Electrochemical etching is used to fabricate porous silicon surfaces for both sides of the Si wafer. The effect of PS on performance of Si solar cells is investigated and the reflected mirrors are manipulated to enhance solar cell efficiency. The process is promising for solar cell manufacturing due to its simplicity, lower cost and suitability for mass production. The PS surface has discrete pores and short-branched pores on the polished wafer side. In contrast, the etched backside of the wafer has smaller pore size, with random pores. PS formed on both sides has lower reflectivity value compared with results in other works. Solar cell efficiency is increased to 15.4% with PS formed on both sides compared with the unetched sample and other results. Using empirical models, the optical properties of the refractive index and the optical dielectric constant are investigated. The porous surface texturing properties could enhance and increase the conversion efficiency of porous Si solar cells. The obtained results are in agreement with experimental and other data.
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Keywords: Porous silicon; Solar cell; Crystalline silicon; Refractive index.
PACS: 61.43.Gt; 88.40.H-; 72.80.Jc; 78.20.Ci.
The amount of reflection from a surface is the main obstacle in efficient solar cell performance. Reflection is related to the refractive index of the material. For instance, the silicon (Si) refractive index is 3.5, (which can rise by up to ~35%), which prevents an electron-hole pair from being generated. This factor could reduce the efficiency of photovoltaic converters. Antireflection Coatings (ARC) could reduce surface reflection, and increase conversion efficiency, extended lifetime and improved the electro- physical and characterization of photovoltaic converters .
Porous Si (PS) is attractive in solar cell applications due to its efficient ARC and other properties such as band gap broadening, wide absorption spectrum and optical transmission range (700-1000 nm). It can also be used for surface passivation and texturization [2-6]. The potential advantages of PS as an ARC for solar cells include surface passivation and removal of the dead layer diffused region. Moreover, PS could convert higher energy solar radiation into spectrum light, which is absorbed more efficiently into bulk Si .
The vibrations, electronic and optical properties of PS have been studied using various experimental techniques. Of these, the electrochemical etching process is a promising technique in fabricating PS [8-11]. According to the quantum confinement model, a heterojunction can be formed between the Si substrate and porous layers because the latter has a wider band gap (1.8-2.2 eV) compared with crystalline Si (c-Si) .
Recently, Ben Rabha and Bessais  used Chemical Vapor Etching (CVE) method to perform front PS layer and Buried Metallic Contacts (BMCs) of multicrystalline Silicon (mc-Si ) solar cells to reduce the reflectivity to 8% in the 450-950 nm wavelength range and induced the simple and low cost technology with 12% conversion efficiency. Yae et al.  have deposited fine platinum (Pt) particles on multicrystalline n-Si wafers by electroless displacement reaction in a hexachloroplatinic acid solution containing HF. The reflectance of the wafers is reduced from 30% to 6% by the formation of porous layer. Brendel  has performed electrochemical etching of porous Si layer into the substrate based on homoepitaxial growth of monocrystalline Si films and yielded a module efficiency of 10%.
This work aims to investigate the effect of PS on performance of Si solar cells. Enhancing solar cell efficiency can be realized by manipulating reflected mirrors. The results are promising for solar cell manufacturing, as they show the simplicity, lower cost, suitability for mass production and to investigate the optical properties of refractive index and optical dielectric constant.
This paper is arranged as follows. Section 2 discusses the experimental procedure, while the experimental and theoretical results are in Section 3. The conclusion is provided in the last section.
N-type Si wafer with a dimension of 1 cm x 1 cm x 283 µm, (111) orientation, resistivity of 0.75 Ω.cm, and doping concentration of 1.8 x 1017 cm-3 was etched through an electrochemical process to produce the porous structure. The wafer was placed in an electrolyte solution (Hydrofluoric Acid (HF): ethanol, 1:4) with a current density of 60 mA/cm2 at an etching time of 15 min for each side. Before the etching process, the Si substrate was cleaned using the Radio Corporation of America method (RCA) to remove the oxide layer, it was then immersed in HF acid to remove the native oxide. The electrochemical cell was made by teflon and has a circular aperture with radius of 0.4 cm, and the silicon wafer is sealed below. The cell consists of two-electrode system with the Si wafer as the anode and platinum as the cathode. The process was carried out at room temperature. After etching, all samples were rinsed with ethanol and dried in the air. Surface morphology and structural properties of the samples under treatment were characterized by using Scanning Electron Microscopy (SEM). PS optical reflectance was obtained by using an optical reflectometer (Filmetrics F20) that includes integrating sphere. Fourier Transform Infrared Spectroscopy (FTIR) of the PS samples were measured. Photoluminescence (PL) spectroscopy measurements were performed at room temperature using He-Cd laser (λ=325 nm).
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To fabricate the solar cell; After (RCA) cleaning and oxidation, the silicon wafer underwent spin coating. A liquid containing photo-resistant material was placed at the center of the wafer. Spinning process was carried out at room temperature at the speed of 300 rpm for 20 sec. After spin coating, the wafer was placed back into the furnace for 20 min at 200 °C to drive out moisture. The mask was designed by the photo plotter technique that was placed directly above the sample and exposed to UV-light for 25 sec to form a patterned coating on the surface. Doping diffusion was carried out using a tube furnace at the temperature of 1100 °C for 60 min using N2 flow gas. The top surface area of the wafer was doped with boron to be P-type. Prior to the contact evaporating process, the oxidation layer was removed using an etching solution of NH4F:H2O, and then mixed with HF with a mole ratio of 1:7. Aluminum evaporation was used for back metal contact, and silver was used for front metallization. Figure 1 shows solar cells setup. Contact annealing was done at 400 °C for 20 min to pledge ohmic contact (see Fig.1) as well as to improve the contact properties. Reflected mirror with reflectivity > 89% was used to enhance solar cell efficiency. The structure of PS solar cells consists of metal mask contact of grid pattern with finger width of 300 µm, and finger spacing of 600 µm.
The fabricated device was analyzed using current-voltage (I-V) measurement, and the lens was placed under solar simulator illumination. A solar cell using unetched c-Si was fabricated under the same conditions for comparison.
Results and discussion
The efficiency of photovoltaic energy conversion must be enhanced to reduce the cost of solar cell modules for energy generation. In this process, photons from solar radiation are falling on a solar cell generate electron and hole pairs, which are collected at the two contact points. A drawback of solar photovoltaic energy conversion is that most semiconducting materials used are sensitive to only a part of the solar radiation spectrum.
Figure 2a shows the cross-section SEM images of chemically treated samples. These images show that the thickness is uniform throughout the obtained porous layer, indicating that the etching process forms a uniform porous density layer on the surface. The SEM images in Fig's. 2 b and c illustrate the treated surface with similar grain geometry due to the isotropic character of HF/ethanol etching and the optimal conditions of current density and etching time. The images show that the entire surface of the sample were etched. Most pores are spherical. The porous surface formed on the front polished side had discrete pores, in addition to short-branched pores. In contrast, the PS surface formed on the unpolished backside is shaped in small pores, which could be attributed to an increase in surface roughness for the unpolished backside proportional to the etching parameter. Figure 3 demonstrates that the three dimensional topographic images of the PS etched surfaces with the pyramidal shape were distributed over the entire surface. The pyramidal shape indicated that the increase in the surface roughness is due to the effect of the etching parameters' effect on the surface characterization. The high degree of roughness of the PS surface implies the possibility of using the porous layer as an ARC because the surface texture reduces the light reflection. The scattering in PS is possibly due to the roughness in relation to the thickness of the porous layer . The attenuation of the reflectivity is due to scattering and transmission at the porous and bulk interfaces [16, 17]. This parameter is important in enhancing the photo conversion process for solar cells. To confirm that PS can be utilized as an ARC, the reflection measurement was done by using optical reflectometry.
The results are shown in Fig. 4 to demonstrate that PS formed on both sides has lower reflectivity value compared with the results of others [13-15] and these results have been confirmed by absorption spectrum as shown in Fig. 5. Figures 6 and 7 show the FTIR spectra of the silicon as grown and PS as function of the reflectivity and absorptive, respectively. The results showed an agreement with the results demonstrated in Fig's 4 and 5. This means that our PS sample has a high absorption and low reflection spectrum as compared with the as grown sample and this may be attributed to the increase of porosity that leads to increase the PS density over the surface of the sample. Figure 8 illustrates the PL spectrum of the PS formed on the unpolished side, revealing a peak at 681.3 nm (1.82 eV) with Full Width and Half Maximum (FWHM) of about 330 mV. For PS formed on the front polished side, the peak located at 666.9 nm (1.86 eV) with a FWHM of about 180 mV is obtained. PS formed on the front polished side revealed blue shift luminescence. This means particles are confined into the lower dimension. The energy gaps of PS are increased to 1.82 and 1.86, respectively. The broadening of the energy gap occurs with a decrease in the crystallite size.
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The results in Figs. 4 and 8 are used to calculate the refractive index and optical dielectric constant of Si and PS using :
where R is reflectivity. The results are given and compared with others in Table 1.
The refractive index is an important physical parameter related to microscopic atomic interactions. Theoretically, the two different approaches in viewing this subject are the refractive index related to density, and the local polarizability of these entities .
On the other hand, the crystalline structure represented by a delocalized picture, will be closely related to the energy band structure of the material, complicated quantum mechanical analysis requirements and the obtained results. Many attempts have been made to relate the refractive index and the energy gap Eg through simple relationships [20-25].
However, these relationships of are independent of temperature and incident photon energy. Here, the various relationships between and will be reviewed. Ravindra et al.  suggested different relationships between the band gap and the high frequency refractive index and presented a linear form of as a function of:
where α = 4.048 and β = −0.62 eV−1.
To be inspired by simple physics of light refraction and dispersion, Herve and Vandamme  proposed an empirical relation as:
where A = 13.6 eV and B = 3.4 eV. Ghosh et al.  took a different approach to the problem by considering the band structural and quantum-dielectric formulations of Penn  and Van Vechten . Introducing A as the contribution from the valence electrons and B as a constant additive to the lowest band gap Eg, the expression for the high-frequency refractive index is written as:
where A = 25Eg + 212, B = 0.21Eg + 4.25 and (Eg+B) refers to an appropriate average energy gap of the material. Thus, these three models of variation with energy gap have been calculated. The calculated refractive indices of the end-point compounds are investigated in Table 1. The optical dielectric constant is calculated using  and depends on the refractive index. In Table 1, the calculated values of using the three models are investigated. Increasing porosity percentage from 60% (front side) to 80% (back side) uses the weight measurements  leads to decreasing refractive index. As with Ghosh et al. , this is more appropriate for studying solar cell optical properties.
The series and sheet resistances, maximum voltage Vm, maximum current Im, open-circuit voltage Voc, and short-circuit current Isc are the prominent parameters in calculating solar cell efficiency.
The increasing efficiency of solar cells fabricated with PS formed on both sides of the wafer compared with one side PS and bulk Si solar cells, respectively is shown in Fig. 9. This is attributed to increasing the open circuit voltage without losing the short circuit current of the solar cells, as shown in Table 2. The porous surface texturing properties could enhance and increase the conversion efficiency of Si solar cells. The results also showed that the efficiency resulting from this procedure is more promising compared with other solar cells fabricated under similar conditions .
PS formed on the unpolished backside of the c-Si wafer showed an increase in surface roughness compared with one formed on the polished front side. The high degree of roughness along with the presence of the nanocrystal layer implies that the surface used as an ARC, which can reduce the reflection of light and increase light trapping on a wide wavelength range. This parameter is important in enhancing the photo conversion process for solar cell devices. PS formed on both sides has low reflectivity value. Fabricated Solar cells show that the conversion efficiency is 15.4% compared with the unetched sample and other results [13,15]. The results of the refractive index and optical dielectric constant of Si and PS are investigated. A good agreement with experimental data is observed.