7.2.1 Textured Surface

Most of the monocrystalline solar cells on the market have surface texture [1,2]. Typical measured texture consists of overlapping pyramids with random heights and locations.

The sizes of the pyramids vary from 2 to 20 μm depending on the etching process. All facets of the pyramids of any size have the same crystal orientation of {111}, which is the densest surface in silicon crystal lattice. The {111} facets have the same angle of 55° with respect to the wafer plane.

Area of the textured surface is $\sqrt{3}\mathrm{=}1.73$ times larger than area of a flat surface on which the pyramids are formed. This ratio is independent of the pyramid size or whether the pyramids are random or regular.

Typically, both the front and the rear surfaces of the silicon wafer are randomly textured, but here we will look at different cases, with flat, regularly textured, and randomly textured pyramids. An example of a randomly textured silicon surface used in simulations is shown in Figure 7.1.

Typical pyramid height is considerably larger than the longest relevant light wavelength. However, different wavelengths in the solar spectrum exhibit very distinct optical behaviors in terms of refraction at the interfaces and in terms of how quickly they get absorbed in silicon. In this work, we use the Sentaurus tool suite [3] for optical and electrical analysis of the solar cells.

7.2.2 Optical Performance of Regular Surface Patterns

Reflectance changes across the solar spectrum and is very sensitive to the surface texture and films deposited on the surface. Transmittance becomes nonzero only for the long wavelengths, because short waves do not get deep enough to reach the rear surface and escape from it.

Figure 7.2 illustrates reflectance as a function of the light wavelength for different wafer surfaces. The legend describes the top surface of the wafer before the slash and the rear surface after the slash. For example, flat/ flat curve is for the wafer with two flat surfaces. About 60% of the short wavelengths are reflected and, therefore, 40% of them absorbed.

At the middle of the relevant solar spectrum, reflectance drops to about 30%, absorbing the other 70%. Toward the long wavelengths, reflectance increases back to about 50%, with the rest split between absorption and transmittance.

Changes to the top surface affect the entire spectrum. Introducing regular pyramids on the top surface moves us to the textured/ flat curve with much better performance than the flat/ flat case, except at the longest wavelengths.

Changes to the rear surface affect only the long wavelengths that can reach it. Introducing regular 4.2 μm tall pyramids to the rear surface moves us to the textured/ textured curve, which brings down reflectance above 1 μm.

On the other hand, the introduction of antireflective nitride film on the top surface dramatically reduces reflectance in the middle of the spectrum without much effect toward the ends of the solar spectrum.

Having antireflective nitride film on the rear surface reflects more infrared light toward the top than the rear surface covered by aluminum. This is important for the solar cells with point rear contacts, because the rear contacts are aluminum and the rest of the rear surface is covered with nitride. Therefore, part of the light reflects off the nitride-covered rear surface, whereas the other part reflects off the aluminum-covered rear surface. The ratio of aluminum contact area to the area of nitride-passivated rear surface determines the overall optical behavior of such solar cells.

So far, we have been analyzing regular texture with the pyramids that are facing up, which is difficult to obtain practically, but is easy to model. It is possible to manufacture regular texture with the pyramids facing down by using photolithography and wet etching. However, the need for the photolithography step makes the process too expensive for competitive manufacturing. Therefore, the industry is using wet etching without any masks, which gives random texture with the pyramids that are facing up.

7.2.3 Regular Versus Random Texture

It is more difficult to model random texture, as it involves a larger simulation domain with multiple overlapping pyramids and requires robust 3D geometry and mesh algorithms to handle such complex geometries. Due to the recent advances in mature simulation tools, such analysis is possible and its results are reported next.

When comparing the reflectance of the structure with regular pyramids to the ones with random texture, one remarkable observation is that the optical performance of random texture is noticeably better than performance of the regular texture, especially in the ultraviolet part of the solar spectrum. Let us find out why.

One hypothesis is that the random texture performs better due to the random lateral locations of the pyramids. Figure 7.3 shows a side view of the regular and random textures that exhibit very different skylines. The regular texture has rows of pyramids that cover exactly half of the area in the range from the foot of the pyramid to the top of the pyramid. The other half of that area belongs to the air between the pyramids.

Now, let us look at the rays that bounce out of the top surface. The rays that bounce at large angles that are close to vertical will definitely escape from the solar cell and will contribute to the wasteful reflectance. The rays with low bouncing angles that are close to the surface have a chance of being recaptured by the other pyramids. Figure 7.3 shows that about half of such rays will be captured by the regular texture, with the other half escaping.

In contrast, shifted pyramids of the random texture cover the entire skyline and can capture all of the low angle rays. This should explain the better optical performance of the random texture.

Let us perform analysis of another structure that can help to confirm this hypothesis. Specifically, let us model reflectance of the surface that has pyramids of the same height but placed at random lateral locations. Moreover, because we can control where those “random” locations are, we can keep the pyramids at the same lateral locations as we had for the true random pyramids. This ensures that there is only one variable changing at a time and the results are cleaner and easier to interpret. A structure like this would be nearly impossible to make experimentally, but is easy to model.

Figure 7.4 proves this hypothesis by confirming low reflectance of the texture with randomly placed pyramids of the same height.

Actually, performance of the artificial texture with randomly placed pyramids of the same height is about 20% higher than the performance of regular pyramids with the same height, which is quite substantial. And it is slightly higher than performance of the true random texture.

Figure 7.5 illustrates why it happens. Due to the limited size of the simulation domain with 20 μm by 20 μm surface and about 100 pyramids, the skyline of the truly random texture has some holes and, therefore, misses some of the low angle rays. In contrast, the artificial texture with randomly placed pyramids of the same height has much better skyline coverage, which explains its superior optical performance.

If we look at the structure with regular pyramids that are facing down, the skyline there is flat as in a random texture with pyramids facing up. However, the random pyramids have an advantage that most of the light scattering events happen at the bottom of the pyramids, because pyramid tips make up only a small portion of the overall surface area. The rays that are coming from the pyramid feet have a good chance of bumping into neighbor pyramids even at slightly upward ray angles.

On the other hand, in regular pyramids that are facing down, most of the surface area and, therefore, most of the scattering events happen close to the top of the skyline. Therefore, any rays that bounce with an upward angle escape into the air, reducing the optical solar cell performance.

To summarize this section, we discussed behavior of different light wavelengths with several types of silicon surface roughness and found that the best optical performance is achieved by random texture. If the randomly placed pyramids have the same or at least similar size, it would further improve the performance, but might be difficult to manufacture.

The next section takes optically generated carriers from this section and discusses how they travel through the cell to its contacts to generate solar power.

7.3.1 Definition of Simulation Cell Structure

7.3.2 Modeling Methodology

To develop an accurate simulation setup for solar cell optimization, all major physical mechanisms need to be modeled properly.

7.3.3 Current Crowding

Consider a solar cell that has 1 mm distance between top contact finger lines and 2.8% rear contact area coverage. The simulated cell power conversion efficiency is 20.93% (Jsc = 26.93 mA/ cm² and Voc = 687 mV). Figure 7.7 demonstrates the cross-sectional view of hole current distribution at different locations.

7.3.4 Optimizing Efficiency of Solar Cells

With the other properties fixed, we vary the rear contact size to change its area coverage. Figure 7.8 illustrates relevant competing physical mechanisms that determine design trade-offs.

Figure 7.9 shows calculated cell power conversion efficiency as a function of the rear contact area coverage. The nonmonotonic trend is a result of multiple competing physical mechanisms and points toward an optimal design around 5% rear contact area coverage. Compared with the design, which has the full backside covered by rear contact, the best design offers more than 1% gain in cell efficiency.

For a different set of p– n junctions, or silicon properties, or contact pitches, the optimum design will be somewhat shifted, but can be found using the same modeling methodology. For instance, when the substrate doping level is low, the high bulk resistance causes a bigger problem in solar cells with smaller rear contact, because current crowding becomes the dominating constraint of the cell efficiency. On the other hand, when substrate doping is high, the low bulk resistance is unlikely to play an important role in determining the cell performance. Therefore, small rear point contacts are desirable with high substrate doping, while the full surface rear contact is preferable when the substrate doping is low.

7.3.5 Comparing 3D with 2D and 1D

Next we compare the three-dimensional simulation results with the simplified two-dimensional and one-dimensional counterparts. To minimize the impact of mesh-related numerical noise, the same meshing strategy is adopted in all simulations.

However, due to the nature of 1D simulation, which only allows variations along one direction ( Y-axis), the structure used in 1D simulation is slightly modified by extending the front contact to cover the whole top surface and removing the heavily doped region under the front contact. The whole rear surface is also fully covered by rear contact, making it impossible to change the rear contact area coverage. Therefore, a valid comparison among 1D, 2D, and 3D simulations can only be drawn from structures with 100% rear area coverage. Two groups of comparison are performed with different parameter settings. Both results show that 1D simulation calculates cell efficiency that is about 2% lower than the 2D or 3D results, which demonstrates that 1D simulation is definitely insufficient to solve problems like this.

A comparison between 3D and 2D simulation results is shown in Figure 7.10. Noticeable discrepancies of up to 0.5% in simulated cell efficiency are observed when rear contact area coverage is small in Figure 7.10. Such discrepancies can be explained by the current crowding effect, which is captured more accurately in 3D simulations. The main geometrical difference between 3D and 2D simulation is that the rear contact has a rectangular shape in 3D, but it is a stripe of infinite length in 2D simulations. Therefore, the current crowding effect is almost doubled in 3D simulation because each contact has four corners compared to two corners in the 2D version, where current crowding takes place. According to Figure 7.10, the low substrate doping makes current crowding a dominating constraint, resulting in a bigger difference between 3D and 2D simulations.

Based on these observations, we conclude that 2D simulations are mostly good enough to produce similar results to 3D simulations, except for certain cases where we see up to 0.5% discrepancy in efficiency. However, it is recommended to use 3D simulations when current crowding effects cannot be neglected.

7.3.6 Junction Optimization

Efficiency of the solar cell is almost insensitive to particular properties of the heavily doped n+ selective emitters, as long as they provide good enough conduction and low enough contact resistance. There are no optically generated carriers there because the selective emitter is in a shadow of the optically opaque silver contact on the top surface. Therefore, carrier recombination is not an issue in the emitters, so they are usually doped as heavily as possible to provide good contact resistance and good conduction.

Conversely, solar cell performance is very sensitive to the properties of blanket n+ junctions. On the one hand, higher doping in the front n-type layer can reduce resistance and, therefore, boost the cell efficiency. On the other hand, higher doping leads to higher recombination rates of minority carriers, which suppresses the cell performance.

The phosphorous oxychloride (POCL) diffusion that is used in the industry to make the n+ junctions creates surface doping of about 2·10²⁰ cm^–3 ± 25%. The 50% doping range happens due to the process variations. For a typical junction depth of 0.4 μm, the efficiency is 18.8% ± 0.25%, as can be seen on Figure 7.11.

Figure 7.11 also shows that a better junction with peak doping of 10¹⁹ cm^–3 and junction depth of 0.6 μm can simultaneously boost the efficiency by 2.25% and significantly reduce the efficiency variability, from 0.5% down to 0.05%. Reduction of variability tightens the efficiency spread and, therefore, improves parametric yield. In terms of process flow, such junctions can be obtained by adding anneal with large thermal budget to the standard POCL process to reduce the surface doping, or to etch away heavily doped surface layer, or to use alternative doping techniques such as ion implantation or plasma doping.

Another option is to keep the conventional POCL doping process, but make shallower junctions of about 0.1 μm deep. This will increase efficiency by about 1%, but will not significantly reduce the variability.

To summarize this section, we discussed several design optimization criteria and found optimization space of 4% in terms of efficiency for the junction design, 1% for the rear contact size, and 4% for the substrate doping. Additionally, we found that 1D modeling is not accurate enough, but 2D modeling gives reasonable results most of the time, with the maximum observed discrepancy with 3D modeling of 0.5% in terms of cell efficiency.

7.3.7 An Alternative Solar Cell Design

Among efforts to boost the performance of monocrystal silicon solar cells, the all-back-contact cell design is regarded as an appealing candidate. Moving all contacts to the back surface and leaving no metallization pattern on the front surface eliminates the optical shading losses and allows the front surface to be optimized without the trade-off between grid shading and series resistance. It is projected that the worldwide fraction of all-back-contact solar cells in production will increase to 35% by 2020 from its current share of 5% [5].

For an all-back-contact solar cell, many options remain to be explored in order to harvest the optimal cell efficiency. Take the front surface doping as an example for which there are at least two approaches. Assuming the same lightly doped n-type substrate, one way is to have a heavily doped n+ layer at the front surface, which reduces the series resistance and provides a passivating drift field. The alternative is a heavily doped p+ layer, which serves as a floating emitter and provides an even larger drift field, but it needs careful design to minimize carrier recombination in the heavily doped surface layer. It is therefore useful to explore the possibilities in the all-back-contact cell design through TCAD simulations.

The comparison among various design options is performed using 3D simulation with Sentaurus TCAD tools, with a simulation work flow and modeling methodologies similar to the point rear contact example described previously.