Molecular-Level Exploration of the Structure-Function Relations Underlying Interfacial Charge Transfer in the Subphthalocyanine/${\mathrm{C}}_{60}$ Organic Photovoltaic System

The arrangement of organic molecules at the donor-acceptor interface in an organic photovoltaic (OPV) cell can have a strong effect on the generation of charge carriers and thereby cell performance. In this paper, we report the molecular-level exploration of the ensemble of interfacial donor-acceptor pair geometries and the charge-transfer (CT) rates to which they give rise. Our approach combines molecular-dynamics simulations, electronic structure calculations, machine learning, and rate theory. This approach is applied to the boron subphthalocyanine chloride (donor) and ${\mathrm{C}}_{60}$ (acceptor) OPV system. We find that the interface is dominated by a previously unreported donor-acceptor pair edge geometry, which contributes significantly to device performance in a manner that depends on the initial conditions. Quantitative relations between the morphology and CT rates are established, which can be used to advance the design of more efficient OPV devices.

Figure 1

SubPC (green) / ${\mathrm{C}}_{60}$ (gray) D-A pairs. There are three categories of D-A pair geometries: (a) on top, (b) hollow, and (c) edge. The related order parameters, $R$ and $\theta$, are defined in (c), where the yellow bead corresponds to the center of mass of the ${\mathrm{C}}_{60}$ and the red and blue beads correspond to the boron and chlorine atoms of SubPC, respectively. The $R$ parameter is the distance between the center of mass of ${\mathrm{C}}_{60}$ and the boron atom. The $\theta$ parameter is the angle between the two vectors, $V_1$ and $V_2$.

Figure 2

The potential of mean force (a) and population of pair geometries (b) for the SubPC/${\mathrm{C}}_{60}$ pair in deposition model V (for the other deposition models introduced below, see Fig. S1 and Sec. I in the Supplemental Material [28]), as a function of the order parameters, $R$ and $\theta$. $R$ and $\theta$ are defined in Fig. 1. The color is scaled by $k_{B}T$. The corresponding ranges of the order parameters for the different spatial pairs are indicated by the rectangular boxes. On top, $R<8.5$ Å and $\theta <{38}^{\circ }$; hollow, $R<9$ Å and ${95}^{\circ }<\theta <{160}^{\circ }$; edge (the majority), $10$ Å $<R<14$ Å and ${40}^{\circ }<\theta <{100}^{\circ }$. Also shown are representative geometries (on top, hollow, and edge) of SubPC/${\mathrm{C}}_{60}$ at each of the three major basins. The setup of deposition model V is shown both before and after equilibration as insets in (b).

Figure 3

The orbital energy diagram for the three representative SubPC/${\mathrm{C}}_{60}$ geometries. The pair’s HOMO, shown in blue and denoted as “H,” is localized on SubPC. The pair’s LUMO, shown in red and denoted as “L,” is localized on ${\mathrm{C}}_{60}$ and contributes to all the CT states. The absorbing excited state involves the LUMO on the donor, which is the pair’s LUMO+3 shown in red. For the on-top geometry, we find an additional absorbing state where the LUMO+4 plays a role (the LUMO+1 on the donor).

Figure 4

The charge of the donor molecule ($Q_D$) in units of $e$ and the excitation energy ($E^{\mathrm{gas}}$) in units of electronvolts for the excited states in different pair geometries. The oscillator strength (OS) is represented by the arrow width. States with a vanishing ($<0.01$) OS are represented by a thin dotted line. The numerical values are listed in Table S2 in the Supplemental Material [28].

Figure 5

The detachment (green) and attachment (magenta) electronic densities of the on-top EX1 and bCT1 states. Here, the detachment and attachment densities demonstrate that the charge density decreased and increased relative to the corresponding electronic states, respectively. Other excited state densities are shown in Fig. S2 in the Supplemental Material [28].

Figure 6

The five initial conditions mimicking the deposition models used in the simulations. Each consists of six layers of 25 SubPC or ${\mathrm{C}}_{60}$ molecules (three SubPC layers $+$ three ${\mathrm{C}}_{60}$ layers). The models differ with respect to the order of layers and the orientation of the molecules in the SubPC layer. Detailed descriptions can be found in the Supplemental Material [28].

Figure 7

Interfacial SubPC/${\mathrm{C}}_{60}$ pairs for the five deposition models in Fig. 6. (a) The percentage of interfacial pairs in the on-top (blue), hollow (red), and edge (yellow) geometries. (b) Only the percentage of interfacial pairs in the on-top geometry in each model. (c) The pair density at the interface of each model.