Photovoltaic properties of two-dimensional van der Waals heterostructure Cs3X2I9/InSe (X = Bi, Sb)

Xiong Xiang-Jie; Zhong Fang; Zhang Zi-Wen; Chen Fang; Luo Jing-Lan; Zhao Yu-Qing; Zhu Hui-Ping; Jiang Shao-Long

doi:10.7498/aps.73.20240434

Abstract
Two-dimensional semiconductor heterostructures have excellent physical properties such as high light absorption coefficients, large diffusion lengths, high carrier mobility rates, and tunable energy band structures, which have great potential in the field of optoelectronic devices. Therefore, designing two-dimensional (2D) semiconductor van der Waals heterostructures is an effective strategy for realizing multifunctional microelectronic devices. In this work, the 2D van der Waals heterostructure Cs₃X₂I₉/InSe of non-lead Perovskite Cs₃X₂I₉ and indium-tin InSe is constructed to avoid the toxicity and stability problems of lead-based Perovskites. The geometry, electronic structure, and optical properties are calculated based on the first-principles approach of density-functional theory. It is shown that the 2D Cs₃Bi₂I₉/InSe and Cs₃Sb₂I₉/InSe heterostructures are of type-II energy band arrangement and have band gaps of 1.61 eV and 1.19 eV, respectively, with high absorption coefficients in the visible range and UV range reaching to 5×10⁵ cm^–1. The calculation results from the deformation potential theory and the hydrogen-like atom model show that the 2D Cs₃X₂I₉/InSe heterostructure has a high exciton binding energy (~0.7 eV) and electron mobility rate (~700 cm²/(V·s)). The higher light absorption coefficient, carrier mobility, and exciton energy make the 2D Cs₃X₂I₉/InSe heterostructures suitable for photoluminescent devices. However, the energy band structure based on the Shockley-Queisser limit and type-II arrangement shows that the intrinsic photoelectric conversion efficiency (PCE) of the 2D Cs₃X₂I₉/InSe heterostructure is only about 1.4%, which is not suitable for photovoltaic solar energy. In addition, the modulation and its effect of biaxial strain on the photovoltaic properties of 2D Cs₃X₂I₉/InSe heterostructures are further investigated. The results show that biaxial strain can improve the visible absorption coefficient of 2D Cs₃X₂I₉/InSe heterostructure, but cannot effectively improve its energy band structure, and the PCE only increases to 3.3% at –5% biaxial strain. The above study provides a theoretical basis for designing efficient 2D van der Waals optoelectronic devices in future.

Keywords:
2D heterostructures /

photoelectric conversion efficiency /

first-principles calculations /

strain engineering
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图 1 (a) Cs₃Bi₂I₉/InSe 和(b) Cs₃Sb₂I₉/InSe 的原子结构俯视和侧视图, 其中a和b为晶格矢量, d为 Cs₃X₂I₉层和 InSe 层之间的层间距离

Figure 1. Top and side views of the atomic structures for the (a) Cs₃Bi₂I₉/InSe heterostructure, and (b) Cs₃Sb₂I₉/InSe heterostructure, where a and b are the lattice vectors and d is the interlayer distance between the Cs₃X₂I₉ and InSe layers.

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图 2 (a) Cs₃Bi₂I₉, (b) Cs₃Sb₂I₉和(c) InSe单体结构的HSE06能带结构

Figure 2. HSE06 band structures of (a) Cs₃Bi₂I₉, (b) Cs₃Sb₂I₉ and (c) InSe monomer structures.

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图 3 (a) Cs₃Bi₂I₉/InSe和(b) Cs₃Sb₂I₉/InSe异质结的能带结构; (c) Cs₃X₂I₉/InSe异质结的载流子迁移机制, 其中红色和蓝色分别代表InSe和Cs₃X₂I₉的电子轨道贡献

Figure 3. Band structures of (a) Cs₃Bi₂I₉/InSe heterostructure and (b) Cs₃Sb₂I₉/InSe heterostructure; (c) carrier migration mechanisms in Cs₃X₂I₉/InSe heterostructures, the red and blue lines represent the electronic orbital contributions for InSe and Cs₃X₂I₉, respectively.

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图 4 (a), (b) 二维Cs₃Bi₂I₉/InSe和Cs₃Sb₂I₉/InSe异质结及其各自层在可见光谱中的光吸收系数

Figure 4. (a), (b) Calculated absorption coefficients of the 2D Cs₃Bi₂I₉/InSe heterostructure and the Cs₃Sb₂I₉/InSe heterostructure and their respective layers in the visible spectrum, respectively.

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图 5 (a) Cs₃Bi₂I₉/InSe和(b) Cs₃Sb₂I₉/InSe vdWHs带边的双轴应变

Figure 5. Biaxial strain on the band edge of (a) Cs₃Bi₂I₉/InSe and (b) Cs₃Sb₂I₉/InSe vdWHs.

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图 6 (a) 双轴应变对 (a) Cs₃Bi₂I₉/InSe和(b) Cs₃Sb₂I₉/InSe光吸收系数的影响; (c) Cs₃X₂I₉/InSe结构PCE图

Figure 6. Biaxial strain on optical absorption coefficients of (a) Cs₃Bi₂I₉/InSe and (b) Cs₃Sb₂I₉/InSe vdWHs; (c) PCE map of intrinsic Cs₃X₂I₉/InSe.

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表 2 300 K下的电子和空穴沿x和y方向的有效质量m(m₀)、DP常数E₁ (eV)、二维弹性模量C_2D (N/m)和载流子迁移速率μ_2D (cm²·V^–1·S^–1)

Table 2. Effective masses m(m₀), DP E₁ (eV), 2D modulus of elasticity C_2D (N/m) and carrier mobility μ_2D (cm²·V^–1·S^–1) for electron and hole along and y directions at 300 K.

Carrier type		m_x	m_y	E_lx	E_ly	C_{2D_ x}	C_{2D_ y}	μ_{2D_ x}	μ_{2D_ y}
Electron	Cs₃Bi₂I₉/InSe	0.22	0.23	8.62	8.62	122.96	122.96	472.80	425.55
Electron	Cs₃Sb₂I₉/InSe	0.24	0.22	7.13	7.13	125.76	123.22	619.99	692.30
Hole	Cs₃Bi₂I₉/InSe	1.16	0.97	6.43	6.43	122.96	122.96	31.39	44.32
Hole	Cs₃Sb₂I₉/InSe	1.01	0.75	8.68	8.68	125.76	123.22	23.04	40.94

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表 1 二维 Cs₃X₂I₉/InSe异质结的晶格常数(a, b)、层间距离(d)、激子结合能(E_b)、带隙(Gap)和晶格失配比(ε)

Table 1. Lattice constants (a, b), interlayer distances (d), exciton binding energy (E_b), band gap (Gap) and lattice mismatch ratio (ε) of 2D Cs₃X₂I₉/InSe heterostructures.

Heterostructure	Lattice/Å	d /Å	E_b /eV	Gap/eV	ε/%
Cs₃Bi₂I₉/InSe	a = 8.32	3.71	0.79	1.61	1.89
Cs₃Bi₂I₉/InSe	b = 8.32	3.71	0.79	1.61	1.89
Cs₃Sb₂I₉/InSe	a = 8.30	3.77	0.73	1.19	1.61
Cs₃Sb₂I₉/InSe	b = 8.30	3.77	0.73	1.19	1.61

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Photovoltaic properties of two-dimensional van der Waals heterostructure Cs₃X₂I₉/InSe (X = Bi, Sb)

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