## 2 Simulation Description  
There are several models commonly used for the optical simulation of absorption and reflectance in thin-film photovoltaic devices. Depending on the dimensions of the structures (layer thicknesses, texture feature size, _etc._) compared to the wavelength of the excitation light, these models can be classified as ray tracing model [17], models based on light scattering effects [18] and finally, rigorous methods which are based on solving [PERSON]'s equation describing the interaction of electro-magnetic waves with the material. Resolving the system of partial differential [PERSON]'s equations can be completed analytically only for problems with simple geometry. Since the geometry of the textured thin-films is usually complex, some type of numerical methods must be employed. The most frequently used numerical methods for this purpose are finite difference time domain [19] and finite element method [20]. Based on the numbers of spatial dimensions there are 1-D, 2-D and 3-D models. While for a number of thin-film photovoltaic simulations the application of 1-D models is sufficient [21], the simulation of non-flat cell layers requires the use of 2-D or 3-D models. In some simulations a combination of models can be used to simulate the cells with higher dimensions [22]. The simulations in this work were based upon finite element method with 2-D geometry. The simulations were carried out using the RF module of COMSOL Multiphysics software package (COMSOL Inc, Burlington, MA, USA) [23]. Since the model geometry is 2-D, with reasonable number of degrees of freedom, a direct solver was used. The simulated thin-film cell based on CIGS absorber material has the following layer structure: Mo (800 nm)/CIGS (500 nm)/CdS (70 nm)/ITO (indium tin oxide) (330 nm). The whole geometry domain was meshed, keeping in mind that the maximum mesh element size does not exceed 1/10 of the wavelength of the excitation electromagnetic wave. The optical properties of materials were described by complex wavelength-dependent refraction index (\(\varepsilon\)). The values of the refraction indexes of all materials used in the simulation were taken from the literature [24,25]. The simulation was carried out at wavelengths in the range of absorption of CIGS material (400-1200 nm). The software calculates the vector of electric field in all nodes of the mesh. The absorption of light in a geometric domain was calculated based on the integration of the electric field strength values within the boundaries of the respective domain. The absorbed power in a node within the domain excited by a single wavelength (\(\lambda\)) can be calculated using the following equation  
\[P_{abs}(\lambda)=\frac{1}{2}\omega\varepsilon^{\prime}\big{|}E(\lambda)\big{|} ^{2} \tag{1}\]  
where \(\omega\) is angular frequency equal to 2\(\pi\lambda\), \(\varepsilon^{\prime\prime}\) is imaginary component of complex permittivity of the respective material, while \(E(\lambda)\) denotes electric field strength at the respective excitation wavelength. The presented texturing is based on introduction of a 2-D periodic texture on the substrate material, and subsequent growth of the solar cell layer stack on such a substrate. The model geometry was simplified assuming the conformal growth of all the layers, causing the angles of the texture in each layer to remain conserved. Although in literature exist more complex models describing the thin-film solar cell layer growth, such as those considering the combination of isotropic and conformal growth [26], they are optimized for silicon based thin-film solar cells. Two different structuring geometries have been explored: triangular (with sharp edges) and convex (with smooth upper edges). The dimensions of the texture period and height have been varied in the range of hundreds of nanometers, which is comparable to the visible light spectrum wavelengths, in order to enable the light scattering within the layers of the solar cell.