Internal Electric Fields in Asymmetric Single-layer Lattices for Enhancing Photocatalytic Solar-to-Hydrogen Efficiency

Two-dimensional materials with intrinsic internal electric field possess promising potential to improve the photocatalytic water-splitting performance. However, the construction of the internal electric field is still a great challenge, which...

stable.To evaluate the in-plane stiffness, we calculated Young's modulus Y(θ) and Poisson's ratio υ(θ) along the in-plane θ, which is given as follow: where and .The Gibbs free energy

𝐴 = (
The change of Gibbs free energy ( ) in water splitting reaction is calculated ∆ using the method proposed by Nørskovet et al 2 .The formula can be expressed as: (3)

Carrier mobility
The carrier mobility of MSi 2 N 3 Y monolayers are calcualted based on the deformation potential (DP) approach 3 , which is expressed by the following equation: where e, ℏ and k B are electron charge, the reduced Planck constant and Boltzmann constant, T means the temperature.C and E d represent the elastic modulus and deformation potential constant.C can be obtained from , where E d is the total energy of the system under uniaxial strain, S 0 is the area of the system, and  is the ratio of lattice parameter under the uniaxial strain along x or y direction on the rectangle cell and.E d is represented by , and E edge is the energy change of   = ∂  ∂ℇ band edge under uniaxial strain.At the meantime, the effective mass m* is calculated from the following relations: where k is wave vector and E(k) represents the energy that corresponding to k.

Solar-to-hydrogen (STH) efficiency
STH efficiency is estimated by the product of the efficiency of light absorption and carrier utilization using the following expression 4 : The efficiency of light absorption is defined as:  Considering the energy loss during carrier migration between different materials, the required over potentials for HER and OER are assumed to be 0. where is the vacuum level difference on the two respective surfaces.∆Φ Table S6.The calculated Over-Potential for HER χ(H 2 ), Over-Potential for OER χ(O 2 ), the photons energy (E), energy conversion efficiency of light absorption (η abs ), carrier utilization (η cu ), and corrected STH (η' STH ) of four monolayers pH=7.

Fig. S1
Fig. S1 The flow diagram of stability evaluation.

Fig. S6
Fig. S6 Band-decomposed charge density of the CBM and VBM for MSi 2 N 4 ,

Fig. S8
Fig. S8 (a)-(d) The imaginary dielectric function ε 2 and the oscillator strength λ as a function of photon energy for MSi 2 N 3 Y monolayers.The red line indicates the direct bandgap calcualted by GW mothod. (ℏ)(ℏ) photocatalytic water splitting for 2D material with vertical intrinsic EF is calculated as

Table S3 .
The calculated band gap at HSE06 level (E g ), the potentials of photo-

Table S5 .
The zero-point energy E ZPE (eV) and entropy TS (eV) of molecules and adsorbates on four structures.