1Density functional studies of the luminescence of Si29H36
Type: Object |
Advantage: None |
Novelty: New |
ConceptID: Obj1
1
Density functional studies of the luminescence of Si29H36
Type: Object |
Advantage: None |
Novelty: New |
ConceptID: Obj1
2
The molecular structures of the ground and the lowest excited state of a Si29H36 cluster have been optimized at the density-functional-theory (DFT) level using the time-dependent perturbation-theory (TDDFT) approach for the excited state.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res1
3
The electronic absorption and emission energies for the fully optimized molecular structures have been calculated at the TDDFT level.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res2
4
The excitation energy calculated for the equilibrium structure of the excited state using the Becke–Perdew (BP) functional was found to be 0.72 eV smaller than the vertical excitation energy for the ground-state structure.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res2
5
The calculated wavelength of the emitted light is 396 nm which agrees well with experiment as the silicon cluster emits blue light.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res3
6
Small structural changes caused by the relaxation of the excited state introduce strains in the ground-state structure.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res4
7
The strain and the relaxation are found to contribute equally to the large red shift of the emitted light.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res4
8
Thus, the present calculations do not support the notion that the potential-energy surface of the excited state has a double-well structure.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con1
Introduction
9
A more detailed understanding of light absorption and light emission processes requires information about the potential-energy surfaces of both the ground and the involved excited states.
Type: Motivation |
Advantage: None |
Novelty: None |
ConceptID: Mot1
10
At absorption, the molecular system is excited from the ground state in its equilibrium geometry to an excited state and during the excitation process the molecular structure is approximately unchanged; the excitation is usually thought to be vertical.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac1
11
However, the ground-state structure is not necessarily optimal for the excited state resulting in a relaxation of the molecular structure of the excited state.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac1
12
The deexcitation giving rise to the luminescence can probably be considered to occur vertically from the relaxed excited state structure.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac1
13
This simplified absorption-emission mechanism suggests that the emitted light is red shifted as compared to the absorbed one.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac1
14
In photophysical studies of ultrasmall nano-sized Si particles, Nayfeh et al1–11. found that the absorption occurs in the ultra-violet (UV) region, whereas the excited Si particles emitted blue light with such a high intensity that one was able to observe the individual particles.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac2
15
Experimental and computational studies suggested that the Si nanoparticles most likely consist of 29 Si atoms which is a magic number for approximately spherically shaped clusters of Td symmetry.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac2
16
Spectroscopic studies showed that the Si cluster is covered by hydrogens.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac2
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac2
18
The electronic absorption spectrum up to the ionization threshold has recently been calculated for the Si cluster at density-functional-theory (DFT) levels and the accuracy of the obtained excitation energies were checked using coupled-cluster response-theory (CC2) calculations.14
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac3
19
At the DFT level using the Becke–Perdew (BP) functional, the excitation energy of the first excited state is 3.85 eV which agrees well with the experimental excitation threshold of 3.7 eV.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac3
20
Calculations at the CC2 level and DFT calculations using a hybrid functional yielded somewhat larger excitation energies, whereas calculations at the coupled-cluster singles (CCS)14 and the closely related configuration-interaction singles (CIS) levels6–8 yielded an excitation threshold of about 6 eV.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac3
21
The calculations also showed that the silicon cluster of 1 nm size possesses a band structure consisting of more than one hundred excited states below the ionization threshold at about 8 eV.14
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac3
22
Experimentally, the excited Si cluster is found to emit blue light which corresponds to an excitation energy of about 3 eV.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac4
23
Thus, the relaxation of the excited state leads to a huge shift of about 0.7 eV.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac4
24
The large red shift of the luminescence has been explained by localized surface states in the Si nanocluster.15
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac4
25
Based on empirical tight-binding and first-principle local-density calculations, Allan et al15. proposed that such states exist under the form of self-trapped excitons at the Si–Si dimers on the nanocluster surface.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac4
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac4
27
They found that the ground state has an all-confining single well, whereas the excited state has a double-well potential.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac4
28
The inner minimum corresponds to a normal nonradiative delocalized excited state with a Si–Si distance of the surface dimer of 2.35 Å, while the outer minimum corresponds to a radiative and trapped excitonic surface state with a Si–Si interspacing of 3.85 Å.1,16
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac4
29
In this work, the molecular structure of the first excited state of the Si29H36 cluster has been fully optimized at the time-dependent density-functional-theory (TDDFT) level.
Type: Goal |
Advantage: None |
Novelty: None |
ConceptID: Goa1
30
The corresponding emission spectrum as well as the absorption spectrum for the ground-state structure have been studied by employing TDDFT calculations.
Type: Object |
Advantage: None |
Novelty: New |
ConceptID: Obj2
31
The potential-energy curve for a relaxation pathway of the first excited state of the Si29H36 cluster has also been investigated.
Type: Object |
Advantage: None |
Novelty: New |
ConceptID: Obj3
Computational methods
32
The molecular structure of the Si29H36 cluster was optimized in the ground and the first excited state using the Turbomole program.17
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp1
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp1
34
Previous calculations showed that at least TZVP basis sets have to be used in order to obtain an accurate excitation spectrum.14
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac5
35
The absorption and emission spectra were calculated using the time-dependent perturbation-theory approach (TDDFT).23,24
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp2
36
The molecular structure of the first excited state was fully optimized at the BP TDDFT level using the Egrad module of Turbomole.25,26
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp3
37
The molecular structure of the ground state of the Si29H36 cluster belongs to the Td point group, whereas the symmetry of the first excited state was found to be D2d.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs1
Results
38
The molecular structure of the Si29H36 cluster is shown in Fig. 1, and the bond lengths of the ground and excited states are given in Table I. Structure changes (ΔR) due to the relaxation of the excited state are also given in the table.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs2
39
When the molecular structure of the Si cluster in the first excited state is assumed to belong to the Td point group, the luminescence energy is red shifted by 0.26 eV as compared to the absorption threshold, while when the cluster is allowed to relax to a D2d structure, the energy decreases by 0.72 eV yielding a deexcitation energy of 3.14 eV.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs3
40
Thus, the wavelength of the emitted light is 396 nm; blue light is emitted as also detected experimentally.1–9
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res5
41
In Table I, one can see that the changes in the bond lengths are rather small.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res6
42
The largest difference of 2.1 pm is obtained for the Si(2)–Si(4) bond.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs4
43
Si(2) is attached to Si(1), which is the central Si atom, and to Si(4) which is a surface Si atom with only one attached hydrogen.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs4
44
See Fig. 1 for the atom numbering.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs2
45
The bonds to the central Si(1) become 1.1 pm longer than for the ground state, while when the Td symmetry is enforced on the excited state, the Si(1)–Si(2) bond becomes 3.3 pm longer than for the ground state.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs5
46
The changes in the bond lengths are remarkably small especially when one considers that the difference between the absorption and emission energies is as large as 0.72 eV.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res7
47
The calculations show that there are two equal sources to the huge red shift: the relaxation of the excited state and the energy shift due to the strain of the ground state.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res8
48
In Table 2, the excitation energies of the first few dipole-allowed excitations are given.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs6
49
In the first three columns, the excitation energy and oscillator strengths obtained using the Td structure of the ground state are given, while the remaining columns contain the corresponding data obtained using the optimized D2d structure of the first excited state.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs6
50
The absorption and emission spectra obtained using the data of Table 2 are displayed in Fig. 2.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs6
51
As the emission spectrum is also constructed from calculated excitation energies and oscillator strengths, not all contributions to the emission are taken into account.27
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met1
52
For the luminescence spectrum, the molecular structure of the 1b2 state has been assumed.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met2
53
Population of higher excited states leads to other molecular structures and different luminescence spectra.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met2
54
By optimizing the doubly degenerate 1e state one obtains a higher luminescence energy of about 3.5 eV, whereas for symmetry reasons, the three individual components of the 1t2 state are identical.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res9
55
The relaxation pathway between the molecular structures of the ground and first excited states is difficult to compute.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met3
56
However, as a first guess one can assume that in the relaxation process the internal coordinates change linearly between the two extremes.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met3
57
The excitation energy plot shown in Fig. 3 is obtained from such an interpolation procedure.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs7
58
As seen in the figure, the excitation energy is a smooth function decreasing from 3.85 eV for the ground-state structure and reaching 3.14 eV for the fully optimized structure of the excited state.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs7
59
The potential-energy curves for the ground and excited states along the same trajectory are shown in Fig. 4.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs8
60
The potential-energy curves for both states are smooth functions with one single minimum each.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs8
61
No avoiding crossing yielding double minima of the potential-energy surface of the excited state, as previously proposed, can be seen in the figure.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res10
62
Fig. 4 shows that energy shift due to the relaxation of the excited state is equally significant to the red shift as the strain-energy contribution of the ground state.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con2
63
The chosen trajectory is not necessarily the exact pathway of the relaxation process.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con2
64
However, the absence of a potential threshold along this trajectory for the excited state shows that the molecular structure of the excited state is, after excitation, relaxed without any barrier.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res11
65
In order to check whether the excited state has an outer potential minimum trapping an exciton state at the surface of the Si cluster, the optimization of the molecular structure of the first excited state was performed without any symmetry constraints i.e. in C1 symmetry starting from a structure with a long Si(3)–Si(5) distance of 3.18 Å.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met4
66
However, no outer potential minimum could be found in the reoptimization of the first excited state.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs9
67
This, and the fact that the absorption and the emission energies are in close agreement with experimental data indicate that the potential-energy curve of the excited state does not possess any outer minimum.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res12
68
The present calculations thus show that it is most unlikely that the potential-energy curve of the excited state has two minima separated by a barrier as previously suggested by Allan et al.15
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con3
69
Instead, the small structural changes due to the relaxation of the excited state result in a lower energy for the excited state and simultaneously the energy of the ground state increases significantily due to the strain.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con4
70
These two contributions seem to be equally responsible for the obtained luminescence shift of 0.72 eV.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con4