation in SiO2 by plasma nitridation and nitrogen distribution in the film,” Appl. Surf. Sci.216 , 41-45 (2003).
9 S. Rauf, S. Lim, and P. L. G. Ventzek, “Model for nitridation of nanoscale SiO2 thin films in pulsed inductively coupled N2 plasma,” J. Appl. Phys.98 , 024305 (2005).
10 E. D. Atanassova, and L. I. Popova, “Plasma nitridation of thin SiO2 films: AES, ELS, and IR study,” J. Nucl. Mater.200 , 421-425 (1993).
11 S. V. Hattangady, H. Niimi, and G. Lucovsky, “Controlled nitrogen incorporation at the gate oxide surface,” Appl. Phys. Lett.66 , 3495 (1995).
12 C. Cavallari, and F. Gualandris, “Plasma Processing for Silicon Oxynitride Films,” J. Electrochem. Soc.134 , 1265 (1987).
13 K. Ueno, T. Kikkawa, K. Tokashiki, “Reactive ion etching of silicon oxynitride formed by plasma-enhanced chemical vapor deposition,” J. Vac. Sci. Technol. B13 , 1447 (1995).
14 B. E. E. Kastenmeier, P. J. Matsuo, J. J. Beulens, and G. S. Oehrlein, “Chemical dry etching of silicon nitride and silicon dioxide using CF4/O2/N2 gas mixtures,” J. Vac. Sci. Technol. A14 , 2802 (1996).
15 P. J. Matsuo, B. E. E. Kastenmeier, J. J. Beulens, and G. S. Oehrlein, “Role of N2 addition on CF4/O2 remote plasma chemical dry etching of polycrystalline silicon,” J. Vac. Sci. Technol. A15 , 1801 (1997).
16 S. Plimpton, “Fast parallel altorithms for short-range molecular dynamics”, J. Comput. Phys.117 , 1 (1995).
17 MedeA: Materials Exploration and Design Analysis, Version, Copyright © 1998-2019 Materials Design, Inc.
18 A. Rahnamoun, and A. C. T. van Duin, “Reactive Molecular Dynamics Simulation on the Disintegration of Kapton, POSS Polyimide, Amorphous Silica, and Teflon during Atomic Oxygen Impact Using the Reaxff Reactive Force-Field Method”, J. Phys. Chem. A118 , 2780-2787 (2014).
19 M. J. Frisch et al, Gaussian 16, Revision A.03, Gaussian, Inc., Wallingford CT, 2016.
20 A. D. Becke, “Density-functional exchange-energy approximation with correct asymptotic behavior,” Phys. Rev. A, 38, 3098 (1988).
21 A. D. Becke, “A new mixing of Hartree–Fock and local density‐functional theories,” J. Chem. Phys., 98, 1372 (1993).
22 C. Lee, W. Yang, and R. G. Parr,“Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density,” Phys. Rev. B, 37, 785 (1988).
23 T. Clark, J. Chandrasekhar, G. W. Spitznagel, and P. v. R. Schleyer, “Efficient diffuse function‐augmented basis sets for anion calculations. III.* The 3‐21+G basis set for first‐row elements, Li–F,” J. Comp. Chem., 4, 294 (1983).
24 M. J. Frisch, J. A. Pople, and J. S. Binkley, “Self‐consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets,” J. Chem. Phys., 80, 3265 (1984).
25 P. Pulay, G. Fogarasi, F. Pang, and J. E. Boggs, “Systematic ab initio gradient calculation of molecular geometries, force constants, and dipole-moment derivatives,” J. Am. Chem. Soc.101 , 2550-60 (1979)
26 C. Peng, and H. B. Schlegel, “Combining Synchronous Transit and Quasi-Newton Methods for Finding Transition States,” Israel J. Chem.33 , 449-54 (1993).
27 C. Peng, P. Y. Ayala, H. B. Schlegel, and M. J. Frisch, “Using redundant internal coordinates to optimize equilibrium geometries and transition states,” J. Comp. Chem.17 , 49-56 (1996).
Article and author information
Du Zhang
Yu-Hao Tsai
Hojin Kim
Mingmei Wang
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Journal of Microelectronic Manufacturing