Dimensional control of the band-gap crossover in layered lead iodide

TL;DR

This study directly visualizes the thickness-driven indirect-to-direct band-gap crossover in PbI$_2$ using ARPES, revealing that the valence-band maximum shifts toward the Brillouin-zone center as films exceed one monolayer. Complementary DFT calculations show the crossover is driven by interlayer coupling and iodine $p_z$ orbital hybridization, with the VBM relocating to $k$-space Γ in multilayers while the conduction-band minimum remains relatively unchanged. The results demonstrate a dimensionality transition from two-dimensional to three-dimensional electronic structure, with 7L PbI$_2$ closely resembling bulk PbI$_2$, and provide a quantitative framework for band-structure engineering in layered semiconductors. This tunable electronic structure has potential implications for designing PbI$_2$-based optoelectronic and photonic devices, where thickness can tailor absorption and emission properties.

Abstract

Before assessing the suitability of a semiconductor for specific applications, the first question to ask is whether it possesses a direct or indirect band gap. This distinction is fundamental, as the operation of devices such as light-emitting diodes, solar cells, and photodetectors is closely tied to the band-gap nature. Semiconductors that exhibit a band-gap crossover, from indirect to direct or vice versa, offer enhanced versatility for optoelectronic applications. Prominent examples include transition metal dichalcogenides and the subject of this study, PbI2. The nature of the band gap, and its crossover, can only be directly determined in reciprocal space by tracking the valence-band maximum and conduction-band minimum. Here, we directly visualize the thickness-dependent crossover of PbI2 from an indirect to a direct band gap using angle-resolved photoemission spectroscopy. Our measurements reveal a shift of the valence-band maximum toward the Brillouin-zone center as the film thickness exceeds a monolayer. Supported by density functional theory calculations, our results show that this crossover is driven by interlayer interactions and the hybridization of iodine pz orbitals. These findings demonstrate the tunable electronic structure of PbI2 and its potential for optoelectronic applications.

Figures (9)

• Figure 1: Growth dynamics of 12 layers of PbI$_2$ on graphene/SiC(0001), probed by a 600 eV He beam aligned along the graphene zigzag direction. (a) Evolution of the GIFAD pattern. (b) Reflectivity curve.
• Figure 2: Structural and electronic properties of the 2H polytype of PbI$_2$. (a) Atomic structure of PbI$_2$, showing a sandwich-like arrangement where a layer of Pb atoms (grey) is positioned between two layers of I atoms (purple and pink). (b) Top view of the monolayer atomic structure, revealing a hexagonal arrangement of iodine atoms surrounding each lead atom. (c) Bulk and surface Brillouin zone with the $k_z=0$ and $k_z=\pi/c$ planes highlighted in green and blue, respectively. (d)–(g) Theoretical band structure of PbI$_2$ obtained from GGA PBE calculations, for different number of layers. The calculations were performed for free-standing PbI$_2$. For multilayers, a slab approach has been used, thus resulting in a multitude of bands that evolve into a continuum in thicker films. Red arrows indicate the position of the minimum band-gap, with tilted (vertical) arrows denoting indirect (direct) band-gaps. The energy axis of each panel has been scaled with respect to its valence band maximum.
• Figure 3: Orbital-resolved band structure for (a) one-, (b) two-, (c) three-, (d) seven-layer PbI$_{2}$ films, and (e) the bulk compound. Grey lines represent the full DFT-calculated bands, while red and blue points indicate the projection onto the $p_z$ orbitals of Pb and I atoms, respectively. The band structure of the thin films refers to the 2D surface-projected Brillouin zone, while the one of the bulk compound refers to the 3D bulk Brillouin zone [see panel (c) of Fig. \ref{['fig:structure']}]. The origin of all energy axes has been set to the valence band maximum.
• Figure 4: (a) Out-of-plane constant energy map at a binding energy of $4$ eV, with green and blue arcs indicating constant photon energy contours. The thickness of the arcs approximates the $k_z$ broadening in ARPES and is equal to $\lambda^{-1}$, where $\lambda$ represents the photoelectron escape depth strocov2003. The transformation to $k$-space was performed assuming an inner potential of $V_0 = 15$ eV. (b) and (c) Constant energy maps for monolayer and seven-layer PbI$_2$, respectively, measured at $k_z = 0$ (photon energy 80 eV), at a temperature of $16$ K, using linearly polarized light with horizontal polarization. Each panel presents four constant-energy contours for binding energies ranging from $5.5$ eV to $2.5$ eV, with a step of $1$ eV.
• Figure 5: Electronic structure of 1 layer (1L) and 7 layers (7L) PbI$_2$ films. (a) and (b) Band structure of, respectively, 1L and 7L films along the $\bar{\text{K}}$-$\bar{\Gamma}$-$\bar{\text{M}}$-$\bar{\text{K}}$ path. (c) and (d) Band structure of, respectively, 1L and 7L films with maximally enhanced contrast for each momentum distribution curve (MDC). The contrast enhancement was achieved by normalizing each MDC to its integrated intensity. The tail of the red arrows indicates the location of the VBM for both films. (e) and (f) Constant energy maps corresponding to a binding energy of $1.8$ eV (i.e. at the valence band maximum) for 1L and 7L films, respectively, under identical measurement conditions. (g) Energy distribution curves (EDCs) corresponding to panels (c) and (d), obtained by integrating over a momentum window of 0.1 Å$^{-1}$ around $\bar{\Gamma}$. The blue (black) curve corresponds to 7L (1L) films. Measurements have been performed at $16$K using photons of $80$ eV and linear horizontal polarization.