This article describes the Phosphors and Fluorescence Model, which is the most sophisticated tool available for simulating photoluminescent materials in OpticStudio. The model is discussed, and then its use is demonstrated through the simulation of a luminescent solar concentrator.
Authored By Zachary Derocher
Introduction
Photoluminescence is the absorption and emission of photons through a process of photo-excitation and radiative relaxation. The effect can be simulated in OpticStudio through the phosphors and fluorescence model. In this article, the phosphors and fluorescence model parameters and usage are discussed, and then the model is demonstrated through the simulation of a quantum dot luminescent solar concentrator (QDSC) system intended for solar energy applications.
Photoluminescence simulation in OpticStudio
With the release of OpticStudio 17, the functionality of the Standard photoluminscent model has been extended. In addition to clarifying spectra definitions, the model now uses the absorption spectrum to calculate mean free path instead of as a scale factor on ray intensity. This allows for more accurate simulation of broadband sources incident on photoluminescent materials, as mean free path now has wavelength dependence.
The photoluminescence mean free path is calculated through a user-specified extinction wavelength (λx), extinction coefficient (ε(λx)), particle density (n), and the user specified absorption spectrum (Ameas(λ)). The Absorption Spectrum has relative units and represents the likelihood that a photon will be absorbed, and it is defined to relate the input and transmitted intensities.
The extinction coefficient (with units of Molar-1cm-1) is provided by the user at a single wavelength, the extinction wavelength. It is a reference scale factor which is used to convert the absorption spectrum to a wavelength dependent extinction coefficient. The extinction coefficient for any input wavelength is calculated according to:
It is known that transmitted power is related to mean free path, l(λ), by:
where x is sample length. From this relation and the defined absorption spectrum, the photoluminescence mean free path can be calculated as:
where from the Beer-Lambert Law, ε(λ) is related to absorption as:
and c is the molar concentration (mol/L) of photoluminescent particles, converted from the user specified particle density n:
Using this definition of mean free path and the known sample length, the probability of the occurence of a photoluminescence event is calculated for each ray. If absorbed, the ray will be re-emitted with an intensity determined by either the quantum yield or excitation spectrum. If quantum yield (Q) is used, as in the example in this article, the emitted intensity is given by:
where the emitted wavelength is selected probabilistically from the user-defined emission spectrum. The emission spectrum is defined in relative units of spectral photon flux (counts/second). The output wavelength is restricted so that it cannot exceed the incident wavelength.
The Mie scatter model can also be optionally included in the simulation. In the Mie scatter model, the mean free path is either specified directly, or determined based on the particle density. If Mie scattering is being considered, then a total mean free path is determined based on both the Mie and Photoluminescence model parameters. Then, if a scattering event is determined to occur for a ray, the type of event is determined probabilistically, based on the ratio of the photoluminescence and Mie mean free paths. For more information on the Mie model, please refer to "How To Simulate Atmospheric Scattering Using a Mie Model".
Quantum dot solar concentrator
Quantum Dot Luminescent Solar Concentrators (QDSCs) are designed to be employed in photovoltaic (PV) systems to improve the cost efficiency of the PV module by increasing the ratio of output to surface area. The bulk of the design is a transparent rectangular substrate of a high index material which is manufactured to house a high density of semiconducting nanoparticles (quantum dots). These nanoparticles are typically designed to absorb light in the 300-450nm range and re-emit to longer wavelengths as efficiently as possible. The PV module is placed on one of the small sides of the rectangular block. Sunlight entering through the top surface of the concentrator may bulk scatter, undergo photoluminescence, or simply pass through the bottom surface and be lost. Scattered or re-emitted light may exit through the escape cone, or be contained within the bulk through TIR. Most designs also employ reflective coatings on the sides and bottom face to improve light containment. Light which is successfully contained within the concentrator bounces around and is eventually collected by the small PV module on the side.
This design is intended to improve concentration ratio and thus cost efficiency; fewer photons are collected, but the expensive PV module's surface area can be greatly reduced. The other advantage relates to the responsivity curve of common PV cells, which typically drops to zero at around 400nm and peaks between 700 and 900nm. With this design, high energy incident light outside of the PV responsivity curve can be downshifted and made usable for the PV module, effectively improving the module's efficiency. Finally, the QDSC is able to concentrate both direct and diffuse sunlight well—a huge benefit over geometric (i.e. mirror) concentrator systems, which are limited to direct sunlight.
Preparing the QDSC simulation in OpticStudio
The file used in the simulation is attached (PL Solar Concentrator.zar). The goal of this simulation is to model a QDSC in OpticStudio, and determine efficiency of the system vs. that of an unconcentrated system. The irradiance vs wavelength captured on the virtual PV module is scaled by responsivity data for an actual PV cell to approximate the efficiency of the simulated concentrated QDSC PV system.
The Basic setup includes a rectangular block of PMMA. The sides and back faces are coated with an ideal 99.5% reflective coating, and the front face is uncoated. The PV module is simulated as an ideal absorbing detector, placed covering one of the concentrator sides, and the interface between the module and the concentrator is assumed to be ideal. System wavelengths and their weights are chosen to match the 1.5 airmass solar spectrum.1 In order to simulate solar radiation angle of incidence correctly, a Lambertian scatter model is used to scatter a small percentage of the incident rays.2 This randomizes a portion of the rays’ angle of incidence to account for rays scattered by atmospheric particles.
Photoluminescence parameters and spectra are approximated based on the research on CuInS2/ZnS quantum dots of Booth et al. and Li et al.3, 4 The extinction coefficient for the quantum dots is set to 1e5 at the 400nm wavelength. A flat quantum yield of 81% is used, an optimistic approximation based on the reported maximum value achieved. Quantum Dot density is chosen as 5E16, to achieve both a high concentration ratio and absorption/re-emission of high-energy photons. This results in a mean free path of 0.523mm at the extinction wavelength. Absorption and Emission spectra are shown below, using the “View Spectrum Files” plot in OpticStudio:
A Mie scatter model is also included. The model’s parameter values are chosen based on the findings of Booth et. al. and Li et al, and the density chosen in the photoluminescence model.3, 4
Simulation results
The resulting flux vs wavelength on the detector object is shown in below. There is an absence of short-wavelength light due to the short photoluminescence mean free path. The 550-650nm range is highly peaked, which matches expectations based on the structure of the absorption and emission spectra. Where the absorption spectrum drops to zero at around 575nm, a large peak in intensity is observed. Furthermore, because the emission spectrum is zero for wavelengths longer than around 710nm, it is observed that the flux vs wavelength curve there drops nearly to zero. This is because longer wavelengths rely purely on Mie and Lambertian scattering in order to be captured by the system, and those effects are weaker than the photoluminescence effects in this system.
When this detector data is folded into a crystalline Silicon (c-Si) solar cell responsivity curve, the approximate cumulative efficiency of the PV module over the wavelength range in question can be estimated.2 The same can be done for the 1W of light incident on the system in order to generate a ‘control’ which represents a bare solar panel in an unconcentrated system.
For a total incident intensity of 1W, the total energy concentrated onto the detector is approximately 0.0712W (1.08E-6 W/mm2) corresponding to a concentration ratio of 5.21. When the flux vs wavelength values are folded into the PV responsivity, a concentrated system efficiency (output/input wattage) of 6.11% is observed (for the reduced solar spectrum used in the simulation). This is near the expected value, as efficiencies of between 3% and 8% have been demonstrated for these types of concentrators under the full solar spectrum.5 When compared to the unconcentrated system, the concentrated system demonstrates an improvement of system efficiency of 585%.
References
- Reference Solar Spectral Irradiance: Air Mass 1.5. http://rredc.nrel.gov/solar/spectra/am1.5/
- University of Oregon Solar Radiation Monitoring Laboratory. http://solardat.uoregon.edu/index.html
- M. Booth, Ph.D. thesis, The University of Leeds School of Physics & Astronomy, 2014, Retrieved from http://etheses.whiterose.ac.uk/8349/1/Matthew_Booth_PhD_thesis.pdf
- C. Li, W. Chen, et al, Scientific Reports 5, (2015).
- W.G.V. Sark, Renewable Energy 49, 207 (2012).
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