1) The document describes a Monte Carlo model developed to simulate exciton diffusion in organic solar cells containing different porphyrin compounds. 2) The model simulated the diffusion and decay of excitons in a cube representing the solar cell material. Results showed less aggregation of PCBM molecules and longer exciton lifetimes for the compound TCO4PP compared to TCM4PP. 3) By varying the simulation parameters, the model determined TCO4PP had significantly longer exciton diffusion lengths than TCM4PP, indicating it could enable up to two times higher efficiencies in organic solar cells.

1. 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

2. 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

3. 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

4. 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

5. 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.

6. 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

7. 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?

8. 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
Hypothesis
Hypothesize 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.

9. Modeling Exciton Diffusion
Primary
• 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

10. Modeling Exciton Diffusion
Secondary
• 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

11. Calculations from the Simulation
From 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).

12. 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

13. 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: ClassBoolean3D
This 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.

14. Sample Code: ClassBoolean3D
This code created the 50 x 50 x 50 nm cube in which the exciton would hop/radiatively
decay. This approach involved

15. 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).

16. 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.

17. 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.

18. 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.

19. Results- Secondary
•Vary the hopsize to get specific relative
quenching efficiency.
•Determine the Exciton Diffusion Length

20. 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!

21. 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.

22. 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

23. 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.

24. 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.

25. 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.

26. 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.

27. 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