### The Shift in Bandgap and Dielectric Constant Due to lattice Expansion in CH3NH3SnI3 Using FHI-aims

#### Abstract

Although methyl ammonium lead iodide, (CH_{3}NH_{3}PbI_{3}) has proven to be an effective photovoltaic material, there remains a main concern about the toxicity of lead, therefore determination of a lead free halide perovskite is of outstanding interest. Sn2+ metal cations are the most obvious substitute for Pb2+ in the perovskite structure because of the similar s2 valence electronic conﬁguration to Pb2+. Sn2+ can form a perovskite with a basic formula **ASnX _{3}** (A= CH

_{3}NH

_{3}and X = halide) because the ionic radius of Sn

^{2+}is similar to that of Pb

^{2+}. With the above similarity, methyl ammonium tin iodide CH

_{3}NH

_{3}SnI

_{3}is one of the common replacement for CH

_{3}NH

_{3}PbI

_{3}in the fabrication of organic-inorganic perovskite solar cells. FHI-aims code was used to perform the simulation of CH

_{3}NH

_{3}SnI

_{3}in this work. Geometry building, parameter optimization, determination of the best exchange functional, k-grid convergence test along with determination of equilibrium lattice constant and geometry relaxation for CH

_{3}NH

_{3}SnI

_{3}were carried out. An energy direct band gap of 1.051 eV was obtained, with an underestimation of 0.249 eV which amount to 19.2% when compared with experimental value. The lattice constant obtained using phonopy with ZPE is close to experimental reported values with an underestimation of 3.01%. The temperature dependent of lattice constant was studied in the temperature range of 0 to 318 K. At the same temperature range, shift in energy bandgap and dielectric constant due to lattice expansion was also investigated.

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