Shift current photovoltaic efficiency of 2D materials

www.nature.com/npjcompumats ARTICLE OPEN Shift current photovoltaic efficiency of 2D materials Mikkel Ohm Sauer 1,2,3 ✉, Alireza Taghizadeh1,3,4, Urko Petralanda 4,5, Martin Ovesen1, Kristian Sommer Thygesen Thomas Olsen 4, Horia Cornean2 and Thomas Garm Pedersen 1,3 ✉ 4,6 , Shift current photovoltaic devices are potential candidates for future cheap, sustainable, and efficient electricity generation. In the present work, we calculate the solar-generated shift current and efficiencies in 326 different 2D materials obtained from the computational database C2DB. We apply, as metrics, the efficiencies of monolayer and multilayer samples. The monolayer efficiencies are generally found to be low, while the multilayer efficiencies of infinite stacks show great promise. Furthermore, the out-of-plane shift current response is considered, and material candidates for efficient out-of-plane shift current devices are identified. Among the screened materials, MXY Janus and MX2 transition metal dichalchogenides (TMDs) constitute a prominent subset, with chromium based MXY Janus TMDs holding particular promise. Finally, in order to explain the band gap dependence of the PV efficiency, a simple gapped graphene model with a variable band gap is established and related to the calculated efficiencies. 1234567890():,; npj Computational Materials (2023)9:35 ; https://doi.org/10.1038/s41524-023-00983-z INTRODUCTION The photovoltaic (PV) effect, i.e. the direct conversion of solar energy to electricity, is a significant part of modern electricity generation. The majority of traditional PV devices are single p-n junction silicon cells, requiring hole- and electron-doped regions1. However, advances in materials technology have unveiled a new venue of PV materials, operating through shift currents (SCs), an example of “bulk photovoltaic effects”2–23. The SC is a second order nonlinear optical response observed in non-centrosymmetric semiconductors5,24, generating a DC current. The name derives from the ‘shift’ of intracell coordinates of an excited electron due to its asymmetrical wave function, which drives the current5. The SC is a transport phenomenon intrinsic to the crystal. Thus, SC PVs do not require p-n junctions to separate optically generated electron-hole pairs. Consequently, the SC generation process is much faster than phonon emission5, as opposed to current generation p-n junction PV devices, where carriers relax to the band edge with excess energy transferred into lattice excitation. Such losses restrict photovoltages in traditional p-n solar cells to values below the band gap, while SC devices can potentially generate above-gap photovoltages5,16,17. The band gap limit is a key component of the Shockley-Queisser efficiency limit, applying to traditional p-n junction cells25. As a result, this limit does not apply to SC devices5,16,17. In general, SCs are generated in non-centrosymmetric materials, which can be further divided into polar and non-polar categories5,16. Polar materials generate SCs in both polarized and unpolarized light5, whereas non-polar materials require polarization5. Experimental SCs have been reported in a wide range of materials, including ferroelectrics6–8, III/V quantum wells9, organic crystals10, and recently two-dimensional interfaces and materials11–14,17,18,20,22. Additionally, it has been shown that excitons play a significant role for second order effects in lowdimensional materials, increasing SCs by almost an order of magnitude at resonance4,14. The increase is significantly larger than the linear optical enhancement provided by excitons in the vicinity of the band gap4,14,17. This difference is attributed to the inter-exciton coupling present in second order optical responses, as demonstrated in a simple tight-binding-based Bethe-Salpeter model4,26. Research on SCs has yet to present any quantitative estimates of SC PV efficiencies from calculations or measurements of 2D materials11–14,17,18,20,22. Furthermore, previous works have had little focus on optimizing the band gap for SCs produced by solar radiation4. The lack of reliable estimates of efficiency and selection criteria constitute important challenges for the field of 2D SC devices. In this work, we calculate and analyze the solar SC PV efficiencies, under idealized conditions, of 326 different dynamically stable, non-magnetic, non-centrosymmetric 2D semiconductors found in the computational database C2DB27,28, 129 of which are non-polar, while 197 are polar, see Fig. 1a. This database contains material properties calculated from density functional theory. The calculation of PV efficiencies is based on the (1) SC spectra, (2) absorption spectra, (3) carrier mobilities, and (4) effective masses of each material, as described in the Methods section. An important distinction between traditional and SC PVs is that different parts of the solar spectrum may produce SCs of opposite sign. Such effects are not found in p-n junction PVs operating through absorption alone. As a consequence, it is advantageous to exclude part of the solar spectrum in SC devices. We therefore implement a low-pass filter, maximizing efficiencies by excluding photons above a certain energy threshold. The schematic in Fig. 1a illustrates PV power produced by SC JSC generated in materials selected from C2DB27,28 under illumination matching the reference air mass 1.5 spectrum29. As shown in the figure, the in-plane current is applied to assess efficiencies. This setup is presumably the most convenient for practical applications, requiring only end contacts. The out-of-plane response is briefly considered. However, collecting such currents would require separate top and bottom electrical contacts. 1 Department of Materials and Production, Aalborg University, 9220 Aalborg Øst, Denmark. 2Department of Mathematical Sciences, Aalborg University, 9220 Aalborg Øst, Denmark. 3Center for Nanostructured Graphene (CNG), 9220 Aalborg Øst, Denmark. 4Computational Atomic-scale Materials Design (CAMD), Department of Physics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark. 5Department of Physics, University of the Basque Country (UPV/EHU), Apartado 644, Bilbao 48080, Spain. 6Center for Nanostructured Graphene (CNG), 2800 Kgs. Lyngby, Denmark. ✉email: ; Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences M.O. Sauer et al. 1234567890():,; 2 Fig. 1 Schematic of computational setup for shift current calculations. a Schematic view of SC power generation from 326 noncentrosymmetric 2D materials from C2DB and the reference air mass 1.5 spectrum29, including a low-pass and polarization filter. The relative proportions of crystal symmetry groups are shown in the pie chart, divided into polar and non-polar materials. b E-J curve applied to calculate output power, with insets showing short circuit and open circuit scenarios. The area of the rectangle underneath the curve indicates the maximum PV pow (...truncated)