Anti-reflective films improve the conversion efficiency of solar cells. However, such films are often narrow-band and even increase reflection for wavelengths outside their operating bandwidth. Nanostructures, on the other hand, can increase the efficiency of single-crystalline (SC) silicon solar cells over a wider range of wavelengths. One such design is a bio-inspired structure array.
In this example, we show how to setup such a simulation and measure the reflection versus the wavelength. We can also gain insight into where the electromagnetic energy is absorbed and where the photoelectrons are created.
The setup for this example follows the guidelines described in Typical simulation setup in FDTD. The structure has a silicon substrate with a square lattice of silicon parabolic structures with period of 500nm. The moth eyes are drawn inside the structure group named "moth eye".
We set x span and y span to be 0.5um for the simulation region, which includes only one unit cell. Since the structure exhibits both symmetry and periodicity, we can choose the boundary conditions as follows:
- x-min bc = x-max bc = antisymmetric
- y-min bc = y-max = symmetric
in order to do the above setting, the 'allow symmetries on all boundaries' checkbox must be enabled first.
We want to know how much power is absorbed in the moth eye structure, so we use two frequency-domain power monitors: R measure the total reflection, which is placed behind the source; T monitor is placed on the interface of moth eye and the substrate to measure the power into substrate. The absorption in moth eye is 1-R-T.
Broadband moth-eye AR coating
Our goal is to calculate the relative absorption of this structure using CW Normalization, therefore we use a plane wave with a wavelength range from 350nm to 850nm, instead of the real sunlight. If you want to calculate the absolute absorption, simply multiply the solar power (see this page).
First we can check that the simulation ran as expected. Right click the time monitor and choose Visualize "E", then the Visualizer plot the amplitude of E vs. time. It can be seen that the fields eventually died down to the minimum shut-off criteria and that the simulation was not on its way to diverging. By choosing its x component, the Ex is plotted as below.
Load silicon_motheye_AR.lsf into the Script File Editor. The first section of the script plots the reflection, transmission, and fields absorbed by the conical structures. From the plot, we can see that wavelengths shorter than 500nm were mostly absorbed by the cones (moth eye), and the wavelength greater than 500nm were mostly absorbed by the substrate. The broadband reflectivity overall is quite low, as expected.
The second section of the script, when enabled, plots the |E|2 profile at the minimum and maximum wavelengths as well as the center wavelength. Notice that in the plot at 350nm, since the conic has high absorption, the |E|2 field is very close to 0 at the conic-substrate interface.
The photoelectrons are created with high density at the location of peak field intensity.
Comparison with reference surface
For a reference comparison, we run a simulation on just the flat silicon substrate. Re-save the simulation with a new name, silicon_motheye_noAR.fsp. Then switch to layout and disable the moth-eye structures. Simulate this new setup and run the same silicon_motheye_AR.lsf file to look at the reflection and transmission. Reload the saved silicon_motheye_AR.fsp. Run the script with the third part (comparison plots) enabled by modifying if(false) to if(true). If we consider anything that transmitted light is all absorbed in the substrate, the following image shows the simulated absorption enhancement by using moth-eye structures.
Chih-Hung Sun et al., "Broadband moth-eye antireflection coatings on silicon", APL 92, 061112 (2008).