LETTER pubs.acs.org/JPCL
Relating Trends in First-Principles Electronic Structure and Open-Circuit Voltage in Organic Photovoltaics Eric B. Isaacs,† Sahar Sharifzadeh, Biwu Ma, and Jeffrey B. Neaton* Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
bS Supporting Information ABSTRACT: Using first-principles density functional theory, and accounting for solid-state polarization effects and electron hole interactions, we calculate excited electronic states at interfaces between C60 and a series of functionalized boron(subphthalocyanine) molecules, a class of donor materials for organic photovoltaic (OPV) devices, and correlate energetics with their measured open-circuit voltages (Voc). For isolated donor and acceptor molecules, a staggered (type-II) interface energy alignment is predicted with an energy offset of several tenths of an electron volt, capable of promoting charge separation. The solid-state charge transfer excited state energy, ECT, obtained by including electronic polarization effects and electron hole interactions, exhibits a near-quantitative linear relationship with Voc. ECT depends sensitively on interface morphology, resulting in a predicted 0.2 0.6 eV spread in energy for the geometries studied here. The agreement between theory and experiment provides insight into possible routes to higher Voc OPVs, and suggests that our approximate approach can enable computational design of Voc for a broad class of molecular-based OPVs. SECTION: Energy Conversion and Storage
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rganic photovoltaic devices (OPVs) are promising candidates for scalable, low-cost solar energy conversion,1 and there is an active effort to design and synthesize novel materials with improved efficiency. In its simplest form, an OPV consists of semiconducting donor (D) and acceptor (A) molecules or polymers, interfaced at the nanoscale in either a planar thin film or bulk heterojunction geometry, sandwiched between electrodes. The electronic properties and atomic-scale structure of the D A interface are crucial to the efficient separation of photogenerated excitons, and are a significant factor in the power conversion efficiency through the open-circuit voltage (Voc).2 For OPVs, Voc typically corresponds to less than half of the incident solar photon energy, and optimizing Voc provides significant opportunity for improvement of device efficiency.3 However, important details of the relationship between Voc and electronic structure at the interface are still not fully understood.4,5 For devices with Ohmic contacts at the electrodes,6,7 Voc is limited by the difference between the highest occupied molecular orbital (HOMO) energy, or ionization potential (IP), of the donor and the lowest unoccupied molecular orbital (LUMO) energy, or electron affinity (EA), of the acceptor.3,6,8 19 Evidence has accumulated to suggest that charge transfer (CT) excited states at the D A interface are an intermediate in the charge separation process in OPVs,20 and that there is a linear relationship between Voc and the CT excited state energy (ECT).13,17,19,21 27 Although increasing Voc is an area of active research, there have only been a limited number of experimental studies of ECT at D A interfaces due to the difficulty in spectroscopically probing interfacial CT states,28,29 limiting the degree to which any linear relationship between Voc and ECT has r 2011 American Chemical Society
been established. In addition, temperature- and disorder-induced energy level broadening30 is also expected to play a significant role in the measured Voc. The ability to predict Voc from first principles would clarify its origin and enable computational design of higher efficiency active layer materials for OPVs. In addition to having a large Voc, OPV materials should be inexpensive to fabricate, have a large overlap between active layer optical absorption and the solar spectrum, and have high electron and hole mobilities to facilitate efficient charge transport. To these purposes, a new class of molecular donors based on boron(subphthalocyanine) (SubPc), are promising.11,31 38 In particular, thiophene-functionalized SubPc and similar dyad molecules (see Figure 1) have a relatively high solubility with low tendency to aggregate and strong absorption in the visible. Initial studies have shown that they behave as chromophores and, when interfaced with C60 in a planar heterojunction, OPV efficiencies greater than 1% are achieved without optimization.31,39 Additionally, the donors are chemically modifiable via the number of thiophene units and the linker between the ligand and SubPc, enabling systematic improvement of their properties. Importantly for theory and simulation, they comprise an excellent set to systematically probe the relationship between the chemical structure of the donor molecules and device performance. In this study, we apply first-principles density functional theory (DFT) to characterize the electronic structure of this class of SubPc derivatives as donor molecules interfaced with C60, and Received: August 23, 2011 Accepted: September 19, 2011 Published: September 19, 2011 2531
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Figure 1. Molecular structures of the donor and acceptor molecules studied in this work. The donors consist of a SubPc moiety that is functionalized. The nT-SubPc consist of n thiophene rings and a benzene ring linked to the SubPc with a C C triple bond for nTaSubPc and an oxygen bond for nTp-SubPc. SubPc-A [2-allylphenoxy(subphthalocyaninato)boron(III)] is similar to nTp-SubPc but contains an allyl group rather than a thiophene chain. C60 buckminsterfullerene is the electron acceptor.
analyze the correlation between measured Voc, the interfacial energy level alignment, and ECT. Crucially, OPVs based on these materials have been studied with identical device architecture and fabrication technique,31,39 allowing the isolation of molecularscale effects relative to extrinsic factors, and thus permitting us to ascribe quantitative meaning to the measured trends in Voc. Although prior studies have investigated the ground- and excitedstate energetics at other D A interfaces,29,40 47 this work compares electronic structure at the D A interface directly to experimental Voc across a class of closely related donor materials. With our parameter-free approach, we establish that, as expected from empirically motivated derivations, the relationship between Voc and ECT is indeed linear. Additionally, we demonstrate that while chemical modification of the donor affects the interface energy alignment by shifting of the IP, the role of interface morphology (which is also molecule-dependent) on ECT is just as significant. These results strongly suggest that precise control of the morphology at the interface is a promising route to improve OPV efficiency, through Voc. The chemical structures of the donor molecules considered in this work, along with the acceptor molecule, C60, are shown in Figure 1. The SubPc moiety consists of a boron atom surrounded by three coupled benzo-isoindole units and forms a nonplanar cone-shaped structure.32 The nTa(p)-SubPc dyads consist of n thiophene rings connected to a benzene unit that is covalently bonded to the SubPc at the boron atom via a C C triple bond (oxygen bond). SubPc-A [2-allylphenoxy-(subphthalocyaninato)boron(III)] consists of an allyl group connected to a benzene group that is linked to a SubPc base through an oxygen bond. DFT calculations are performed within the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE)48 using the Q-Chem 3.2 package.49 For isolated molecules, the atomic orbitals are expanded in the all-electron 6-311++G** basis set of Pople, while D A pairs are treated with the Christiansen Ross Ermler Nash Bursten large-basis (CRENBL) shape-consistent relativistic
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effective core potentials (ECPs) and corresponding basis sets50 augmented with 6-311++G** polarization functions (“CRENBL**”). The quality of the all-electron basis set is evaluated against planewave DFT calculations within the Vienna ab initio simulation package (VASP).51 53 The validity of the ECP is tested by against all-electron calculations (see Supporting Information for basis set convergence details). The isolated D and A molecular structures are optimized within GGA-PBE with forces on all atoms converged to less than 0.015 eV/Å and total energies converged to less than 0.03 meV. The optimized molecular structures are in good agreement with available X-ray crystallography data for 2Tp-SubPc, 4Tp-SubPc, and SubPc-A.31,37 For D A pairs, the donor-C60 distance is determined within PBE (and, in instances, augmented with empirical van der Waals corrections54,55 for comparison) for several C60 locations, as illustrated in Figure 2 for 2Ta-SubPc as an example. In each case, the hexagonal face of C60 is placed closest to the donor molecule and oriented in a staggered configuration to minimize C C and/or C H repulsion. The influence of empirical dispersion interactions54,55 is studied for 2Tp-SubPc-C60, with the C60 nearest to the benzene ring and led to closer D A distance (by ∼0.4 Å) and stronger D A binding energy (from 60 meV to 0.4 eV) than with PBE. However, the change in IP and EA for the D A pair (see below) is on the order of only 0.01 eV and the difference in calculated ECT (see below) is only 0.04 eV. IPs and EAs for the isolated and pair systems, initially in the gas phase, are calculated with the ΔSCF approach,56 where addition and removal energies are computed as total DFT57,58 energy differences for the appropriately charged and uncharged systems. In order to model their solid-state environment, we consider the molecule in a linear dielectric medium and account for the screening from the dielectric when computing the energy to add or remove a charge. In the simplest solvation model, the molecule is represented as a sphere in a continuous dielectric of constant εr. In this sphere-in-a-dielectric model, which has previously been applied to a wide range of organic materials,59 the polarization energy associated with the solid state is taken to be that due to addition or removal of a charge from the center of a sphere of radius R and is computed as P = (e2/2R)[(εr 1)/εr] such that the solid-state gap is Esolid-state gap = Egas-phase gap - 2P. Here, the gas-phase gap, Egas-phase gap, is defined as IP EA. For all interfaces, we set εr to 4, a typical value for organic semiconductors in between that of SubPc and C60.33,60,61 R is determined as the radius of a sphere whose volume is equivalent to the volume of the charge density around the molecule, as calculated within the Gaussian 09 code62 (see Supporting Information for details). We confirm, by means of a self-consistent polarizable continuum model (PCM),63 the validity of two assumptions in the above sphere-in-a-dielectric model: (1) that the molecule can be represented as a sphere and (2) that the electronic wave functions of the gas-phase molecule are not significantly modified by the dielectric. Within the PCM, the molecule is contained in a cavity defined by either its electronic density or overlapping atom-centered spheres and the DFT energy for either the charged or neutral state is optimized self-consistently in the presence a continuous dielectric outside of the cavity. The dielectric constant is again set to εr = 4. (See ref 63 for a review of this method, and the Supporting Information for details of our calculations.) The results of our gas-phase calculations for the IP and EA of the thiophene SubPc dyads, SubPc-A, and C60 are summarized 2532
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Figure 2. Possible donor acceptor configurations for 2Ta-SubPc. Similar configurations are considered for all donor molecules.
Figure 3. Predicted gas-phase HOMO and LUMO energy level diagram for the functionalized SubPc donor molecules studied in this work and the acceptor, C60. The values of IP and EA, in electron volts, are shown next to the corresponding HOMO and LUMO levels, respectively. The gas-phase energy level alignment shows a type-II interface between donor molecules and C60.
in the energy level diagram of Figure 3. The different functional groups on the donor molecule lead to a systematic shift of the frontier molecular orbital energies. Both the IP (the quantity of interest for the donor molecules) and the molecular HOMO LUMO (IP EA) gap decrease with the length of the attached ligand, consistent with the increased delocalization of the electronic wave function for the larger ligands. Interestingly, replacing the C C triple bond linker (nTa-SubPc) with the oxygen linker (nTp-SubPc) does not change the electronic structure significantly, although it modifies the preferred bend angle of the ligand, as shown at the bottom of Figure 3. The calculated values of the C60 IP and EA of 7.5 and 2.7 eV are in excellent agreement with the experimental values of 7.5 7.6 and 2.7 eV,64 66 and prior computed values of 7.6 and 2.9 eV,67 respectively. Although there are no experimental gasphase energetics yet on these donor molecules for comparison,
the trends in the donor molecule IPs and EAs are well-reproduced by a contemporary long-range hybrid DFT functional (Baer Neuhauser Livshits (BNL);68 see Supporting Information for details). This is particularly true for the nT-SubPc molecules, but as it turns out less so for SubPc-A due to the limitation of our computational approach. As discussed in the Supporting Information, the ΔSCF approach, when used with standard local and semilocal functionals, tends to underestimate IP-EA (HOMO/LUMO) gaps of large molecules, with the error increasing with the molecular size (see, for example, ref 26 in the Supporting Information). The gap of the significantly smaller SubPc-A molecule is expected to be more accurate than that of the relatively larger nT-SubPc molecules, which, due to their similar size, are treated on a nearly equal footing at the level of ΔSCF-PBE. Thus, while trends in predicted excitation energies of the nT-SubPc-C60 would be expected to be quite good due to 2533
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Table 1. The Polarization Energy and Computed Solid-State Transport Gap (eV) As Predicted with the Sphere-in-aDielectric Electrostatic Model Psphere
Eg,sphere
2Ta-SubPc
0.9
2.4
2Tp-SubPc
1.0
2.2
4Ta-SubPc
0.9
1.9
4Tp-SubPc
0.9
1.9
SubPc-A C60
1.0 1.0
2.8 2.7
molecule
their similar size, quantitative differences are anticipated (and calculated) for the smaller SubPc-A system. The frontier orbital energy offsets between the donors and C60 are consistent with a staggered (type-II) interface. Both the IP and EA of the donor are smaller than the IP and EA of C60, by 0.7 1.7 eV and 0.4 1.0 eV, respectively. Additionally, when we incorporate the influence of the D A interface or solid-state effects (via bulk polarization) on the HOMO and LUMO energies, the trend in energy level alignment is almost unchanged. For the former, we expect and see an insignificant shift of the frontier orbital energies at the D A interface with respect to the isolated donor and acceptor due to the weak interaction between them.69 For D A pairs (within the range of interface geometries considered), the HOMO (LUMO) corresponds to the HOMO (LUMO) of the isolated donor (acceptor) and the IP and EA change by 0.03 and 0.09 eV, respectively, for the thiophene SubPc-C60 systems, while for the SubPc-A-C60, the IP is reduced and the EA is increased by as much as nearly 0.2 and 0.07 eV, respectively. For the latter, the simple sphere-in-a-dielectric electrostatic model predicts a reduction of donor HOMO energies and an increase of the C60 LUMO energy by 0.9 1.0 eV (selfconsistent PCM gives similar values of 0.7 1.1 eV) due to bulk polarization (see Table 1). The lowest-energy CT excited state is expected to involve a transition from the donor HOMO to acceptor LUMO, due to the type-II level alignment and noncovalent interaction between D and A. Given their close proximity, electron hole interactions will be significant and will strongly contribute to ECT. To account for this, we compute the CT state excited state energy in the EA Eb where the exciton Mulliken limit70 as ECT = IP binding energy is Eb = e2/4πε0εrr, and r = ÆψHOMO,D|r|ψHOMO,Dæ ÆψLUMO,A|r|ψLUMO,Aæ is taken to be the average distance between the electron and hole. Here, ψHOMO,D and ψLUMO,A are the HOMO of the donor and LUMO of the acceptor, respectively, and r represents the spatial separation between the centroids of the dominant pair of orbitals involved in the CT excitation, which are taken from DFT-PBE. The thiophene-SubPc dyads themselves are a donor (ligand)acceptor (SubPc) system, with the computed ΔSCF IP energy offset ranging from 0.1 (2Ta-SubPc) to 0.7 eV (4Tp-SubPc). Consequently, within PBE, the HOMO is localized on the thiophene chain, while the LUMO is localized on the SubPc base. For the smaller SubPc-A molecule, the HOMO (localized on the ligand) and HOMO-1 (delocalized over the molecule) have nearly degenerate DFT eigenvalues (
