Size-effects on shift-current in layered CuInP$_2$S$_6$

TL;DR

The study addresses why CuInP2S6 exhibits large bulk photovoltaic responses and how thickness controls this effect. Using first-principles DFT with spin–orbit coupling and Wannier-based shift-current calculations across 1–4 layers, the authors map the intrinsic shift-current contribution and its 2D scaling after a suitable rescaling. They find that the shift-current alone underestimates observed currents and that a pronounced size effect suppresses shift-conductivity toward the bulk, with particular multi-layer configurations (notably four-layer) maximizing the integrated 2D response; SOC further enhances the BPVE. The work also suggests that interface-induced band bending, ballistic/phonon/exciton processes, or ionic effects may dominate in real devices, guiding future design of BPVE-based photovoltaics in 2D ferroelectrics. Overall, the results emphasize the interplay between band topology, depolarization fields, and interfaces in optimizing BPVE in few-layer CuInP2S6.

Abstract

Two-dimensional ferroelectrics have recently emerged as a promising avenue for next-generation optoelectronic and photovoltaic devices. Due to the intrinsic absence of inversion symmetry, 2D ferroelectrics exhibit bulk photovoltaic effect (BPVE), which relies on hot, non-thermalized photo-excited carriers to generate a photo-induced current with enhanced performances thanks to efficient charge separation mechanisms. The absence of a required p-n junction architecture makes these materials particularly attractive for nanoscale energy harvesting. Recent studies have reported enhanced BPVE in nanometer-thick CuInP$_2$S$_6$ ferroelectric embedded between two graphene wafers, driven by relatively strong polarization and reduced dimensionality. Short circuit photocurrent density values have been observed to reach up to mA/cm$^2$. In this paper, we demonstrate that the shift-current mechanism alone cannot fully account for these high conductivity values, suggesting that additional mechanisms may play a significant role. Furthermore, our work confirms the existence of a strong size effect, which drastically reduces the shift-conductivity response in the bulk limit, in agreement with experimental observations.

Figures (17)

• Figure 1: a CuInP$_2$S$_6$ monoclinic structure: Cu is reported in in blue, In in pink, P in grey, S in yellow. b The electronic band structure of the CIPS monolayer, bi-layer, four-layer, bulk configurations. The direct band gap is localized at $\Gamma$. c The atomic orbital projected DOS of the four layer structure. d Top panel: filled central bars represent the Homo-Lumo band gap: the colored labels report the corresponding values; black-border transparent bars represents the intra-layer averaged band gap: 1.34 eV and 1.48 eV respectively for the 2 and 4 layers slabs; transparent bars represents the optical gap extracted with Tauc analysis: 1.65 eV, 1.27 eV, 0.52 eV, 1.49 eV for 1-layer, 2-layer, 4-layers and bulk configurations. Bottom panel: the z component of the polarization as a function of slab thickness. Bulk phase P$_z$ obtained with Berry-phase is reported in black; with Born-effective charges in blue; layer-decomposed P$_z$: single-layers in yellow, bi-layer in red, 4 layers in green.
• Figure 2: The imaginary diagonal components of the permittivity tensor for the single layer (yellow, top left panel), bi-layer (red, top right panel), 4-layers (green, bottom left), bulk (blue, bottom right) configurations. Different components are reported with different line styles.
• Figure 3: The shift current tensor components (in $\mu A \cdot V^{-2}$) corresponding to light linearly polarized along the lab reference frame axes for the bulk (blue line), 4-layers (green line), bi-layer (red line), mono layer (orange line) configurations.
• Figure 4: The weighted, and in-plane averaged, shift current density $\bar{j}_{k} = \frac{1}{2}(j_{ixx}+j_{iyy})$ along x (top panel), y (central panel) and z (bottom panel) directions, to the solar light spectrum when incident along z direction and penetrating a film of: 1 layer of CIPS, 6.7 nm thick (orange), 2 layers (red), 4 layer (green). The bulk case is reported in dashed blue as a comparison.
• Figure 5: The electronic bands with and without vdW semi-empirical corrections in blue and red, respectively.