Fig shows the experimental and modelled amplitude component

Fig. 4 shows the experimental and modelled amplitude component Ψ; phase difference Δ; transmission T of the CH3NH3PbI3 perovskite which are used to determine the optical constants as a supplementary method. The CH3NH3PbI3 perovskite film thickness has been determined to be 173nm and 40nm surface roughness with 89% void. The optical constants n and k deduced from this modelling are compared with other data sets in Fig. 5(a) and (b) respectively.
Acknowledgement This work was supported by the Australian Government through the Australian Renewable Energy Agency (ARENA) (Grant no. ARENA 1-SRI001). Responsibility for the views, information or advice expressed herein is not accepted by the Australian Government.
Computational methods Density-functional theory (DFT) calculations were carried out with the plane-wave code PWscf of the Quantum Espresso software package [2], using the Perdew–Burke–Ernzerhof PBE exchange-correlation functional [3], Vanderbilt ultrasoft pseudopotentials [4] and a plane wave kinetic perk inhibitor cutoff of 30Ry. k-point meshes for Brillouin zone integrations were generated by the Monkhorst–Pack scheme [5], and the fractional occupation numbers of the electronic states were determined by a Gaussian broadening [6]. Atomic positions and lattice parameters were relaxed by minimizing the atomic forces and the stress tensor, with a convergence threshold for the largest residual force and stress component of 5meV/Å and 0.1kbar, respectively. Bulk second order elastic constants (SOEC) were calculated by finite deformations of the conventional face-centered cubic (fcc) unit cell with 4atoms, Cartesian basis vectors and lattice constant a. The lattice is distorted by applying a small strain , which transforms the basis vectors , , to the new vectorswhere is the 3×3 identity matrix. The three independent elastic constants of the cubic lattice C11, C12 and C44 were determined by using the deformation strains proposed by Mehl et al. [7]:The first deformation is a homogeneous volume change, which changes the total energy of the unit cell byV0 is the equilibrium volume of the unit cell and B is the bulk modulus. For a cubic lattice B is related to the elastic constants byThe second deformation is a volume conserving orthorhombic strain with energy changeand the third deformation is a volume conserving monoclinic shear with energy changeFrom the bulk modulus B and the difference the two elastic constants C11 and C12 are given byFor all three deformations a series of total energy calculations was performed for a small set of finite strain values x. The energy values as function of x were fitted to a polynomial and the elastic constants were determined from the second derivative of the polynomial at the minimum. Specifically, the bulk modulus B was calculated by varying the lattice constant a between 7.64Bohr and 8.04Bohr in steps of 0.04Bohr, which corresponds to strain values between −2.4% and +2.7%. A polynomial of degree 4 was fitted to the 11 data points. The minimum of the curve gives the equilibrium lattice constant, which was used as starting point for the calculation of and C44. The deformations proposed by Mehl have the advantage that the energy is an even function of the strain x. Thus, only positive values for x have to be considered. For the calculation of the strain parameter x was changed between 0 and +0.084 in steps of +0.012 (8 values) and for the calculation of C44 we used 7 values of x between 0 and +0.12 in steps of +0.02. An even polynomial of degree 6 was fitted to the calculated total energy values. The Young׳s modulus was calculated by a similar quastistatic approach as the SOEC. The unit cell is chosen in such a way that one axis is parallel to the direction of the applied strain and the two other axes are perpendicular to the first one. Then a set of finite tensile and compressive strains x is applied and for each strain x the cell vectors perpendicular to the strain direction and the atomic positions are relaxed (Poisson contraction). From the energy changeThe Young׳s modulus is calculated by taking the second derivative of a polynomial fitted to the energy versus strain values.