In this paper, a n-i-p planar heterojunction simulation of Sn-based iodide perovskite solar cell (PSC) is proposed. The solar cell structure consists of a Fluorine-doped tin oxide (FTO) substrate on which titanium oxide (TiO₂) is placed; this material will act as an electron transporting layer (ETL); then, we have the tin perovskite CH₃NH₃SnI₃ (MASnI₃) which is the absorber layer and next a copper zinc and tin sulfide (CZTS) that will have the function of a hole transporting layer (HTL). This material is used due to its simple synthesis process and band tuning, in addition to presenting good electrical properties and stability; it is also a low-cost and non-toxic inorganic material. Finally, gold (Au) is placed as a back contact. The lead-free perovskite solar cell was simulated using a Solar Cell Capacitance Simulator (SCAPS-1D). The simulations were performed under AM 1.5G light illumination and focused on getting the best efficiency of the solar cell proposed. The thickness of MASnI₃ and CZTS, band gap of CZTS, operating temperature in the range between 250 K and 350 K, acceptor concentration and defect density of absorber layer were the parameters optimized in the solar cell device. The simulation results indicate that absorber thicknesses of 500 nm and 300 nm for CZTS are appropriate for the solar cell. Further, when optimum values of the acceptor density (N_A) and defect density (N_t), 10¹⁶ cm⁻³ and 10¹⁴ cm⁻³, respectively, were used, the best electrical values were obtained: J_sc of 31.66 mA/cm², V_oc of 0.96 V, FF of 67% and PCE of 20.28%. Due to the enhanced performance parameters, the structure of the device could be used in applications for a solar energy harvesting system.

With the application of a homogenization theory, based on the Fourier formalism (which provides efficient and exact formulas by which to determine all the components of the effective stiffness and mass density tensors, valid in the regime of large wavelengths), a new approach to calculate the effective quasi-static response in three-dimensional solid-solid phononic crystals is reported. The formulas derived in this work for calculating the effective elastic parameters show a dependence, in terms of summations over the vectors, of the reciprocal lattice by the discretization of the volume of the inclusion in small parts (e.g., small cubes), to obtain a system of equations from which we define the effective response. In particular, we present the numerical results calculated for several cubic lattices with solid constituents and different shapes of inclusions in the unit cell versus the filling fraction, as well as for fixed values of it. By this means, we analyzed the effect of the type of Bravais lattice of the materials, and the geometry of the inclusions that constitute the three-dimensional phononic array, on the resulting effective anisotropy. Finally, our theory confirms other well-known results with previous homogenization theories as a particular case study. In this regard, the examples and results shown here can be useful for the design of metamaterials with predetermined elastic properties.

A homogenization theory that can go beyond the regime of long wavelengths is proposed, namely, a theory that is still valid for vectors of waves near the edge of the first zone of Brillouin. In this paper, we consider that the displacement vector and the magnetic induction fields have averages in the volume of the cell associated with the values of the electric and magnetic fields in the edges of the cell, so they satisfy Maxwell’s equations. Applying Fourier formalism, explicit expressions were obtained for the case of a photonic crystal with arbitrary periodicity. In the case of one-dimensional (1D) photonic crystals, the expressions for the tensor of the effective bianisotropic response (effective permittivity, permeability and crossed magneto-electric tensors) are remarkably simplified. Specifically, the effective permittivity and permeability tensors are calculated for the case of 1D photonic crystals with isotropic and anisotropic magnetic inclusions. Through a numerical calculation, the dependence of these effective tensors upon the filling fraction of the magnetic inclusion is shown and analyzed. Our results show good correspondence with the approach solution of Rytov’s effective medium. The derived formulas can be very useful for the design of anisotropic systems with specific optical properties that exhibit metamaterial behavior.

The authors wish to make the following corrections to this paper [1]: replace: (37) $$\frac{1}{{\epsilon }_z}=\frac{f}{{\epsilon }_m}=\frac{1-f}{{\epsilon }_d}$$ and (39) $$\frac{1}{{\mu }_z}=\frac{f}{{\mu }_m}=\frac{1-f}{{\mu }_d}$$ with the correct expressions: (37) $$\frac{1}{{\epsilon }_z}=\frac{f}{{\epsilon }_m}+\frac{1-f}{{\epsilon }_d}$$ and (39) $$\frac{1}{{\mu }_z}=\frac{f}{{\mu }_m}+\frac{1-f}{{\mu }_d}$$