Hexagonal 2D covalent organic frameworks from nonpolar and symmetric electron-accepting substituents for electron transport layers in near-infrared PeLEDs

Abstract

We conducted high-throughput calculations on the structure library of two-dimensional covalent organic frameworks (2D COFs), with the aim of finding new candidate materials as electron transport layers (ETLs) for the high-performance perovskite light-emitting diodes (PeLEDs). Starting with nearly 400 unique 2D COFs with hexagonal (hcb) topology, 23 candidates for β-ketoenamine linked 2D COFs composed of 1,3,5-triformylphloroglucinol (Tp) and linear diamines are identified by band structures. Interestingly, 2 β-ketoenamine linked 2D Tp-DAAQ and 2D Tp-DABDA with electron-accepting substituents, are the most promising candidates due to the optimal band edge and effective mass. Further, the nonpolarity of the Tp-DAAQ molecule makes it a more favorable choice for the ETL, as confirmed by nonadiabatic molecular dynamics that 2D Tp-DAAQ with anthraquinone diamine linker has a longer e–h nonradiative recombination time. This work provides a paradigm for the design of high-performance ETLs.

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1. Introduction

Perovskite light-emitting diodes (PeLEDs) have experienced rapid development in recent years and are approaching the efficiency of organic light-emitting diodes (OLEDs), showing great potential for commercialization.^1–7 However, nonradiative recombination is encountered in carrier transport, resulting in energy loss.^8,9 Currently, the development of ideal electron transport layers (ETLs) for PeLEDs is an important research direction to improve device performance,^10,11 in terms of its important role in lowering the potential barrier for electron injection from the cathode into the emitting layer (EML).^12,13 Presently, ZnO is commonly used as an ETL material due to its ease of preparation and processing, and its relatively low cost.^14,15 However, the energy level mismatch and mismatched mobility with hole transport layer (HTL) cause electron and hole transport imbalance and nonradiative recombination. Many efforts have been devoted to finding ETLs with suitable energy level and mobility.

To improve the device performance, the ETLs for PeLEDs need to meet the following requirements: (1) possess similar mobility as HTL; (2) the conduction band minimum (CBM) is higher than or close to the CBM of EML, while the valence band maximums (VBM) is much lower than that of EML; (3) have stable physicochemical properties. Two-dimensional covalent organic frameworks (2D COFs) have a regular, conductive π–π stacking structure, leading to higher carrier mobility.¹⁶ In addition, through the interfacial modulation, the chemical or physical properties of the interface of 2D COFs can be modified, and thus have potential to achieve better band alignment, and display superior charge transfer pathways. These advantages make 2D COFs as the promising candidates for the ETLs. Previous studies have shown that five possible topologies in the case of 2D covalent plane, namely hexagonal (hcb),¹⁷ kagome (kgm),¹⁸ tetragonal (sql),¹⁹ rhombille (kgd),²⁰ and triangular (hxl).²¹ In particular, 2D COFs with hcb topology usually have good electrical conductivity compared to other topologies due to their graphene-like planar structure, in which carbon atoms are arranged in hexagonal shape to form highly conjugated π orbitals.^22–24 What new properties would these materials with hcb topology have? To our knowledge, attempts in this area have never been reported systematically.

Here, we screened close to 400 2D COFs with hcb topology in the core-cof/CoRE-COF-Database^25,26 to find potential candidates for ETLs in PeLEDs. After systematic studies, β-ketoenamine linked candidates 2D Tp-DAAQ (2,6-diaminoanthraquinone)²⁷ and 2D Tp-DABDA (2,5-diaminobenzene-1,4-disulfonic acid),²⁸ consisting of Tp (1,3,5-triformylphloroglucinol) and different linear diamine linkers, stood out among nearly 400 materials. In both 2D Tp-DAAQ and 2D Tp-DABDA, the linear diamine linkers have electron-accepting substituents =O and –SO₃H, with a low VBM and a suitable CBM. Furthermore, the dipole moment (EDM) of the monomer molecule Tp-DAAQ is zero making it a more favorable material for the ETL. Nonadiabatic molecular dynamics (NAMD) confirms that 2D Tp-DAAQ with anthraquinone linear diamine linker has a longer e–h nonradiative recombination time scale compared to 2D Tp-DABDA and is a good candidate for ETL in PeLEDs.

2. Computational details

All the ground state properties are calculated using the PWmat²⁹ and Vienna Ab Initio Simulation Package (VASP).³⁰ Electron–ion interactions are described by using the all electron projector augmented wave (PAW) method.³¹ The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional is used to approximate correlation of electrons within the many-body wave function.³² Since the PBE generalization will underestimate the band gap, the Heyd–Scuseria–Ernzerhof (HSE06) functional is used to calculate the more accurate energy band structures.³³ The Hefei-NAMD software package is used to calculate excited state processes.³⁴ For more details on the calculation, see the ESI.†

3. Result and discussion

As a transport layer material in PeLEDs, a suitable band structure and matching energy levels with EML are essential. We screened close to 400 2D COFs with hcb topology connected by five different linkages, namely boronate anhydride, boronate ester, nitrile cyclotrimerization, imine, and hydrazone,³⁵ as shown in Fig. 1. Among them, hydrazone-linked 2D COF materials undergo spontaneous structure change during the DFT optimization, which implies that these are unstable, and some examples are listed in Fig. S1.† For the other four modes, the VBM and CBM of some 2D COFs are flat bands, which lead to an infinite effective mass of carriers and cannot be used as transport layer materials in PeLEDs. Several representatives of each linked mode are selected as examples (Fig. S2–S5†). There is an unexpected finding in the imine-linked 2D COFs that the CBMs of β-ketoenamine linked 2D COFs³⁶ consisting of linear diamine linkers with the Tp are not flat bands, which have potential as ETL materials, as displayed in Fig. S6–S9.†^{27,28,37–51} Eventually, we screened out 23 2D COFs with different diamine linkers (Fig. 1). For the convenience of the later discussion, we use Tp + linker to name the 2D COF materials, and the full names of linkers are given in Table S1.† The lattice constants of these 23 2D COFs are listed in Table S2.† In addition to the above 2D COFs, another class of more recently studied materials are sp² carbon conjugated 2D COFs, as shown in Fig. S10.† The calculated lattice parameters are shown in Table S3.† Band structure plots in Fig. S11† indicate that the VBMs and CBMs of these kinds of materials are flat bands with infinite effective mass, and are therefore unsuitable as ETLs in PeLEDs.

Fig. 1 High-throughput computational screening model. Structures downloaded from the experimental library are sequentially passed through multiple computational filters, such as cohesive energies, energy bands, and carrier dynamics, in order to remove materials unsuitable for use as ETLs in PeLEDs and ultimately screen out 2 potential candidates that could be ETLs.

Before studying their electronic properties, we first evaluate the stability of these 23 2D COFs by calculating the cohesive energy (E_coh). Taking 2D Tp-DAAQ (C₆₀H₃₀N₆O₁₂) as an example, the equation is E_coh = (60E_C + 30E_H + 6E_N + 12E_O − E_C60H30N6O12)/108, where E_C, E_H, E_N, E_O, and E_C60H30N6O12 are the total energies of a single C atom, a single H atom, a single N atom, a single O atom, and E_C60H30N6O12 monolayer, respectively. According to the definition, a more positive value of E_coh indicates a stronger bonding. The cohesive energies of 23 β-ketoenamine linked 2D COFs are calculated within 6.5–7.5 eV per atom, as shown in the insert of Fig. 2, which is greater than the 3.71 eV per atom for silicon.⁵² Although the relative stability of these materials cannot be directly determined by comparing their cohesive energies, the more positive E_coh clearly demonstrate that these 2D COFs are strongly bonded network.

Fig. 2 The energy levels of different materials acting as ETLs (23 β-ketoenamine linked 2D COFs) and EML (CsPbI₃) in PeLEDs. The inset shows the cohesion energies of 23 β-ketoenamine linked 2D COFs.

In PeLEDs, the band edges affect carrier transport and recombination significantly. To achieve efficient electron transport, the CBM of the ETL should be higher or closer to that of the EML, while its VBM must be much deeper than that of the EML to prevent holes from entering the ETL through the EML. Thus, the band edge is the second criterion of screening. PBE functional will underestimate the band gap, so the more accurate HSE06 is used to calculate the band edges, as shown in Fig. 2. The screening results show that 2D Tp-DAAQ and 2D Tp-DABDA, consisting of diamine linkers with symmetrical electron-accepting substituents, not only have the suitable CBMs to transport electrons, but also the quite deep VBMs can effectively block the passage of holes, which is comparable to that of ZnO (VBM of −7.39 eV, CBM of −4.2 eV).⁵³ As stated above, the β-ketoenamine linked 2D COFs consisting of diamine linkers with symmetrical electron-accepting substituents can effectively reduce both VBM and CBM, and have better matching energy levels with the EML.

What kind of interesting electronic properties would this particular structure have? To answer this question, we calculated their highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) in terms of the minimum construction unit, with the HOMO–LUMO gaps of 2.92 and 3.66 eV in Tp-DAAQ and Tp-DABDA, respectively (Fig. 3a), and band edges enclosing the corresponding 2D COFs, as displayed in Fig. 3b and c (left panel). The electrons of Tp-DABDA on HOMO and LUMO are distributed throughout the molecule. In Tp-DAAQ, electrons are more localized in the center at HOMO, while electrons are dispersed along the chain at LUMO, and this large difference between the HOMO and LUMO wave functions can facilitate the generation of intramolecular charge transfer.⁵⁴ We further calculated the EDMs and obtained values of 0 and 2.32 Debye in Tp-DAAQ and Tp-DABDA, respectively, indicating that Tp-DAAQ is a nonpolar molecule while Tp-DABDA is a polar molecule (Fig. 3a). Nonpolar molecules have no significant charge difference in chemical bonding, so they are not strongly affected by the electric field during the transport between electrons and holes, which can reduce the scattering of carriers and improve the efficiency of electron and hole transport. To gain more insight into the electronic properties of 2D Tp-DAAQ and 2D Tp-DABDA, we calculated their projected density of states (PDOS). As can be seen from the Fig. 3b and c (right panel), the VBM of 2D Tp-DAAQ is contributed by C-2p, O-2p, and N-2p, and the CBM is provided by C-2p and O-2p. In 2D Tp-DABDA, the VBM and CBM are both provided by C-2p, O-2p, and N-2p. These results are consistent with the calculation of the projected energy bands (Fig. S12 and S13†).

Fig. 3 (a) Calculated HOMO/LUMO of Tp-DAAQ (left panel) and Tp-DABDA (right panel) molecules. Red values represent dipole moments (EDMs). (b) Band structure (left panel) and density of states (right panel) in 2D Tp-DAAQ. (c) Band structure (left panel) and density of states (right panel) in 2D Tp-DABDA. VBM is set to zero. (d) Calculated VBMs in 2D Tp-DAAQ with different electron-accepting substituents.

The other question that arises is whether all β-ketoenamine linked 2D COFs with symmetric electron-accepting substituents in the linear diamine linkers are likely to be suitable band edges for PeLEDs? To address this query, we calculated their band edges by replacing =O with substituents –CN, –NO₂, and –F in 2D Tp-DAAQ, as shown in Fig. 3d. This presents an inverted volcanic relationship, where the VBM is the lowest and the band gap is the largest when the electron-accepting substituent is =O. While the systems with substituents –CN, –NO₂, and –F, the positions of VBMs and CBMs are not suitable for ETLs (Table S4†). We have studied the effect of electron-accepting substituents in the diamine linkers on the band edge, so how about the band edges of 2D COFs of the diamine linkers with electron-donating substituents? To this end, –OH and –CH₃ are used to replace =O in the diamine linker in 2D Tp-DAAQ, thus calculating their band edges to answer this question. The calculated VBMs and CBMs are listed in Table S4,† and excessively high VBMs make them unsuitable for ETLs. The above results demonstrate that β-ketoenamine linked symmetric 2D Tp-DAAQ and 2D Tp-DABDA are potential candidates for ETLs in PeLEDs.

Mobility is also a factor that affects transport efficiency.¹⁰ Excessive mobility can cause excess electrons to aggregate at the interface of ETL/EML, while low mobility cannot transport electrons. Because the systems are large, calculating their mobility is expensive. Accordingly, we evaluate their mobility by calculating the effective mass. The larger the effective mass, the smaller the mobility. Calculations show that the effective masses of 2D Tp-DAAQ and 2D Tp-DABDA are 7.80 and 3.89 m₀, respectively, which are greater than the widely used effective mass of 2.95 m₀ of monolayer ZnO (Fig. S14†). The reduced mobility compensates for the high mobility of ZnO and reduces the carrier aggregation at the ETL/EML interface, resulting in an increase of carrier recombination.

In general, more donor is more favorable for transporting electrons in the donor–acceptor structures.^55–58 However, if the donor–acceptor structure is used as ETLs in PeLEDs, two conditions need to be satisfied simultaneously: (1) the energy level should be matched with that of the perovskite; (2) the transport rate should be similar to that of the hole transport rate. The only ones that fulfill the above two conditions are 2D Tp-DAAQ and 2D Tp-DABDA of the donor–acceptor structures.

To understand the charge transfer between the ETL and EML interfaces, we built an ETL/EML heterojunction to calculate its charge transfer. CsPbI₃, as a direct band gap material, possesses advantages such as low density of defect states and is a potential high-quality EML material in near-infrared PeLEDs (Fig. 2).^59,60 Due to the large size (632 atoms) of 2D Tp-DAAQ/CsPbI₃ (Fig. S15†), it is impractical to perform calculations on it. Accordingly, only 2D Tp-DABDA/CsPbI₃ heterojunction is constructed as an example to study the transport efficiency. In 2D Tp-DABDA/CsPbI₃ heterojunction, van der Waals interactions between the interfaces are found due to the Pb–O distance (3.69 Å) being larger than the covalent radii of Pb (1.46 Å) and O (0.66 Å)⁶¹ and approximately equal to the van der Waals radii of Pb (2.3 Å) and O (1.4 Å).⁶² See ESI† for computational details and stability discussions, including electron localization function (ELF) and deformation charge density (DCD) (Fig. S16a and b†).

To intuitively determine the charge transfer at the heterojunction interface, the plane-averaged charge-density difference (Δρ) is calculated along the z direction as Δρ = ρ_{heterojunction} − ρ_CsPbI3 − ρ_Tp-DABDA, where ρ_{heterojunction}, ρ_CsPbI3, and ρ_Tp-DABDA represent the plane-averaged charge-densities of heterojunction and isolated CsPbI₃ and 2D Tp-DABDA, respectively. Δρ > 0 for electron accumulation; Δρ < 0 for electron depletion. Fig. S14d† shows the direction of electron transport from 2D Tp-DABDA to CsPbI₃ at the 2D Tp-DABDA/CsPbI₃ interface. The above analysis confirms that 2D Tp-DAAQ and 2D Tp-DABDA do have potential as ETLs in near-infrared PeLEDs.

Suppression of e–h nonradiative recombination is an effective way to obtain high-performance PeLEDs under the premise of carrier injection balance.⁶³ When an electron or hole is excited to an excited state, the nonradiative recombination will occur by the action of a single particle such as a phonon. However, the process of nonradiative recombination is complex, including generalized recombination dynamics of the photo-generated carriers and interfacial induced dynamics.⁶⁴ Understanding the origin of nonradiative recombination and suppressing it is key to achieving high-performance PeLEDs. Here, we investigated the interface-induced nonradiative recombination in 2D Tp-DAAQ and 2D Tp-DABDA by the NAMD method using Hefei-NAMD software. Since HSE06 has the same band gap trend as the PBE (Table S2†), excited state calculations and discussions are conducted using the PBE approach to minimize the computational cost. The time scales of e–h nonradiative recombination for 2D Tp-DAAQ and 2D Tp-DABDA are 8.24 and 0.88 ns, respectively, as shown in Fig. 4a. e–h recombination time scales (τ) are fitted using an exponential function P(t) = exp(−t/τ). In NAMD simulations, the main factor of e–h recombination time is the nonadiabatic coupling (NAC), the larger the NAC, the faster the excited state process.³⁴ The equation is given by:

where 〈φ_j|∇_RH|φ_k〉 is electron–phonon (e–ph) coupling strength, ε_k − ε_j is the energy difference between the band gap, and Ṙ is the velocity of the nuclei. These three factors simultaneously determine the value of NAC. Firstly, the band gaps of 2D Tp-DAAQ and 2D Tp-DABDA are similar, and such a small band gap difference may not affect the e–h recombination time scale. Secondly, the Fourier transform (FT) diagram can reflect the e–ph information between different energy states, that is, the corresponding 〈φ_j|∇_RH|φ_k〉. The FT spectra of the energy gap between the CBM and VBM states of 2D Tp-DAAQ and 2D Tp-DABDA with time are given in Fig. 4c and d. Note that both systems have only small low-frequency phonons, which leads to significantly smaller nuclear velocities, which in turn reduces the NAC and the e–h nonradiative recombination time. However, the amplitude of energy level oscillation in 2D Tp-DABDA is large (Fig. 4f), leading to the stronger e–ph and thus accelerating e–h nonradiative recombination. In contrast, the energy oscillation amplitude is particularly small in 2D Tp-DAAQ (Fig. 4e), which leads to a longer recombination time scale. This is because the 2D Tp-DAAQ structure is quite flat and its conjugation effect is stronger than that of 2D Tp-DABDA. Thus, the oscillation amplitude of 2D Tp-DAAQ is significantly weaker. After calculation, the NAC values obtained for 2D Tp-DAAQ and 2D Tp-DABDA are 0.98 and 2.32 meV, respectively, as shown in Fig. 4b.

Fig. 4 (a) e–h recombination time scale in 2D Tp-DAAQ and 2D Tp-DABDA. (b) Nonadiabatic coupling (NAC) and decoherence time (τ_ϕ) in 2D Tp-DAAQ and 2D Tp-DABDA. Fourier transform for (c) 2D Tp-DAAQ and (d) 2D Tp-DABDA. Energy evolution of KS states in (e) 2D Tp-DAAQ and (f) 2D Tp-DABDA.

Since the studied e–h nonradiative recombination times are generally longer, the dephasing time (τ_ϕ) can have a significant effect on them.⁶⁵ The larger the τ_ϕ, the faster the dynamics process and the faster the nonradiative recombination. There are many methods to calculate τ_ϕ, here, the DISH method is used to calculate the quantum dephasing time in both systems. The calculated τ_ϕ of 2D Tp-DAAQ and 2D Tp-DABDA are 20 and 5.69 fs, respectively (Fig. 4b). By comparing the results in Fig. 4a, it can be found that the determinant of NAC is greater than the effect of τ_ϕ in this system. Calculations based on ground and excited states of 2D COFs confirm that β-ketoenamine linked 2D Tp-DAAQ with anthraquinone diamine linker is the most promising ETL candidate for near-infrared PeLEDs.

4. Conclusion

In summary, we propose a material design guide to discover the ETLs as near-infrared PeLEDs by high-throughput and NAMD simulations, as demonstrated in β-ketoenamine linked 2D COFs with an anthraquinone linear diamine linker. We first perform computational screening in the core-cof/Core-cof-Database, a large experimental structure library containing 400 2D COF crystal structures with hcb topology. By calculating the energy band structures, we identify a total of 23 possible ETL candidates consisting of Tp and linear diamines in near-infrared PeLEDs. Among them, 2D Tp-DAAQ and 2D Tp-DABDA with symmetric electron-accepting substituents can significantly reduce the VBMs and CBMs, resulting in them have more suitable band edges. Furthermore, the EDM of Tp-DAAQ molecule is 0 debye, while the EDM of Tp-DABDA molecule is 2.3 debye, making Tp-DAAQ more likely to become an ETL material. Finally, the NAMD calculations show that the e–h recombination time scales of 2D Tp-DAAQ and 2D Tp-DABAQ are 8.24 ns and 0.88 ns, respectively, which indicates that 2D Tp-DAAQ with anthraquinone diamine linker is the most promising candidate for ETL in near-infrared PeLEDs.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (No. 52202247, 22279059) and the Training Program of the Major Research Plan of the National Natural Science Foundation of China (91964103), the Fundamental Research Funds for the Central Universities (No. 30921011106).

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05200a

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