Modeling of CVD processes implies dealing with “molecular” issues, related to the precursor and its gas- or plasma-phase reactivity (including its behavior at sublimation conditions), as well as with “surface” problems, concerning the growth surface interactions with the precursor molecule and other eventual gaseous species under CVD operating conditions. As a matter of fact, these interactions directly affect the whole process, from precursor adsorption to material growth. Despite a single “optimum” methodology to tackle the whole CVD process is currently not available, different sets of computational approaches may be adopted in order to address the above problems.
The precursor chemistry deeply affects the properties of CVD-derived materials, and research efforts are devoted to the design of novel precursors simultaneously exhibiting a high volatility, a vaporization free from undesired side reactions and a clean conversion into the target material. Such a synthetic activity would strongly benefit from knowledge of chemico/physical properties and possible decomposition pathways for the precursor molecule. Whereas experimental data can be gathered rather easily by, for example, spectroscopic techniques, their atomistic-level interpretation is often very difficult to be extracted. On the other hand, despite the fact that computational investigations could provide valuable insight, modeling of actual CVD precursors presents several nontrivial aspects. For instance, many precursors for technologically relevant nanostructures contain transition metals,[2, 7, 8] whose theoretical treatment is still challenging (see, e.g. Ref.  and references therein). Highly correlated methods, such as coupled cluster (CC), would be needed to obtain accurate results. Moreover, as different spin multiplicities may be possible, methodologies for open-shell systems based on multideterminant reference functions, like multireference configuration interactions, multireference perturbation theory (MRMP2), or complete active space self consistent field, with second order perturbation theory (CASPT2), would be the optimal choice. Nevertheless, because correlated methods scale steeply with system size, their application to most CVD precursors is currently unfeasible, and most of the computational studies on transition-metal-based systems are performed within the density functional theory (DFT) framework.[6, 9]
An alternative strategy is the use of combined approaches, as reported in a recent study, taken from the heterogeneous catalysis literature, concerning acetylene cyclotrimerization over a CrSi2O3H2 model of the Cr(II)/silica catalyst. As spin state changes are known to occur in this reaction, reference CASPT2 calculations were performed to determine the spin states energy gap, followed by a massive benchmarking of several DFT approximations. Subsequently, the potential energy surfaces corresponding to the singlet, triplet, and quintet spin multiplicities were explored by the combination of DFT functional/basis set that better reproduced the CASPT2 results, leading to the identification of the most probable reaction pathway. In perspective, such a strategy might be also applied to problems related to CVD precursors.
Indeed, a similar combined approach has been applied to a relevant and still open question in CVD: the growth of Cu(I) nanostructures from Cu(II) precursors, observed even under oxidizing conditions. In trying to understand such a finding, which apparently challenges traditional notions in chemistry, knowledge of the precursor behavior is the first and necessary step. The gas-phase fragmentation of the Cu(II) precursor, the Cu(hfa)2TMEDA complex (Fig. 2a), was studied by ElectroSpray Ionization-Mass Spectrometry (ESI-MS). The results indicated that a hfa− diketonate ligand loss converts the precursor in the [Cu(hfa)TMEDA]+ ion (Fig. 2b), which, in turn, releases a neutral β-diketone (Hhfa) forming a species, [CuTMEDA(-H)]+, in which copper is coordinated by a dehydrogenated diamine. First-principles molecular dynamics (FPMD) at 473 K was adopted to describe the conditions of the ESI-MS experiment, whereas a statistical sampling approach was adopted to model the fragmentation reactions, which are generally “rare events” for the time scales accessible to standard FPMD. Simulations highlighted that the diamine transfers a proton to the diketonate ligand and coordinates the metal center, forming a six-membered ring (Fig. 2c). This mechanism was validated by locating the transition and final states with a hybrid functional and by performing electronic structure analyses, which indicated homolitic cleavage of the diamine CH bond and the Cu(II)Cu(I) conversion. The [Cu(I)TMEDA(-H)]+ ring structure stability was confirmed at the MP2 and CCSD(T) levels. This example evidences that a multitechnique computational toolbox for dealing with different time and length scales, synergistically combined with experiments, represents, to date, one of the most valuable approaches to the “molecular” issues of CVD processes. These integrated approaches are particularly useful for the investigation of transition-metal precursors exhibiting properties and reactivity strongly dependent on the nature of the metal center M. For instance, the first fragmentation stage of M(hfa)2TMEDA occurs by release of a neutral ligand (TMEDA) for M = Fe(II), and with loss of a charged hfa− ligand for M = Cu(II). The microscopic rationale of such a different behavior has been provided by combined experimental–theoretical studies.[18, 19] It is also worth observing that in situ analyses, such as MS or optical emission spectroscopy, can be extremely insightful in PE-CVD processes, where they permit to detect both ground-state and excited species. In perspective, combination of these experimental techniques with theory may hence provide an important piece of information to also understand the fascinating world of plasma environments.
Figure 2. (Left) Sketch of the M(hfa)2TMEDA “second generation”[7, 8] precursor molecular structure. The diketonate and the diamine ligands are hfa (1,1,1,5,5,5-hexafluoro-2,4-pentanedionate) and TMEDA (N,N,N′,N′-tetramethylethylenediamine), respectively, while M is a first-row transition metal (e.g., Fe, Co, Cu, and Zn). (Right) Graphical representation of the Cu(hfa)2TMEDA precursor (a) and its subsequent fragmentation stages [Cu(hfa)TMEDA]+ (b) and [CuTMEDA(-H)]+ (c). Color codes: Cu, yellow; O, red; N, blue; F, green; C, grey; H, white. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
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In the simulation of CVD processes, the growth surface needs to be modeled by considering the role of several key process variables, such as substrate temperature and surface structure/composition, taking also into account the eventual influence of the reaction atmosphere. Either cluster models or slab geometries with periodic boundary conditions could in principle be employed. Cluster models offer the possibility of using high level of theory, but they are plugged by a poor description of surface and temperature effects, and should be better adopted only when adsorption/decomposition processes are localized in a limited spatial region, and restricted to insulating supports. On the other hand, simulations with periodic slab geometries would provide a more realistic representation of the system, including both metallic and semiconducting substrates.
Upon modeling the heterogeneous stages of CVD processes, a key variable to be accounted for is temperature, and a methodology which could describe conditions far from the minimum energy (0 K) region should be adopted. In spite of the possibility of using molecular dynamics or Monte Carlo approaches, force-field-based techniques are normally not suitable for the description of surface reactions due to difficulties of classical methodologies in dealing with bond cleavage-formation events. Approaches characterized by an explicit description of the electronic structure should hence be adopted.
A detailed survey of computational studies on atomic layer deposition, a synthetic route related to the family of CVD techniques, can be found in Ref. . Here we focus on few examples, mainly based on FPMD or tight-binding molecular dynamics (TBMD), all characterized by the fact that both temperature and electronic structure of substrate surface and precursor(s) were explicitly taken into account. Owing to its lower computational cost with respect to FPMD (about 5000 fold faster), TBMD can be applied when larger model systems and longer time scales need to be considered. This is the case of a recent TBMD simulation study of Si thin film deposition by PE-CVD, modeling precursor adsorption/product desorption on/from the growth surface. When the plasma-activated precursors (SiH3 radicals) reached the substrate (a hydrogen-terminated Si(001) surface model), processes such as hydrogen abstraction from the surface, SiH3 adsorption on unsaturated Si atoms as well as electron injection to the surface were observed. TBMD results were validated by performing static first-principles (DFT) energy calculations for the most relevant structures. Upon dealing with such kinds of simple precursors, even the more accurate FPMD could be employed, but both the model size and simulation length should be reduced. A representative example related to the same system is the study of the surface H-abstraction step by the SiH3 radical. A set of FPMD simulations were performed to model SiH3 collision with the surface. Techniques for the sampling of rare events (e.g., nudged elastic band (NEB), metadynamics, and bluemoon ensemble) are, in general, needed for simulating chemical reactions. In this case, activation energies were comparable with thermal energies, thus allowing to observe directly along the simulations either H-abstraction or SiH3 recoil into the gas phase; then, minimum free energy paths for this reaction were calculated by NEB, proving that H-abstraction was nearly barrierless. The actual probability of H-abstraction, not accessible to FPMD, was estimated by performing many classical MD simulations with empirical potentials validated against the FPMD results. SiH3 absorption/diffusion processes on the surface were explored by a combination of statistical sampling techniques (metadynamics/NEB), highlighting a very complex surface chemistry for such an apparently simple species. A similar picture emerged by studying, with analogous approaches, the SiH3 and GeH3 decomposition pathways on Ge(100) and Si(100), respectively.
FPMD may provide insight on elementary steps of CVD surface processes, but its computational cost limits the application range to small-scale systems. Modeling of actual CVD growth processes is currently accessible to large-scale kinetic Monte Carlo simulations, which, however, need rate constants determined from first principles as input parameters. Such a scenario has stimulated the development of multiscale models for the CVD growth, that comprise a set of submodels tailored for dealing with different length scales. On the other hand, the study of the plasma-activated SiH3 formation and of its reactivity with other plasma-generated species requires a very high theory level and should be performed with post-HF methods.
In general, prediction of the behavior of CVD precursors becomes more difficult upon increasing molecular complexity, as several concomitant decomposition processes may take place. This phenomenon has been evidenced by modeling a CVD precursor for copper deposition, Cu(hfa)(tvms) (tvms = tetravinylmethylsilane), on metal surfaces. Different FPMD runs were performed, in which a Cu(hfa)(tvms) molecule was forced to collide on the substrate with different initial orientations and velocities. During simulations, the molecule was observed to decompose upon contact with the growth surface, irrespective of the initial orientation and temperature, while decomposition products were found to depend on the initial conditions. Moreover, different products were obtained using the same sets of initial conditions for the precursor but passivated surface models. This example highlights that the role of the growth surface in the first stages of the deposition process is still an open issue, which surely deserves further consideration.
Up to now, examples related to the surface behavior of small, already activated precursors[22, 23, 26-28] and of a coordinatively insaturated transition-metal precursor have been considered. In both cases, the structure of the precursor molecule allows Si or Cu to directly interact, and finally bind, with surface atoms. Moving a level up in complexity, understanding how the surface-metal bond formation could take place becomes a challenge when the metal center is fully saturated by ligands' atoms (as, e.g., in second generation CVD precursors,[7, 8] see Fig. 2). In such cases, thermal activation processes at the growth surface may lie at the origin of precursor reactivity, which is still largely unknown and difficult to be predicted. By means of 750 K FPMD simulations, a novel behavior, the fast rolling motion of the precursor on heated surfaces (“rock and roll on a hot floor”) has been revealed. Such rolling diffusion (Fig. 3), that is accompanied by precursor vibrational excitation, could trigger decomposition by promoting intermolecular collisions on the substrate, and configures itself as a general activation route for a broad variety of processes at hot surfaces. In fact, it is worth noticing that a similar surface diffusion mechanism, the molecular tumbling of propene molecules on Si(100), has been recently proposed in a scanning tunneling microscopy/computational study. The possible appearance of similar phenomena in molecule-to-material conversion processes represents, therefore, an additional challenge for modeling studies. An explicit description of surface bimolecular/multimolecular events would also be needed in order to provide a thorough understanding of the nanostructure growth mechanisms, and this would require large size models and longer simulation times.
Figure 3. Successive snapshots of a FPMD simulation showing the rolling motion of the Cu(hfa)2TMEDA precursor on a CVD substrate model (hydroxylated SiO2) maintained at 750 K. Color codes: Cu, yellow; O, red; N, blue; F, green; C, grey; H, white; Si, black. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
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Computational studies of the behavior of CVD molecular precursors may, therefore, disclose important information on chemical events initiating the nucleation of the target nanostructure, an issue of key relevance for the optimization of well-defined synthetic strategies. Simulation of relevant elementary steps of the nucleation and growth processes is now accessible through the TBMD methodology, that in principle could be eventually extended, via an accurate parametrization, to the growth of transition-metal nanostructures. On the other hand, as illustrated by the presented examples, the superior FPMD methodology could be profitably adopted for CVD phenomena occurring on smaller time and space scale, like, for example, the temperature-induced activation and fragmentation of complex molecular precursors at the growth surface.