Exceptionally high charge mobility in phthalocyanine-based poly(benzimidazobenzophenanthroline)-ladder-type two-dimensional conjugated polymers

Two-dimensional conjugated polymers (2DCPs), composed of multiple strands of linear conjugated polymers with extended in-plane π-conjugation, are emerging crystalline semiconducting polymers for organic (opto)electronics. They are represented by two-dimensional π-conjugated covalent organic frameworks, which typically suffer from poor π-conjugation and thus low charge carrier mobilities. Here we overcome this limitation by demonstrating two semiconducting phthalocyanine-based poly(benzimidazobenzophenanthroline)-ladder-type 2DCPs (2DCP-MPc, with M = Cu or Ni), which are constructed from octaaminophthalocyaninato metal(ii) and naphthalenetetracarboxylic dianhydride by polycondensation under solvothermal conditions. The 2DCP-MPcs exhibit optical bandgaps of ~1.3 eV with highly delocalized π-electrons. Density functional theory calculations unveil strongly dispersive energy bands with small electron–hole reduced effective masses of ~0.15m0 for the layer-stacked 2DCP-MPcs. Terahertz spectroscopy reveals the band transport of Drude-type free carriers in 2DCP-MPcs with exceptionally high sum mobility of electrons and holes of ~970 cm2 V−1 s−1 at room temperature, surpassing that of the reported linear conjugated polymers and 2DCPs. This work highlights the critical role of effective conjugation in enhancing the charge transport properties of 2DCPs and the great potential of high-mobility 2DCPs for future (opto)electronics.


S3
Theoretical calculations of model compounds were performed using the Gaussian 16 program. 1 The B3LYP functional was used for geometry optimization in the ground state.
The 6-31G (d) basis set was used. The dispersion correction was conducted by Grimme's D3 version with the BJ damping function. 2 All geometry optimization was done in the gas phase.
For transition state (TS) calculation, all the structures were optimized in gas phase by using B3LYP level of density functional theory with the 6-31G* basis. To confirm the accuracy of the TS, frequency calculation was performed. The Gibbs free energies of reaction (∆ r G o ) at room temperature (298 K) can be calculated using following equations 3 : where H corr is the thermal correction to Enthalpy; E tot is the correction to the internal thermal energy; k B is the Boltzmann constant; T is the temperature; G corr is the thermal correction to Gibbs free energy (thermal Free Energies); S tot is the correction to the internal Entropy; ε 0 is the total electronic energy and nuclear repulsion energy. In our case, the isomerization process represents the reaction.

Structural modeling and Pawley refinement of 2DCPs
Density functional theory (DFT) calculations were carried out using the Vienna ab-initio Simulation Package (VASP) 4,5 version 5.4.1. The electronic wave-functions were expanded in a plane-wave basis set with a kinetic energy cutoff of 500 eV. The geometry optimization convergence was set to forces acting on the ions were smaller than 0.015 eV A -1 .
Electron-ion interactions were described using the projector augmented wave (PAW) method 6,7 . Generalized gradient approximation (GGA) 8 of the exchange-correlation energy in the form of Perdew-Burke-Ernzerhof (PBE) was applied 9 . We used DFT+U approach to describe the localized d-orbitals of Cu and Ni ions. The effective Coulomb (U) and exchange (J) terms were set to 4 and 1 eV, respectively 10 , such approach was already S4 successfully applied for similar systems 11 . Monkhorst-Pack Gamma-centered grid 12 with 2×2×1 dimension was used for K-point sampling of the Brillouin zone for the monolayer during the geometry optimization and 4×4×1 for band structure calculations. In the computational protocol for the three-dimensional (3D) stacking of the studied 2DCPs, the K-point grid dimension was changed to 2×2×5 for the geometry optimization and 4×4×10 for the band structure calculations, and Grimme-D2 correction for the interlayer dispersion interactions was applied 13 . In order to determine the full high-symmetry K-points in the Brillouin zone a VASPKIT 14 code for pre-and post-processing of the VASP calculated data was used. The PBE-D2 method can lead to a relative error up to 3% in lattice parameter for metal-organic frameworks 15 . Thus, an error of 3% was considered during calculating the PXRD patterns of the final structures. The 2DCP monolayer was modeled by adding a large vacuum space, 10 Å, in the direction normal to the monolayer. The unit cell used in the calculations of the 3D models contains two layers. All the models were subject of full geometry optimization (cell parameters and ionic positions). The corresponding electronic band structures were evaluated along the Γ-X-M-Γ and Γ-X|Y-Γ-Z|R 2 -Γ-T 2 |U 2 -Γ-V 2 path in the Brillouin zone for the monolayer and multilayered structures, respectively. The effective masses for the electrons and holes were calculated by parabolic fit of the VBM and CBM using SUMO Python toolkit 16 or manually in the case of nearly degenerated electronic states (see details in Supplementary Tables 1 and 2).
For Pawley refinement, the unit cells of the models were refined in the 2θ range ca.
2.5−40° with the experimentally obtained PXRD pattern in the Reflex module of the BIOVA Materials Studio 2020 with fixed atom coordinates.

Section B. Materials and Synthetic Procedures
All the solvents and reagents were purchased from commercial suppliers and used without purification. Octaaminophthalocyaninato metal(II) (4-M) was synthesized according to a literature procedure. 17 Naphthalenetetracarboxylic dianhydride (1) and

Supplementary Scheme 3. Competitive reactions between 5, 2 and 2-Me.
Competitive reactions between the anhydride 5 (1 equiv) and two o-diamines of 2 (1 equiv) and 4,5-dimethyl-1,2-phenylenediamine (2-Me, 1 equiv) are examined at 90 °C for 6 h. (with M = Zn). The program ACD/Labs was used for the prediction. 22 6 was not detected by MALDI-TOF MS, which suggests that such a large and rigid ring-fused compound is not able to fly during the measurement. It's noted that the synthesized 2DCP (2DCP-ZnPc) from 7-Zn was barely crystalline, which can be ascribed to the catalytic ability of Zn 2+ in this condensation reaction 19 to disturb the interlayer arrangement of phthalocyanines. The Raman spectra present peaks matching well with those of the commercial copper phthalocyanine (CuPc) and BBL 1DCP. As is known, the double-integration (DI) of an EPR spectrum is proportional to the magnetic susceptibility, the temperature dependence of which can indicate whether a spin is localized or not: the susceptibility of localized spins is temperature-dependent while it is not for delocalized spins. 29 For 2DCP-NiPc, the DI is calculated and plotted versus temperature in Supplementary Figure 44b. It can be seen that DI depends strongly on temperature.
Moreover, the DI can be well fitted to the Curie-Weiss law which also describes temperature dependence of magnetic susceptibility of localized spins. In a word, these data indicate that the EPR signal of the sample mainly comes from localized spins, which do not delocalize prior to external excitation (e.g., optical excitation).    The 2DCP-NiPc film is continuous, which also contains many big 2DCP-NiPc particles on top of the bottom film (Supplementary Figure 52). However, many pinholes are observed in the 2DCP-CuPc film, which indicates higher defect density than that in the 2DCP-NiPc   To provide more insights, we have performed fluence-dependent THz photoconductivity measurements. We found that, in our available pump fluence range, the photoconductivity of (Supplementary Figure 60a,c) increases with the pump fluence, while the normalized dynamics overlap within the experimental error (Supplementary Figure 60b,d).

2DCP-MPcs
This result indicates that the charge carrier lifetime, or equivalently the decay rate, does not depend on the pump fluence in the pump-fluence range used in the study. Based on the data, we can safely conclude that the monomolecular recombination e.g., trap-assisted recombination, dominates the charge carrier decay. Given the extremely high charge carrier mobility, we exclude geminate charge recombination as the main recombination channel. We investigated the charge transport properties of 2DCP-MPc in power form: a sample geometry that has been widely used to investigate 2D c-COFs by THz spectroscopy. 17,30,34 The 2DCP-MPc powder samples were first sandwiched between two fused silica substrates to form ∼10s of µm thick thin films. By measuring the transmitted THz traces with and without photoexcitation in the time domain (E pump (t) and E 0 (t)) and further converting them into the frequency domain by Fourier transform (E pump ( ) and E 0 ( )), we can obtain their complex photoconductivity ( ( )) following the thin-film approximation: 0 ( ) where Z 0 = 377 Ω is the impedance of free space, 1 and 2 are the refractive indices of the media before and after the sample, and is the excitation thickness. We use = 1 to obtain the sheet complex sheet photoconductivity ( ( )).
( ) of 2DCP-MPc powder samples was fitted by the DS model, which provides a phenomenological description of confined charge transport in the material: where c is the backscattering probability and is the DS relaxation time. Here we use the DS relaxation time to approximate the Drude scattering time, which is in reality a function of both the DS relaxation time and diffusion time 35 .
Photoconductivity measurements yield spectral responses that differ from the Drude behavior (Supplementary Figure 62b).

Section D. Supplementary Tables
Supplementary Table 1. Effective masses of 2DCP-MPc monolayers obtained from band structure calculations. Different fitting methods were used to obtain the effective masses.

2DCP-MPc
Effective masses (m 0 ) at different K-paths [a] Note that ℎ * is mathematically negative. However, to avoid misunderstanding in the calculation, we use and present all ℎ * in this work in the absolute value.  We describe the photoconductivity decay of 2DCP-MPc films by a bi-exponential function as follows:

Supplementary Table 4. A comparison of charge carrier mobilities of 2DCP-MPcs (films and powders) with 1DCPs (including graphene nanoribbons) and other organic 2D
framework materials (e.g., COFs, MOFs) measured by THz spectroscopy at ambient temperature.
In our work, we estimate the charge carrier mobility at the dc limit. For Drude-Smith-type charge transport, this reads: = * (1 + ). For Drude-type transport, this reduces to = * (as c = 0). We provide a comprehensive summary of values together with and as well as the inferred * from calculation. The stacking modes of the layer-stacked polymers and the theoretical calculation methods for effective mass calculation are also offered, i.e., AA, AA-s (AA-slipped), ABC. Note that most polymers were synthesized as powder samples. Only the film samples are labeled film.
As non-contact THz spectroscopy was employed to reveal the intrinsic charge carrier  [b] Reduced m* of electron and hole.