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Solar Energy

PV: Engineering and Advanced Concepts

Multi-junction cells in practice


In the last quiz we explored the theoretical performance improvement that could be achieved by using multi-junction cells. To find ultimate efficiency in the previous quiz, we assumed we had a perfect sorting mechanism that directed each photon to the junction that would convert it most efficiently.. In this quiz, we’ll look at some real ways to sort photons of different energies, and also look at how to estimate efficiencies for real multi-junction cells.

One method to “sort” photons is using an optical device. For example, imagine we had a prism - sunlight incident on the prism would be split into different directions based on the different refraction for different wavelengths. We could then place cells with different bandgaps under the part of the spectrum that they convert most efficiently.

When an optical device is used to redirect photons to their corresponding junction, you can add up the power output from all cells individually. In this case each cell can be treated similarly to a normal single junction cell, except that it’s exposed to a specially tailored spectrum instead of the normal solar spectrum. Suppose we have a prism which has a transmittance of 70% and separates the solar spectrum into three bands which each contain one third of the energy of the total solar spectrum. These three bands are converted to electricity by 3 PV cells with efficiencies of 30%, 50%, and 60% when illuminated by their corresponding band. What is overall efficiency (in percent) of this MJ PV cell setup?

Real MJ cells which use an optical device typically use dichroic mirrors rather than a prism to send photons of different energies to the different junctions. Dichroic mirrors are surfaces which reflect photons with certain energies while allowing other photons to be transmitted.

Whether dichroic mirrors or prisms are used, it is challenging to efficiently split up the solar spectrum into bands corresponding to different PV junctions. In these types of multi-junction PV systems, the optical device typically accounts for a significant portion of the overall losses.

While designing efficient optical devices for this type of multi-junction PV cell is challenging, the actual PV cell portion is simple, as each junction can be treated like a single junction cell. This means that fabrication of the cells is not necessarily more complicated than the fabrication of regular cells, and we already have all the tools we need to simulate their performance. In this case, you can treat each junction as its own single-junction cell, the only difference from previous approaches is that each cell is only illuminated by a certain band of the solar spectrum.

Most MJ cells currently being developed use a much different strategy. Rather than having an optical device sort photons, different PV materials are layered on top of each other, with the highest bandgap junctions going on top. The top layer absorbs the highest energy photons, but lets lower energy photons pass through to the junction underneath. The next junction then absorbs the photons it is able to convert, and the lower energy photons are transmitted further. Photons continue passing through the structure this way until they have been absorbed or pass through all the junctions. This layered approach simplifies the system optics: the MJ cell structure performs the photon sorting itself, so there is no need for an external optical device.

While the layered cell structure avoids needing an optical device to sort photons, that doesn’t mean this approach is without challenges. One challenge is that since layers are grown directly on top of each other, the PV materials achieving good crystal structure require that all the materials are “lattice-matched” which means that they have similar atomic spacing. This limits the materials that can be used together. If materials with very different atomic spacing are used, there will be flaws and dislocations in the crystal structure near the interface between the two materials.

Another challenge is that in this approach all the cells are connected electrically in series, which means they need to operate at the same current. With this arrangement for an MJ cell, the output current from the cell is the operating current, while the output voltage is the sum of the voltages across each junction. For a 3J cell with the IV curves given in the plot below, which current would lead to reasonable electrical output from each cell?

We can predict the performance of this type of layered MJ cell with a similar treatment as we used for single junction cells before, however we will need to change some of our assumptions. Which of the following assumptions we used to model single-junction cell performance still holds for our layered MJ cell model?

So how can we actually model the performance of a layered multi-junction PV cell? We can use a modified approach that borrows many of the equations we’ve used previously to model single-junction PV cells. In the approach we’ll use, the first step is to choose the PV materials that will go into our PV cell, the thickness of each layer, and the order of the layers (i.e., which material will go on the top of the cell, which material will go second, and so on). With the structure of the cell determined, we can use absorption data for each material, along with that layers’ thickness, with the detailed balance principle to determine the minimum required recombination rate of each layer at zero voltage.

\[R_{c0} = 2A\int_{E^*}^\infty \alpha(E) \frac{2 \pi E^2}{h^3 c^2} \frac{1}{e^{E/k_BT} - 1} dE\]

The recombination rate still has the same dependence on carrier density, so it varies with voltage based on the same dependence we found earlier.

\[R_c = R_{c0} e^{V/V_c} \]

We can then use the absorptance of each layer to determine the photogeneration rate of each layer. The first layer is exposed to the full solar spectrum, which absorbs some portion of that spectrum (exciting electron-hole pairs in the process). The remaining portion of the spectrum reaches the second layer, which absorbs a different portion of the spectrum, and this continues on through all the layers. This gives us the photogeneration rate in each layer.

\[G_s = AF \int_0^{\infty} \alpha(E) Q_{solar}(E) dE \]

With the photogeneration and recombination rates for each layer, we can determine the short-circuit current and open-circuit voltage for each layer:

\[I_{SC} = q(G_s - R_{c0})\] \[V_{OC} = V_c\ln(\frac{G_s}{R_{c0}})\]

With \(I_{SC}\) and \(V_{OC}\) for each layer, we can generate IV curves for each layer of our multi-junction PV cell. In each layer, the current-voltage relation is given by

\[I = q(G_s - R_{c0}e^{V/V_c}) \approx I_{SC} - qR_{c0}e^{V/V_c}\]

Finally, we can calculate the overall power output of the cell. The power output is given by the operating current of the cell times the sum of the voltage at each junction for that operating current. We can find the operating current which maximizes output power, and the efficiency of the multi-junction PV cell is simply given by this output power divided by the incident solar power. \[\eta = \frac{P_{PV}}{P_{inc}}\]

The code environment below is set up to model the efficiency of layered multi-junction cells using the approach described on the previous pane. The table below lists the materials that you can choose from, as well as their bandgap energies and a nominal thickness (how thick a layer of that material should be to absorb most photons above its bandgap energy).

MaterialName in python codeBandgap [eV]Nominal thickness [um]
Gallium Phosphidegap2.6120
Indium Gallium Phosphideingap1.845
Cadmium Telluridecdte1.52
Gallium Arsenidegaas1.422
Amorphous Siliconasi1.45
Indium Phosphideinp1.2720
Indium Gallium Arsenideingaas0.755

To add a layer in the model, create a layer object, and define its material (this must follow the naming convention given in the table and is case sensitive) and thickness (in micrometers). Some layers have already been created in the default code, so you can follow the example given for those layers. You can also choose a recombination factor for each layer - a value of 1 corresponds to the minimum required recombination rate calculated from the detailed balance principle, and larger values correspond to more realistic recombination rates when non-radiative radiation is considered.

The multi-junction cell is arranged in the list “MJPVcell.” Be sure to include each layer in that list, and be sure that they are in the correct order: the layer you want on the top of the cell should be first in the list.

Finally, you can also change the temperature of the PV cell (the default value is \(\SI{300}{\kelvin}\)) and the concentration ratio of incident sunlight, if you’d like to explore the effects of those parameters.

Running the code will calculate the efficiency of your chosen multi-junction PV cell, as well as a pair of plots. The first plot shows the incident solar spectrum, as well as the spectrum after each layer in the cell. The second plot shows the IV curve of each layer, as well as the operating current (and corresponding voltage in each layer) that leads to the maximum power output.


You can use this code to explore some questions on your own, if they interest you: - Do thicker layers always lead to higher efficiencies, or are there cases where increasing layer thickness decreases efficiency? - Does adding a new layer always increase efficiency or does it ever lead to a decrease?

Note: the code is all written for you, so you only need to change the layers making up the PV cell to explore MJ PV cell efficiency. However, if you’re interested in looking at the specifics of the calculation, the code includes commenting and documentation, so you can see exactly how the program is written.

[Should it be noted that many of these combinations wouldn’t be possible in real life due to lattice mismatch?]

Using multiple-junctions in a PV cell can improve efficiency, and some MJ cells have already demonstrated efficiencies higher than the SQ limit for single junction cells. While MJ cells offer the potential for improved performance, they also involve new challenges and are expensive to make, so they are mostly used in specialized applications. One place that is common to see MJ PV cells is on spacecraft, since on a spacecraft cost is a minor concern compared to achieving a high efficiency.


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