Empirical Modeling of Electron Transport in Fe/Ti Layered Double Hydroxide Using Exponential, Gaussian and Mixed Gauss–Exponential Distribution

Fe/Ti-layered double hydroxide (LDH) has been hydrothermally prepared and characterized using X-ray diffraction, scanning electron microscopy, atomic force microscopy, Fourier transform infrared spectroscopy, and UV-visible diffuse reflectance spectroscopy for evaluation of its structure, morphology, and optical properties. The purpose of doping Ti 4+ with Fe 3+ toward the synthesis of Fe/Ti LDH is to extend the absorption of the nanomaterial to longer wavelength, which is known to exhibit higher electron transport performance. To provide a practical realization, electron transport modeling across the band gap has been interpreted using exponential, Gaussian, and mixed Gauss-exponential distribution. The conduction band energy ( E C ) has been calculated by using the observed values of band gap ( E g ) and ξ-potential of the LDH. A detailed study has been undertaken to investigate the pattern of theoretical density of the LDH on the basis of unknown ( E C = 0) and known (calculated) values of E C . Fermi-Dirac statistics has been used extensively for estimating the occupancy probability of electron (e - )-hole (h + ) pair formation within the valence and conduction bands, respectively, with different temperatures, as well as for given energy levels. Monte Carlo simulations have also been performed to evaluate the suitability of the choice of the model, on the basis of the probability of availability of e - s within the conduction band. To provide a practical realization of the suggested models, electronic transition across the band gap of Fe/Ti LDH has been extensively investigated.