JOURNAL OF ENGINEERING RESEARCH AND TECHNOLOGY, VOLUME 1, ISSUE 2, JUNE 2014 73 Antireflection Coatings Combining Silicon Nitride with Silicon Nanoparticles M. Beye1, F. Ndiaye2, and A. S. Maiga2 1 Department of Applied Physics, Gaston Berger University of Saint Louis, Senegal. 2 Laboratory of Electronics, Data Processing, Telecommunications and Renewable Energies, Saint Louis, BP 234, Senegal Abstract—In this work, solar cell antireflection coatings (ARC) combining silicon nitride layer with silicon nanoparticles are investigated. Two configurations are considered: silicon nanoparticles on a SiNX layer surface and partially embedded in a SiNX layer. Numerical results show that this ARC concept performs better in the configuration where silicon nanoparticles are placed on the dielectric layer. A silicon nitride refractive index of 2.3 is found to be more advantageous, yielding a low weighted reflectance of 2.1% in the wavelength range 300 – 1100 nm. The stability of the reflectance for oblique incidence with angles lower than 40° was also observed. With this new ARC concept, a relative increase of 8.6% in the short circuit current density over a solar cell with the standard Si3N4 coating can be expected. Index Terms—Silicon nitride, silicon nanoparticles, antireflection coatings I INTRODUCTION Silicon nitride (SiNX) layers are largely used in photovoltaic (PV) applications due to their interesting optical and electrical properties [1]. Planar layers of this and other dielectric materials, generally used as antireflection coatings (ARCs) in solar cells and other optoelectronic devices, are often optimized for a single wavelength. Therefore, they reduce the reflection from a surface in a narrow wavelength range. It has been shown that an optimized SiNX double layer has a little advantage over the standard Si3N4 single layer [2, 3]. Scattering from metal particles has been demonstrated to efficiently couple light into waveguide modes in thin semiconductor layers due to their surface plasmon resonances [4, 5]. Metal and dielectric nanoparticles have been also largely used to enhance light absorption in thin film solar cells [6 - 12]. Metal nanoparticles embedded in a dielectric layer [13, 14] and patterned on it or directly onto a substrate [15, 16] have been found to reduce the reflection from a solar cell active layer surface over a broad spectral range. Recently, a new approach not involving metals has been proposed, in which a two-dimensional periodic array of cylindrical silicon nanoparticles on a Si3N4 spacer layer is used. Simulations and experimental results showed a weighted reflectance lower than 2% over the spectral range 450 – 900 nm for angles of incidence up to ± 60° [17]. In this work, we consider a solar cell antireflection coatings combining silicon nitride layer with silicon nanoparticles in two configurations: silicon nanoparticles on a SiNX layer surface and partially embedded in a SiNX layer. The effect of the dielectric layer refractive index and the one related to the incorporation of silicon nanoparticles in the dielectric layer on the performances of this ARC concept are investigated. II MODELS DESCRIPTION AND OPTIMIZATION PROCEDURE We consider a silicon solar cell surface of length L and width l, on which a regular array of spherical silicon nanoparticles is arranged as schematically shown in Fig. 1. In this figure r is the radius of a particle and p the period of the two-dimensional array. The two configurations considered in this work are shown in Fig. 2. Figure 1: Schematic representation of a regular array of spherical silicon nanoparticles. (a) (b) Figure 2: Schematic representations of ARCs: (a) Silicon nanoparticles on a SiNX layer surface; (b) Silicon nanoparticles embedded in a SiNX layer. Antireflection coatings combining silicon nitride with silicon nanoparticles, M. Beye*, F. Ndiaye, and A. S. Maiga (2014) 74 For each configuration, a modified transfer matrix method [18, 19, 20] is used to calculate the reflectance from the silicon surface. The ARC structures represented in Fig. 2 can be considered as composed of two layers (therefore, three interfaces) on a Si substrate (Fig. 3). The amplitude of the uniform electrical field, E, at any position in a layer, can be divided into two components: the transmitted, E+, and the reflected component, E–. The field amplitudes at the top and bottom side of an interface are related by the so-called transmission or refraction matrix of the interface, Ik–1,k, as follows [19]:                       ' ' ,1 1 1 kE k E kkI kE k E (1) where           1,1 ,11 ,1 1 ,1 kkr kkr kkt kkI (2) The Fresnel coefficients of transmission, tk–1,k, and reflection of the interface, rk–1,k, are defined as follows [20]:  For the s polarization: k qknkqkn kqkn kkt    11 112 ,1 (3) k qknkqkn kqknkqkn kkr    11 11 ,1 (4)  For the p polarization : kqknkqkn kqkn kkt 11 112 ,1    (5) k qknkqkn kqknkqkn kkr 11 11 ,1    (6) where nk is the complex refractive index of the k-th layer and 2 0sin0 1          kn n kq  (7) θ0 is the angle of incidence. The field amplitudes at the top and bottom side of the k-th layer are related by the so-called propagation matrix of the layer, Pk, as follows [18]:                      kE k E kP kE k E ' ' (8) where         )exp(0 0)exp( ki ki kP   (9) The phase shift, δk, due to the wave passing through the k-th layer is given by: )cos( 2 kkdknk            (10) where λ is the wavelength of the incident light, nk is again the complex refractive index of the k-th layer, dk its thickness, and θk is the propagation angle following Snell’s law (n0 sinθ0 = n1 sinθ1 = n2sinθ2 = n3sinθ3). The above matrix transformations can be applied for the 2 layers and 3 interfaces in Fig. 3, resulting in:                                       ' 3 ' 3 2221 1211 ' 3 ' 3 23212101 0 0 E E TT TT E E IPIPI E E (11) The product matrix resulting from the above procedure is a 2 x 2 matrix called system transfer matrix T. The complex reflection coefficient of the multilayer can be calculated from the elements of the system transfer matrix as follows [18, 19]: 11 21 0 ' 3 0 0 T T E E E r       (12) from which the reflectance, R, is obtained as │r│2. It is clear that to calculate R, we need to know the complex refractive index of each layer and its thickness. For the ARC configuration shown in Fig 2.a, the first layer can be considered as a composite material consisting of silicon nanoparticles in air (we suppose that nair = n0 ≈ 1) with a thickness d1 equal to the diameter of the nanoparticles and the second is a homogeneous SiNX spacer layer of thickness d2. For the configuration shown in Fig. 2b, two layers of composite materials can be considered with the host media consisting of air and SiNX, respectively. The complex refractive index of a material is related to its permittivity by the well-known formula: ε = n2. Therefore, knowing the permittivity, we can calculate the complex refractive index. The Maxwell-Garnett effective medium approximation is used to calculate the effective permittivity of the composite Figure 3: Notation of electric field amplitudes in the two-layer ARC structure. The prime is used for waves at the down side of an interface. JOURNAL OF ENGINEERING RESEARCH AND TECHNOLOGY, VOLUME 1, ISSUE 2, JUNE 2014 75 materials formed by silicon nanoparticles in air and in SiNX. This effective permittivity is given by [21]:        fbfi fbfi beff    21 1221    (13) where εb is the permittivity of the host (base) material, εi the permittivity of the particle’s materials and f the volume fraction of the particles in the host medium. For a layer of thickness d, its volume can be expressed as: Vlayer = L×l×d. For simplicity, we will take L = l = 1 cm. The volume of a spherical particle of radius r is: Vp = 4πr 3/3. The number of particles on the surface can be expressed as: Np = (L/p)×(l/p). Thus, the volume fraction of the particles in the corresponding layer is: f = (Np×Vp) /Vlayer. Optical data for silicon are taken from [22]. For silicon nitride, optical constants are calculated using data provided in the appendix of [23]. The reflectance weighted over the AM1.5G solar spectrum (Air Mass 1.5 Global: terrestrial solar spectral irradiance on a surface of specified orientation under specified atmospheric conditions) is evaluated in the wavelength range 300 – 1100 nm to take into account the influence of the photon flux and the solar cell internal quantum efficiency. This parameter is defined as [24]:               max min max min       dIQEF dRIQEF wR (14) where F is the photon flux, IQE the solar cell internal quantum efficiency, defined as the number of electrons collected per photon not reflected and R the reflectance. The photon flux, F, is related to the irradiance, I, by the following expression [25]:   ch I F      (15) where λ is the wavelength of the incident light, h the Planck's constant and c the speed of light. Irradiance data are taken from [26]. The short circuit current density (JSC) is also evaluated as an important solar cells parameter. For a single junction solar cell, it is given by [23]:           dAIQEFqscJ   max min (16) where A(λ) is the absorption by silicon. We suppose in this work that IQE = 1, meaning that all not reflected photons are collected. Thus, in equation (4), A(λ) can be replaced by [1 – R(λ)]. III SILICON NANOPARTICLES ON A SINX LAYER SURFACE The weighted reflectance under normal incidence from the silicon surface in the configuration shown in Fig 2.a is about 17.3% for an array of spherical particles of diameter 125 nm, spaced by 450 nm and a Si3N4 layer thickness of 60 nm with a refractive index of 2.0. These values are the optimal ones found in [15] for cylindrical nanoparticles. This high reflectivity suggests that the dimensional parameters have to be re-optimized since the shape of the particles has changed. The dependences of the weighted reflectance (Rw) on the period (p) of the regular array and the spacer layer thickness (d2) are shown in Fig. 4. The parameters used in the calculations are displayed in Table I. It can be seen that there is an optimum both in the period and in the thickness. It is clear from the insets of Fig. 4a-b that these optimal values are about 840 nm for the period and 66 nm for the spacer layer thickness. It has been argued that the optimum in the array period is related to the fact that a smaller period results in a strong interparticle coupling effect and a large period corresponds to a small surface coverage, reducing the overall light scattering. The optimum in the spacer layer thickness is because thicker spacer layers lead to reduce the near field-coupling, while thinner layers cause a shift of the Plasmon resonance [16]. The reflectance under normal incidence from the silicon surface in the configuration with new optimized parameters is shown in Fig. 5. Reflectance curves from a bare silicon surface (a) (b) Figure 4: Dependences of the weighted reflectance on the dimensional parameters for a particle diameter of 125 nm: (a) Period dependence of Rw; (b) Thickness dependence of Rw. TABLE 1 Parameters used in the calculations. Parameters For Fig. 4a For Fig. 4b Diameter of particles (d1) 125 nm 125 nm Period (p) variable 840 nm Spacer layer thickness (d2) 60 nm variable Antireflection coatings combining silicon nitride with silicon nanoparticles, M. Beye*, F. Ndiaye, and A. S. Maiga (2014) 76 and coated with a standard 80 nm thick S3N4 are also shown for comparison. The optimization of the dimensional parameters, except the particle’s diameter, results in a decrease of the weighted reflectance from 17.3% to 3.2%. The strong reduction of the reflection is explained by the combined effect of the preferential forward scattering of the incident light by the silicon nanoparticles and the destructive interference from the SiNX layer [17]. The scattering from particles is known to depend strongly on the dielectric environment. Figure 6 represents the dependence of the weighted reflectance on the SiNX refractive index. For the optimal dimensional parameters found in Fig. 4, it appears that an optimal refractive index of about 2.3 leads to a weighted reflectance of 2.1%. However, it is well known that the extinction coefficient and, the absorption within a SiNX layer, slightly increases in the lower wavelength range for high refractive indices [23]. Therefore, the pronounced antireflection effect for higher index may be partly compensated by the increased absorption within the layer. This claim may be verified by taking into account the dispersion of SiNX optical constants. A good antireflection coating must be stable in a wide range of angles of incidence. Figure 7 shows the angular dependence of the weighted reflectance for the configuration shown in Fig. 2a with the optimal parameters. It appears that the reflectance shows a good stability for angles of incidence under 40°. An evaluation of the short circuit current density from equation (16) shows that for a solar cell with the standard Si3N4 single layer ARC, a theoretical JSC value of 38.4 mA/cm 2 can be expected, whereas, for this new ARC concept with the optimal parameters this value is 41.7 mA/cm2, corresponding to a relative increase of about 8.6%. IV SILICON NANOPARTICLES PARTIALLY EMBEDDED IN A SINX LAYER For the configuration of silicon nanoparticles on a SiNX layer with the optimal parameters (diameter 125 nm, period 840 nm, spacer layer thickness 66 nm, refractive index 2.3) let’s incorporate gradually the nanoparticles in the dielectric layer. We can define a factor, Femb, corresponding to the portion of a particle embedded in the SiNX layer. Here, the maximum value of Femb is 66/125 or about 0.52, representing the ratio of the optimal spacer layer thickness over the optimal diameter of nanoparticles. The increase of the weighted reflectance with the factor Femb (Fig. 8) permit to conclude that the embedded silicon nanoparticles in the SiNX layer yield a negative effect. Therefore, the proposed ARC performs better in the configuration where silicon nanoparticles are placed on the SiNX layer. Figure 5: Reflectance under normal incidence from a bare silicon surface (black), a silicon surface coated with a 80 nm thick Si3N4 layer (green) and with a 60 nm thick SiNX layer on which silicon nanoparticles of diameter 125 nm and spaced by 450 nm are arranged (red). Figure 6: Dependence of Rw on the SiNX refractive index for optimal dimensional parameters (diameter 125 nm, period 840 nm and spacer layer thickness 66 nm). Figure 7: Angular dependence of the WR for the ARC configuration with optimal parameters. Figure 8: Dependence of Rw on the parameter Femb under normal incidence for the ARC with optimal parameters. JOURNAL OF ENGINEERING RESEARCH AND TECHNOLOGY, VOLUME 1, ISSUE 2, JUNE 2014 77 V CONCLUSION Two configurations of antireflection coating combining silicon nanoparticles and silicon nitride layer are considered. The antireflection performances of this combination are found to be better in the configuration where silicon nanoparticles are placed on the SiNX layer. For this configuration, a SiNX refractive index of 2.3 provides better performances, yielding a low weighted reflectance of 2.1% in the wavelength range 300 – 1100 nm. Stability of the reflectance for oblique incidence with angles lower than 40° is observed. A relative increase of 8.6% in the short circuit current density over a silicon solar cell with the standard Si3N4 coating can be theoretically expected. Partially embedded silicon nanoparticles in the dielectric layer yielded a negative effect. The new ARC concept proposed in this work can be used for efficiency improvement in silicon solar cells. ACKNOWLEDGMENTS The authors would like to thank the staff members of the Department of Applied Physics: A. Ndiaye, D. Diouf and M. Sene for helpful discussions and suggestions. This work was also supported by the University Gaston Berger (Grant N° 0003765). REFERENCES [1] M. 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Perova, “Numerical methods for calculation of optical properties of layered structures”, Proc. of SPIE Vol. 7521 (2010) 75210G-1–75210G-10. [21] R. Ruppin, “Evaluation of extended Maxwell-Garnett theories”, Optics Communications 182 (2000) 273–279. [22] M. A. Green and M. Keevers, "Optical properties of intrinsic silicon at 300 K ", Progress in Photovoltaics 3, 3 (1995) 189–192. [23] H. Nagel, A. G. Aberle, and R. Hezel, “Optimized Antirereflection Coatings for Planar Silicon Solar Cells using Remote PECVD Silicon Nitride and Porous Silicon Dioxide”, Progress in Photovoltaics 7 (1999) 245–260. [24] D. Bouhafs, A. Moussi, A. Chikouche, and J. M. Ruiz, “Design and simulation of antireflection coating systems Antireflection coatings combining silicon nitride with silicon nanoparticles, M. Beye*, F. Ndiaye, and A. S. Maiga (2014) 78 for optoelectronic devices: Applications to silicon solar cells”, Solar Energy and Solar Cells 52 (1998) 79–93. [25] S. A. Boden and D. M. Bagnall, “Sunrise to Sunset Optimization of Thin Film Antireflective Coatings for Encapsulated, Planar Silicon Solar Cells”, Progress in Photovoltaics 17 (2009) 241–252. [26] American Society for Testing and Materials (ASTM), “Standard Tables for Reference Solar Spectral Irradiance at air mass 1.5: ASTM G-173-03”, (2003). M. Beye obtained his PhD in Applied Physics in 2013 from Gaston Berger University. He received his MS (2005) in Semiconductor Materials and Structures and BS (2003) degrees from the Saint- Petersburg Electrotechnical University (Russia). He held different teaching positions since 2006, particularly at the Department of Applied Physics of the Gaston Berger University which he joined in 2010. He has also worked at the Laboratory of Electronics, Data Processing, Telecommunications and Renewable Energies. His research interest includes antireflection coating technologies, solar cells and related topics, nanotechnology, environment. F. Ndiaye is a PhD Student at the Laboratory of Electronics, Data Processing, Telecommunications and Renewable Energies of the Gaston Berger University. She is working on the relations between environmental conditions and PV module performances. A. S. Maiga obtained his PhD in 1993 from the University of Rennes (France). He is now an Associate Professor at the Department of Applied Physics of the Gaston Berger University. He is also leading the Laboratory of Electronics, Data Processing, Telecommunications and Renewable Energies.