In this application example we calculate the field distribution in a silicon nanowires based solar cell. This is one of many advanced options how to construct better solar cells. As the solar cell performance highly depends on the local absorption of light, FDTD can be an useful tool for exploring in which regions of the sample the light gets absorbed.
The example shown here is related to radial junction solar cell structures presented in Ref. 1. Two different models were constructed as shown on the left image. In model “A” a periodic array of structured is created using single NW/aSi/ITO column and periodic boundary conditions. This can be used to evaluate effect of column spacing films thicknesses, length or tilt on resulting structure performance. In model “B” 3×3 differently tilted columns are used as basic building block for periodic array construction. This is useful to estimate effects of random column orientation. In principle this could be expanded up to 7×7 array basic building block, however for even larger building blocks the computation would be too long and memory demanding.
All the optical data were taken from SOPRA database. Structure was illuminated from top or from bottom by a linearly polarised plane wave. Glass at the bottom of the structure was treated as infinitely extending. Voxel spacing was 7 nm. Geometrical parameters of a single column were as follows in first set of simulations (radii of nested cylinders capped by spheres and apparent thickness of the film if seen from side):
|material||cylinder radius||film thickness|
|Si NW||28 nm|
|(i) a:Si-H||161 nm||67 nm|
|(n) a:Si-H||182 nm||11 nm|
|TCO||350 nm||84 nm|
Bottom ITO thickness was 630 nm. All these parameters can be changed and were considered only as initial values, a bit smaller than ideal values, to speed up the first test calculations.
As an example of numerical results here we show resulting time averaged spatial distribution of absorption in single column structure illuminated from top (left) and bottom (right), for 500 nm illumination wavelength. Visualisation was performed using Paraview.
Similar calculation can be performed for any wavelength within range of our optical data (and reasonable ratio between wavelength and voxel spacing). Here a set of simulation snapshots for different wavelengths is shown for single column structure illuminated from bottom:
If we run full spectral calculation, we can get also dependences of summed local absorption in different parts of the solar cell, for distinct materials. A preliminary result for bottom illuminated regular structure is shown below (note that number of steps for longer wavelengths was too small for reaching steady state). Spectral calculations using optical database are performed for each wavelength separately, so this type of calculations is already computationally demanding - we had used CMI high performance computing system for these preliminary calculations.
Geometrical model can be made even more complex, e.g. by adding scanning probe microscope tip to the structure. This geometry is similar to what we use in photoconductive AFM measurements. After adding simple tetrahedral tip we get the volume absorption like shown belos: (left) geometry, (center) 400 nm illumination, (right) 600 nm illumination:
Sample parameter file: silicon nanowire.
A simulation of a single silicon nanowire composed of multiple different materials, illuminated from bottom. Absorption in different materials is evaluated.
 A. Fejfar, M. Hývl, A. Vetushka, P. Pikna, Z. Hájková, M. Ledinský, J. Kočka, P. Klapetek, A. Marek, A. Mašková, J. Vyskočil, J. Merkel, C. Becker, T. Itoh, S. Misra, M. Foldyna, LW. Yu, P. R. I Cabarrocas, Correlative microscopy of radial junction nanowire solar cells using nanoindent position markers, Solar Energy Materials and Solar Cells 135 (2015) 106-112