Simulating optical behaviors of multi-layered solar devices via the transfer-matrix method
Eva Beeching, Dustin Hemphill
Slippery Rock University, Department of Physics and Engineering

Project Goals
• Study electromagnetic properties of
inorganic nanopillar devices.
• Calculate absorption spectra from
multi-layered solar devices, including a
nanopillar array.
• Compare simulation results with
experimental data
• Understand limitations of simulation
technique, differences between
experimental and simulated spectra

Methods
• Start with a 1-D model instead of full
3D nanopillars.
• Create stacked layers of uniform
dielectric materials.
• Transfer Matrix Method can be used to
calculate overall transmission and
reflectance from a many layered
structure.
• Simulate model using input parameters
to match sample.
• Compare to absorption data from UVVis spectrophotometer.

The Transfer Matrix Method

Transmission and Reflection Spectra

• The transfer matrix method is used to
analyze the propagation of quantum
particles or waves through a medium
• The transfer matrix is the mechanism
that describes the incoming light wave in
terms of the outgoing wave of each layer.

T
R

• Assumes no energy losses
in layers
• Requires each layer of the
structure to be a uniform
slab of dielectric material.
• Cannot simulate the true 3D
nanopillar structure.

300 400 500 600 700 800 (nm)

• For a plane wave incident on a layered
structure, the transfer matrix method
calculates how much of the light is both
transmitted through and reflected by the
layered structure.

Future directions
Fig 3. Transmission spectra of the MATLab simulation
(above right) which matches closely with the spectra
achieved by [1] (above left) for the same wavelength
range. However, the reflection spectra differ.

Simulation and Parameters
The simulation [2] uses input parameters of
permeability, permittivity, and thickness of
each layer, as well as number of layers to
produce transmission and reflection spectra,
and absorption spectra.

Absorption Spectra

• Computationally study the
effect of nanopillar structures
by estimating effective
optical properties of the
nanopillar layer.
• Explore the feasibility of
using a more advanced
numerical technique, such as
rigorous coupled-wave
analysis (RCWA) to calculate
absorption spectra from a
true nanopillar structure.

References
Fig 4. Simulation absorption spectra (above left) vs
observed spectra [3] taken via UV-Vis (above right). They
both show peaks around 275 nm, however are markedly
different after this wavelength.

Multilayered Solar Devices

Discussion of Results
Fig 1. Multilayered solar devices made
of flexible organic polymers offer
advantages over traditional solar cells,
namely in cost efficiency. Adding a
nanopillar structure aims to enhance the
light absorption of the layered device.

Drawbacks of TMM

Fig 2. Example of the input code for the
simulation of a light wave passing
through structure of PEDOT:PSS
(polymer layer), ITO (conductor layer)
and glass substrate, using literature values
of permeability and permittivity.

• The above data is for a 3-layered structure of PEDOT:PSS,
ITO, and glass substrate.
• This simulation produces accurate transmission data,
however the absorption and reflection do not match
observed data or literature values. Reasons for this could
include the fabricated samples not being perfect thin films
(i.e., inconsistent thicknesses).

[1] Rumpf et al. “IMPROVED
FORMULATION OF SCATTERING
MATRICES FOR SEMI-ANALYTICAL
METHODS THAT IS CONSISTENT WITH
CONVENTION”, Progress In
Electromagnetics Research B, Vol. 35,
241–261, 2011
[2] Sathyanarayan Rao
(2021). Transmittance and Reflectance
Spectra of Multilayered Dielectric Stack
using Transfer Matrix
Method (https://www.mathworks.com/m
atlabcentral/fileexchange/47637transmittance-and-reflectance-spectraof-multilayered-dielectric-stack-usingtransfer-matrix-method), MATLAB Central
File Exchange. Retrieved April 3, 2021.
[3] Beeching (2019) Study of Optical
Properties of composite layers of MEHPPV nanopillars and PEDOT:PSS films.