gmp007/optical-modeling

Optical Modeling (Transfer Matrix): Modeling the light propogation, light absorption, transmission, and reflection in a multi-layer thin-film stack and current in solar cells.

Optical-Modeling :

Modeling the light propogation, light absorption, transmission, and reflection in a multi-layer thin-film stack.

The model is based on a transfer matrix method, which can be found in the following paper:

L. A. A. Pettersson et al., “Modeling photocurrent action spectra of photovoltaic devices based on organic thin films ”, J. Appl. Phys. 86, 487-496 (1999) [link to the paper]

What it can do?

OpticalModeling class

The OpticalModeling object is designed to model the light propogation in a stack of thin films with different materials at normal incidence. It can be used to calculate the following properties for thin films:

• Light absorption
• Transmission
• Reflection

And the following properties in solar cells under standard AM 1.5 solar irradiation at normal incidence:

• Electric field profile
• Charge carrier generation rates (equivalent to photon absorption rate)
• Jsc (short circuit current density, assuming 100 % IQE, i.e. all absorbed photons are converted into charge carriers)

OpticalModeling Examples

Below are some example output figures for a device stack consisting of these materials at the given thickness (their refraction indices are included in the Index_of_Refraction_library_Demo.csv file):

Layer No.	Material	Thickness		note
0	Glass	N/A		substrate
1	ITO	145 nm		transparent electrode
2	ZnO	120 nm		window layer
3	PbS	250 nm		main light absorbing layer
4	Au	150 nm		gold electrode

""" set up user input """
# (Name_of_material, thickness_in_nm)
Device = [
("Glass" , 100), # layer 0 # thickness of "thick" substrate can be set to an arbitrary number 
("ITO"   , 145), # layer 1
("ZnO"   , 120), # layer 2
("PbS"   , 250),
("Au"    , 150)
]
libname = "Index_of_Refraction_library_Demo.csv"
Solarfile = "SolarAM15.csv" # Wavelength vs  mW*cm-2*nm-1
wavelength_range = [350, 1200] # wavelength range (nm) to model [min, max]

Run the simulation by creating an OpticalModeling object and the call the RunSim method:

# initialize an OpticalModeling obj OM
OM = OpticalModeling(Device, libname=libname, WLrange=wavelength_range)
OM.RunSim()

And then you woul get the following output figures

Absorption, Transmission, Reflection of each material in the device stack

Carrier generation (photon absorption) rate at different wavelengths and position.

Position vs carrier generation (photon absorption) rate in the device.

This is basically the summation of the generation rates over different wavelengths for each position in the figure shown above)

Electric field profile in each material at different wavelengths and position.

Position vs electric field in the device at selected wavelengths

(selected slices of the figure above)

Finally, by calling JscReport() method,

OM.JscReport() # print and return a summary report

it would print out a brief summary that looks like this in the console :

"""
Summary of the modeled results between 350.0 and 1200.0 nm

Layer No. Material  Thickness (nm)  Jsc_Max (mA/cm^2)
        1      ITO             145               2.61
        2      ZnO             120               0.97
        3      PbS             250              24.07
        4       Au             150               1.47
"""

===

OMVaryThickness

The OMVaryThickness object is a subclass of OpticalModeling. It adds some features so that you can vary the thickness of one or two layers in the thin film stack to see how the properties of interest – either absorption (and thus Jsc) in 'any' layer, transmission, or reflection) – respond to the change of thickness.

For example, you can change the thickness of layer2, and watch how the following properties changes with respect to it:

• Transmission of the whole stack
• Reflection of the whole stack
• Absorption in layer1, layer2, layer3...

This feature would be very helpful for design of experiments. Below are some example outputs by using the OMVaryThickness object.

Examples for OMVaryThickness

These examples use the same device stack to that in the example for OpticalModeling. First create a VaryThickness object and then call the method VaryOne() with the desired parameters to run the simulation

OMVaryThickness Example 1

In this example, we vary the thickness of the PbS layer (ToVary=3) and set the target to PbS itself (target=3).

VT1 = OMVaryThickness(Device, libname="Index_of_Refraction_library_Demo.csv", WLrange=[350, 1200])
VT1.VaryOne(ToVary=3, t_range=range(50, 601, 10), target=3)

The absorption in the PbS vs the thickness of PbS

The Jsc from PbS vs the thickness of PbS.

OMVaryThickness Example 2

In the second example, we vary the thickness of the ZnO layer (ToVary = 2)to see how the properties of the PbS layer (target = 3) change with it.

VT2 = OMVaryThickness(Device, libname="Index_of_Refraction_library_Demo.csv", WLrange=[350, 1200])
VT2.VaryOne(ToVary=2, t_range=range(20, 551, 10), target=3)

As you can see, because of the interference effects in thin films, the absorption of the PbS layer is not a monotonic function of the thickness of ZnO. It also shows strong wavelength dependence: every wavelength shows a different behavior. This example demostrates the usefulness of the OMVaryThickness object for the design of experiments.

Absorption in PbS vs thickness of ZnO

Jsc from PbS vs thickness of ZnO

Plot other target layers

Once the simulation has been done after calling VaryOne(), we can just call the PlotVaryAbs(target) and PlotVaryJsc(target) methods to generate this plot again or generate other plots (different target layers) without running the simulation again. We can call

VT2.PlotVaryAbs(target=2) # ZnO layer

to get the absorption in the ZnO layer, which increases with the thickness of itself:

Absorption in ZnO vs thickness of ZnO

If, instead, we use target 1 (ITO layer)

VT2.PlotVaryAbs(target=1) # ITO layer

we get the absorption of the ITO layer with respect to the thickness of the ZnO layer. (ITO is very transparent to the visible light but it could show strong absorption in the near-infrared (>750nm) ). This figure probably does not provide too much useful information in practical, but I found the inteference pattern very beautiful (science!) -- I intentionally simulated a lot of data points to make the overlap of all curves look more interesting. That's why I decided to show it here.

Beautiful patterns: Absorption in ITO with respect to the thickness of ZnO

In addition to the absorption in each layer, we can also use "T" to plot the transmision,"A" for the total absorption (sum over all layers), and "R" for reflection in the device stack with respect to the thickness of the ToVary layer.

VT2.PlotVaryAbs(target="T") # Transmission
VT2.PlotVaryAbs(target="A") # absorption
VT2.PlotVaryAbs(target="R") # Reflection

The transmission is very low (< 1%) because there is an opaque electrode (150 nm of gold).

The overall absorption in the device stack

The reflection of the device: everything not absorbed is reflected back!

More example figures for OMVaryThickness

How to Run OpticalModeling

There is a RunModeling.py file desgined to take user inputs and then run the optical modeling based on your inputs. To run the simulation, simply provide a library of the refraction indices of the materials of interest and specify the materials and thickness in the thin film stack in the RunModeling.py file and the run it. You can get the some output figures with options to save the data as .csv files and figure in your desired format (such as .pdf vector graphics or .png raster graphics). More information on how to run it and how to specify inputs, and how to save data/figures can be found in the comments in the RunModeling.py file.

How to Run VaryThickness

There is a RunVaryOneThickness.py file desgined to take user inputs and then run the optical modeling based on your inputs.