Fig. 4
From: Cross-plane coherent acoustic phonons in two-dimensional organic-inorganic hybrid perovskites

The CLAP velocities of 2D RPs. a n′(λ) curves for N = 1–6 in the below-bandgap range, and n′(λ) for N = ∞ taken from literature. b Measured CLAP velocities plotted against N (number of inorganic layers), shown in black. Calculated results from the bead-spring model is shown in green. c Schematic illustration of the coarse-grained bead-spring model. In the upper figure, the green rectangle encloses a single unit cell, half of which, highlighted by a cyan rectangle, was considered in the bead-spring model, as illustrated in the lower figure. d The pairs of the spring constants that give the calculated velocities exactly matching the experimental ones for N = 1–6. Dependence of elastic modulus along the cross-plane direction in e and velocity in f on the number of inorganic layers plotted for various kb values (with ka fixed at 17 N m−1). Result for MAPbI3 (average value of its lower and upper bounds) is shown in black dashed lines