Paraboloid Structured Silicon Surface for Enhanced Light Absorption: Experimental and Simulative Investigations
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In this paper, we present an optical model that simulates the light trapping and scattering effects of a paraboloid texture surface first time. This model was experimentally verified by measuring the reflectance values of the periodically textured silicon (Si) surface with the shape of a paraboloid under different conditions. A paraboloid texture surface was obtained by electrochemical etching Si in the solution of hydrofluoric acid, dimethylsulfoxide (DMSO), and deionized (DI) water. The paraboloid texture surface has the advantage of giving a lower reflectance value than the hemispherical, random pyramidal, and regular pyramidal texture surfaces. In the case of parabola, the light can be concentrated in the direction of the Si surface compared to the hemispherical, random pyramidal, and regular pyramidal textured surfaces. Furthermore, in a paraboloid textured surface, there can be a maximum value of 4 or even more by anisotropic etching duration compared to the hemispherical or pyramidal textured surfaces which have a maximum h/D (depth and diameter of the texture) value of 0.5. The reflectance values were found to be strongly dependent on the h/D ratio of the texture surface. The measured reflectance values were well matched with the simulated ones. The minimum reflectance value of ~4 % was obtained at a wavelength of 600 nm for an h/D ratio of 3.75. The simulation results showed that the reflectance value for the h/D ratio can be reduced to ~0.5 % by reducing the separations among the textures. This periodic paraboloidal structure can be applied to the surface texturing technique by substituting with a conventional pyramid textured surface or moth-eye antireflection coating.
KeywordsSolar cells Surface modification Reflectance Light trapping Paraboloid structure
The cost of the solar energy can be reduced by enhancing solar cell efficiency using some advanced technology to fabricate solar cells with reduced losses [1, 2], namely, reflection , recombination , and resistive losses [5, 6]. The surface texturing of the wafers is an important part of the silicon (Si) solar cell’s fabrication process in R&D and production levels . This process can be utilized to enhance the absorption of light due to enhancing the back surface reflectance and path length of light and reduction in front surface reflection. This process also encourages the carrier collection near the junction.
For a bare Si surface, the reflection loss is around ~30 % due to reflection of light from the front surface resulting in a small amount of absorption which yields poor efficiency. To reduce these losses, several techniques have been invented. Out of all the methods created and invented, surface texturing has been widely used to reduce the reflection losses. It reduces the front surface reflection, increases the internal reflections, and also increases the light path lengths inside the cell due to the overall light absorption increasing. Several surface texturing methods, like mechanical grooving , reactive ion etching , laser texturing , alkaline , and acidic texturing  have been used to increase the absorption of light inside the solar cell. Alkaline and acidic texturing has been widely used for the commercial production of Si wafer-based solar cells.
Alkaline anisotropic etchants like sodium hydroxide (NaOH) and potassium hydroxide (KOH) at low concentrations and temperatures of 80–90 °C can form square base pyramidal structures randomly distributed over the cell surface. The reflectance value of ~12 % was obtained at a wavelength of 600 nm for the random pyramidal structure . Baek et al.  also made a regular pyramidal structure using electrochemical etching. In a regular pyramidal structure, the reflectance value is reduced to ~10 %. The pyramidal structures allow for multiple reflections and hence trap any incoming ray light and reduce the reflection.
Several attempts have been made in previous studies to explain the variation of the reflectance values by taking scanning electron microscopy (SEM) images of the texture surface and theoretical modeling of reflectance [7, 14, 15, 16, 17]. Previous studies [7, 14, 15, 16, 17] have assumed that the acid textured surfaces are a part of the hemisphere, and also, the variation of reflectance with a h/D (depth and diameter of the texture) ratio was also determined. In case of the texture surface as a part of the hemisphere, the minimum reflectance value of ~15 % can be achieved for a maximum achievable value of an h/D ratio of 0.5.
Macdonals et al.  developed a masked reactive ion etching (RIE) method, which is better than the wet acid, maskless reactive ion etching method. Xi et al.  observed a part of hemispherical structure in acid texturization and calculated that reflectivity at 500 nm start declining when the h/D exceeds 0.29.
Several researchers have introduced analytical models for Si nano-wire mats , and nano-holes . Kim and Kim  used ultrasonic vibration during alkaline texturing of multicrystalline Si (mc-Si) to improve uniformity. Gangopadhyay et al.  obtained 14.0–14.5 % efficiency in an industrial production line with a yield >95 % by using mc-Si substrates of large size and textured them in a solution of NaOH-NaOCl at 80 °C to restrict the step height to <5 μm. Si nano-structures have been characterized using various techniques [23, 24]. Tsujino et al.  used metallic catalysts for acid texturization. Hazeland and Hu  formed a titled pyramidal structure by using potassium carbonate, which shows a lower reflectance compared to polished surfaces. Campbell et al.  suggested that top surface reflection could be eliminated by using a tilted pyramidal structure. Wang et al.  wire textured the mc-Si wafers by using a self-assembled mask. Houser et al.  used nano-imprint lithography for solar cell texturization, whereas Xu et al.  developed lithography-free sub 100 nm nano-cone array antireflection layers for the application of solar cells. Houser et al.  found that the texture surface is a part of paraboloids. It was found that acid textured surfaces are not always part of the hemisphere but also have a parabolic structure. The paraboloid structure has more potential to reduce the reflection loss.
In this work, we investigated the Si texture surface as a part of paraboloid and developed a model for surface reflection of paraboloid texture surfaces. This model was used to predict the reflectance as a function of wavelength and h/D ratio for the paraboloid textured Si surface. This model considers the reflection from the entire solar spectrum, bulk absorption, and the contribution of the rear surface to light trapping. In the case of parabola, there is more possibility that the light could be concentrated inside the Si solar cell compared to the hemispherical, random pyramidal, and regular pyramidal textured surfaces. For hemispherical or pyramidal textured surfaces, the maximum h/D value can reach 0.5, whereas in paraboloid textured surfaces, the maximum h/D value can reach a maximum of 4 or even more by anisotropic chemical etching.
Modeling of Parabolic Textured Surface
The values θ i and θ t lie between 0° and 90°.
Here, k n is the no. of reflection (no. of times the light reflected back on the surface, which is an incident on point P n,1).
It can be seen that for a lower wavelength, there is no rear surface reflection effect, as the light gets absorbed due to a high absorption coefficient for a lower wavelength. However, for a higher wavelength, the value of R r has a huge effect on the total reflection. The refracted light along direction PS incident on back surface at Q making an angle (θ i–θ t) with normal (MM’) to the rear surface as shown in Fig. 1b. This incident beam PS on rare surface again split into two parts, first reflected one along QR direction making the same angle (θ i–θ t) with MM’, whereas transmitted beam goes along QT direction (making angle θ t’ with MM’).
Here, h << t w, t w is the wafer thickness and x w is the path length traveled by the refracted light inside the Si wafer, which make an angle of (θ i–θ t) with the normal (MM’) of rare plane surface. As the light pass through the wafer, its attenuation factor increases hence probability of light gets absorbed within the wafer increases and reflectivity decreases.
For (θ i–θ t) ≥ critical angle, total internal reflection will occur.
The Eqs. (1)–(16) were used to calculate the theoretical values of the reflectance of paraboloid front texture surfaces.
Si paraboloid micro-pore arrays were prepared on B-doped p-type <100> Si wafers with a resistivity of 1~10 Ωcm and wafer thickness (t w) of 550 μm by electrochemical etching method. In order to make Si pore arrays with a parabolic shape, we first oxidized the wafers to get a silicon oxide (SiO2) mask using thermal oxidation. A square pattern of 2 μm × 2 μm size was obtained on SiO2 using photolithography. The patterned samples were dipped in a KOH etchant at 80 °C to make inverse-shaped pyramidal notches that would act as regions for concentrating an electrical bias. The electrochemical etching was performed in a solution of hydrofluoric acid, dimethylsulfoxide (DMSO), and deionized (DI) water. A thin aluminum layer was deposited on the backside of the wafer to produce an Ohmic contact between the Si wafer and working electrode by DC magnetron sputtering method. The electrochemical etching was performed under a constant current density mode of different biases in a Teflon bath. A platinum wire was used as a counter electrode. The Si wafer with Al back contact acted as a working electrode. The sample area exposed to the electrolyte solution was approximately 2 cm2. The etch rate was approximately 1.1~1.3 μm/min, and the pore length was controlled by etching time under otherwise nominally identical conditions.
Field emission scanning electron microscopy (FE-SEM) images of the front and cross-sectional view of paraboloid textured Si surfaces were taken under ×5000 magnification using the Hitachi FE-SEM, Model S-4800. The reflectance measurements were carried out with a wavelength range of 300–1200 nm using the UV-Vis-NIR spectrophotometer, Model Cary-5000.
Results and Discussion
Figure 1 shows the schematic of ray tracing in the parabolic structure instead of the paraboloid for picture clarity. In this diagram, the axis of parabola is assumed along the x-axis. A ray falls along the axis of parabola. Similar to the parabolic mirror, the ray incident on any point P n,1 (x n,1, y n,1) of the inner surface of the parabola will pass through the focal point F. The vertex O of the parabola is assumed as origin (0, 0). The distance of point P from the y-axis is h, which is known as height or depth of textures, and at the same point, the diameter of the circular ring is D. The distance between points F and O is a. Hence, the latus rectum of the parabola is 4a (as taken in the theoretical section for calculations). When a ray is incident on point P at an incident angle, θ i is split into two parts. The first reflected part goes in the air along the PF direction while making the same reflected angle as θ i. Another refracted part goes along the PS direction while making an angle θ t.
The h/D values along with surface area ratio of untexture (a 1) to texture (a 2) with etching duration (t e )
Etching duration (s)
Spacing between textures (d, μm)
a 1/a 2
After using the passivating layer, the recombination at the surface can be reduced to a very low value. The passivating layer can also work as ARC. Thus, paraboloid structure combined with the passivating layer can be used in PV devices for better performance.
The paraboloid texture surfaces of Si with different h/D ratios were obtained by anisotropic chemical etching using external bias in order to increase the h/D ratio. The paraboloid texture surface has a lower reflectance value than the hemispherical, random pyramidal, and regular pyramidal texture surfaces. An optical model was developed to simulate the light trapping and scattering effects of paraboloid Si textured surfaces. The model was experimentally verified by measuring the reflectance values for different h/D ratios. The h/D ratio of the textured surface was varied up to 3.75. The measured reflectance values matched well with the simulated one in the wavelength of 300–1200 nm. The minimum experimental reflectance value of ~4 % was obtained at a wavelength of 600 nm for the h/D ratio of 3.75. Simulation results showed that the reflectance value could be reduced to less than 1 % by reducing the separation among paraboloid textures.
This study was carried out with the support of the DGIST R&D Program (No. 15-EN-01 &15-HRMA-01) funded by the Ministry of Science, ICT, and Future Planning of the Korean government.
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