2D silicon square grating solar cell

One of the major challenges in designing solar cells is to maximize the efficiency. One common practice is to add a layer of grating on top of the substrate to minimize the large back reflections of solar radiation from the upper surface of solar cells at the air-semiconductor interface.

solar_grating.ldev

Simulation setup

The patterned Silicon solar cell can be set up as a 2D simulation in FDTD. Open the solar_grating.fsp file. The rectangular groove structure in the reference paper by Chong et al. is modeled. Periodic boundary conditions are used in the x direction to account for the fact that the structure is essentially infinite in the x direction.

We use a plane wave source with a wavelength range from 300 nm to 1100 nm to account for the frequency range of interest in a silicon solar cell. The resultant spectrum is then multiplied by the spectrum of the Sun since the system is linear. For more details on this technique, visit the FDTD solar cell methodology section.

The analysis group, "solar_generation" contains a script that calculates the number of absorbed photons. A parameter sweep named "polarization" is used to run the simulation and calculate the generation rates for 0 and 90 degree polarizations, which are then combined in the electrical solver (CHARGE) to get the generation rate for unpolarized illumination. Two .mat files (Gen_s.mat, Gen_p.mat) are generated once the sweep is run. These .mat files contain the optical generation rates that are imported into CHARGE.

Results

FDTD

Open the solar_cell_grating.fsp file and run the 'polarization' sweep. Once the sweep is done, results will be available which can be viewed by right-clicking on the sweep object and by selecting 'Visualize'. The sweep provides the (ideal) short-circuit current (Jsc), generation rate (G), absorbed power profile (Pabs), and total absorbed power (Pabs_total) as a function of frequency, for 0 and 90 degree polarizations. All of the values are scaled by a factor of 0.5 so that adding them for the two polarization cases will provide the result for the unpolarized solar spectrum AM1.5G.

Absorbed optical power at 500 nm for 0 degree pol (log scale)

Absorbed optical power at 500 nmfor 90 degree pol (log scale)

Generation rate for 0 degree polarization angle (log plot)

Generation rate for 90 degree polarization angle (log plot)

The ideal short-circuit current for the 0 and 90 degree polarizations are found to be around 13 and 14 mA/cm², respectively. Adding them together, we get the ideal short-circuit current for the unpolarized sunlight to be about 27 mA/cm².

The sweep also creates two .mat files Gen_s.mat and Gen_p.mat which can be found in the sub-folder 'solar_grating_polarization'.

CHARGE

Open the solar_grating.ldev file. Under the CHARGE solver in the objects tree, right click on Gen_s, open the edit window, and then using the browse button, import the Gen_s.mat file. Click LOAD and OK. Repeat the same procedure for the Gen_p object and import the Gen_p.mat file.

The solar cell has been fully modeled in the CHARGE simulation. In order to confirm the ideal result, we will first turn off any non-ideal effects such as bulk and surface recombination. Notice that the silicon material used in the simulation is named "Si (Silicon) ideal." This is just a copy of the Si material with all recombination processes disabled. Run the simulation (for zero bias) and execute the following command in the script window,

? getdata("CHARGE","emitter.I")/(getnamed('CHARGE','norm length')*getnamed("CHARGE simulation region","x span"));

You should see the result, J_sc ~ 22 (mA/cm²). This result is lower than what we obtained in FDTD. The reason is that the short circuit current calculated in FDTD is normalized to the length of solar cell without the contact region whereas CHARGE results are normalized to the width of the simulation region (10 um in this case) including contact shadowing as well as limited number of grating teeth.

We will now switch back to layout mode, and change the silicon material properties to include non-idealities such as bulk and surface recombinations. The carriers generated will now have the chance to recombine before they are collected at the contact and the distance they will be traveling is different depending on which groove they are generated under.

Select the "substrate" from the Objects Tree, open the Edit rectangle window, and change the material from "Si (Silicon)_Ideal", to "Si (Silicon)" from the 'Material' tab. This will change the material to the 'real' Silicon, including the effects of bulk and surface recombinations. Next select the structure group called 'ribs' and change the 'material' variable from "Si (Silicon)_Ideal", to "Si (Silicon)". The properties of Silicon in the material database can be tailored to the particular Silicon wafer and how it was fabricated. 'Surface Recombination Velocity' of electrons and holes at the SiO₂-Si interface can be set to be 100 cm/s by choosing "SiO2 (Glass) - Sze" and "Si" as materials for a surface recombination boundary condition and setting the surface recombination velocities for electrons and holes appropriately. The surface recombination at the Ag-Si interface can also be set to 1000 cm/s in a similar manner. With the recombination models enabled, the photo-generated carriers in the bulk silicon now have the chance to recombine before they are separated by the built-in fields and are collected at the contacts.

Click Run. To get the value of generation current, type the following line of script into the script prompt:

? getdata("CHARGE","emitter.I")/(getnamed('CHARGE','norm length')*getnamed("CHARGE simulation region","x span"));

You should see the result, J_sc ~ 21 (mA/cm²). This result is now less than that of the ideal case. Both recombination in silicon and surface recombination at the interface of silicon with the oxide have contributed to this reduction.

The table below summarizes the results:

This is a good example of a case where optical simulation is not sufficient by itself to model the device characteristics and the simulation of the solar cell in CHARGE brings to our attention the otherwise ignored effects of recombination. We can also generate voltage-current plots by sweeping the base bias. Switch back to the layout mode and click the edit button for base bias value to modify it. Check the DC box and set the voltage to rage from 0 to 0.7 Volts in 15 steps.From an optical perspective, the patterned solar cell performs similarly to the planar solar cell; however, the electrical simulation in CHARGE reveals that this optical enhancement is reduced by the recombination effects, and specifically by surface recombination effects. The reason for this is that the rectangular grating increases the surface area of the structure at the interface between the oxide and Silicon materials. The loss due to surface recombination in this case is about 2%.

We will run this simulation for both cases of ideal and non ideal silicon materials. For the non ideal silicon, we will consider the effects of both bulk and surface recombination. Run the simulation for both ideal and non ideal materials. After the simulation is done, open and run the script file solar_cell_2d_FOMs.lsf to generate the J-V plots. The figure below shows the results from the ideal silicon material as well as silicon with recombination effects on the same plot:

J-V characteristics of the solar cell

Bulk and surface recombination have decreased the short circuit current by ~ 6% as can be extracted from the y crossing of the plot. The open circuit voltage for the solar cell can also be extracted from the x crossing of the plot.

Similarly power curves can be generated. The plots for both cases are shown below:

Output power versus bias voltage

Efficiency values can be extracted from this plot by dividing the maximum power by the input power of 100 mW/cm². The efficiency in the case with bulk and surface recombination effects is lower by about 9%.

$$\eta_{ideal}=11\% \\\eta_{recomb} = 10\%$$

Reference

T.K. Chong, J. Wilson, S. Mokkapati, K. Catchpole, “Optimal wavelength scale diffraction gratings for light trapping in solar cells,” J. Opt. A, 14, 024012 (2012)