A comprehensive understanding of the chemical vapour deposition of cadmium chalcogenides using Cd[(C6H5)2PSSe]2 single-source precursor: a density functional theory approach

Background The phosphinato complexes of group IIB are of great interest for their potential toward technological applications. A gas phase mechanistic investigation of the chemical vapour deposition of cadmium chalcogenides from the decomposition of Cd[(C6H5)2PSSe]2, as a single source precursor is carried out and reported herein within the framework of density functional theory at the M06/LACVP* level of theory. Results The results reveal that the activation barriers and the product stabilities on the singlet potential energy surface (PES) favour CdS decomposition pathways, respectively. However, on the doublet PES, the activation barriers favour CdS while the product stabilities favour CdSe decomposition pathways, respectively. Contrary to the previously reported theoretical result for Cd[(iPr)2PSSe]2, CdSe decomposition pathways were found to be the major pathways on both the singlet and the doublet PESs, respectively. Conclusion Exploration of the complex gas phase mechanism and a detailed identification of the reaction intermediates enable us to understand and optimise selective growth process that occur in a chemical vapour deposition.Graphical abstract Structure of Cd[(C6H5)2PSSe]2 single-source precursor

II-VI nanostructure semiconductors have been of considerable interest in the past decade due to their unique optical and electrical properties, and good candidates for the building blocks of functional Nano devices such as field-effect transistors (FETs), [26,27] photo detectors (PDs), [28,29] light-emitting diodes (LEDs), [30] photovoltaic (PV) devices [31,32] and logic circuits [33,34]. Semiconductor materials such as CdSe, CdTe, and CdSe x Te 1−x are the bases of modern electronic devices. CdSe is one of the most promising semiconducting materials with potential applications in solar cells, [35,36] γ-ray detectors, [37] thin film transistors, [38] etc. Doped semiconductor Nano crystals with transition metals have attracted much attention due to their unique properties [39][40][41].
Gas-phase chemistry for the chemical vapour deposition (CVD) of metal precursors has been the subjects of theoretical investigations as gas-phase reactions, in particular, are found to play a key role in CVD process which has a number of important industrial and commercial applications. Theoretical data on single-source precursor bearing the thioselenophosphinate groups, [R 2 PSeS], are lacking in literature. Very recently, we have undertaken a theoretical study on several single source precursors (SSPs) to deposit metal chalcogenides via the gas phase decomposition process [42][43][44][45][46]. Spurred by the success of the use of SSPs and motivated by their potential to reduce the environmental impact of material processing, we have been keenly interested in investigating new routes to prepare SSPs. In addition, ligands binding strength on single-source metal precursor can be employed to tune the decomposition kinetics of the complex. Contrary, multiple-source routes often use highly toxic and/or oxygen or moisture sensitive gases, or very volatile ligands, such as: (CH 3 ) 2 Cd (Et 3 ) 3 Ga, H 2 E (E = S or Se) or EH 3 (E = N, P or As).
In continuation of our research into thioselenophosphinato metal complexes, we have investigated the possibility of the gas phase decomposition of single source precursors within Cd[(C 6 H 5 ) 2 PSSe] 2 complex. To gain insight into the complete reaction features, theoretically we have employed density functional theory technique. The reaction kinetics is also studied, employing standard transition state theory to evaluate the rate constant of the elementary reactions involved.

Computational details
All calculations were carried out with Spartan'10 v1.1.0 Molecular Modelling program [47] at the DFT M06/ LACVP* level in order to maximize the accuracy on the chemically active electrons of the reactions while minimizing computational time. LACVP* basis set uses the Hay-Wadt ECP basis set for cadmium, [48] and the 6-31G* basis set for all other atoms [49] as implemented in Spartan [47]. Zhao and Truhlar [50] recently developed the M06 family of local (M06-L) and hybrid (M06, M06-2X) meta-GGA functionals that show promising performance for the kinetic and thermodynamic calculations without the need to refine the energies by post Hartree-Fock methods. The M06 is reported to show excellent performance for transition metal energetics [50] and is therefore strongly recommended for transition metal chemistry [51].
The starting geometries of the molecular systems were constructed using Spartan's graphical model builder and minimized interactively using the sybyl force field [52]. The equilibrium geometries of all molecular species were fully optimized without any symmetry constraints.
Frequency calculations were carried out for all the stationary points at the corresponding level of theory to characterize the optimized structures as local minima (no imaginary frequency) or as transition states (one imaginary frequency) on the potential energy surfaces. The connecting first-order saddle points, the transition states between the equilibrium geometries, are obtained using a series of constrained geometry optimization in which the breaking bonds were fixed at various lengths and optimized the remaining internal coordinates.
The rate constants were computed using the transition state theory for the selected reaction pathways [53,54].
where ΔG ‡ is the activation free-energy, ΔG o is the Gibbs free energy, and k B and h are the Boltzmann and Planck constants, respectively.

Results and discussion
Optimized geometry of Cd[(C 6 H 5 ) 2 PSSe] 2 precursor Table 1 shows the M06/LACVP* calculated geometries for the Cd[(C 6 H 5 ) 2 PSSe] 2 and Cd[( i Pr) 2 PSSe] 2 precursors. The Cd-Se bond lengths are in the range of 2.99-3.02 Å which are slightly longer than the Cd[( i Pr) 2 PSSe] 2 precursor 2.81 Å [42]. The bond angle of Se 1 -Cd-S 1 (79.1°) is more acute than the Se-Cd-Se angle in Cd[(SeP i Pr 2 ) 2 N] 2 [111.32 (6)u] [56]. The average Cd-Se bond lengths, 3.01 Å, as expected are longer than the Cd-S distance, 2.59 Å. The S-Cd-Se angle (79°) is smaller than the S-P-Se angle (119°) due to the large amount of repulsion between the lone pairs of electrons of phosphorus with those of cadmium. The wider Se 1 -Cd-Se 2 bond angle of 159.4° was as a result of the proximity of the non-coordinating Se-donor atoms to the Cd(II) atom.
The geometry around P 1 and P 2 is a distorted tetrahedral (Se 1 -P 1 -S 1 and S 2 -P 2 -Se 2 : 118.5 and 118.7). The structure of Cd[(C 6 H 5 ) 2 PSSe] 2 precursor adopts a symmetric and puckered macro cyclic framework, with the two phenyl rings directly attached to phosphorus atoms being parallel to each other. The Se-P-Se bond angles are enlarged from ideal tetrahedral Se 1 -P 1 -S 1 and S 2 -P 2 -Se 2 : 118.5 and 118.7, respectively, and are considerably slightly larger than those in Cd[( i Pr) 2  (1) The following discussions are aimed at elucidating the detailed mechanistic scenario and thereby providing a molecular level understanding of the complete reaction features associated with Cd[(C 6 H 5 ) 2 PSSe] 2 precursor. Twenty four reactions have been investigated in total: seven energy minima and seventeen transition states. The relative energies and the optimized geometries of all the species involved in the (C 6 H 5 )PSSe-Cd-Se and (C 6 H 5 ) PSSe-Cd-S decomposition are depicted in Figs. 1 and 2. Unimolecular decomposition of R1 via pathway 1 is associated with the elimination of phenyl radical leading to the formation of a (C 6 H 5 ) 2 PSSe-Cd-SeSP(C 6 H 5 ) intermediate, INT1/d (Fig. 2). This dissociation pathway passes through a singlet transition state TS1/s with a barrier height of 40.64 kcal/mol and reaction energy of 34.58 above the initial reactant on the doublet potential energy surface. This barrier is significantly lower than the barrier for the formation of the ( i Pr) 2  Scheme 4 Proposed decomposition pathway of (C 6 H 5 )P(Se)S-Cd intermediate [38][39][40][41] accounts for the dissociation of the phenyl radical being 2.93 Å away from the associated P atom. INT5/s is produced at an energy level of 18.42 kcal/mol below the INT3/d. The phenyl-dissociation transition state, TS5/d, possesses an activation barrier of 32.83, ∼4 kcal/mol lower than pathway 3 discussed above.
It was reckoned that the (C 6 H 5 )PSSe-Cd-Se INT4/s intermediate produced in Scheme 1 may then decompose in two ways, either through the formation of CdSe or ternary CdSe x S 1−x . The energetics of such reaction was investigated and it was found that the activation barrier and the reaction energy for the formation of CdSe through a singlet transition state is +73.97 and −29.86 kcal/mol, respectively. The formation of ternary CdSe x S 1−x has an activation barrier and a reaction energy of +71.43 and −26.83 kcal/mol, respectively. The activation barrier for the formation of the CdS by the dissociation of the Cd-S and Cd-Se bonds from (C 6 H 5 ) PSSe-Cd-S INT5/s intermediate is +95.15 kcal/mol (Fig. 5). This is much higher than the barrier for the formation of the ternary CdSe x S 1−x .
As shown in Figs. 2 and 3, the final decomposition pathways that were considered have a higher activation barrier. It is worth noting that the higher energy values of the transition states associated with the final pathways are consistent with the strained, four cantered nature of the calculated transition state structures. The lowest barrier (∼60 kcal/mol) on the potential energy surfaces is ternary CdSe x S 1−x dissociation pathway. A rate constant of 7.88 × 10 −7 s −1 , 1.86 × 10 8 mol L −1 and 1.61 × 10 −4 mol L −1 s −1 were estimated for this pathway ( Table 2). In terms of energetic, the formation CdSe is the thermodynamically more stable product on the reaction PES (Fig. 2). The rate constant along this pathway is 1.86 × 10 8 mol L −1 ( Table 2). Though Opoku et al. [42] found the CdS-elimination pathway as the most favoured pathway and ternary CdSe x S 1−x elimination as the most disfavoured one in their calculation using Cd[( i Pr) 2 PSSe] 2 analogue, the present study suggest the ternary CdSe x S 1−x formation pathway as the most favoured pathway followed by CdSe and CdS-elimination pathways among the several possible decomposition pathways discussed above for the gas-phase thermal decomposition of Cd[(C 6 H 5 ) 2 PSSe] 2 precursor.
As outlined before, another plausible decomposition route originating from R1 is Cd-Se and Cd-S elimination (Scheme 3). The fully optimized geometries of all the reactants, intermediates, transition states (TS), and products involved in the Cd[(C 6 H 5 ) 2 PSSe] 2 decomposition are shown in Fig. 4. Decomposition of R1 proceeds through the dissociation of Cd-Se and Cd-S bonds on one side of the ligand via a singlet transition state to form a (C 6 H 5 ) 2 PSSe-Cd intermediate on the doublet PES, which is like the loss of a phenyl radical in Scheme 1. This process is associated with an activation barrier and a reaction energy of 43.48 and 28.41 kcal/mol above the initial reactant, R. The (C 6 H 5 ) 2 PSSe-Cd intermediate, INT6/d, formed can enter into three successive reactions.
As shown in Fig. 4, further decomposition of INT6/d may lead to the formation of CdSe (shown in Scheme 3) through Cd-S and P-Se elimination. This passes through the transition state TS11/d and requires a barrier height of 28.68 kcal/mol above the INT6/d; the corresponding reaction energy is 37.80 below the reactant. The Cd-S bond elongates from 2.48 Å in the complex to 2.87 Å in the transition state, and the P-Se bond also elongates from 2.20 Å in the complex to 2.96 Å in the transition state. at TS12/d and free energy of −29.11 kcal/mol (Fig. 4). Therefore, the results suggest that the dissociation of CdS is kinetically preferred over the dissociation of CdSe.
A subsequent decomposition via INT6/d, leads to the formation of a ternary CdSe x S 1−x . This process needs to go over a barrier of 28 Among the three possible heterolytic dissociations pathway, the CdSe dissociation pathway is slightly the most stable species on the reaction PES, with a free energy of about 0.03 kcal/mol lower than the CdS. The results suggest that, the heterolytic pathway of CdSe through the [(C 6 H 5 ) 2 PSSe] − anion is highly competitive with the CdS pathway. Moreover, in terms of kinetic, the CdS dissociation is the most favourable pathway than the CdSe and ternary CdSe x S 1−x pathways and a rate constant of 3.17 × 10 −1 s −1 was estimated ( Table 2). In an alternate dissociation route involving the dissociation of P-S and P-Se bonds, INT7/s gives rise to the formation of a ternary CdSe x S 1−x . This process is associated with an activation barrier of 41.57 kcal/mol and passes through a singlet transition state TS17/s. The resulting product being 3.42 kcal/mol below INT7/s is ∼18 and ∼11 kcal/mol less stable than the CdSe and CdS dissociation pathway, respectively.
However, CdSe is comparable, located only at 0.25 and 0.19 kcal/mol higher than CdS and ternary CdSe x S 1−x . Therefore one of the three pathways is not overwhelming to the other but instead competing even if CdS dissociation is a little more favourable. The rate constants along CdS pathway were 1.53 × 10 −3 s −1 and 2.32 × 10 −5 mol L −1 s −1 (Table 2). Moreover, all the reactions were predicted to be exergonic, ranging from ~ 3-21 kcal/mol. However, the results further suggested that the formation of CdSe is the most stable species on the reaction PES.
In order to provide a direct comparison of activation energy data for a phenylphosphinato complex and its isopropyl analogue, the Cd[(C 6 H 5 ) 2 PSSe] 2 complex was prepared as a model for Cd[( i Pr) 2 PSSe] 2 complex. Precedent for the modelling of phenyl complex is provided by the virtually identical decomposition patterns for the isopropyl complex [42]. DFT results for phenyl group could then be compared to our previously reported data for the isopropyl complex [42]. The activation barrier and reaction energy of the two precursors are presented in Table 3.
The kinetics and thermodynamics of organic and inorganic substituents, and radical reaction pathways may be affected by the size of structural features of either the

Table 1 Comparison of the calculated geometries of Cd[(C 6 H 5 ) 2 PSSe] 2 and Cd[( i Pr) 2 PSSe] 2 precursor at the M06/LACVP* level of theory (bond lengths in angstroms and bond angles in degrees)
a Data from Ref. [38] Bond lengths M06/LACVP* Bond angles M06/LACVP* P  substrate or the dissociation species. Since any homogeneous decomposition of electron transfer reaction requires appropriate orbital overlap, features that diminish such overlap will reduce the corresponding rate constants. Increasing substitution across the phosphinato complex, increases the activation barrier of the phenyl group, which are significantly greater than the isopropyl analogue. This suggests that the steric congestion afforded by this bulky substituent imposes significant energy on the electron transfer processes. Thus increased alkyl substitution may increase the chemical reaction of the decomposition process and decrease the activation barrier. Therefore, the kinetic stabilities of the resulting ligands depend on the steric congestion about the central phosphorus; more congested compounds are resistant to decomposition, while those with more accessible phosphorus centres react rapidly. Moreover, the activation barrier data of the phenyl and isopropyl group may also suggest that the C-Ph bond is more difficult to break than the C-i Pr bond. This is consistent with the homolytic bond strength of the C-i Pr moieties [42]. If C-i Pr bond cleavage were involved in the rate determining step, phenyl complex would be expected to require higher deposition temperatures relative to the isopropyl complex. The stronger C-Ph bond may also affect growth rate and composition of the deposited films. Additionally, these data suggest that replacing the phenyl moiety with a group that will cleave more readily could decrease the deposition temperature and improve the compositional characteristics of the cadmium chalcogenides films.

Spin density analysis
The spin density distribution map of some intermediates and transition states complexes obtained on the doublet PES has been explored on the M06/6-31(d) level of theory.
In Fig. 6a-c, most of the spin densities are distributed on the ligand with less metal contribution. As shown in Fig. 6d, the spin density is entirely distributed on the cadmium atom that coordinates to the ligand.
In Fig. 7a-c, additional spin density is symmetrically delocalised on the phenyl group with little or no spin on the phosphorus atom.
In Fig. 8a-c, the spin density is exclusively localised on the selenium atom with less metal contribution. Additional spin density is symmetrically delocalised on the phenyl group that coordinate to the phosphorus atom.

Orbital analysis
The single occupied molecular orbital (SOMO) analysis of some intermediates and transition states complexes has also been explored at the same level of theory. In Fig. 9a-c, the electron density distribution on the cadmium atom resembles that of d-xy orbital; a significant contribution from the ligand was also observed. The  Fig. 6 Spin-density distribution for a (C 6 H 5 ) 2 PSSe-Cd-SeSP(C 6 H 5 ), b (C 6 H 5 ) 2 PSSe-Cd-Se, c (C 6 H 5 ) 2 PSSe-Cd-S and d (C 6 H 5 ) 2 PSSe-Cd complexes. Isosurfaces ± 0.003 a.u SOMO of (C 6 H 5 ) 2 PSSe-Cd + complex shows a strong localisation of electron density on the cadmium atom as compare to the ligand.

Conclusion
The Cd[(C 6 H 5 ) 2 PSSe] 2 complex was tested to determine its suitability as a single-source precursor for cadmium chalcogenides thin films. The decomposition of Cd[(C 6 H 5 ) 2 PSSe] 2 as a single source precursor, is investigated using density functional theory at the M06/LACVP* level. Kinetically, the dominant pathways for the gas-phase decomposition of Cd[(C 6 H 5 ) 2 PSSe] 2 were found to be CdS elimination pathways on both the singlet and the doublet PESs. However, on the basis of the dissociation energy of the reactions and with the detailed identification of the reaction intermediates, it is clearly shown that CdSe elimination pathways are the dominant pathways on both the singlet and the doublet PESs. Comparison of energetics of the phenyl group to the isopropyl analogue, allows evaluation of  the effect of the phosphinato bond dissociation energy on final decomposition products. The isopropyl precursor is superior to phenyl for barrier deposition due the tendency of the stronger phosphinato bond of phenyl to result in dissociation of the C-Ph fragments. The exploration of chemical kinetics and the construction of global potential energy surfaces for the decomposition of SSPs are believed to provide a comprehensive fundamental molecular level understanding of the reaction mechanism involved in the chemical vapour deposition.
Authors' contributions NKA and AAA proposed and designed research subject; FO carried out the computation studies and wrote the paper. NKA and AAA helped in the result and discussion and edit the final manuscript; All authors read and approved the final manuscript.