For example blendICT Excitation energy of the first ICT state of the blend EHOMO HOMO energy. Bottom panel: two-dimensional representation of the transition density matrix (TDM) site for the S1, S4, and S11 excited states (from left to right) of the P5/PCBM composite system.
Organic solar cell device architecture
Single-layer devices
The presence of organic compounds in the active layer paves ways for easy modifications, and it has been shown to greatly affect the PCE. As mentioned in the previous paragraph, the design of the active layer is a key component of device manufacturing.
Bilayer devices
Bulk heterojunction (BHJ) device
Working principle of OSCs
- Light absorption
- Exciton diffusion
- Exciton dissociation
- Charge transport and collection
The first step in the photovoltaic process is the absorption of light by the photoactive material. The rate of charge transfer is usually described by Marcus' classical theory, which will be discussed in Chapter 2.
Characterization of organic solar cells
Open circuit voltage
In the case of BHJs, charge separation effectively occurs at the interface, so Voc strongly depends on the gap between the HOMO energy of the donor and the LUMO energy of the acceptor. EHOMOD and ELUMOA are the HOMO and LUMO levels of the donor and acceptor, respectively.
Short-circuit current density
Fill factor
Vocis defined as the maximum voltage transferred by the solar cell when the current is zero. If Rs is high, the voltage drops less across the diode, and the current increases more slowly with voltage.
Motivation
The introduction of fluorine, chlorine and bromine atoms into the side chain of a conjugated polymer and a small molecule has been shown to improve the PCE of OSCs.[41–. Many studies in the literature show that the introduction of π-bridges such as furan, thiophene and thiazole greatly affects the optoelectronic properties.
Outline of the thesis
Here MA is the mass of nucleus A, ZA and ZB are the atomic numbers of nucleus A and nucleus B respectively. RAB, riA and row are respectively the distances between the nuclei A and B, electrons and nucleus A, and the two electrons i and j.
Born-Oppenheimer approximation
Mean-field approximation and Hartree-Fock method
The electron-electron correlation effects can be introduced by various post-HF methods such as configuration interaction, M¨oller-Plesset perturbation theory,[46]. Instead of using ab initio correlated wave function theory methods, DFT- and TD-DFT-based methods, which offer a good balance between accuracy and computational cost, are generally used to obtain the structures and properties of conjugated oligomers and small molecules, which are used in active layers of OPVs.
Density functional theory
The Hohenberg-Kohn theorems form the basis of DFT.[52] The first Hohenberg–Kohn theorem states that the ground state electron density function can determine all the properties of a molecule in a ground electronic state. The non-interacting part can be easily treated, which constitutes a large part of the electronic energy, and a relatively small part is associated with the interacting part, which can be calculated using a density function.
Approximate exchange-correlation functionals
There are many other hybrid functionals reported in the literature, such as PBE0[56], HSE[57] and O3LYP.[58]. DFT has been the method of choice to describe organic donors, acceptors and donor-acceptor mixture systems in the literature.
London dispersion corrections
Out of these two, E(2) is the most important term.[64] This expression with the standard zero damping formula is given as. Cnij represents the average n-order scattering coefficients for atomic pairs ij,rij is their internuclear distance, and fd,n(rij) is the damping function.
Time-dependent density functional theory
The symbol vs1(r, t) is the linear change of the effective potential, vs(r, t), of the time-dependent KS system, and it can be written as. One of the other linear-response approaches that is widely used is the Casida formalism.[73]
Marcus theory
In the above equation, λ and ∆Gij represent the total reorganization energy and the change in free energy, respectively.
Reorganization energies
Usually, the two-sphere implicit Marcus formula in a continuum solvent[83,84] shown in Eq. For example, the external reorganization energy for composites with fullerene or substituted fullerene systems is about 0.1-0.3 eV and a value within this range has been used in many places in the literature giving good results. In the thesis, we have used a value of 0.3 eV for λext.
Electronic coupling and the generalized
The GMH method was developed by Cave and Newton[94, 95] based on the work of Mulliken[96, 97] and Hush.[98] Derivations of the GMH formula can be found in Refs.[99, 100] Consider a two-state system described by adiabatic wave functions ψ1 and ψ2 corresponding to the two adiabatic energies E1 and E2. The transition dipole moment between ground and excited states can be written from the adiabatic states as µ12=hψ1|r|ψ2i.
Free energy changes and exciton binding energy
In one of the earlier works, a device based on BDT and benzotriazole (denoted as P1) reported a PCE of ~4%.[1] Subsequent work by Yu and co-workers[2] reported medium-band conjugate polymers based on BDT and either a pyridazine-fused triazole (denoted as P2) or a cyano-substituted pyridine-fused triazole (denoted as P3) . P4 is again modified by replacing one of the hydrogens on one of the thienyl rings with a fluorine atom resulting in P5.
Computational Methodologies
Oscillation frequencies are calculated for all optimized geometries and found to be true. We note here that the HOMO and LUMO energies are calculated using the models described below. EA, IP and λ are calculated at the HSE06/6-31G(d,p) level based on neutral and charged optimized geometries.
Theoretical methodology for charge transport properties
Here Vab is the charge transfer integral, λ is the reorganization energy, T is the room temperature and kBand~ are the Boltzmann and Planck constants respectively. As is clear from the expression, the charge transfer rate depends on the charge transfer integral and the reorganization energy. The charge transfer integral describes the strength of electronic coupling between two identical and symmetrical molecules.
Results and discussion
- Optimized geometries and electronic properties of all polymers 37
- Spectral properties
- IPs and EAs
- Reorganization energies
- Charge transfer integrals, rates of diffusion and charge mo-
- Conclusions
In the case of LUMOs, the densities are delocalized over all but one of the donor BDT units to the end point. The data in the table shows that the contributions of BDT/thiophene/triazole units increase as we move towards the center of the tetramers. On the other hand, P7 has the smallest and P1 the largest of the electron transfer rates.
Computational Details
For A1, A5 and A9, the results in Table 4.2 show that the B3LYP functional produces better Eg1 compared to the other functionals. Therefore, the CAM-B3LYP functional, which includes long-range corrections, is used here to handle these ICT excited states of the mixts. Post-processing of excited state calculations to analyze excited state characters and charge transfer lengths is performed using Multiwfn[141].
Results and discussion
Donor SMs
- Molecular geometries in ground state
- Frontier molecular orbitals, open-circuit voltages
- Light absorption properties
This shows that halogen substitution in the lateral side chains has little effect on the electron density distribution of the SMs. Halogen atoms have a crucial effect on the energies of HOMOs and LUMOs of the SMs. ELL values, the energy difference between the donor's LUMO energy and PCBM, are shown in Table 4.4.
A1-A12/PCBM composite systems
- Structures and properties
- Intermolecular charge transfer and charge recom-
Results of TDDFT studies and analysis of the results with Multiwfn software are shown in Table 4.6. In particular, excitation energies of first ICT states, corresponding foscs, charge transfer lengths (lCT) of the twelve composites are plotted. Since the eg,Blend1 values for the blends are almost the same, the difference in the Eb values is due to the IP values as shown in Table 4.7.
Conclusions and outlook
A device based on the donor BDTT, thienothiophene p urate and the benzoxadiazole polymer acceptor[196] was found to have a PCE of 7.05%. As the above discussion shows, the insertion of π-bridge affects the photovoltaic performance of OSCs. Using computational studies based on density functional theory methods, we aim to have a detailed insight into the effect of π-bridge units on the structures of these donors and the photovoltaic properties of OSCs.
Computational Methodologies
All these calculations are performed with the def2-SV(P) basis set using the TURBOMOLE V7.1 software.[147] We denote the above method as RI-PBE-D3/def2- SV(P). Following geometry optimizations, single-point calculations at M06-2X/6-311G(d,p) level in chloroform solvent (denoted as CPCM-M062X/6- 311G(d,p)) are performed using the Gaussian 09 software. M06-2X functional was chosen for the blends as this functional performed well for other donor-acceptor blends in literature. For these donor-acceptor blends, excited states that include charge-transfer states are calculated using the CAM-B3LYP series-separated functional with 6-311G(d,p) basis set (denoted as TD-CPCM-CAMB3LYP/6- 311G(d,p)).
Results and discussion
Ground state molecular geometries
Frontier molecular orbitals and open-circuit voltages
Therefore, the variation of HOMO and LUMO levels with respect to the π-bridges depends on the molecular structure. However, in our case the structure of the tetramer results in an up-shift of the HOMO value. Consequently, its incorporation as a π-bridge is a well-known strategy to lower the HOMO/LUMO levels.[209-212] Also in our case, P5 having thiazole π-bridge units has the deepest HOMO among the tetramers.
Optical absorption and excited-state properties
For the LUMO, the distribution is over the entire molecule except for the terminal BDTT unit. The addition of π-bridges does not change the scenario much, and as shown in Figure C3, similar distributions are observed. In addition, the fosc values of P2-P5 are also larger than those of P1 due to the increased conjugation length.[213] It is also observed that the newly designed tetramers exhibit better η values compared to that of P1.
Structures and properties of the D/A blends, charge transfer
This shows that while the λmax values of the newly designed composites are close to each other, they are blue-shifted with respect to that of P1/PCBM. Excitation energies, corresponding oscillator strengths, ICT and types of excited states of the composite systems P1/PCBM and P2-P5/PCBM are tabulated in table 5.6. Diagonal and off-diagonal elements of the TDM matrix reveal local and charge-transfer characters, respectively.
Rates of charge transfer and charge recombination processes 86
Comparing FuP1 with P1, it is observed that the insertion of the furan units between donor and acceptor results in smaller angles for φ2 and φ3. Our results for φ2 and φ4 showing increased rigidity and flatness of the backbone after the insertion of thiazole π bridge are in agreement. From the above discussion, it can be concluded that the energies of HO-MOs and LUMOs in π-bridged system vary depending on the type of donor and acceptor components of the molecule.
The calculated HOMO and LUMO levels of NDI are also shown in Figure 6.3 and it is clear that the HOMO and LUMO energies of all oligomers are appropriately positioned with respect to the NF acceptor energy levels. The excitation energies of the ICT first states (eg, blendICT ), the corresponding foscat and lCT are listed in Table 6.6.
