For a long period, there was a resolution gap between numerical modeling and experimental measurements, making it hard to conduct a direct comparison between them, but they are now developing in parallel. In this work, we numerically study diffusive ionization wave and fast ionization wave discharge experiments using recently published electric-field-induced second-harmonic (E-FISH) data together with a classical fluid model. We propose a pressure-E/N range for the drift diffusion approximation and a pressure-grid range for the local field/mean energy approximation of the fluid model. The three-term Helmholtz photoionization model is generalized using parameters given for N 2 , O 2 , CO 2 , and air. The capabilities of the classical fluid method for modeling the inception, propagation, and channel breakdown stages are studied. The calculated electric field evolution of the ionization is compared with E-FISH measurements in the discharge development and gap-closing stages. The influence of electrode shape and predefined electron density on the streamer morphology and the long-standing inception problem of the ionization waves are discussed in detail. Within the application range of the classical fluid model, good agreement can be achieved between calculation and measurement.

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Development of hybrid organic−inorganic lead halide perovskites is still hampered by the toxicity of lead and their structural stability in air. Hence, the research of lead-free alternatives is extremely important to promote the development of perovskite-based photovoltaics. Here, we construct lead-free tin (Sn)-and germanium (Ge)-based two-dimensional (2D) hybrid organic−inorganic perovskites, (BA) 2 GeX 4 and (BA) 2 SnX 4 (X = I, Br, and Cl), and explore their geometrical, electronic, and light absorption characteristics via first-principles calculations. The lattice constants will increase from (BA) 2 MCl 4 , (BA) 2 MBr 4 to (BA) 2 MI 4 (M = Ge, and Sn), owing to the increase in halogen ionic radius in the order of Cl − (1.81 Å) < Br − (1.96 Å) < I − (2.20 Å). Meanwhile, (BA) 2 GeX 4 materials show less lattice constants by ∼3−4% along a axis and ∼2−4% along b axis, respectively, than those of (BA) 2 SnX 4 materials. Moreover, both the 2D tin and germanium halide perovskites have direct band gaps; (BA) 2 GeX 4 exhibits values of 1.54, 2.10, and 2.55 eV, while (BA) 2 SnX 4 exhibits values of 1.53, 1.98, and 2.49 eV, for X = I, Br, and Cl, respectively. In particular, the estimated effective masses of electrons/holes in 2D-(BA) 2 GeX 4 and (BA) 2 SnX 4 are 0.15−0.23/0.16−0.27 m e and 0.14−0.18/0.14− 0.19 m h at Γ−X and 0.16−0.29/0.12−0.14 m e and 0.22−0.35/0.12−0.14 m h at Γ−Y, respectively, about half of those in BA 2 PbI 4 and BA 2 PbBr 4 . Furthermore, the density of states (DOS) and partial DOS results suggest that the contributions to the valence and conduction band are mostly made by the components of halogen p state orbitals and metal p state orbitals, respectively. Furthermore, the band-decomposed charge densities of the conduction band minimum and valence band maximum results imply that the distorted inorganic [GeX 6 ] 4− and [SnX 6 ] 4− octahedra have a direct influence on the band gaps. Our results indicate that this series of homologous 2D tin and germanium halide perovskites are a promising class of stable and efficient light-absorbing materials for photovoltaic and/or photoelectronic applications.