Optimization and Understanding of Exciton Diffusion in Organic Solar Cells via Novel Monte Carlo Modeling

Taesoo Daniel Lee, North Carolina School of Science and Mathematics

Introduction • Energy Issues

– Earth’s increasing depletion of fossil fuels and nonrenewable energy sources has called for alternative energies such as organic solar cells

• Organic Solar Cells and Benefits – Potential to become more efficient than inorganic solar cells

(which are toxic and expensive)– Cheap, less toxic, easy to manufacture

• Computational Monte Carlo Modeling– Quick and easy to compute thousands of different results – Able to model interdependent relationships between input

variables– Multiple probabilistic iterations at the click of a mouse– Saves money

Background Information

The bulk heterojunction solar cell is the most common organic solar cell. It is a heterogeneous mixture of acceptor and donor material.

Pros Cons

Easy to assemble, high performance

Cannot control morphology

The bilayer junction is easily manufactured with an anode and cathode. The only issue is getting an exciton, an electrically neutral bound electron-hole pair, to reach an interface without emitting heat or light.

Improve Organic Photovoltaics• Increasing the exciton diffusion

length (LD)• The length an exciton hops

inside the junction before reaching the interface.

• Longer the LD, the more photocurrent and voltage, better performance

• LD is impacted by light absorption and chemical interactions within the cell

Background Information (continued)

• Porphyrins– Light absorbing molecules that contain four pyrrole rings. – Captures photons and promotes efficient electron transfer – Used to increase light absorption in organic solar cells. – Tetrakis (4-carbomethoxyphenyl)

Synthesized by Walter Research Group

TCM4PP has methyl groups (single carbon chains).

TCO4PP has octyl groups (eight-carbon chains).

Photoluminescence decay data via Time-Correlated Single Photon Counting for these two compounds were chosen because of their impressive diffusion lengths of 15-30 nm that had been calculated before.

Introduction of Problem

• Problems with aggregation of PCBM (phenyl-C61-butyric acid methyl ester) molecules (electron acceptor) – Leads to lower efficiencies and quicker

photoluminescence decay– Shorter lifetime and shorter diffusion lengths for

excitons, meaning lower photocurrent– One of the leading detrimental problems with

organic bulk heterojunction solar cells

GGuiding Question

•Compare the PCBM aggregation of TCM4PP and TCO4PP and analyze the morphology of these two organic compounds using a Novel Monte Carlo model in order to ultimately help optimize semiconductor blends, thus leading to a deeper understanding of organic solar cells to improve efficiencies.

•Can we make high efficiency bi-layer organic solar cells using the same methodology?

Materials- Microsoft Excel - Photoluminescence Decay

Data Set of TCM4PP and TCO4PP acquired from local lab (Walter Research Group)

- Computer with a C++ Program/ GNU Compiler

- 3-4 months to write code

HypothesisHypothesize that TCO4PP will experience a longer diffusion length and a smaller decrease in relative quenching efficiency because of the structural difference between the octyl and methyl chains.

Hypothesize that there will more aggregation in TCM4PP in comparison to TCO4PP. When the molecules are excited, I hypothesize that the shorter methyl chains could potentially cause an imbalance in electron mobility because TCM4PP molecules may be too close to each other, possibly annihilating each other.

Modeling Exciton DiffusionPrimary• Created an Diffusion Monte Carlo

software through C++. • PL decay data of TCM4PP and TCO4PP

from lab was fitted and simulated by my software.

• Models the diffusion of excitons in the semiconductor blend while keeping the hopsize constant and varying the PCBM fraction in a 50 x 50 x 50 nm box from the modeling.

Equations are based on the Einstein- Smoluchowski’s Theory of Diffusion (integrated into code)

Model was written to simulate the hopping of excitons in the box to the right. Iterations gave you the number of radiatively decayed excitons

Modeling Exciton DiffusionSecondary • Vary the hopsize to get a certain

quenching efficiency • Generated exciton diffusion lengths

and simulated photoluminescence decay of exciton.

• Algorithm varying the hopsize based on the inequality to the right.

• Processes iterations until the inequality holds true for the biggest possible hopsize.

• Big hopsize= longer exciton diffusion length= better performance in organic solar cell

Calculations from the SimulationFrom Data Set

Generated from Model

The primary experiment calculated the number of relatively quenched excitons, and the number generated was utilized to find the relative quenching efficiency (equation to right) in the cell . This was plotted vs. the variable volume fractions (each volume fraction was run in the model).

Screenshots from Simulation

Each iteration

Mean root square displacement of excitons.

Mean root square displacement in one dimension

Average exciton displacement from the original position in 3D

One-dimensional average displacement

Code from Simulation• Several classes were created because they are essentially an expanded concept of

data structures- they can function as members • Importing previous classes

Sample Code: ClassBoolean3DThis code created the 50 x 50 x 50 nm cube in which the exciton would hop/radiatively decay. Boolean 3D is one of the basic operations done for 3D models. It sets and defines the cell on the grid.

Sample Code: ClassBoolean3DThis code created the 50 x 50 x 50 nm cube in which the exciton would hop/radiatively decay. This approach involved

Sample Code: Class Quencher: “double” initialized the presence of a decimal, in this case x2, y2, and z2 because it indicates that x2, y2, and z2 are decimal coordinate points. Class Quencher set new coordinates for a quencher, checks for boundary conditions, and calculates the distance of the exciton to the center of the simulation cube. Also randomized the position of the quencher molecule (PCBM material).

Benefits of Monte Carlo Modeling • Allows for a deeper understanding of exciton diffusion in the

morphologies of organic semiconductor-fullerene blends. • Excitons undergo a random walk in this medium and decay

radiatively when contacted with a quenching site. • Data can be graphed in a PL decay- number of radiatively decayed

excitons vs. time. • Relies on the comparison between polymer’s emission with and

without the quencher, so it is not as advanced. • Ability for optimization and numerical integration, and with the

degrees of freedom that excitons can move in all six directions, tracking exciton diffusion was fairly accurate.

• Simulation’s ability to run over and over again to obtain the distribution of unknown excitons in semiconducting polymer.

Results- Primary• Aggregation: Data from the Monte Carlo Model was analyzed. • The hopsize of the exciton was kept constant. • Relative quenching efficiency was graphed along with an increasing volume

fraction of PCBM. • The different curves were examined for aggregation of PCBM molecules.

• More aggregation in TCO4PP

The model assumes that the diffusion length is most accurate at low volume fractions (0.06%)

The red (0.20%) and green (0.23%) curves deviate from the blue curve, indicating heavy aggregation. This indicates that as volume fraction of PCBM increases, the aggregation increases and inhibits electron mobility.

The model assumes that at the lowest volume fraction (0.028%), the diffusion length is the most accurate.

TCO4PP is the better molecule because PCBM aggregates less. There is almost no deviation between the 0.2%, 0.028%, and 0.3% PCBM volume fraction curves, meaning there there is almost no aggregation, which is good for the solar cell!

The boxes with “dots” show the excitons in the medium at a given volume fraction. The model was written to generate .bmp images of these cross-sections.

Results- Secondary •Vary the hopsize to get specific relative quenching efficiency.

•Determine the Exciton Diffusion Length

PL (photoluminescence) decay data, shown to the left, depends on the composition of polymer-PCBM blends, and can provide information about exciton kinetics.

At high PCBM volume fractions, most of the excitons are quenched, resulting in a shorter PL decay time and leveling of the relative quenching efficiency curves.

The PL decay of many polymers is mono-exponential, especially in the case of P3HT because of the lack of interchain interactions between the isolated molecules in the solvent.

Longer exciton lifetimes in TCO4PP!

Results

• TCO4PP demonstrated a longer lifetime (almost doubled the lifetime of TCM4PP)

• Longer exciton diffusion lengths in TCO4PP, meaning TCO4PP does not aggregate as much as TCM4PP.

• The diffusion lengths of TCO4PP are almost twice as long as TCM4PP, indicating that organic solar cells using TCO4PP may see up to two times their original efficiency.

Discussion• Better to use lower concentrations of PCBM when

determining LD organic semiconductors.

• The deviation in TCM4PP between the 0.06, 0.20, and 0.23 curves were expected. – Reasonable to assume that the formation of clusters

during the solvent evaporation in the manufacturing process is more likely in blends of higher PCBM fractions.

– Formation of clusters is indicated by the aforementioned deviation.

Example of Aggregation

Discussion

As hypothesized, TCO4PP experienced a much smaller decrease in relative quenching efficiency compared to TCM4PP. The bonding operative in these units is described as a cooperation between H-O bonding, involving the C5H9O2 groups of the PCBM molecule, and fullerene-fullerene attraction.

Conclusion • Developed deeper understanding and discoveries of morphologies of porphyrins/polymers.

• Determination of longer diffusion lengths with TCO4PP for up to two times more efficient organic solar cells.

• Investigated the effect of PCBM aggregation on organic semiconductor performance.

• Novel and computational model to simulate molecular interactions of excitons in organic semiconductor.

–Allows for a deeper understanding of exciton diffusion in the morphologies of organic semiconductor blends that traditional lab work cannot achieve.

–Expedience of time, and saves money.

Impact

• How do we want to treat our environment? – Computational science revolutionizes the improvement of

organic solar cells– We can observe molecular interactions at a level

impossible in the lab– Improvement of organic solar cells brings us one step

closer to a cleaner and more green world• Can we use computing to find ideal materials for

usage in organic solar cells? Yes– Benefits: saves time, money, and insight into levels never

done before, hence the novelty.

Future Work

• Using different types of quenchers such as TiO2., which is already established as an exciton quencher in DSSC.

• Thermal annealing- integrating temperature into diffusion. – Temp increases, probability of photon absorption by excitons

increases as well. • Clarify and understand obscurities regarding molecular

orientation and metal-organic framework• Making the code for the Monte Carlo Model open-source

and integrating more parameters. – Beauty of research is making efforts collaborative: two minds

work better than one.

Acknowledgements

• Dr. Myra Halpin– Provided guidance and support

• Walter Research Group, UNC-Charlotte– Provided photoluminescence decay data set for two compounds (TCM4PP and

TCO4PP)

• Mr. Oleksandr Mikhnenko, UC-Santa Barbara– Provided guidance, helped to edit code and offer improvements