Radiative lifetimes of several doublet and quartet states of silicon boride
Graphical abstract
The radiative lifetimes are approximately 1 – 10, 0.1 – 1, 1, 10 – 100, and 1 – 10 μs for the A4Π, D4Σ–, E4Π, d2Σ+, and e2Π states, respectively; and those are of the order of 0.1 – 1000, 0.1 – 100, 1 – 10,000, 1 – 1000 ms for the b2Δ, c2Σ–, B4Δ, and C4Σ+ states, respectively. Of the transitions between the quartet states, the A4Π – X4Σ–, D4Σ– – X4Σ–, E4Π – X4Σ–, and E4Π – A4Π transitions are strong, whereas the B4Δ – A4Π, C4Σ+ – A4Π, and E4Π – B4Δ transitions are weak. Of the transitions between the doublet states, the e2Π – b2Δ and e2Π – c2Σ– transitions are relatively strong, whereas the b2Δ – a2Π transition is relatively weak. The radiative lifetime of a particular υ changes quickly as J increases for lower vibrational levels of the B4Δ, C4Σ+, b2Δ, c2Σ–, and d2Σ+ states; whereas the radiative lifetime of a particular υ increases or decreases as J increases for the other states.
Introduction
Currently, boron–silicon alloys are garnering interest because of their potentially important applications in semiconductor materials and thermoelectric devices [1], [2], [3]. Chemical vapour deposition is a method employed to prepare these alloys, particularly thin films or plates [4], [5], [6]. Therefore, for a better understanding of such processes, the spectroscopic parameters and transition properties of the vapour species in the B–Si binary system are important. To the best of our knowledge, even for the simplest silicon boride (SiB) radical, few spectroscopic parameters and transition properties are currently available experimentally [5], [6], [7], [8] or theoretically [1,[9], [10], [11], [12], [13].
Only four experimental groups have measured the spectroscopic parameters and transition properties of the SiB radical [5], [6], [7], [8]. Verhaegen et al. [5] performed the first mass spectrometric experimental study, in which the ground–state dissociation energy D0 of SiB in the gas phase was determined to be 23783.68 ± 2098.53 cm–1. Viswanathan et al. [6] measured the ground–state D0 in the gas phase as 26081.17 ± 1003.12 cm–1. Knight et al. [7] performed the first experimental spectroscopic measurements in neon matrices at 4 K and confirmed the ground state as X4Σ–. Brazier et al. [8] first observed the gas–phase spectrum of SiB and measured the emissions from the A4Π – X4Σ– and D4Σ– – X4Σ– systems using a corona excited supersonic expansion source. For the A4Π – X4Σ– system, the emissions measured were from υ’ = 0 – 5 to υ’’ = 0 – 11 and for the D4Σ– – X4Σ– system, they were from υ’ = 0 to υ’’ = 0 – 3.
At least six research groups [1,[9], [10], [11], [12], [13] have calculated the spectroscopic parameters and transition properties of SiB. Boldyrev and Simons [9] performed the first theoretical study at the MP2(fu11)/6-31G*, MP2(fu11)/6-311+G*, QCISD(T)/6-311+G(2df), and SCF/6-31G* levels of theory and reported the Re and ωe values of several states. Ornellas and Iwata [10] calculated the potential energy curves (PECs) and dipole moment functions of several states using the internally contracted multireference configuration interaction (icMRCI) method as well as the natural orbitals generated from a state-averaged density matrix, and determined the transition dipole moments (TDMs) of the transitions between quartet states. Employing these PECs and TDMs, Ornellas and Iwata [10] evaluated the spectroscopic parameters of involved states, calculated the Franck–Condon (FC) factors and Einstein A coefficients of the spontaneous emissions, and determined the radiative lifetimes of only a few states. Oyedepo et al. [11] calculated the spectroscopic parameters of the X4Σ– and a2Π states employing the multireference correlation–consistent composite approach. Tai et al. [1] and Tam et al. [12] calculated the ground–state D0 value using the CCSD(T)/complete basis set (CBS) approach. Xing et al. [13] calculated the PECs of numerous states using the complete active space self–consistent field (CASSCF) method, followed by the icMRCI approach. Using the PECs obtained, they [13] determined the spectroscopic parameters of the involved states.
Summarising the experimental and theoretical results reviewed previously [1,[5], [6], [7], [8], [9], [10], [11], [12], [13], we can draw two main conclusions: (1) Only the emissions of the A4Π – X4Σ– system from υ’ = 0 to υ’’ = 0 – 3 and those of the D4Σ– – X4Σ– system from υ’ = 0 – 5 to υ’’ = 0 – 11 were measured in the gas phase [8]. However, no radiative lifetimes of any state have been determined experimentally to date. (2) Of the states involved in this study, the TDMs, Einstein A coefficients, and FC factors of only the A4Π – X4Σ–, D4Σ– – X4Σ–, and E4Π – X4Σ– systems were calculated. The radiative lifetimes of the A4Π, D4Σ–, and E4Π states were evaluated based on the contributions from only the A4Π – X4Σ–, D4Σ– – X4Σ–, and E4Π – X4Σ– systems, respectively [10]. This study was performed to comprehensively understand the transition properties of several lowest–lying quartet and doublet states of SiB, namely X4Σ–, A4Π, B4Δ, C4Σ+, D4Σ–, E4Π, a2Π, b2Δ, c2Σ–, d2Σ+, and e2Π.
Section snippets
Theory and method
The ground and first–excited states of B atoms are 2Pu and 4Pg, the atomic energy levels of which are 0.00 and 28652.63 cm–1, respectively [14]. The ground, first and second –excited states of Si atoms are 3Pg, 1Dg, and 1Sg, the atomic energy levels of which are 0.00, 6298.85, and 15394.37 cm–1, respectively [15]. Thus, the first four dissociation limits of SiB are Si (3Pg) + B (2Pu), Si (1Dg) + B (2Pu), Si (1Sg) + B (2Pu), and Si (3Pg) + B (4Pg). Based on group theory, the Si (3Pg) + B (2Pu)
Results and discussion
Fig. 1 shows the PECs of the X4Σ–, A4Π, B4Δ, C4Σ+, D4Σ–, E4Π, a2Π, b2Δ, c2Σ–, d2Σ+, and e2Π states of SiB, which were obtained by the icMRCI + Q/56 + CV + DK calculations. As shown in Fig. 1, the E4Π state contains an evident barrier, at the top of which the potential energy is higher than that at the dissociation limit. The calculations in this work confirm that this barrier was formed by the avoided crossing of this state with the 34Π state, the transition properties of which were not
Conclusions
The PECs were calculated for the X4Σ–, A4Π, B4Δ, C4Σ+, D4Σ–, E4Π, a2Π, b2Δ, c2Σ–, d2Σ+, and e2Π states of the SiB radical and the TDMs were computed for all dipole–allowed transitions between these states using the icMRCI approach. The properties of the transitions originating from the A4Π, B4Δ, C4Σ+, D4Σ–, E4Π, b2Δ, c2Σ–, d2Σ+, and e2Π states were evaluated. According to the transition properties calculated in this study, we obtained the following main conclusions:
- (1)
The radiative lifetimes were
Author statement
We have reviewed the final version of the present manuscript and approve it for publication. We promise that this manuscript has not been published in whole or in part nor is it being considered for publication elsewhere.
Declaration of Competing Interest
All the authors of the present paper disclose no actual or potential conflict of interest including any financial, personal, or other relationships with other people or organizations within three years of beginning the submitted work that could inappropriately influence, or be perceived to influence, their work.
Acknowledgment
This work is sponsored by the National Natural Science Foundation of China under Grant No. 11274097.
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Cited by (1)
Transition properties among Ω states originating from X <sup>2</sup>Π, A <sup>2</sup>Σ<sup>+</sup>, B <sup>2</sup>Π, C <sup>2</sup>Σ<sup>+</sup>, a <sup>4</sup>Π, b <sup>4</sup>Σ<sup>+</sup>, c <sup>4</sup>Δ, and d <sup>4</sup>Σ<sup>–</sup> states of SiP molecule
2021, Journal of Quantitative Spectroscopy and Radiative TransferCitation Excerpt :Many of these applications require the spectroscopic parameters and transition properties of these molecules. Thus far, the transition properties of several Si–containing diatomic molecules like SiC [1,2], SiN [3,4], SiO [5,6], SiS [7], and SiB [8] have been reported, and many of these Si–containing diatomic molecules have been searched successfully in outer space [9–11]. However, for molecules containing Si and P, even for the simplest SiP, few experimental or theoretical transition properties are currently available in the literature, as summarized by Santos and Ornellas [12].