Radiative Lifetime Distribution Research Articles

Rovibrational properties of the A1Π – X1Σ+ system of the AlCl radical

The potential energy curves of the X1Σ+ and A1Π states of aluminum monochloride radical and the transition dipole moments between them were calculated using the icMRCI approach. Core–valence correlation and scalar relativistic corrections were applied. The extrapolation of the potential energies to the complete basis set limit was considered to improve the quality of the potential energy curves. In order to accurately calculate the rovibrational transition positions of the A1Π – X1Σ+ system, the experimental Te value of the A1Π state was used to improve the reliability of the ab initio results. The radiative lifetimes of all vibrational states of the A1Π state were calculated and compared with the available experimental and theoretical results. The variation of the radiative–lifetime distribution with the rotational quantum number was obtained. The rovibrational transition positions, Einstein A coefficients, oscillator strengths, and Franck–Condon factors of the P, Q, and R branches of the vibronic emissions of this system were calculated up to J = 150. The Einstein A coefficients were large for numerous vibronic bands, indicating that these transitions were easily measured via spectroscopy. A Comparison with available measurements shows that the transition properties reported herein are accurate.

Investigations on transition properties of X2Σ+, A2Π, B2Σ+, C2Π, and a4Σ+ states, and their Ω states of BO

The transition properties were calculated for the X2Σ+, A2Π, B2Σ+, C2Π, and a4Σ+ states, and eight Ω states of BO. The calculations were performed using the CASSCF method, followed by the icMRCI approach. Core–valence correlation and relativistic corrections were included. The radiative lifetimes of the first 16 vibrational levels were roughly 1.5–1.6 μs for the A2Π state, 96–177 ns for the B2Σ+ state, and 16.7–18.5 ns for the C2Π state. The B2Σ+ – X2Σ+ and C2Π – X2Σ+ transitions were strong, followed by the A2Π – X2Σ+, B2Σ+ – A2Π, and C2Π – A2Π transitions. The radiative lifetime of the first 16 levels was approximately 4.9–10.4 ms for the a4Σ+1/2 state, 0.21–24 ms for the a4Σ+3/2 state, 2.9–3.6 μs for the A2Π1/2 state, 3.5–3.8 μs for the A2Π3/2 state, 134–230 ns for the B2Σ+1/2 state, 23.2–25.4 ns for the C2Π1/2 state, and 23.0–25.2 ns for the C2Π3/2 state. Among all spin–forbidden transitions generated from the a4Σ+ state, the a4Σ+1/2 – X2Σ+1/2 and a4Σ+3/2 – X2Σ+1/2 transitions were relatively strong. The transition properties reported herein were compared with the experimental results. The variation of the radiative–lifetime distribution with the rotational angular quantum number was evaluated for A2Π1/2, A2Π3/2, B2Σ+1/2, C2Π1/2, and C2Π3/2 states. It is expected that the transition properties calculated in this study can provide some useful guidelines for future experimental and theoretical investigations.

Transition properties of the X1Σ+, I1Σ−, A1Π, D1Δ, B1Σ+, and a3Π states of carbon monoxide

This work calculated the potential energy curves of the X1Σ+, I1Σ−, A1Π, D1Δ, B1Σ+, a3Π, a’3Σ+, d3Δ, and e3Σ− states of the carbon monoxide, the transition dipole moments between the X1Σ+, I1Σ−, A1Π, D1Δ, and B1Σ+, states, and the transition dipole moments of the a3Π – X1Σ+ spin–forbidden transition. The calculations were made using the CASSCF method, followed by the icMRCI approach. The radiative lifetime of the first 16 levels was approximately 9.8–11 ns for the A1Π state, 6.3–23.7 ns for the B1Σ+ state, and 0.24–553 ms for the D1Δ state. The Einstein A coefficients, band origins, and Franck–Condon factors of the spontaneous bands from all electric dipole–allowed transitions were calculated. The A1Π – X1Σ+, B1Σ+ – X1Σ+, and B1Σ+ – A1Π transitions were strong, whereas the A1Π – I1Σ− and D1Δ – A1Π transitions were weak. The spin–forbidden transition from the a3Π state to the X1Σ+ state were calculated. The a3Π1 – X1Σ+0+ transition was much stronger than the a3Π0+ – X1Σ+0+ transition. The radiative lifetimes of the first 16 vibrational levels were approximately 12.6–25.5 ms and 10–105 s for the a3Π1 and a3Π0+ states, respectively. The radiative–lifetime distribution depending on J at a certain υ was calculated at υ ≤ 15 and J ≤ 70 for the A1Π and a3Π1 states. Comparison of the transition properties reported herein with the available measurements shows that these results are accurate.

Transition properties among Ω states originating from X 2Π, A 2Σ+, B 2Π, C 2Σ+, a 4Π, b 4Σ+, c 4Δ, and d 4Σ– states of SiP molecule

The potential energy curves of X 2Π, A 2Σ+, B 2Π, C 2Σ+, a 4Π, b 4Σ+, c 4Δ, and d 4Σ– states of SiP molecules and the transition dipole moments of the transitions between these states were calculated using the CASSCF method, followed by the icMRCI approach. The radiative lifetimes of the first 16 vibrational levels were 0.27 – 66 and 1.5 – 2.38 × 104 ms for the A 2Σ+ and b 4Σ+ states, respectively. Those were 146 – 497, 93 – 254, 23.9 – 30.3, and 0.85 – 1.1 µs for the B 2Π, c 4Δ, d 4Σ–, and C 2Σ+ states, rspectively. The spin–orbit coupling constants of the X 2Π, B 2Π, a 4Π, and b 4Σ+ states were evaluated. Including the spin–orbit coupling effect, the radiative lifetimes of the A 2Σ+1/2, B 2П1/2, B 2П3/2, C 2Σ+1/2, a 4П–1/2, a 4П1/2, a 4П3/2, a 4П5/2, b 4Σ+1/2, and b 4Σ+3/2 states were calculated. The lifetimes of the first 16 levels were 0.35 – 0.42, 3.1 – 5.5, 1.3 – 5.8, and 30 – 57 s for the a 4П–1/2, a 4П1/2, a 4П3/2, and a 4П5/2 states, respectively. And those were 2.3 – 268 and 2.6 – 257 ms for the b 4Σ+1/2 and b 4Σ+3/2 states, respectively. The SOC effect made the radiative lifetimes of the A 2Σ+, B 2Π, and C 2Σ+ states become longer. Among the spontaneous emissions between these Ω states, those from the C 2Σ+1/2 state to the X 2П3/2, X 2П1/2, and A 2Σ+1/2 states were the strongest. The results indicated that the strong emissions originated from the lower levels of the C 2Σ+1/2 state. Furthermore, almost all of these strong emissions were in the visible region. All emissions generating from the a 4П–1/2, a 4П1/2, a 4П3/2, and a 4П5/2 states are extremely weak. The radiative–lifetime distribution of each level υ versus the rotational quantum number J was evaluated for several Ω states.

Radiative lifetimes of A 2Π, B 2Σ+, a 4Σ+, and b 4Δ states of CP radical

The potential energy curves of X 2Σ+, A 2Π, B 2Σ+, a 4Σ+, and b 4Δ states and their Ω states of CP were calculated using the icMRCI approach. The transition dipole moments between these states were computed. To improve the accuracy of the potential energy curves, core–valence correlation and scalar relativistic corrections were considered. The radiative lifetimes were approximately 10 μs for the A 2Π3/2 and A 2Π1/2 states and 100 ns for the B2Σ+1/2 state; those were approximately 10, 10 – 100, 10, 0.1 – 1, and 10 ms for the a 4Σ+1/2, a 4Σ+3/2, b 4Δ1/2, b 4Δ3/2, and b 4Δ5/2 states, respectively. The spontaneous emissions from the B 2Σ+1/2 – X 2Σ+1/2 system were strong, followed by the A 2Π3/2 – X 2Σ+1/2, A 2Π1/2 – X 2Σ+1/2, B 2Σ+1/2 – A 2Π3/2, and B 2Σ+1/2 – A 2Π1/2 transitions. The strong emissions from the A 2Π3/2 – X 2Σ+1/2 and A 2Π1/2 – X 2Σ+1/2 systems were in the infrared region; those from the B 2Σ+1/2 – X 2Σ+1/2 system were in the visible and ultraviolet regions; and those from the B 2Σ+1/2 – A 2Π3/2, and B 2Σ+1/2 – A 2Π1/2 systems were of visible light. A simple comparison shows that the effect of the spin–orbit coupling on the radiative lifetimes of the A 2Π and B 2Σ+ states was significant. The radiative–lifetime distribution of each level υ versus the rotational quantum number J was evaluated for υ ≤ 15 and J ≤ 70.5.

Radiative lifetimes of A2Π, B2Σ+, 22Π, 12Σ–, C2Δ, and a4Σ+ states of carbon monosulfide cation

The transition dipole moments of the dipole–allowed transitions between the X2Σ+, A2Π, B2Σ+, 22Π, 12Σ–, and C2Δ states of the carbon monosulfide cation were calculated using the complete active space self–consistent field method, followed by the internally contracted multireference configuration interaction approach. The transition dipole moments of the spin–forbidden transitions from the a4Σ+ state to the X2Σ+ and A2Π states were computed. The radiative lifetimes were of the order of 1 – 10 µs, 100 ns, 1 µs, 10 – 100 µs, and 1 – 10 µs for the A2Π, B2Σ+, 22Π, 12Σ–, and C2Δ states, respectively. The transition frequencies, Einstein A coefficients, and Franck–Condon factors of all these spontaneous vibronic emissions from these systems were calculated. The emissions from the A2Π – X2Σ+, B2Σ+ – X2Σ+, B2Σ+ – A2Π, 22Π – A2Π, and C2Δ – A2Π systems were strong, suggesting that the 22Π state could be measured in a spectroscopy experiment via 22Π – A2Π transition. Those from the 22Π – B2Σ+, 12Σ– – 22Π, and C2Δ – 22Π systems were weak. The radiative lifetimes of the a4Σ+1/2 and a4Σ+3/2 states were approximately 10 ms. Among these spin–forbidden transitions, the emissions from the a4Σ+3/2 – A2Π3/2 system were relatively strong. The radiative–lifetime distribution of each vibrational level versus the rotational quantum number was evaluated for the A2Π, B2Σ+, 22Π, 12Σ–, C2Δ, and a4Σ+ states.

Radiative lifetimes of several doublet and quartet states of silicon boride

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.

Radiative lifetimes of the 11Σ–, 11Δ, 21Σ+, a3Π, 13Σ+, d3Δ, and e3Σ– states of carbon monosulfide

Numerous experimental and theoretical investigations studied the transition properties of the A1Π – X1Σ+ system of carbon monosulfide. However, only a few transition properties are currently available except for the A1Π state. Therefore, this study calculated the properties of the dipole-allowed transitions arising from the 11Σ–, 11Δ, 21Σ+, a3Π, 13Σ+, d3Δ, and e3Σ– states and the spin–forbidden transition from the a3Π to the X1Σ+ state. The radiative lifetimes were approximately 10 ns for the 21Σ+ state, 10 μs for the e3Σ– state, 10 – 100 μs for the d3Δ state, and 10 – 1000 μs for the 13Σ+ state. The emissions from the 21Σ+ – X1Σ+ system were strong. The radiative lifetimes were of the order of 0.1 – 1000 ms for the 11Δ state and 0.1 – 105 ms for the 11Σ– state. The lower the vibrational level of the 11Δ and 11Σ– states was, the longer the radiative lifetime became, suggesting that the spontaneous emissions arising from the lower vibrational levels of the two states were difficult to be measured through spectroscopy. The radiative lifetimes were of the order of 1 – 10 and 1 ms for the a3Π1 and a3Π0+ states, respectively; whereas those of the a3Π2 and a3Π0– states were extremely long. The radiative–lifetime distribution varying with the rotational angular quantum number J was investigated at J ≤ 70 for a particular vibrational level of the 11Σ–, 11Δ, 21Σ+, a3Π, 13Σ+, d3Δ, e3Σ–, a3Π1, and a3Π0+ states.

Radiative lifetimes and transition properties of boron monoxide cation

The transition dipole moments of dipole–allowed transitions between the following states were calculated in this study: X1Σ+, A1Π, B1Σ+, C1Δ, D1Σ–, and E1Π; a3Π, b3Σ+, c3Σ–, d3Π, and e3Δ, and those of the spin–forbidden transitions from the a3Π state to the X1Σ+ state of boron monoxide cation. The CASSCF method was used, followed by the valence icMRCI approach. The radiative lifetimes of the vibrational states were of the order of 1 – 10 μs for the A1Π state; 10 ns for the D1Σ–, e3Δ, and the first well of the B1Σ+ states; 1 – 1000 ns for the second well of the B1Σ+ state; 100 ns for the d3Π state; 0.1 – 1 μs for the b3Σ+ and E1Π states; 10 – 100 μs for the C1Δ state; and 10 – 10,000 μs for the c3Σ– state. The transition from the first well of the B1Σ+ state to the X1Σ+ state and that from the double well of the B1Σ+ state to the A1Π state were the strongest, followed by the D1Σ– – A1Π, E1Π – A1Π, d3Π – a3Π, and e3Δ – a3Π transitions. The transition from the second well of the B1Σ+ state to the X1Σ+ state was the weakest, followed by the C1Δ – A1Π, E1Π – B1Σ+, E1Π – C1Δ, E1Π – D1Σ–, c3Σ– – a3Π, and e3Δ – d3Π transitions. The variation in the radiative–lifetime distribution with the rotational angular quantum number J was evaluated. The radiative lifetimes of the vibrational states were of the order of 1 – 10 ms for the a3Π1 state and 10 ms for the a3Π0+ state. The a3Π1 – X1Σ+0+ and a3Π0+ – X1Σ+0+ transitions were weak. The transition properties reported herein may provide useful guidelines for related experimental and theoretical investigations in the near future.

Plasmonic enhancement of intrinsic carbon nanodot emission

In this Letter we characterize both the photophysical and plasmonic enhanced photophysical properties of carbon nanodots produced by a combustion method. In addition, we have found that max entropy analysis of luminescence decay reveals inhomogeneous distribution of radiative lifetimes. Further, while quantum yields of intrinsic carbon nanodots emission are low [<2%], when in close proximity to plasmonic supporting materials, carbon nanodots emission can be enhanced 30 times (30×).

Microscopic modeling of photoluminescence of strongly disordered semiconductors

A microscopic theory for the luminescence of ordered semiconductors is modified to describe photoluminescence of strongly disordered semiconductors. The approach includes both diagonal disorder and the many-body Coulomb interaction. As a case study, the light emission of a correlated plasma is investigated numerically for a one-dimensional two-band tight-binding model. The band structure of the underlying ordered system is assumed to correspond to either a direct or an indirect semiconductor. In particular, luminescence and absorption spectra are computed for various levels of disorder and sample temperature to determine thermodynamic relations, the Stokes shift, and the radiative lifetime distribution.

Lifetime distribution and non-radiative processes in chromium doped aluminosilicate glass

We present luminescence decay measurements of an aluminosilicate glass doped with chromium for different combinations of excitation and emission wavelengths, obtained between 10–300K. The luminescence lifetime distribution of the 4T2→4A2 transition has been obtained using the exponential series method and modelled by considering the radiative lifetime distribution in the sample and the effect of non-radiative internal conversion. Good fits to the data have been obtained. The distribution of the radiative luminescence lifetimes shows that there is little correlation between 4T2 energies and the magnitude of odd parity distortions. The distribution of the energy barrier for non-radiative processes indicates that a significant contribution to barrier crossing comes from tunnelling and that the Cr3+ potential wells must be modelled using confinement potentials rather than simple harmonic approximations.

Luminescence lifetimes of single molecules in disordered media

Linewidth measurements for single terrylene molecules in polyethylene at a temperature of 30 mK indicate that there is a distribution of lifetimes for the terrylene molecules with a relative standard deviation of ∼20%. An analysis of the linewidth–line area correlation shows that the variations arise from approximately equal radiative and nonradiative contributions. A simple model suggests that the distribution of radiative lifetimes in disordered media is a general effect caused by the same interactions responsible for inhomogeneous broadening. In addition to the transition frequency, the luminescence lifetime of a probe molecule can be used to study the nano-environment of the probe.

Luminescence kinetics and emission lifetime distribution of Cr 3+-doped aluminosilicate glass

Luminescence decay measurements of Cr 3+ ions in an aluminosilicate glass have been recorded for different combinations of excitation wavelength, emission wavelength and temperature. The luminescence lifetime distribution has been obtained using the exponential series method and modelled by considering the radiative lifetime distribution in the sample and the effect of non-radiative internal conversion. At low temperatures, the luminescence decays are little affected by changes in experimental parameters and this allows the distribution of the intrinsic radiative lifetimes to be determined. From these data, it is determined that the main factors that influence the inhomogeneous broadening of the absorption and emission spectra, the strength of the crystal field and the magnitude of even parity distortions, are only weakly correlated with the magnitude of the odd parity distortions that principally determine radiative lifetime. A model of the temperature dependence of the luminescence lifetime distribution provides an estimate of the distribution of the energy barrier for the non-radiative processes in this system. The results of this fit show that a significant contribution to barrier crossing comes from tunnelling and that the Cr 3+ potential wells must be represented by confinement potentials rather than simple harmonic approximations.

Nonradiative recombination and its influence on the lifetime distribution in amorphous silicon (a-Si:H).

We present a detailed analysis concerning the influence of the defect density ${\mathit{N}}_{\mathit{D}}$ on the low-temperature (T=10 K) geminate recombination kinetics. It is shown that the lifetime distribution of a-Si:H, measured by frequency-resolved photoluminescence spectroscopy, can be explained quantitatively if it is assumed that radiative recombination is directly competing with nonradiative tunneling into defect states. This allows us to determine the radiative lifetime distribution with high accuracy, which in turn provides the unique opportunity to describe the recombination kinetics entirely, i.e., including its nonradiative contribution. Interesting and nonintuitive consequences that are related to the competition model are discussed.

Discontinuous change of photoluminescence lifetime with temperature in hydrogenated amorphous silicon

The radiative lifetime distribution G(τ) in a-Si:H has been evaluated for monochromatized photoluminescence (PL). Although the PL intensity in a steady state was almost constant at temperatures lower than 50 K, G(τ) exhibited a drastic change in this temperature range; G(τ) at 13 K was dominated by a single component peaked at 1 ms, whereas another component grew up gradually at around 10 μs with increasing temperature. In this case, the lifetime changes discontinuously from 1 ms to 10 μs. Based on G(τ) evaluated for various conditions, PL mechanism in a-Si:H is reconsidered.

Radiative and non-radiative tunnelling in glow-discharge and sputtered amorphous silicon

Abstract Photoluminescence decay measurements are reported for doped and undoped glow-discharge a-Si, and for a-Si prepared by sputtering in a hydrogenated atmo-sphere. It is concluded that a distribution of radiative lifetimes is present, due either to non-crystalline disorder or to a donor-acceptor pair mechanism. The main competitive mechanism is tunnelling to defects.

Photoluminescence and lifetime studies on plasma discharge a-Si

A detailed study has been made of the photoluminescence (PL) behaviour of high T D, undoped, glow-discharge a-Si, prepared by the Dundee group. Our measurements include temperature and field quenching of the luminescence and PL decay in the region 2 ns to ∼20 μs. Some recombination models for a-Si are briefly reviewed in the light of these results. Preliminary life-time data on doped a-Si are also presented and used to discuss our earlier measurements on the PL efficiency of doped samples. We conclude that a distribution of radiative lifetimes is present in a-Si, due to disorder. The main competitive non-radiative process is tunnelling to defects.