Effect of the Push–Pull Electronic Structure of Nonfullerene Acceptor Molecules on the Interfacial Charge Dynamics in Heterojunction Organic Solar Cells

Abstract

Nonfullerene acceptor (NFA) molecules have attracted significant attention in high‐efficient heterojunction organic solar cells (OSCs) due to their push–pull electronic structures. Herein, using a universal quantum model for an organic donor/acceptor interface composed of a polymer donor and an NFA molecule, effect of the NFA molecular electron push and pull ability on the interfacial charge dynamics in the case of donor excitation is focused on. It is confirmed that energy and charge transfer coexist and compete during the interfacial charge dynamics, by which an interfacial hybrid state is created, and the quantitative correlations of the generation rates for different component states (e.g., donor exciton, acceptor exciton, and charge transfer state) with the NFA molecular electron push and pull ability are separately clarified. It is found that, by strengthening the NFA molecular electron push ability, competition between charge and energy transfer presents a nonmonotonous behavior; by strengthening the electron pull ability, charge transfer is always promoted and energy transfer is inhibited. This study provides a microscopic understanding for the interfacial charge dynamics modulated by tuning the NFA molecular push–pull electronic structure and thus sheds light on further improving the performance of heterojunction OSCs by rational designs of NFA molecules.

Introduction

Benefitting from the development of nonfullerene acceptors (NFAs), the power conversion efficiency (PCE) approaching 19% has been achieved in single-junction organic solar cells (OSCs).^[1,2] Compared with fullerene acceptors (FAs), NFAs present different aspects of advantages, such as the tunable energy levels,^[3,4] strong absorption in the visible-to-near-infrared wavelength range,^[5,6] and various molecular aggregation structures.^[7,8] Despite molecular diversity, most of the high-performance NFA molecules (e.g., ITIC and Y6) have push–pull electronic structure, where the central group has stronger electron push ability, the terminal groups have stronger electron pull ability, and sometimes π-bridges connecting the central group and the terminal groups.^[9,10] Up to now, different strategies have been explored to strengthen the electron push ability of the central group, such as extending the conjugation length,^[11,12] introducing strong electron push group (e.g., alkoxy or alkyl amino side groups),^[13,14] and inserting quinone resonance structure.^[15] To strengthen the electron pull ability of the terminal groups, one usually introduces halogen atoms (e.g., fluorine and chlorine).^[16–19] The push–pull electronic structure of NFA molecules can result in their intramolecular charge transfer character, reducing the binding energy of their excited states.^[20–23] Recent works have successively reported that the excited states in NFA molecules might behave in intra- and intermolecular charge transfer (CT) states,^[24,25] which can dissociate into free charges even at room temperature without the assistance of a donor/acceptor (D/A) energy offset.^[24–26]

In FA-based OSCs, we know that polymer donors usually act as the light-absorbing components due to the poor absorption of FA molecules,^[27] such that charges mainly originate from the donor excitation via experiencing the interfacial electron transfer into FA molecules.^[28] In NFA-based OSCs, polymer donors and NFA molecules usually have complementary absorption; thus, charge generation presents diverse channels. When the donor molecule is photoexcited, the excited electron transfers into NFA molecule.^[20,22,23] When NFA molecule is photoexcited, the excited hole transfers into donor molecule.^[10,21,25] Recently, a third charge generation channel was revealed in the case of donor excitation,^[29–34] that is, energy transfer (or exciton transfer) into NFA molecule first occurs due to its smaller energy gap compared with the donor molecule. Up to now, it has been confirmed that the interfacial energy transfer from the donor to NFA molecule coexists and competes with charge transfer.^{[29,30,32,33]} In addition, following energy and charge transfer, there appears the hybridization of exciton and CT state at a D/A interface.^[35–37] Synergistic effect of the interfacial energy and charge transfer (or the rational hybrid between exciton and CT state) has been reported to promote the charge generation and reduce the nonradiative voltage loss in NFA-based OSCs.^[35,36]

An effective strategy to modulate the interfacial charge dynamics is to tune the push–pull electronic structure of an NFA molecule, including the electron push ability of the central group and/or the electron pull ability of the terminal groups.^[37–41] For instance, using the fluorination for the terminal groups of NFA molecules, Xu et al. reported that the generation rate of CT state increases in its hybridization with the local exciton state, thus facilitating charge generation.^[37] The experimental results by Li et al. also confirmed that the fluorinated NFA molecule favors the charge transfer in OSCs.^[41] Despite these advances, how to optimize the interfacial charge dynamics by rational designs of NFA molecular push–pull electronic structures remains an open question to further improve the performance of NFA-based OSCs. In view of this, we focus on the microscopic understanding for the interfacial charge dynamics modulated by tuning the push–pull electronic structure of an NFA molecule and thus clarify the quantitative correlation of the hybrid exciton and CT state with different NFA molecular push–pull electronic structures.

Experimental Section

With the rapid development of NFA molecules in applications of OSCs, different theoretical models and methods have been used to study their unique excited state and charge characteristics.^{[21,24,26,42,43]} For instance, by density functional theory (DFT) and time-dependent DFT (TD-DFT) methods, Cui et al. systematically investigated the structure–property relationship and excited-state CT characteristics based on two types of NFA molecules.^[42] In addition, Zhu et al. investigated the effect of different intermolecular aggregations on the exciton binding energy in NFA molecules by a self-consistent quantum mechanics/embedded charge approach.^[21] Recently, by emphasizing the intramolecular push–pull electronic structure and intermolecular aggregation of typical NFA molecules, we theoretically proposed a universal synergistic charge transfer model incorporating both the intra- and intermolecular pathways.^[24,43] In this work, to clarify the effect of the NFA molecular push–pull electronic structure on the interfacial charge dynamics, we further construct an organic D/A interface composed of a polymer donor and a NFA molecule (see Figure 1a), where the quasi-1D-conjugated skeleton of the two molecules and the intramolecular push–pull electronic structure of NFA molecule are emphasized. The molecular chain with sites 1–92 represents a polymer donor and the chain with sites 93–128 an NFA molecule. Figure 1b schematically describes the molecular structure of a typical NFA molecule, consisting of a central group (C), two π-bridges (π), and two terminal groups (T).

[IMAGE OMITTED. SEE PDF]

For the modeled polymer donor and NFA molecule, we used an extended version of the 1D Su–Schrieffer–Heeger (SSH) tight-binding model to describe their electronic and lattice features. The total Hamiltonian consisted of intramolecular (H_intra) and intermolecular parts (H_inter). H_intra can be expressed as the sum of H_i,intra1$H_{\text{intra}}=\sum _i{H}_{i,\text{intra}}=\sum _i(H_{i,\text{elec}}+H_{i,\text{latt}})$

H_i,elec denotes the electronic Hamiltonian of one molecule, where i represents the molecular index. Due to the homogeneous electronic structure of polymer donor, $H_{\mathrm{D},\text{elec}}$ is expressed as2$\begin{array}{c}{H}_{\mathrm{D},\text{elec}}=\sum _{n,\mathrm{s}}{\Delta }_{\mathrm{D}}{C}_{\mathrm{D},n,\mathrm{s}}^{+}{C}_{\mathrm{D},n,\mathrm{s}}-\sum _{n,\mathrm{s}}\left[t_0-{\alpha }_{\mathrm{D}}(u_{\mathrm{D},n+1}-u_{\mathrm{D},n})-{(-1)}^n{t}_e\right]\\ (C_{\mathrm{D},n+1,\mathrm{s}}^{+}{C}_{\mathrm{D},n,\mathrm{s}}+C_{\mathrm{D},n,\mathrm{s}}^{+}{C}_{\mathrm{D},n+1,\mathrm{s}})\\ +U\sum _n\left(C_{\mathrm{D},n,\uparrow }^{+}{C}_{\mathrm{D},n,\uparrow }-\frac{1}{2}\right)\left(C_{\mathrm{D},n,\downarrow }^{+}{C}_{\mathrm{D},n,\downarrow }-\frac{1}{2}\right)\\ +V_{\parallel }\sum _n(C_{\mathrm{D},n}^{+}{C}_{\mathrm{D},n}-1)(C_{\mathrm{D},n+1}^{+}{C}_{\mathrm{D},n+1}-1).\end{array}$

For the electronic Hamiltonian ($H_{\mathrm{A},\text{elec}}$) of an NFA molecule, we focused on its push–pull electronic structure, divided into three parts.3$H_{\text{A,elec}}=H_{\text{A,elec}}^{\mathrm{C}}+H_{\text{A,elec}}^{\text{π}}+H_{\text{A,elec}}^{\mathrm{T}}$

$H_{\text{A,elec}}^{\mathrm{C}}$ describes the central group ($103\le n\le 117$), written as4$\begin{array}{c}{H}_{\text{A,elec}}^{\mathrm{C}}=-\sum _{n,\mathrm{s}}\left[t_0-{\alpha }_{\mathrm{A}}(u_{\mathrm{A},n+1}-u_{\mathrm{A},n})-{(-1)}^n{t}_1\right]\\ (C_{\mathrm{A},n+1,\mathrm{s}}^{+}{C}_{\mathrm{A},n,\mathrm{s}}+C_{\mathrm{A},n,\mathrm{s}}^{+}{C}_{\mathrm{A},n+1,\mathrm{s}})\\ +\sum _{l=1}^4{t}^{\prime }(C_{\mathrm{A},4l+99,\mathrm{s}}^{+}{C}_{\mathrm{A},4l+102,\mathrm{s}}+C_{\mathrm{A},4l+102,\mathrm{s}}^{+}{C}_{\mathrm{A},4l+99,\mathrm{s}})\\ +\sum _{l^{\prime }=1}^3{t}^{\prime }(C_{\mathrm{A},4l^{\prime }+101,\mathrm{s}}^{+}{C}_{\mathrm{A},4l^{\prime }+104,\mathrm{s}}+C_{\mathrm{A},4l^{\prime }+104,\mathrm{s}}^{+}{C}_{\mathrm{A},4l^{\prime }+101,\mathrm{s}})\\ +\sum _{l=1}^4{\Delta }_{\text{on}}(C_{\mathrm{A},4l+99,\mathrm{s}}^{+}{C}_{\mathrm{A},4l+99,\mathrm{s}}+C_{\mathrm{A},4l+102,\mathrm{s}}^{+}{C}_{\mathrm{A},4l+102,\mathrm{s}})\\ +\sum _{l^{\prime }=1}^3{\Delta }_{\text{on}}(C_{\mathrm{A},4l^{\prime }+101,\mathrm{s}}+C_{\mathrm{A},4l^{\prime }+104,\mathrm{s}}+C_{\mathrm{A},4l^{\prime }+104,\mathrm{s}}^{+}{C}_{\mathrm{A},4l^{\prime }+104,\mathrm{s}})\\ +U\sum _n(C_{\mathrm{A},n,\uparrow }^{+}{C}_{\mathrm{A},n,\uparrow }-\frac{1}{2})(C_{\mathrm{A},n,\downarrow }^{+}{C}_{\mathrm{A},n,\downarrow }-\frac{1}{2})\\ +V_{\parallel }\sum _n(C_{\mathrm{A},n}^{+}{C}_{\mathrm{A},n}-1)(C_{\mathrm{A},n+1}^{+}{C}_{\mathrm{A},n+1}-1)\end{array}$

$H_{\text{A,elec}}^{\text{π}}$ describes the π-bridges ($100\le n\le 102\text{\hspace{0.17em}and\hspace{0.17em}}118\le n\le 120$), written as5$\begin{array}{c}{H}_{\text{A,elec}}^{\text{π}}=-\sum _{n,\mathrm{s}}\left[t_0-{\alpha }_{\mathrm{A}}(u_{\mathrm{A},n+1}-u_{\mathrm{A},n})\right](C_{\mathrm{A},n+1,\mathrm{s}}^{+}{C}_{\mathrm{A},n,\mathrm{s}}+C_{\mathrm{A},n,\mathrm{s}}^{+}{C}_{\mathrm{A},n+1,\mathrm{s}})\\ +U\sum _n(C_{\mathrm{A},n,\uparrow }^{+}{C}_{\mathrm{A},n,\uparrow }-\frac{1}{2})(C_{\mathrm{A},n,\downarrow }^{+}{C}_{\mathrm{A},n,\downarrow }-\frac{1}{2})\\ +V_{\parallel }\sum _n(C_{\mathrm{A},n}^{+}{C}_{\mathrm{A},n}-1)(C_{\mathrm{A},n+1}^{+}{C}_{\mathrm{A},n+1}-1)\end{array}$

$H_{\text{A,elec}}^{\mathrm{T}}$ describes the terminal groups ($93\le n\le 99\text{\hspace{0.17em}and\hspace{0.17em}121}\le n\le 127$), written as6$\begin{array}{c}{H}_{\text{A,elec}}^{\mathrm{T}}=-\sum _{n,\mathrm{s}}\left[t_0-{\alpha }_{\mathrm{A}}(u_{\mathrm{A},n+1}-u_{\mathrm{A},n})-t_2\cos \left(\frac{n\pi }{2}\right)\right]\\ (C_{\mathrm{A},n+1,\mathrm{s}}^{+}{C}_{\mathrm{A},n,\mathrm{s}}+C_{\mathrm{A},n,\mathrm{s}}^{+}{C}_{\mathrm{A},n+1,\mathrm{s}})\\ -\sum _n{{\Delta }^{\prime }}_{\text{on}}{C}_{\mathrm{A},n,\mathrm{s}}^{+}{C}_{\mathrm{A},n,\mathrm{s}}\\ +U\sum _n(C_{\mathrm{A},n,\uparrow }^{+}{C}_{\mathrm{A},n,\uparrow }-\frac{1}{2})(C_{\mathrm{A},n,\downarrow }^{+}{C}_{\mathrm{A},n,\downarrow }-\frac{1}{2})\\ +V_{\parallel }\sum _n(C_{\mathrm{A},n}^{+}{C}_{\mathrm{A},n}-1)(C_{\mathrm{A},n+1}^{+}{C}_{\mathrm{A},n+1}-1)\end{array}$

${\Delta }_{\mathrm{D}}$ represents the on-site energy of an electron on site n of polymer donor, introduced to tune the interfacial energy-level structure. ${\alpha }_i$ is the electron–lattice (e–l) interaction constant. $u_{i,n}$ is the displacement of site n. $C_{i,n,\mathrm{s}}^{+}$ ($C_{i,n,\mathrm{s}}$) is the creation (annihilation) operator of an electron on site n with spin s $(s=\uparrow ,\downarrow )$. $t_0$ denotes the nearest-neighbor electron-hopping integral for a uniform bond structure. $t_{\mathrm{e}}$, $t_1$, and $t_2$ are the symmetry-breaking parameters, which are used to describe the lattice feature of the polymer donor, the NFA molecular central group, and the NFA molecular terminal groups, respectively. $t^{\prime }$ describes the electron hopping between the neighboring sites of a heteroatom X (e.g., sulfur and nitrogen atom) in the NFA molecular central group. U and $V_{\parallel }$ are the on-site and off-site Coulomb interaction strengths in a molecule.

H_i,latt in Equation (1) denotes the Hamiltonian for lattice part of one molecule, including elastic potential energy and kinetic energy, described classically as7$H_{i,\text{latt}}=\frac{K}{2}{\sum _n(u_{i,n+1}-u_{i,n})}^2+\frac{M}{2}\sum _n{\stackrel{.}{u}}_{i,n}^2.$

K denotes the elastic constant between the nearest neighbor sites and M the mass of a site.

The intermolecular Hamiltonian (H_inter) is written as8$\begin{array}{c}{H}_{\mathrm{int}\text{er}}=-\sum _{n^{\prime },\mathrm{s}}{t}_{\perp \text{DA}}(C_{\mathrm{D},n^{\prime },\mathrm{s}}^{+}{C}_{\mathrm{A},n^{\prime },\mathrm{s}}+C_{\mathrm{A},n^{\prime },\mathrm{s}}^{+}{C}_{\mathrm{D},n^{\prime },\mathrm{s}})\\ +V_{\perp }\sum _{n^{\prime }}(C_{\mathrm{D},n^{\prime }}^{+}{C}_{\mathrm{D},n^{\prime }}-1)(C_{\mathrm{A},n^{\prime }}^{+}{C}_{\mathrm{A},n^{\prime }}-1).\end{array}$

$t_{\perp \text{DA}}=\frac{t_0}{10}\exp (1-d_{\text{DA}}/5)$ is the intermolecular hopping integral between the vertical neighbor sites of the donor and acceptor, depending on the corresponding intermolecular distance $d_{\text{DA}}$. $V_{\perp }$ shows the intermolecular Coulomb interaction strength. $\sum _{n^{\prime }}$ means to sum the sites for the coupling region between donor and acceptor.

Finally, the model description for the NFA molecular push–pull electronic structure should be stressed. To consider the effect of heteroatoms on the electron push ability of the molecular central group, we introduced ${\Delta }_{\text{on}}$ in Equation (4) to describe the contribution of heteroatoms to on-site energy of a neighboring site. Furthermore, the electron pull ability of the molecular terminal groups can be effectively tuned by halogenation (e.g., fluorination or chlorination), where we introduced ${{\Delta }^{\prime }}_{\text{on}}$ in Equation (6) to describe the on-site energy of a fluorinated or chlorinated site. Therefore, the electron push ability of the molecular central group and the electron pull ability of the molecular terminal groups can be tuned by changing the value of ${\Delta }_{\text{on}}$ and ${{\Delta }^{\prime }}_{\text{on}}$, respectively. Figure 1c sketches the interfacial electronic structure of the modeled D/A interface with both ${\Delta }_{\text{on}}=0\text{\hspace{0.17em}eV}$ and ${{\Delta }^{\prime }}_{\text{on}}=0\text{\hspace{0.17em}eV}$. $\Delta E_{\text{LUMO}}$ ($\Delta E_{\text{LUMO}}=E_{{\text{LUMO}}_{\mathrm{D}}}-E_{{\text{LUMO}}_{\mathrm{A}}}$) represents the energy difference between the lowest unoccupied molecular orbital of the donor (LUMO_D) and acceptor (LUMO_A) and $\Delta E_{\text{HOMO}}$ ($\Delta E_{\text{HOMO}}=E_{{\text{HOMO}}_{\mathrm{A}}}-E_{{\text{HOMO}}_{\mathrm{D}}}$) that between the highest occupied molecular orbital of the acceptor (HOMO_A) and donor (HOMO_D). For the present values of parameters (see Section S1, Supporting Information for parameter details), we got $\Delta E_{\text{LUMO}}=0.24\text{\hspace{0.17em}eV}$ and $\Delta E_{\text{HOMO}}=-0.16\text{\hspace{0.17em}eV}$. In view of the interfacial charge transfer, $\Delta E_{\text{LUMO}}$ and $\Delta E_{\text{HOMO}}$ corresponded to the energy offset of electron and hole charge transfer, respectively. From earlier works,^{[12,24,37,38]} we have known that the energies of both LUMO_A and HOMO_A can be shifted up by increasing the value of ${\Delta }_{\text{on}}$ (see Figure 2a), while the energies of both LUMO_A and HOMO_A shifted down by increasing the value of ${{\Delta }^{\prime }}_{\text{on}}$ (see Figure 2b). Here, it should be stressed that the energy shift amplitudes of LUMO_A and HOMO_A are different in either of the two cases, such that the interfacial electronic structure of the modeled D/A interface can be effectively tuned by changing the value of ${\Delta }_{\text{on}}$ and ${{\Delta }^{\prime }}_{\text{on}}$, respectively.

[IMAGE OMITTED. SEE PDF]

During the dynamical simulations, an exciton is formed in donor as the initial state, which can be gained by iteratively calculating the coupled Equation (S1) and (S2) (see Section S2, Supporting Information for details). To simulate its migration process toward the D/A interface, we used a half-Gaussian distribution function to turn on the intermolecular interaction9$t_{\perp \text{DA}}(t)=\{\begin{array}{c}\frac{t_0}{10}\exp (1-d_{\text{DA}}/5)\text{exp}\left[-{(t-t_{\mathrm{c}})}^2/t_{\mathrm{w}}^2\right]t\hspace{0.17em}\le \hspace{0.17em}{t}_{\mathrm{c}}\\ \frac{t_0}{10}\exp (1-d_{\text{DA}}/5)t\text{\hspace{0.17em}>\hspace{0.17em}}{t}_{\mathrm{c}}\end{array}$

We set t_c = 80 fs and t_w = 20 fs in all the following simulations. It means that the intermolecular configuration of the D/A interface becomes stable around t_c = 80 fs. After that, the exciton experienced evolutions. Using a quantum nonadiabatic evolution method, we could gain the temporal evolution of the lattice displacement $u_{i,n}(t)$ and the electronic state ${\psi }_{i,\text{μ,s}}(n,t)$ (see Section S3, Supporting Information for details).

Results and Discussion

Firstly, let us consider the effect of the electron push ability (${\Delta }_{\text{on}}$) of the molecular central group on the interfacial charge dynamics. Due to the upshifting of LUMO_A and HOMO_A, we note that there exists a conversion for the interfacial electronic structure from a type-II to type-I at a critical value of ${\Delta }_{\text{on}}$ (${\Delta }_{\text{on}}=0.3\text{\hspace{0.17em}eV}$, see Figure 2a). Experimentally, such a conversion has been confirmed by Ming et al.,^[12] where the electron push ability of central group was strengthened by extending its conjugation length. As follows, the interfacial charge dynamics in cases of ${\Delta }_{\text{on}}=0.2\text{\hspace{0.17em}eV}$ (a type-II structure) and ${\Delta }_{\text{on}}=0.5\text{\hspace{0.17em}eV}$ (a type-I structure) will be separately presented.

In the case of ${\Delta }_{\text{on}}=0.2\text{\hspace{0.17em}eV}$, Figure 3a,b separately display the time evolution of the net charge distribution $q_{i,n}=e({\rho }_{i,n,n}-1)$ (${\rho }_{i,n,n}$ indicates the density matrix, see Equation (S5), Supporting Information) and the total net charge quantities $Q_i=\sum _n{q}_{i,n}$ in donor and acceptor. We can see that charge transfer takes place after the donor exciton arrives at the D/A interface, by which there appear negative charges (≈0.05 e) in acceptor and positive charges (≈0.05 h) in donor. To give a deeper understanding for this result, Figure 3c demonstrates the time evolution of the transferred electron (ξ_A,e) and hole (ξ_A,h) charges into acceptor (see Equation (S8) and (S9) in Section S4, Supporting Information for details). It is found that both the excited electron and hole charges in donor exciton transfer into acceptors during the interfacial charge dynamics. However, their transfer dynamics are different due to the larger energy offset of electron charge transfer ($\Delta E_{\text{LUMO}}\text{=0}\text{.14}\text{eV}$) than that of hole charge transfer ($\Delta E_{\text{HOMO}}=-0.04\text{eV}$). On the one hand, the transfer quantity of electron charges (ξ_A,e = 0.86 e) is more than that of hole charges (ξ_A,h = 0.81 h) after the evolution tending to be stable; on the other hand, their transfer dynamics are not synchronous on timescale, that is, the electron charge transfer is faster than hole charge transfer. As a result, there appear net negative charges in the acceptor and net positive charges in donor, whose quantity presents an apparent oscillation at the initial time (60–110 fs), as presented in Figure 3b.

[IMAGE OMITTED. SEE PDF]

In particular, by comparing the transferred electron charges (ξ_A,e) and hole charges (ξ_A,h) into acceptor (see Figure 3c), we obtain that energy (or exciton) transfer from donor to acceptor also takes place in addition to the net charge transfer (usually referred to as charge transfer). As experimentally reported, energy transfer coexists with charge transfer during the interfacial charge dynamics,^{[29,30,33,34]} by which an interfacial hybrid state is created.^{[30,35–37,44]} However, due to the technical limitations, it is difficult to distinguish the possible component states (including donor exciton, acceptor exciton, and CT state) and especially their respective generation rate η. In view of this, we focus on the time evolution of η for the possible component states during the energy and charge transfer dynamics. η_DE (generation rate for donor exciton) and η_AE (generation rate for acceptor exciton) are separately obtained by ${\eta }_{\text{DE(AE)}}=\text{min}\left[{\xi }_{\text{D(A),e}},{\xi }_{\text{D(A),h}}\right]\times 100\%$, where $\text{min}\left[{\xi }_{\text{D(A),e}},{\xi }_{\text{D(A),h}}\right]$ means to select the smaller value between ξ_D(A),e and ξ_D(A),h. η_CT (generation rate for CT state) is obtained by ${\eta }_{\text{CT}}=|{\xi }_{\text{D(A),e}}-{\xi }_{\text{D(A),h}}|\times 100\%$. As presented in Figure 3d, we can see that the interfacial state corresponds to a pure state (i.e., a donor exciton) at the initial time. After the exciton arrives at the D/A interface, the value of η_DE is quickly reduced by the energy and charge transfer process. Correspondingly, there appear acceptor exciton and CT state at the D/A interface. Finally, the D/A interface lies in a hybrid state consisting of 81% acceptor exciton, 5% CT state, and still 14% donor exciton. In other words, during the interfacial charge dynamics, energy and charge transfer coexist with an efficiency of 81% and 5%, respectively.

In the case of ${\Delta }_{\text{on}}=0.5\text{\hspace{0.17em}eV}$, the modeled D/A interface turns to be a type-I electronic structure, where the energy offset of hole charge transfer ($\Delta E_{\text{HOMO}}=0.19\text{eV}$) is larger than that of electron charge transfer ($\Delta E_{\text{LUMO}}\text{=\hspace{0.17em}0}\text{.03}\text{eV}$). So, the transfer quantity of hole charges into the acceptor (ξ_A,h = 0.90 h) is more than that of electron charges (ξ_A,e = 0.82 e), as presented in Figure 4a, where we can also see that the hole charge transfer is faster than electron charge transfer. It makes the charge transfer dynamics to be fundamentally different from the result in the case of ${\Delta }_{\text{on}}=0.2\text{\hspace{0.17em}eV}$. The time evolution of the total net charge quantity Q_i in donor and acceptor is displayed in Figure 4b. It is found that there appear net positive charges (≈0.08 h) in acceptor and net negative charges (≈0.08 e) in donor, that is, the donor polymer actually acts as a “hole donor” in the case of ${\Delta }_{\text{on}}=0.5\text{\hspace{0.17em}eV}$. For the created hybrid state after the interfacial charge dynamics, we get that it consists of 82% acceptor exciton, 8% CT state, and still 10% donor exciton (see Figure 4c).

[IMAGE OMITTED. SEE PDF]

Comparing the results of the above two cases, the interfacial charge dynamics can exactly be modulated by tuning the electron push ability (${\Delta }_{\text{on}}$) of the NFA molecular central group, which is mainly realized by its impact on the difference value (${\delta }_{\Delta E}=|\Delta E_{\text{LUMO}}-\Delta E_{\text{HOMO}}|$) between the energy offsets of electron and hole charges transfer. To give a systematic result, the inset of Figure 5a shows the value of ${\delta }_{\Delta E}$ as a function of ${\Delta }_{\text{on}}$. It is found that the value of ${\delta }_{\Delta E}$ first decreases and then increases with increasing the value of ${\Delta }_{\text{on}}$, and there exists a critical value of ${\Delta }_{\text{on}}$ (${\Delta }_{\text{on}}=0.34\text{\hspace{0.17em}eV}$), at which ${\delta }_{\Delta E}=0$. It means that the energy offsets of electron and hole charge transfer are the same in the case of ${\Delta }_{\text{on}}=0.34\text{\hspace{0.17em}eV}$, such that the electron and hole charges transfer from donor to acceptor are equivalence (see Figure S1a, Supporting Information). As a result, both donor and acceptor keep electric neutrality unchanged during the interfacial charge dynamics (see Figure S1b, Supporting Information). This result supports that only energy transfer takes place, by which the created interfacial hybrid state consists of 86% acceptor exciton and 14% donor exciton (see Figure S1c, Supporting Information).

[IMAGE OMITTED. SEE PDF]

In cases of ${\Delta }_{\text{on}}<0.34\text{\hspace{0.17em}eV}$, the value of ${\delta }_{\Delta E}$ presents a decreasing tendency with increasing the value of ${\Delta }_{\text{on}}$. It gradually eliminates the difference between electron and hole charge transfer from donor to acceptor, such that the charge transfer is inhibited and the energy transfer promoted. Reflected in the variation of the generation rate η for different component states after the interfacial charge dynamics (see Figure 5a), the value of η_CT decreases and the value of η_AE increases with increasing value of ${\Delta }_{\text{on}}$. In cases of ${\Delta }_{\text{on}}>0.34\text{\hspace{0.17em}eV}$, however, the value of ${\delta }_{\Delta E}$ presents an increasing tendency with increasing value of ${\Delta }_{\text{on}}$. As a result, the value of η_CT increases and the value of η_AE decreases. So, the competition between charge and energy transfer is not monotonous in the modulation for the interfacial charge dynamics by strengthening the NFA molecular electron push ability. There exists a critical strength, below which the molecular electron push ability favors the energy transfer and inhibits the charge transfer and beyond which the molecular electron push ability favors the charge transfer and inhibits the energy transfer.

Now, let us turn to the effect of the electron pull ability (${{\Delta }^{\prime }}_{\text{on}}$) of the NFA molecular terminal groups on the interfacial charge dynamics. As presented in Figure 2b, both LUMO_A and HOMO_A shift down with increasing the value of ${{\Delta }^{\prime }}_{\text{on}}$, such that the modeled D/A interface keeps type-II electronic structure unchanged. A result for the interfacial charge dynamics with a typical value of ${{\Delta }^{\prime }}_{\text{on}}=0.3\text{\hspace{0.17em}eV}$ is displayed in Figure S2, Supporting Information. We obtain that the result is similar with that in the case of ${\Delta }_{\text{on}}=0.2\text{\hspace{0.17em}eV}$ due to their similar interfacial electronic structures. The difference is that the difference value between the energy offsets of electron and hole charges transfer (i.e., ${\delta }_{\Delta E}$) is apparently larger in the case of ${{\Delta }^{\prime }}_{\text{on}}=0.3\text{\hspace{0.17em}eV}$, by which the electron charges are much easier to be transferred into acceptor than hole charges, both in charge quantity and in timescale. As a result, the charge transfer efficiency is remarkably improved, and the generation rate of CT state reaches up to η_CT = 29% after the interfacial charge dynamics. To give a systematic result, the inset of Figure 5b presents the value of ${\delta }_{\Delta E}$ as a function of ${{\Delta }^{\prime }}_{\text{on}}$, where we can see that it keeps an increasing trend. It results in the continuous increase for the generation rate of CT state and reduction for the generation rate of acceptor exciton, as shown in Figure 5b. So, by strengthening the electron pull ability of the NFA molecular terminal groups, we can effectively improve the charge transfer and reduce the energy transfer.

Conclusion

In summary, we employ a universal quantum model to focus on the effects of the NFA molecular electron push and/or pull ability on the interfacial charge dynamics in NFA-based OSCs. It is confirmed that energy and charge transfer coexist and compete during the interfacial charge dynamics, by which an interfacial hybrid state is created with the component states including donor exciton, acceptor exciton, and CT state. The quantitative correlations for the generation rates of different component states with the NFA molecular electron push and pull ability are separately clarified. The results support a critical strength for the electron push ability of NFA molecular central group, below which energy transfer is promoted and charge transfer inhibited; otherwise, charge transfer is promoted and energy transfer inhibited. By strengthening the electron pull ability of NFA molecular terminal groups, charge transfer is always promoted and energy transfer correspondingly inhibited.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (grant nos. 11674195 and 21961132023), the Major Program of Natural Science Foundation of Shandong Province (grant no. ZR2019ZD43), and the Natural Science Foundation of Shandong Province (no. ZR2022MA007).

Conflict of Interest

The authors declare no conflict of interest.

Data Availability Statement

Research data are not shared.

References

Y. Cui, Y. Xu, H. Yao, P. Bi, L. Hong, J. Zhang, Y. Zu, T. Zhang, J. Qin, J. Ren, Z. Chen, C. He, X. Hao, Z. Wei, J. Hou, Adv. Mater. 2021, 33, 2102420.

P. Bi, S. Zhang, Z. Chen, Y. Xu, Y. Cui, T. Zhang, J. Ren, J. Qin, L. Hong, X. Hao, J. Hou, Joule 2021, 5, 2408.

J. Hou, O. Inganäs, R. H. Friend, F. Gao, Nat. Mater. 2018, 17, 119.

Y. Ji, L. Xu, X. Hao, K. Gao, Sol. RRL 2020, 4, 2000130.

H.-W. Cheng, C.-Y. Juan, A. Mohapatra, C.-H. Chen, Y.-C. Lin, B. Chang, P. Cheng, H.-C. Wang, C. W. Chu, Y. Yang, K.-H. Wei, Nano Lett. 2021, 21, 2207.

C. Yan, S. Barlow, Z. Wang, H. Yan, A. K.-Y. Jen, S. R. Marder, X. Zhan, Nat. Rev. Mater. 2018, 3, 18003.

D. Li, X. Zhang, D. Liu, T. Wang, J. Mater. Chem. A 2020, 8, 15607.

H. Lai, Q. Zhao, Z. Chen, H. Chen, P. Chao, Y. Zhu, Y. Lang, N. Zhen, D. Mo, Y. Zhang, F. He, Joule 2020, 4, 688.

Y. Lin, J. Wang, Z.-G. Zhang, H. Bai, Y. Li, D. Zhu, X. Zhan, Adv. Mater. 2015, 27, 1170.

J. Yuan, Y. Zhang, L. Zhou, G. Zhang, H.-L. Yip, T.-K. Lau, X. Lu, C. Zhu, H. Peng, P. A. Johnson, M. Leclerc, Y. Cao, J. Ulanski, Y. Li, Y. Zou, Joule 2019, 3, 1140.

M. A. Alamoudi, J. I. Khan, Y. Firdaus, K. Wang, D. Andrienko, P. M. Beaujuge, F. Laquai, ACS Energy Lett. 2018, 3, 802.

R. Ming, J. Wang, W. Gao, M. Zhang, J. Gao, W. Ning, Z. Luo, X. Liu, C. Zhong, F. Zhang, C. Yang, Small Methods 2019, 3, 1900280.

H. Yao, Y. Chen, Y. Qin, R. Yu, Y. Cui, B. Yang, S. Li, K. Zhang, J. Hou, Adv. Mater. 2016, 28, 8283.

H. Lin, M. A. Adil, Q. Zhang, J. Zhang, Q. Wang, Org. Electron. 2021, 93, 106167.

H. Xu, Y. Yang, C. Zhong, X. Zhan, X. Chen, J. Mater. Chem. A 2018, 6, 6393.

S. Wan, Y. Ma, D. Cai, W. Lin, P. Wang, J. Wang, Q. Zheng, Adv. Funct. Mater. 2021, 31, 2010436.

L. Hou, J. Lv, F. Wobben, V. M. Le Corre, H. Tang, R. Singh, M. Kim, F. Wang, H. Sun, W. Chen, Z. Xiao, M. Kumar, T. Xu, W. Zhang, I. McCulloch, T. Duan, H. Xie, L. J. A. Koster, S. Lu, Z. Kan, ACS Appl. Mater. Interfaces 2020, 12, 56231.

S. Dai, F. Zhao, Q. Zhang, T.-K. Lau, T. Li, K. Liu, Q. Ling, C. Wang, X. Lu, W. You, X. Zhan, J. Am. Chem. Soc. 2017, 139, 1336.

G. P. Kini, S. J. Jeon, D. K. Moon, Adv. Mater. 2020, 32, 1906175.

Y. Song, X. Liu, Y. Li, H. H. Nguyen, R. Duan, K. J. Kubarych, S. R. Forrest, J. P. Ogilvie, J. Phys. Chem. Lett. 2021, 12, 3410.

L. Zhu, Z. Tu, Y. Yi, Z. Wei, J. Phys. Chem. Lett. 2019, 10, 4888.

L. Perdigón-Toro, H. Zhang, A. Markina, J. Yuan, S. M. Hosseini, C. M. Wolff, G. Zuo, M. Stolterfoht, Y. Zou, F. Gao, D. Andrienko, S. Shoaee, D. Neher, Adv. Mater. 2020, 32, 1906763.

X. Zhu, G. Zhang, J. Zhang, H.-L. Yip, B. Hu, Joule 2020, 4, 2443.

Y. Ji, L. Xu, H. Yin, B. Cui, L. Zhang, X. Hao, K. Gao, J. Mater. Chem. A 2021, 9, 16834.

R. Wang, C. Zhang, Q. Li, Z. Zhang, X. Wang, M. Xiao, J. Am. Chem. Soc. 2020, 142, 12751.

L. Zhu, J. Zhang, Y. Guo, C. Yang, Y. Yi, Z. Wei, Angew. Chem., Int. Ed. 2021, 60, 15348.

P. Cheng, X. Zhan, Chem. Soc. Rev. 2016, 45, 2544.

A. A. Bakulin, A. Rao, V. G. Pavelyev, P. H. M. van Loosdrecht, M. S. Pshenichnikov, D. Niedzialek, J. Cornil, D. Beljonne, R. H. Friend, Science 2012, 335, 1340.

S. Karuthedath, J. Gorenflot, Y. Firdaus, N. Chaturvedi, C. S. P. De Castro, G. T. Harrison, J. I. Khan, A. Markina, A. H. Balawi, T. A. D. Peña, W. Liu, R.-Z. Liang, A. Sharma, S. H. K. Paleti, W. Zhang, Y. Lin, E. Alarousu, S. Lopatin, D. H. Anjum, P. M. Beaujuge, S. De Wolf, I. McCulloch, T. D. Anthopoulos, D. Baran, D. Andrienko, F. Laquai, Nat. Mater. 2021, 20, 378.

Y. Zhong, M. Causa’, G. J. Moore, P. Krauspe, B. Xiao, F. Günther, J. Kublitski, R. Shivhare, J. Benduhn, E. BarOr, S. Mukherjee, K. M. Yallum, J. Réhault, S. C. B. Mannsfeld, D. Neher, L. J. Richter, D. M. DeLongchamp, F. Ortmann, K. Vandewal, E. Zhou, N. Banerji, Nat. Commun. 2020, 11, 833.

B. R. Gautam, R. Younts, J. Carpenter, H. Ade, K. Gundogdu, J. Phys. Chem. A 2018, 122, 3764.

P. Li, J. Fang, Y. Wang, S. Manzhos, L. Cai, Z. Song, Y. Li, T. Song, X. Wang, X. Guo, M. Zhang, D. Ma, B. Sun, Angew. Chem., Int. Ed. 2021, 60, 15054.

H.-W. Cheng, H. Zhang, Y.-C. Lin, N.-Z. She, R. Wang, C.-H. Chen, J. Yuan, C.-S. Tsao, A. Yabushita, Y. Zou, F. Gao, P. Cheng, K.-H. Wei, Y. Yang, Nano Lett. 2019, 19, 5053.

A. Karki, J. Vollbrecht, A. J. Gillett, P. Selter, J. Lee, Z. Peng, N. Schopp, A. L. Dixon, M. Schrock, V. Nádaždy, F. Schauer, H. Ade, B. F. Chmelka, G. C. Bazan, R. H. Friend, T.-Q. Nguyen, Adv. Energy Mater. 2020, 10, 2001203.

G. Han, Y. Yi, J. Phys. Chem. Lett. 2019, 10, 2911.

F. D. Eisner, M. Azzouzi, Z. Fei, X. Hou, T. D. Anthopoulos, T. J. S. Dennis, M. Heeney, J. Nelson, J. Am. Chem. Soc. 2019, 141, 6362.

Y. Xu, H. Yao, L. Ma, L. Hong, J. Li, Q. Liao, Y. Zu, J. Wang, M. Gao, L. Ye, J. Hou, Angew. Chem., Int. Ed. 2020, 59, 9004.

M.-S. Niu, K.-W. Wang, X.-Y. Yang, P.-Q. Bi, K.-N. Zhang, X.-J. Feng, F. Chen, W. Qin, J.-L. Xia, X.-T. Hao, J. Phys. Chem. Lett. 2019, 10, 7100.

C. Huang, X. Liao, K. Gao, L. Zuo, F. Lin, X. Shi, C.-Z. Li, H. Liu, X. Li, F. Liu, Y. Chen, H. Chen, A. K.-Y. Jen, Chem. Mater. 2018, 30, 5429.

W. Liu, X. Xu, J. Yuan, M. Leclerc, Y. Zou, Y. Li, ACS Energy Lett. 2021, 6, 598.

S. Dai, J. Zhou, S. Chandrabose, Y. Shi, G. Han, K. Chen, J. Xin, K. Liu, Z. Chen, Z. Xie, W. Ma, Y. Yi, L. Jiang, J. M. Hodgkiss, X. Zhan, Adv. Mater. 2020, 32, 2000645.

Y. Cui, P. Zhu, X. Shi, X. Liao, Y. Chen, J. Phys. Chem. C 2021, 125, 10250.

Y. Ji, L. Xu, X. Mu, W. Wang, K. Gao, J. Mater. Chem. C 2022, 10, 10106.

K. Li, D.-H. Xu, X. Wang, X.-Y. Liu, Phys. Chem. Chem. Phys. 2021, 23, 2097.