Hybrid perovskites for photovoltaics: Insights from first principles

The methylammonium lead iodide perovskites at the core of recently proposed solar cells with exceptionally large quantum conversion efficiency are studied by first-principles methods. Large absorption coefficients (0.03–0.04 nm${}^{-1}$ for wavelength $\sim$500 nm) and small effective masses suited for both $n$-type and $p$-type transport are obtained as a consequence of their peculiar structural and electronic characteristics. In particular, the presence of a direct gap between highly dispersed Pb(6$s$)-I($5p$) valence bands and Pb($6p$) conduction bands is the key ingredient at the basis of their excellent performance in photovoltaic applications.

Figure 1

Top panels: Three-dimensional view (left) and top-view (right) of the unit cell for $M$PbI${}_3$. Bottom panels: same for $M$PbI${}_2$Cl. Color code: yellow (C), gray (N), cyan (H), red (I), violet (Pb), orange (Cl).

Figure 2

Calculated band energies for $M$PbI${}_3$ (left) and $M$PbI${}_2$Cl (right panels). Labels indicate the atomic and orbital character for each group of bands ($M$ labels molecular states). In the bottom panels the enlargement around the band gap is shown. $k$-point coordinates (unit of 2$\pi$/$a$) are $X$ = (1/2,0,0), $L$ = (1/2,1/2,0), $M$ = (1/2,1/2,a/2c), $Z$ = (0,0,a/2c).

Figure 3

Atomic- and orbital-projected DOS for $M$PbI${}_3$ (left panels) and $M$PbI${}_2$Cl (right panels). Each panel refers to the atomic species indicated by the label. Orbital contributions are represented by different colors: $s$ states in blue, $p$${}_x$-$p$${}_y$ states in red, $p$${}_z$ states in green, and $d$ states in orange. For the molecule, $sp$${}^3$ states are in black.

Figure 4

Calculated optical properties for $M$PbI${}_3$ and $M$PbI${}_2$Cl: real and imaginary dielectric function ($\epsilon$), refractive index ($n$), absorption coefficient ($\alpha$), and absorbance ($A$) through a perovskite film of 150 nm (see text). For each quantity, planar ($xx$ = $yy$) and orthogonal ($zz$) components are separately shown. Absorption for typical semiconductors [33] is reported for comparison.

Figure 5

Atomic- and orbital-projected DOS for $M$PbI${}_2$Cl with the molecule oriented along the [100] direction. Each panel refers to the atomic species indicated by the black label. The orbital character is indicated by labels of corresponding color: $s$ states in blue, $p_x$-$p_y$ states in red, $p_z$ states in green, and $d$ states in orange. For the molecule, $s{p}^3$ states are in black.

Figure 6

Calculated optical properties for the [100]-oriented $M$PbI${}_2$Cl. Top panel: real and imaginary dielectric function ($\epsilon$). Bottom: absorption coefficient ($\alpha$). For each quantity, planar ($xx$ = $yy$) and orthogonal ($zz$) components are separately shown.

Figure 7

Structure of the $2\sqrt{2}\times 2\sqrt{2}\times 2$ supercell for [100]-oriented $M$PbI${}_2$Cl [panels (a) and (b)], [110]-oriented $M$PbI${}_2$Cl [panels (c) and (d)], and [110]-oriented $M$PbI${}_3$ [panels (e) and (f)]. The reference system indicated by black solid arrows refers to the $\sqrt{2}\times \sqrt{2}\times 2$ tetragonal unit cell, while $a$ and $b$ are 45${}^{\circ }$-rotated axes of the conventional cubic cell. Small arrows indicate the important $M$-$I$ distances shortened by the octahedral rotations (see text). Atomic colors are yellow (C), gray (N), cyan (H), red (I), violet (Pb), green (Cl).