International Journal of Scientific & Engineering Research, Volume 4, Issue 6, June-2013 2890

ISSN 2229-5518

FDTD Optical Simulation to Enhance Light

Trapping

Badri Narayan Mohapatra, Rashmita Kumari Mohapatra

Abstract-Thin film silicon solar cells, which are commonly made from microcrystalline silicon (μc-Si) or amorphous silicon (a-Si), have been considered inexpensive alternatives to thick polycrystalline silicon (polysilicon) solar cells. However, the low solar efficiency of these thin film cells has become a major problem, which prevents thin film silicon cells from being able to compete with other solar cells in the market. One source of inefficiency is the light reflection off the interface between the thin film cell’s top Transparent Conducting Oxide (TCO) and the light absorbing silicon. In this paper, we demonstrate the use of nanocone textured ZnO as the antireflection surface that mitigates this problem. The tapered structure of the nanocone forms a smooth transition of refractive index on the interface between the TCO (ZnO) and the silicon, effectively acting as a wideband Anti-Reflection coating (AR coating).Finite Difference Time Domain simulation is used to estimate the optimal ZnO nanocone parameter (periodicity and height) to be applied on a single junction microcrystalline silicon (μc-Si) solar cell. Relative improvement over 25% in optical performance is achieved in the simulated structure when compared to state-of- the-art μc-Si cell structure. Cheap and scalable colloidal lithography method is then developed to fabricate ZnO nanocone with the desired geometry. Since the ZnO texturing technique works by depositing ZnO on nanocone-textured glass substrate, the technique is potentially applicable to Transparent Conducting Oxides other than ZnO as well, making it a useful TCO texturing technique for solar cell applications.

Index Terms -Fdtd optical simulation, μc-Si solar cell model, μc-Si solar cell Texture simulation.

1. INTRODUCTION:

Solar cell is a very attractive method of harvesting energy. There is little doubt that solar cell is the future of energy due to the abudandance of sunlight and the solar cell’s environmentally friendly nature. Since the cells source of energy is the sunlight itself, we need not be concerned about running out of power in the long run which is the case for fossil fuel energy. Furthermore, the solar power entering the Earth is enormous. Most of the solar cells in the market are currently made from silicon [2]. Silicon is the preferred solar cell material due to the abundance of silicon on the Earth crust, and due to the fact that the absorption peak of silicon is very close to that of the solar spectrum’s peak. Unfortunately, silicon is an indirect band-gap material, making it a poor light absorber (compared to other direct band-gap materials such as GaAs, which is significantly more expensive). To compensate for this poor absorbance, early solar cell technology uses thick single crystalline silicon wafer up to a few hundred micron thickness, effectively making the cell expensive to produce. This is where the thin-film technology comes in. Solar cell manufacturers build thin-film silicon cells not by cutting up expensive silicon ingots, but rather by depositing thin layers of 17 materials, including 1-2 μm silicon (100x less silicon compared to silicon wafers), on a substrate like coated glass, metal or plastic. The absorbing semiconductor does not have to be very thick, so thin-film silicon solar cells are cheap, durable, lightweight, and easy to use. However, thin layer of
absorbing material obviously means less light is absorbed by the solar cell, and the cell efficiency is reduced. This is why light trapping is becoming very important for thin film silicon solar-cell. Light reflection, refraction, and scattering (light trapping schemes) have to be taken into account to produce more efficient solar cell while keeping the solar cell structure constraint intact. The structure constraint here means all the components of a solar cell, including the glass, Transparent Conducting Oxide (TCO), p-i-n silicon junction, and a back reflector. These components are required in order to obtain a working, readily usable thin-film solar cell. Their presence in thin-film silicon solar cell adds some additional layers of inefficiency that we need to take iinto account. For this thin-film structure, there are some methods which can be done to improve efficiency. Layer thicknesses can be adjusted to optimize light absorption in the silicon. Interface between layers can be chemically random-textured so that light is scattered inside the cell and effectively follows a longer path in the silicon (higher absorption). In this work, we present a method aimed at replacing the chemically random textured interface with a submicron periodic texture. Submicron periodic texture has been known as a great anti-reflection coating since it acts as a smooth transition of refractive indices between material layers [3-5]. Furthermore, the submicron texture also scatters light like a randomly textured interface. A full solar cell structure will be used to study this effect. It will later beshown that a crucial interface to apply the submicron periodic texture is the interface

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between the top TCO and the μcSi [6]. To study and optimize the effect of this anti-reflection submicron
texture, we are using Finite Difference Time Domain (FDTD) optical simulation. Similar solar cell optical simulation work using FDTD simulation has previously been done [7-10], but our work will be applied to the single junction thin film μcSi cell structure .The result is then compared to the same solar cell structure that uses chemically etched ZnO texture currently used in commercial thin-film silicon solar cell. Enhancement over 20% in the cell’s short circuit current is predicted from the FDTD simulations, making the submicron periodic texture a potentially useful feature for thin-film silicon solar cell. A method to fabricate the submicron periodic texture over the entire wafer area is then developed so that we can use the texture to experimentally confirm the cell’s optical enhancement in the near future.

2.THEORY:

2.1.Finite Difference Time Domain (FDTD) Optical

Simulation:-

Finite Difference Time Domain (FDTD) is a simulation technique to solve electromagnetic field equations across a wide ride of frequency with a single simulation. In this technique, we define a material structure in space and discretize the simulation space into xy coordinates (for
2D simulation) or xyz coordinates (for3D structure). A
short pulse of light is then propagated through the area
of interest (simulation area) in the material structure. We discretize the time domain into small time steps and solvethe light pulse propagation’s electromagnetic equation (Maxwell’s equations) for each time step in a leapfrog manner. In the beginning, the electric field components of the equations are determined for a specific time step. Afterwards, the magnetic field components are solved at the next time step. This process is repeated multiple times until the light propagation is completed and the electromagnetic field in the simulation area is below a certain threshold. After solving the light propagation in the time domain, we obtain the electromagnetic field profile as a function of space and time. Since a short light pulse in the time domain corresponds to a wide pulse in the frequency domain, we can perform Fourier transform on the electromagnetic field profile we have previously acquired, in order to obtain electromagnetic field profile as a function of space and frequency. Further processing of this frequency domain electromagnetic field spatial profile can be used to determine light absorption inside

the structure. A brief summary of the FDTD method is shown in Figure1.
Figure1.FDTD simulation flowchart
The FDTD optical simulation method is advantageous
since it can be used to solve electromagnetic equations,
not only for planar structure (1D) but also for more complex 2D and 3D structures. It is also very useful since by solving Maxwell’s equations in one time domain simulation, we simultaneously solve the electromagnetic field profile in the material structure for a wide range of frequencies. Furthermore, it does not require manual parameter tuning since the only information that the method requires is the geometry of the material structure and the optical properties (n, k) of the materials involved in the simulation. The disadvantage of this method, however, is that it is very computationally expensive. For each simulation time step, it is necessary to record the time domain electromagnetic field spatial profile as well as to Fourier transform this spatial profile for each frequency of interest. Therefore, a large amount of computation time and memory is required for the FDTD simulation.

2.2μc-Si Solar Cell Model for Optical Simulation:

It is important to estimate how much improvement we can achieve in a single junction μc-Si solar cell through light trapping. In order to do so, we used the FDTD technique to simulate the optical performance of single junction μc-Si cell. For the optical simulation portion of this work, we used a single junction microcrystalline silicon (μc-Si) cell structure developed by Bosch Solar Energy in 2010 (Figure 2). It has the following layer thicknesses:
1. Glass (SiO2) : 3 mm
2. Boron-doped Zinc Oxide (B:ZnO) : 1600 nm
3. p-type microcrystalline silicon (p-μcSi) : 10 nm
4. Intrinsic microcrystalline silicon (i-μcSi) : 1500 nm
5. n-type amorphous silicon (n-aSi) : 20 nm
6. Boron-doped Zinc Oxide (B:ZnO) : 400 nm
7. Perfect back reflector : 10 nm

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interfaces between the different layers are no longer planar.

Figure2.FDTD model for a planar single junction μc-Si cell
The (n, k) data for each of the materials involved in this FDTD optical simulation is provided by Robert Bosch as well. Using these material data and layer thicknesses, we were able to construct the solar cell structure using Numerical FDTD Solutions software.

2.3QE and Jsc Extraction from the Simulated Solar Cell

Structure:-

The FDTD optical simulation was constructed to study the light trapping efficiency of our solar cell structure.
Since this work is focused on the optical performance of
Figure3.Placement of the data collection monitors in (a)
planar structure, (b) textured structure

To fix this problem, we use rectangular 2D electric field monitors

to record E(x, y, f ) in the area around the textured interface.

However, we need to be able to distinguish whether a certain (x, y) coordinate is composed of intrinsic μc-Si or composed of another material. In order to do this, we put rectangular 2D refractive index monitors covering exactly the same area that the rectangular electric field monitors cover. The light absorption only in the intrinsic μc-Si can be found by integrating the electromagnetic power absorption from the coordinates where the refractive index in the coordinate is equal to the refractive index of intrinsic μc-Si. In pseudo-code, it means we perform the following operation

for each frequency f:

our cell, the most relevant parameter to be extracted using this optical simulation is the number of photons absorbed by the solar cell that can contribute to the generation of electron-hole pairs, which leads to the generation of electric current. In the case of our single junction μc-Si cell, only light absorption in the intrinsic μc-Si layer can contribute to this electric current. Since this is the case, we have to extract our absorption data carefully so that absorption in the other layers is not included in the calculation. In the case of planar structure, this task can be done very easily. One can simply put an electric field monitor at the beginning and at the end of the layer of interest. In Figure 3.(a) below, we put an electric monitor named ‘Input’ below the 10 nm p-type μc-Si layer and an electric field named
‘Output’ above the 20 nm n-type a-Si layer. These electric
field monitors store E(x, f ), which we can use to calculate the electromagnetic power P( f ) passing through the monitors. In this case, the electromagnetic power absorbed by the intrinsic μc-Si layer can simply be written as
Pabs = Pinput (f) − Poutput(f)………..(1)
When we have to calculate light absorption in a textured
solar cell (Figure 3.(b)), the simulation setup becomes slightly more complicated. We can no longer use electromagnetic power passing through planar monitors to calculate electromagnetic power absorption since the

𝑃𝑎𝑏𝑠 = 0

for each x coordinate:

for each y coordinate:

if 𝑛(𝑥, 𝑦, 𝑓) == 𝑛(𝑓) for intrinsic μc-Si:

𝑃𝑎𝑏𝑠 (𝑓) = 𝑃𝑎𝑏𝑠 (𝑓) + 𝜋𝑓 ∗ 𝑑𝑥 ∗ 𝑑𝑦 ∗ 𝐸2 (𝑥, 𝑦, 𝑓) ∗ 𝐼𝑚 (∈0

𝑛2 (𝑥, 𝑦, 𝑓))……….. (2)

where the last term in equation (4) corresponds to the

electromagnetic power absorption in dx*dy area on the simulation grid coordinates (x, y). Note that since this particular example is a

2D simulation, the absorbed power 𝑃𝑎𝑏𝑠 is represented in

Watt/meter.

At the end of this operation, we will obtain light absorption only in the intrinsic μc-Si within the monitor area. Combining the use of these 2D monitors with planar electric field monitors we have used previously will enable us to extract light absorption in the entire μc-Si layer. The absorbed power is dependent on the intensity of the incoming electromagnetic pulse

we used in this FDTD simulation though, so it is much more useful to calculate the quantum efficiency (QE) instead, which is the actual optical characteristic of the solar cell. QE is a good standard for optical simulation since it ignores electron-hole recombination. For this FDTD optical simulation, the QE is obtained using the formula:

𝑄𝐸(𝑓) = 𝑃𝑎𝑏𝑠 (𝑓) ………………………………….(3)

𝑃𝑝𝑢𝑙𝑠𝑒 (𝑓)

The QE curve is useful to show the spectral efficiency of our solar

cell device. However, sometimes it is more convenient to describe solar cell performance by comparing single numbers instead of comparing different QE curves. The number of electron-hole pairs which the cell generates under standard 1 Sun light illumination (Figure 2) is a good choice for this

purpose, as it reflects the optical efficiency of the solar cell. This

number directly corresponds to the short circuit current density

(Jsc) that the cell produces, which can be calculated using the

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formula:

𝐽𝑆𝐶 = 𝑞 ∫ 𝑏𝑠 (𝐸) ∗ 𝑄𝐸(𝐸)𝑑𝐸……………………(4)

where 𝑏𝑠 (𝐸) is the intensity of the solar spectrum for
photon with energy E , and QE(E)is the quantum photon
conversion efficiency of the cell, in which we have
ignored the electron-hole recombination effect. In the
following sections, we will describe our solar cell’s optical performance using this short circuit current

density 𝐽𝑆𝐶 .
Figure 4.ASTM G173-03 Reference Spectra [15]

3.Result & Disscussion

3.1FDTD Simulation of μc-Si Cell with Different Textures:- Flat Cell (Baseline)-

Apart from the layer thicknesses and the material data,
we need to take the light trapping geometry, which is the focus of this work, into account. In order to do so, we have prepared 3 different types of solar cell model using the same materials and layer thicknesses:
1. Planar single junction μc-Si cell (Section 2.3)
2. Single junction μc-Si cell with industrial HCl-etch
textured ZnO (Section 2.4)
3. Single junction μc-Si cell with periodic submicron ZnO
texture

The planar cell is used as the baseline, since theoretically this structure will have the lowest optical performance since it has no light scattering and anti-reflection mechanism. Our Lumerical FDTD simulation model for this cell is shown in Figure 2, and the resulting optical performance is shown in Figure 5.
Figure5.QE curve of a flat single junction μc-Si Cell

3.2Cell with Industry Standard LPCVD B:ZnO

We would like to compare the optical performance of our submicron periodic ZnO texture not only to a planar single junction μc-Si cell, but also to a single junction μc-Si cell with
industry standard textured ZnO. For the simulation part of this work, we worked with boron doped ZnO that Bosch grows using Low Pressure Chemical Vapor Deposition (LPCVD) process.
When B-doped ZnO is grown with this method, the

surface of the ZnO is automatically randomly textured with feature size that increases with the thickness of the ZnO (Figure 6).
Figure6.SEM image of 1500 nm thick B:ZnO texture (left) and 3000 nm thick B:ZnO (right) grown by Bosch. The texture feature size increases with film thickness.
We are using Bosch’s 1600 nm B:ZnO for our FDTD simulation. The texture of this B:ZnO has previously been characterized by Bosch using Atomic Force Microscope (AFM). In Atomic Force Microscopy, a small cantilever with an even smaller tip on its end is used to physically trace the geometry of the sample. The sample deflects the cantilever and modifies the intensity of the laser beam that the cantilever reflects to the light detector, allowing the AFM to characterize the sample height using the cantilever deflection (Figure 7). The B:ZnO texture that Bosch obtained using the AFM is shown in Figure 8.

Figure7. AFM principle of operation

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Figure8.1600 nm B:ZnO texture characterized using the
AFM.
To perform 2D FDTD simulation, we imported a texture line from the AFM characterization into our FDTD optical simulation model. For simplicity, we assumed that the rest of the material layers have the same texture as our B-doped ZnO. The FDTD optical simulation model for this structure and the resulting optical performance is shown in Figure 9. As we can see from the simulation result, randomly texturing the ZnO allows us to
increase the cell’s Jsc from 17.4 mA/cm2 to 20.3 mA/cm2,
a relative increase of 17 %. It can also be seen that our
simulation result agrees very well with the experimental measurement

obtained by Bosch.
Figure9.FDTD simulation model and the resulting QE curve for single junction μc-Si cell withLPCVD B:ZnO texture. SimulatedJsc = 20.3 mA/cm2. Measured Jsc =
20.6 mA/cm2.

3.3 Cell with Periodic 2D ZnO Texture

We propose that a ZnO textured with submicron
periodic texture can provide optical enhancement to the
solar performance when compared to an industry standard B:ZnO. The simplest way to test this hypothesis in a simulation would be to substitute each B:ZnO texture on our simulation model with a submicron periodic texture, similar to the optical simulation work performed in the references [17-18]. However, we would like to be able to test this
hypothesis experimentally as well, which means we
have to consider the way we make the submicron periodic texture on our ZnO. There is limited literature
on methods to texture ZnO, and most texturing methods result in random feature size and aspect ratio. On the
other hand, there are many known and controllable methods to texture silicon dioxide (SiO2), and it is most likely easier to deposit conformal ZnO on a textured SiO2 surface and obtain ZnO texture from such deposition. As such, we have opted to form our FDTD simulation by putting conformal layer of ZnO on textured SiO2 instead.We used two different types of tapered geometry as our submicron periodic texture.The first one is a triangular texture, and the second one is a sinusoidal texture (Figure 10 and 11). Since the texture is periodic in the x-axis, the cell structure is periodic as well, allowing us to put periodic boundary conditions on the left and the right sides of the structure. We varied the period of the texture from 200-700 nm, and varied the height of the texture from 200-600 nm, and the resulting Jsc from this optical simulation are shown in the corresponding tables.

Figure10.2D FDTD simulation model for the triangular texture.

Figure11.2D FDTD simulation model for the sinusoidal texture.
From this 2D optical simulation, two results can be observed:
1. Submicron periodic texture on ZnO does improve
light trapping in μc-Si Cell, and there exist geometries that improve light absorption over random HCl-etched ZnO. For 2D texture with 600 nm height and 700 nm period we can achieve Jsc > 23
mA/cm2, compared to 20.5 mA/cm2 Jsc that a cell with
industrial HCl-etched ZnO texture achieves.
2. The exact geometry of the tapered texture (triangle or
sinusoidal) does not affect the submicron anti-reflection

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effect as much as the texture feature size does. This flexibility is important since fabricating perfectly sharp
triangular glass texture might
be considerably harder and more expensive than
fabricating smoother texture.

3.4Cell with Periodic 3D ZnO Texture

We further extended our FDTD optical simulation to
three dimensional periodic textures.We believe the 3D version of our optical simulation is necessary since it is easier to manufacture 3D texture than 2D texture in an actual micro fabrication. Furthermore, our initial attempts on 3D FDTD simulations indicated that the anti-reflection (AR) effect is strengthened when we use
3D texture instead of 2D texture for the same feature
size. To construct our 3D simulation structure, we

followed the same procedure as in 2D. We constructed a textured glass with periodic boundary condition and put conformal material layers on it to form the single junction μc-Si cell (Figure 12 (b)). Only light absorption in the intrinsic μc-Si layer got included in the Jsc calculation. We attempted several other geometries as well in our 3D FDTD simulation (Figure 12 (c) and (d)).
Figure12. Usage of the periodic 3D texture in the μc-Si cell 3D FDTD simulation.
Since 3D FDTD simulations require enormous amounts
of computational resources, we had to limit our simulation to texture feature size that can potentially provide better AR effect.
A few considerations were taken into account:
1.Initial work on AR effect indicates that 2D texture with
small periodicity and large height provides the best AR effect. Increasing texture periodicity will reduce the AR effect slightly.
2. When the entire device structure is taken into
account, 2D simulations (Table 1 and 2) seem to indicate
that larger height and periodicity improve the light absorption more effectively.
3. It is easier to fabricate texture with large periodicity and height (low aspect ratio) rather than fabricating
texture with small periodicity and large height (high aspect ratio). Taking these considerations into account, we decided to focus on large periodicity and height as our simulation domain and limited our 3D FDTD simulation parameters to 600-900nm periodicity and 500-

700nm height. The result of our 3D simulation is presented in Table 3 -5
Figure13.Other 3D structures done for simulation
It has to be noted that due to limited computational
resources, we were using lower accuracy setting to complete these 3D simulations. Because of this, the Jsc is overestimated by 1-2 mA/cm2 for each of these simulations. Nevertheless, it can be seen that ZnO with
3D submicron periodic texture can enhance Jsc in our

single junction μc-Si cell up to 25-26 mA/cm2, a 25-30% relative increase in light absorption over industrial HCl- etched ZnO texture which only provides a Jsc of 20.5 mA/cm2. Figure 14 compares the simulated quantum efficiency (QE) between different ZnO textures (assuming perfect carrier collection), showing that the improvement is seen over a large range of wavelengths.

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Figure14.Simulated QE of different ZnO textures. Both the 2D and 3D periodic ZnO textures have 600 nm
periodicity and 700 nm height.

4. Conclusion:

Light trapping is an essential technique to improve the optical performance of thin film solar cells. While the solar cell material’s capability to absorb light sets the upper limit of the
solar cell’s performance, it is often the case that there are
improvements which can be done to bring the cell’s performance closer to its upper limit. In this work, we studied the optical performance of a single junction μc-Si solar cell. Using FDTD optical simulation, we concluded that the largest loss of light absorption in this cell structure happens on the interface between the front ZnO layer and the light absorbing intrinsic μc-Si layer. The problem on this interface lies on the fact that there is a steep change of refraction index when light travels from the ZnO layer to the μc-Si layer, which reflects a significant fraction of the light entering the solar cell. By texturing the front ZnO with a periodic and tapered submicron geometry, we can create a smooth transition of refractive index between the two layers. This reduces the reflection of the incoming light and increases the light absorption in the solar cell structure.

5.Future Work:

By the end of our work, we obtained submicron ZnO texture that was predicted by our FDTD simulation to improve the optical performance of our single junction μc-Si solar cell. Our FDTD simulation predicted that the submicron ZnO nanocone texture will improve the cell’s optical performance when compared to that of a cell which uses the industrial state-of-the-art randomly textured ZnO. Our simulation also showed that the optical improvement is seen across a wide range of wavelengths due to the AR effect of our tapered submicron geometry. Further optimization work on the texture fabrication process might also be needed once the μc-Si cell has been deposited on our current ZnO texture and has been characterized.

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