The prediction of the morphology and PCE of small molecular organic solar cells

Abstract

The efficiency of bulk heterojunction (BHJ) solar cells depends strongly on the morphology of the electron donors and electron acceptors in the active layer. Here we use Dissipative Particle Dynamics (DPD) simulation to predict the donor–acceptor morphology and graph theory to predict the efficiency of small molecular organic solar cells (SM OSCs). We focus on a recently reported small molecular organic solar cell based on a new molecule donor, DTS(PTTh₂)₂ and three molecules DR3TBDTT, DR3TBDTT-HD, and DR3TBD2T with a benzo[1,2-b:4,5-b′]dithiophene (BDT) unit. With our theoretical approach, we are able to study the critical factors affecting the morphology and efficiency such as, the chemical structure of the conjugated molecular, fullerene functional group, solvents, additives, blend ratio, and processing conditions (e.g., annealing temperature). Our results are consistent with experimental conclusions and provide useful guidelines for improving the efficiency of small organic solar cells.

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1 Introduction

In the circumstance of reduced availability of energy, as a new generation of solar cells, organic solar cells (OSCs) are attracting more and more attention worldwide due to their potential to be cost effective and flexible solar energy conversion devices.^1–4 In the past few years, many research efforts have been focused on polymer solar cells and impressive results were achieved.^5–10 To date, power conversion efficiencies (PCE) over 10% have been obtained for both solution-processed single-junction polymer solar cells and the tandem devices.² Small molecule OSCs are of great interest to the research community owing to the distinct advantages of small-molecule semiconductors, such as well-defined structures, and batch-to-batch stability.³ With consistent effort, the PCE of small-molecule OSCs had been improved from 0.03% to 10.08% in the past few years.^11–25 However, there is still much work needed to be done to overcome the hurdles of low PCE of small-molecule OSCs.

In order to find ways to overcome these limitations, computational approaches have been utilized for deciphering the roles of different variables that could improve the PCE and lifetime of an OPV cell.²⁶ A number of such studies have focused on some or all of the pertinent steps in solar energy conversion in an OPV device. These steps in chronological order are: (1) the absorption of light and excitons (i.e., electron–hole pair) generation; (2) the diffusion of the excitons to an interface; (3) the separation of the excitons into electrons and holes; (4) the transport of these electrons and holes to their corresponding electrode; and (5) the transfer of electrons and holes from the electrode to an external circuit. It is believed that the third step needs optimization in a bulk heterojunction (BHJ) design.²⁶ Here the design consists of a mixture of an electron donor and an electron acceptor (fullerene based molecules), which tends to form a phase segregated morphology. The phase segregation leads to a marked increase in the interfacial area between the donor and acceptor thus facilitating excitons separation. However, the ultimate goal is to achieve sizes of the donor and electron acceptor domains commensurate with the excitons diffusion length so that a higher number of excitons can reach the donor–acceptor interface. The importance of the morphology of polymer bulk heterojunctions could be found in the reviews, such as, Liu et al.²⁷ and Ruderer and Müller-Buschbaum.²⁸

Recently, three molecules named DR3TBDT-HD, DR3TBDTT and DR3TBD2T with a benzo[1,2-b:4,5-b′]dithiophene (BDT) unit and fullerene derivatives have been used as electron donor and acceptor materials.^29,30 The effects of blend ratio,³¹ additives^32,33 have been investigated to improve its morphology and efficiency. However, it is not clear how the chemical structures and the processing conditions affect the morphology and the efficiency. Here we combine DPD simulations and graph theory to predict the morphology and the efficiency of these small molecules organic solar cells. We study the effects of blend ratio of donor/PC₇₁BM, the annealing temperature of system, the additives, and the desolvation process. Our results are consistent with experimental conclusions and provide useful guidelines for improving the efficiency of small organic solar cell.

2 Simulation methods

2.1 DPD simulation

DPD was first proposed by Hoogerbrugge and Koelman^34,35 and later improved by Groot et al.³⁶ It is essentially a coarse-grained molecular dynamics (CGMD) method with a stochastic thermostat. In the DPD method, each bead represents a group of atoms and their movements are governed by:Where v_i, r_i and F_i represent the velocity, position vectors and total force acting on bead, respectively. Due to the significant reduction in the number of degrees of freedom, DPD can be used to simulate complex systems for much longer time. The forces acting on each bead can be divided into three components: conservative forces (F^C_ij), dissipative forces (F^D_ij) and random forces (F^R_ij).

All the three forces act only within a cut-off radius r_c, which is taken as the unit of length in the simulation. The conservative force represents a soft repulsive interaction in linear form:

Where r_ij = r_j − r_i, r_ij = |r_ij| and r̂_ij = r_ij/|r_ij|. The parameters a_ij, which represent the maximum repulsion between beads i and j, can be related to the Flory–Huggins parameter as follows:Where ρ represents the bead density of the system and a_ii is the repulsion parameter between the same beads. By matching the compressibility of water, a_ii and ρ are related through

The dissipative forces F^D_ij are the drag forces and the random forces F^R_ij represent the thermal noise of the system:

Where γ is the friction parameter, σ is the noise amplitude parameter and v_ij = v_i − v_j. The following equations should be satisfied to ensure the canonical ensemble equilibrium conditions and the fluctuation–dissipation relation:

σ² = 2γk_BT (9)

We use γ = 4.5, k_BT = 1, and thus σ = 3 according to eqn (9). F^S_i acts between consecutive beads within the same molecule, and has the following form:

Where C is the spring constant, and C is set to be 4 in this paper.³⁷

2.2 Predict the efficiency by using graph theory based on the morphology of the active layer

To improve the efficiency of organic solar cells, it is essential to understand the role of morphology and tailor fabrication process to get desired morphologies. Wodo et al.³⁸ provide a comprehensive suite of physically meaningful morphology descriptors, which reflect the complex nature of the BHJ and the underlying device physics. They formulate and implement a graph-based framework to efficiently construct this comprehensive suite. This approach is motivated by the equivalence between a discretized 2D/3D morphology image. These morphology descriptors are further classified according to the physical processes of the photovoltaic process: excitons diffusion, excitons dissociation into free charge carriers, and charge transport. We obtain the 3D morphology from our DPD simulation firstly. Then we use the following three descriptors³⁸ to characterize the discrete morphology. The descriptors are f_abs, f_diss, f_out.

f_abs Fraction of donor materials. Light is absorbed by the electron donor to generate the excited hole–electron pairs (excitons) in the active layer. We should find the fraction of donor materials.

If there is only donor and acceptor in the morphology, we could use f_abs respectively. However, our study involves solvent/additive in addition to donor and acceptor. It is necessary for us to modify descriptor f_abs to indicate the fraction of average donor/acceptor density.

([small rho, Greek, macron]_D: the average density of donor; [small rho, Greek, macron]_A: the average of density of acceptor).

f_diss Fraction of photoactive material within 10 nm distance (excitons diffusion length) to the interface.

By finding the fraction of donor material within this distance to the donor–acceptor interface, we identify the fraction of donor material that can theoretically contribute to this stage. Donor material distributed beyond this distance to the interface has a significantly lower chance of being useful.

f_out Fraction of materials with useful domains connected to the electrode.

Only regions with a connection to the electrode constitute paths for charge to travel and consequently can contribute to current generation. If charges are created in islands or “cul-de-sacs” with no direct connection to appropriate electrode, they eventually recombine.

Wodo et al. further define a “performance indicator” as product of these three fractions.

f = f_absf_dissf_out (15)

They imply that f is a good marker for J_sc. J_sc is a direct measurement of the device performance. In addition, the magnitude of short circuit current density is a quantity which is strongly affected by the morphology.^39,40

The size of the interface and the domain size affect the charge collection efficiency. When the interface area is big, the domain size will be small. There is an optimum interface area of the morphology for the efficiency. Young Min Nam et al.’s experimental results⁴¹ show that, when the domain size is about 6 nm, the active layer shows the optimum PCE. Meanwhile, Peter K. Watkins et al.⁴² use dynamical Monte Carlo model to evaluate the relationship between interface area and efficiency. Watkins et al. evaluated the “excitons dissociation efficiency” and “charge collection efficiency” separately and they conclude that there is an optimum interface area. We use the relationship of interface area and internal quantum efficiency derived from Watkins et al. and the optimum domain size 6 nm based on Young Min Nam et al.’s experimental results. And the descriptor is defined as the following:

A is the interface area.

When we use graph theory to estimate the efficiency, we use the empirical factors (f_abs, f_diss, f_out, f_interface) to represent different factors affecting the efficiency. We don't explicitly consider the process of the generation of the excition, the dissociation of the excition, and the charge transfer. Thus our model doesn't include all the factors affecting the final efficiency and overestimates the final efficiency. For example, Lin et al. explicitly investigate the charge-transfer processes at pentacene-C60 interface by using simulations.⁴³ They found that the positional relationship between donor and acceptor materials plays a critical role for the charge-transfer process. It will be interesting and challenging to simulate the charge transfer process of small molecule OPV explicitly and incorporate the factor into our model to improve the accuracy of the estimated efficiency.

In summary, the power conversion efficiencies based on morphology descriptors is defined as:

PCE = f′_absf_dissf_outf_interface (17)

3 Models and parameters

We model donor and acceptor molecules in a coarse-grained manner to simulate these systems on a length scale that is large enough to examine the blend morphology, while retaining necessary details at molecular level. As shown in Fig. 1, we model a donor using four coarse-grained beads. The acceptor or the solvent is represented by one bead. The additive (PDMS) is represented by three beads.

Fig. 1 Chemical structures of donor, acceptor, solvent and additive are represented by coarse-grained beads. (a) Chemical structures of C1 (DR3TBDTT-HD), C2 (DR3TBDTT), C3 (DR3TBDT2T)²⁹ are represented by coarse-grained beads A, B, D and C. (b) The fullerene derivative is represented by one coarse-grained bead Z. (c) The additive PDMS is represented by three coarse-grained beads, G, F, F. (d) The solvent chloroform is represented by one coarse-grained bead S.

To obtain the solubility parameters and interaction potential parameters of particles, we construct the amorphous structures of each fragment and perform molecular dynamics with COMPASS force-field^44,45 by using the Forcite module of Materials Studio software package to obtain cohesive energy, solubility parameters (δ_i)^46–48 and volume. According to Groot et al.,⁴⁹ we choose a standard volume of bead V_m, and this DPD bead is equal to N_m (real-space renormalization factor) water molecules (30 ų). Then we obtain the length scale, time scale and the number of step. The formulas are listed as following:

r_c = (ρV_bead)^1/3 = (3 × 100)^1/3 = 6.7 Å = 0.67 nm (18)

The Newtonian equation of position and velocity of particles is solved by a modified version of the velocity Verlet algorithm.⁵⁰ In the simulation, the radius of interaction, the particle mass, and the temperature were chosen as r_c = m = kT = 1 and σ = 3.67, while the particle density ρ = 3 (taking into account the computational efficiency, ρ = 3 is a reasonable choice).^34,35 The only parameter to be determined is the maximum repulsive force a_ij, which is chosen according to the linear relation with Flory–Huggins χ parameters.⁵¹

a_ij = a_ii + 3.27χ, a_ii = 25 (21)

The Flory–Huggins χ parameter can be obtained from experiments, free energy of mixing, or solubility parameter.^52,53 Here we obtain the χ through the solubility parameter (Table 1). And we obtain the solubility parameters from molecular dynamics (MD) simulations. A high-quality force field COMPASS (condensed-phase optimized molecular potentials for atomistic simulation studies)^54–56 is adopted, which is known to accurately reproduce experimental structures, densities, and solubility parameters.⁵⁷ MD simulations are performed under NPT thermodynamic ensemble. In our MD simulations, we obtain the cohesive energy (δ).⁵⁸ Then we get the Flory–Huggins χ parameter by the eqn (22).

Where V is the arithmetic average of molar volumes of two beads, δ_i and δ_j are the solubility parameters of beads i and j, respectively. R is perfect gas constant. T is the temperature of system. Then we obtain the repulsive force a_ij according to the eqn (21). The calculation results are listed in Table 3.

Table 1 Parameters derived for the coarse-grained beads defined in Fig. 1

	A	B	C1	C2	C3	D	S	F	G	Z
Solubility parameter	17.6	14.8	15.8	15.1	16.1	9.26	15.5	11.3	10.02	20.5
Vmol (Å)	170	82	923.5	579	1048.6	83.68	96.74	141.01	126.4	1003
M (g mol^−1)	130	84	872	578	956	29	29	89	58	1030

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Table 2 The parameters of DPD simulation

Parameter	Value	Meaning
aii	25	Repulsion between identical particle types
T*	1.0	Reduced temperature
Vm	100 Å^3	The volume of standard bead
Nm	3	Number of water molecules represented by one bead
δt	0.02	Time step
T	103.55 ps	Characteristic time scale
rc	0.67 nm	Range of soft repulsive interaction
N	25000 step	The number of step
CS	4.0	Spring constant

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Table 3 The interaction parameters a_ij between beads at 346.4 K

	A	B	C	D	F	G	S	Z
A	25.00
B	26.01	25.00
C	26.86	25.52	25.00
D	34.48	37.68	47.56	25.00
F	31.87	25.57	25.14	25.43	25.00
G	33.83	27.55	43.64	25.10	25.16	25.00
S	25.62	25.05	25.05	28.70	27.40	28.50	25.00
Z	28.92	37.75	43.64	58.35	45.83	27.40	35.10	25.00

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In DPD method, the simulation length scale and time scale of molecular motions are much larger than ordinary molecular dynamics (MD) simulations. We choose the particle mass and the temperature and interaction range as units of mass, energy, and length, hence r_c = m = kT = 1, and the simulated time is expressed in the natural unit of time.⁴⁹ The simulation boxes of sizes in our DPD simulation is 32 × 32 × 32 r_c³. ​The parameters of DPD simulations are summarized in Table 2.

4. Result and discussion

4.1 The effect of the blend ratio on the morphology and the efficiency

The blend ratio of donor and acceptor is one of the most important factors affecting the morphology of BHJ solar cells. Jiaoyan Zhou et al.,²⁹ Yanming Sun⁵⁹ and Aung Ko Ko Kyaw⁶⁰ illustrated the importance of the ratio of small molecular donor/PC₇₁BM. Here we study the morphology and domain size of small molecular donor/PC₇₁BM for different composition ratio. Fig. 2 shows the equilibrated morphology for different molar percentage of PC₇₁BM: 33.3%, 50%, 66.7%, and 75%. In addition, we studied three different small molecules C1, C2, C3 as the donor, as shown in Fig. 2a–c respectively. The predicted efficiencies are summarized in Fig. 2a–c. The domain sizes are summarized in Fig. 2d–f.

Fig. 2 (a) The dependence of Power Conversion Efficiency (PCE) on the molar percentage of PC₇₁BM for C1/PC₇₁BM; (b) the dependence of Power Conversion Efficiency (PCE) on the molar percentage of PC₇₁BM for C2/PC₇₁BM; (c) the dependence of Power Conversion Efficiency (PCE) on the molar percentage of PC₇₁BM for C3/PC₇₁BM; (d) the dependence of the domain size on the molar percentage of PC₇₁BM for C1/PC₇₁BM; (e) the dependence of the domain size on the molar percentage of PC₇₁BM for C2/PC₇₁BM; (f) the dependence of the domain size on the molar percentage of PC₇₁BM for C3/PC₇₁BM; domain size is derived from the volume divided by the interface area. The optimum domain size favorable for efficiency is around 6 nm.

Fig. 2a–c show consistent results that, when percentage of PC₇₁BM is 66.7%, the efficiency is the highest. By analyzing the domain sizes as shown in Fig. 2d–f, we can see that when the domain size is around 6 nm, the efficiency is good. In order to rationalize the different factors affecting the efficiency, we list the factors in Table 4.

Table 4 Morphology descriptors depends on the blend ratio of C1/PC₇₁BM

Factor	Molar percentage of PC71BM	33.3%	50%	66.7%	75%
fabs	Fraction of light absorbing material	89.6%	79.5%	64.8%	54.8%
fdiss	Fraction of photoactive material within d < 10 nm to the interface	81.8%	83.0%	87.5%	87.4%
fout	Fraction of useful domains connected to the electrode	6.8%	22.9%	95.1%	97.8%
F	f = fabs* fdiss* fout	5.0%	15.1%	54.0%	46.8%
PCE	Power conversion efficiency	0.5%	2.3%	10.3%	9.7%

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As shown in Table 4, among the various factors, f_out is the most important factor for different blend ratios. When the percentage of PC₇₁BM is 33.3% or 50%, the islands or ‘cul-de-sacs’ morphology is formed. Such morphology is poor for the fraction of useful domains connected to the electrode and leads to poor efficiency. Thus for 33.3% and 50%, f_out is low and the final efficiency is low. Meanwhile, when the percentage of PC₇₁BM is high, such as 75%, f_abs is limited, since the donor is responsible for absorbing the light. In conclusion, 66.7% percentage shows the best efficiency.

When Zhou et al.²⁹ made the device of C1, C2, C3 with PC₇₁BM, they chose the blend ratio as (1 : 0.8 w/w). It corresponds to the volume percentage of PC₇₁BM: 66.7%, which is the best blend ratio based on our results. Aung Ko Ko Kyaw et al.⁶⁰ studied the dependence on the percentage of PCBM. They concluded that, when the weight: weight ratio between DTS(PTTh₂)₂ and PCBM is 70 : 30 or 60 : 40 shows the best mobility and performance, which is close to our best blend ratio for C1, C2, C3 with PC₇₁BM: (1 : 0.8 w/w).

4.2 The effect of the annealing temperature on the morphology and the efficiency

We then investigated how the annealing temperature affects the morphology, PCE and the domain size of SM OSC (see Fig. 3). In the DPD simulation, we set the reduced temperatures (T*) to the corresponding physical temperature. A rough but simple estimation of the value of this reduced temperature in terms of physical temperature can be given by the equation^61,62: T = 133T^∗ − 33 to simplify the relationship between T and T*. The reduced temperatures T^* = 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, and 1.6 correspond to physical temperature T = −6.4, 20.2, 46.8, 73.4, 100, 126.6, 153.2, and 179.8 °C.

Fig. 3 (a) The dependence of Power Conversion Efficiency (PCE) on the temperature of PC₇₁BM for C1/PC₇₁BM; (b) the dependence of Power Conversion Efficiency (PCE) on the temperature for C2/PC₇₁BM; (c) the dependence of Power Conversion Efficiency (PCE) on the temperature for C3/PC₇₁BM; (d) the dependence of the domain size on the temperature for C1/PC₇₁BM; (e) the dependence of the domain size on the temperature for C2/PC₇₁BM; (f) the dependence of the domain size on the temperature for C3/PC₇₁BM; the molar percentage of PC₇₁BM is 66.7%.

Fig. 3 shows that the morphology and PCE are the best when the reduced temperatures is 1.0, namely, the physical temperature is 100 °C.⁶³ Similarly, temperature has been found to be an important parameter for morphology and efficiency, experimentally.^64,65 Upon changing the heating temperature, the extent of phase separation evolves and finally forms phase-separated network-like morphology, which benefits the efficiency of the device.

4.3 The effect of the additives on the morphology and the efficiency

Kenneth R. Graham et al.⁶³ investigated the effect of macromolecular additive, polydimethylsiloxane (PDMS) on the performance of solution processed molecular bulk heterojunction solar cells. Their results show that PDMS has a strong influence on film morphology, with a significant decrease in film roughness and feature size observed. As a general, the additive has a higher solubility for PC₇₁BM than the donor material.³² This increases donor aggregation and leads to the formation of high ordered D and A phases, thus improving device performance.

Here we investigated how the Degree of Polymerization (DP) of PDMS affects the morphology and PCE of OSC. As shown in Fig. 4, the introduction of PDMS will improve the PCE. For C1, C2, and C3, PCE will increase, when there is PDMS introduced. In addition, our results show that, when DP of PDMS is equal to 20, PCE will be slightly better than other DP values (e.g. DP = 4, or 100). This is consistent with Kenneth R. Graham's⁶⁶ results. Graham et al. showed that the PCE is enhanced from 1.42% without additive to 2.35% with 410 g mol⁻¹ PDMS, which corresponds to DP around 4.4.

Fig. 4 The dependence of the power conversion efficiency (PCE) on the degree of polymerization (DP) of PDMS as additive in the active layer formed by C1, C2, or C3 with PC₇₁BM. We highlight DP = 4, 20, or 100. When DP = 20, it leads to the best PCE.

As summarized in Table 5, we can see that the domain size will increase as PCE, when there is PDMS introduced.²⁹ Our results show that, when there is PDMS introduced, f will increases, which corresponds to the short current. Our f values are consistent with the short current from experiments.²⁹ Our approach is useful to illustrate the effect of additives and will be useful for rational design of additives.

Table 5 The effect of the additive on the PCE, domain size, short current, and morphology descriptors

Donor: PC71BM		C1		C2		C3
		Without additive	With additive	Without additive	With additive	Without additive	With additive
PCE (%)	Exptl.^29	6.07	6.50	7.22	7.80	11.66	11.73
	Modeling	6.95	10.30	10.19	10.49	10.04	10.35
Domain size (nm)	Exptl.^29	15–35	20–45	10–30	15–40	8–30	15–35
	Modeling	5.76	6.02	6.26	6.24	5.79	5.83
J (mA cm^−2)	Exptl.^29	12.16	11.75	12.92	12.95	11.66	11.73
f (%)	Modeling	52.8	53.9	50.2	51.8	55.0	56.4

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In addition, we studied the desolvation process based on DPD simulation and graph theory. Fig. 5 shows the change of PCE and morphology during desolvation process. Based on our results, we can see that the aggregation level of PC₇₁BM phase is becoming large with the evaporation of the solvent and percolating network of electron-donor and electron-acceptor materials is formed. And the PCE increases in the desolvation process. Our approach is able to provide the dynamical process during desolvation and will be useful for optimizing the desolvation procedure in the fabrication.

Fig. 5 PCE and morphology of C1/PC₇₁BM evaluated from DPD simulation and graph theory during desolvation process. X_S/A represents the percentage of the solvent.

5 Conclusions

In this work, we use dissipative particle dynamics simulation and graph theory to predict the morphology and efficiency of small molecular organic solar cell. Our simulations explore the effects of the structural parameters on the morphology. We compare our results with recent experiments and provide a quantitative and qualitative analysis for the experiments studies.

Certainly the Small molecule as the donor is the good choice for organic solar cells. In summary, we combine atomistic simulation with mesoscale simulation to predict the morphology of BHJ solar cells and the optimal parameters for morphology of BHJ solar cells. For the effect of the blend ratio, we find that the molar ratio of PC₇₁BM 66.7% leads to the best performance. In addition, we study the effect of temperature and the additives on the morphology and the performance of small molecular organic solar cell. Our approach is useful to illustrate the mechanism and the important factors for organic solar cell. And it could be used to optimize other important factors to improve the performance of organic solar cell.

Acknowledgements

The work is supported by the National Basic Research Program of China (973 Program, Grant No. 2012CB932400), the National Natural Science Foundation of China (Grant No. 91233115, 21273158, and 91227201), a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). This is also a project supported by the Fund for Innovative Research Teams of Jiangsu Higher Education Institutions, Jiangsu Key Laboratory for Carbon-Based Functional Materials and Devices, Collaborative Innovation Center of Suzhou Nano Science and Technology.

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