Radiative lifetimes of several doublet and quartet states of silicon boride

Highlights

• Lifetimes are 1–10, 0.1–1, and 1 μs for the A⁴Π, D⁴Σ^–, and E⁴Π states, respectively.

• Lifetimes are 10–100 and 1 – 10 μs for the d²Σ⁺ and e²Π states, respectively.

• Lifetimes are 0.1–10³ and 0.1–10² ms for the b²Δ and c²Σ^– states, respectively.

• Lifetimes are 1–10⁴ and 1–10³ ms for the B⁴Δ and C⁴Σ⁺ states, respectively.

• A⁴Π – X⁴Σ^–, D⁴Σ^– – X⁴Σ^–, E⁴Π – X⁴Σ^–, and E⁴Π – A⁴Π transitions are strong.

Abstract

In this study, the potential energy curves were calculated for the X⁴Σ^–, A⁴Π, B⁴Δ, C⁴Σ⁺, D⁴Σ^–, E⁴Π, a²Π, b²Δ, c²Σ^–, d²Σ⁺, and e²Π states of silicon boride. The transition dipole moments were computed for all dipole–allowed transitions between these states. The complete active space self-consistent field method was used for calculations, followed by the valence internally contracted multireference configuration interaction approach. The radiative lifetimes were approximately 1 – 10 μs, 0.1 – 1 μs, 1 – 10,000 ms, 1 – 1000 ms, and 1 μs for the A⁴Π, D⁴Σ^–, B⁴Δ, C⁴Σ⁺, and E⁴Π states, respectively. Of these transitions between the six lowest–lying quartets, the spontaneous emissions from the A⁴Π – X⁴Σ^–, D⁴Σ^– – X⁴Σ^–, E⁴Π – X⁴Σ^–, and E⁴Π – A⁴Π systems were strong, whereas those from the B⁴Δ – A⁴Π, C⁴Σ⁺ – A⁴Π, and E⁴Π – B⁴Δ transitions were weak. The radiative lifetimes were approximately 0.1 – 1000 ms, 0.1 – 100 ms, 10 – 100 μs, and 1 – 10 μs for the b²Δ, c²Σ^–, d²Σ⁺, and e²Π states, respectively. Of the transitions between the a²Π, b²Δ, c²Σ^–, d²Σ⁺, and e²Π states, the spontaneous emissions from the e²Π – b²Δ and e²Π – c²Σ^– systems were relatively strong, whereas those from the b²Δ – a²Π transition were relatively weak. The transition frequencies, Einstein A coefficients, and Franck–Condon factors of all spontaneous vibronic bands from these transitions were calculated. The results obtained in this study were compared with experimental and other theoretical values. The radiative–lifetime distribution varying with rotational angular quantum number J was calculated when J ≤ 50.5 for a particular vibrational level of these 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 R_e and ω_e 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.