Electronic structure and stability of the $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{PbB}{\mathrm{r}}_3$ (001) surface

The energetics and the electronic structure of methylammonium lead bromine ($\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{PbB}{\mathrm{r}}_3$) perovskite (001) surfaces are studied based on density functional theory. By examining the surface grand potential, we predict that the $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Br}$-terminated (001) surface is energetically more favorable than the $\mathrm{PbB}{\mathrm{r}}_2$-terminated (001) surface, under thermodynamic equilibrium conditions of bulk $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{PbB}{\mathrm{r}}_3$. The electronic structure of each of these two different surface terminations retains some of the characteristics of the bulk, while new surface states are found near band edges which may affect the photovoltaic performance in the solar cells based on $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{PbB}{\mathrm{r}}_3$. The calculated electron affinity of $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{PbB}{\mathrm{r}}_3$ reveals a sizable difference for the two surface terminations, indicating a possibility of tuning the band offset between the halide perovskite and adjacent electrode with proper interface engineering.

Figure 1

(a) The optimized cubic $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{PbB}{\mathrm{r}}_3$ perovskite structure. The $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3$ dipole is assumed to be pointing in opposite directions in adjacent atomic layers along the [001] direction to ensure the whole structure is nonpolar. (b) The layer-resolved density of state (LDOS) as a function of energy along the $z$ direction in nonpolar bulk $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{PbB}{\mathrm{r}}_3$.

Figure 2

The atomic structure of $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{PbB}{\mathrm{r}}_3$(001) slabs with $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Br}$ [(a) and (b)] and $\mathrm{PbB}{\mathrm{r}}_2$ [(c) and (d)] surface terminations. There are two surfaces for each termination, to account for the opposite orientations of the $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3$ moieties (dipoles): [(a) and (c)] has the dipole is pointing into the first $\mathrm{PbB}{\mathrm{r}}_2$ layer (the “dipole-into” slab); [(b) and (d)] has the dipole is pointing away from the first $\mathrm{PbB}{\mathrm{r}}_2$ layer (the “dipole-away” slab). The first $\mathrm{PbB}{\mathrm{r}}_2$ layer is marked using orange horizontal dotted line and the dipole orientations are indicated by orange arrows.

Figure 3

The surface stability diagram for $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{PbB}{\mathrm{r}}_3$. The blue (pink) region indicates where the $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Br}$ ($\mathrm{PbB}{\mathrm{r}}_2$) surface termination is stable. The narrow red region is the stable range of chemical potentials for growth of bulk $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{PbB}{\mathrm{r}}_3$ in thermodynamic equilibrium. Three representative points A (Pb-rich/Br-poor), B (Pb-moderate/Br-moderate), and C (Pb-poor/Br-rich) are chosen for comparing the surface grand potential difference between the $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Br}$ and $\mathrm{PbB}{\mathrm{r}}_2$ surface terminations.

Figure 4

The electronic band structure of the $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{PbB}{\mathrm{r}}_3$ slabs with the (a) $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Br}$ and (b) $\mathrm{PbB}{\mathrm{r}}_2$ surface (001) terminations. The bands are shown along lines connecting high-symmetry points in the Brillouin zone with $\overline{\mathrm{\Gamma }}$(0,0,0), $\overline{X}$ (0,1/2,0), and $\overline{M}$ (1/2,1/2,0). The bands are colored according to the relative contribution from bulk or surface, at a given energy. The surface (bulk) character is indicated by blue (red) color. The purple color implies that the surface and bulk bands strongly hybridized. The reference energy is placed at the CBM.

Figure 5

The electrostatic potential energy profile across $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{PbB}{\mathrm{r}}_3$ (001) slabs, with the (a) $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Br}$ and (b) $\mathrm{PbB}{\mathrm{r}}_2$ surface terminations. The sharp dips in the potential energy correspond to $\mathrm{PbB}{\mathrm{r}}_2$ monolayers, whereas shallower dips are due to $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Br}$ monolayers. The flat region corresponds to the vacuum energy. All the energies are referenced with respect to the VBM.