新型四元硫族化合物光伏特性的高通量筛选和第一性原理研究

康家兴; 严全河; 曹浩宇; 孟威威; 徐飞; 洪峰

doi:10.7498/aps.73.20240795

摘要

本工作提出了一种对Cu₂ZnSnS₄中Zn元素异价取代策略, 探讨了新型四元硫族化合物A₂M₂M'Q₄ (A = Na, K, Rb, Cs, In, Tl; M = Cu, Ag, Au; M' = Ti, Zr, Hf, Ge, Sn; Q = S, Se, Te)作为新型太阳能电池吸收层材料的应用潜力. 利用第一性原理高通量计算, 评估了1350种A₂M₂M'Q₄化合物热力学稳定性、带隙、光谱极限最大效率和声子色散谱等特性. 结果表明, 有10种热力学和动力学稳定的候选材料, 它们表现出合适的带隙, 并展现出高的光吸收性能, 光谱极限最大效率的理论值均超过30%. 它们的电子结构和光学性质类似于Cu₂ZnSnS₄, 有望应用于高效单结薄膜太阳能电池. 本文数据集可在https://www.doi.org/10.57760/sciencedb.j00213.00006 中访问获取.

关键词:

Abstract

In recent decades, the demand for clean energy has promoted extensive research on solar cells as a key renewable energy source. Among the various emerging absorber layer materials, Kesterite-type semiconductors have aroused significant interest. Especially, Kesterite Cu₂ZnSnS₄(CZTS) stands out as a promising candidate for low-cost thin-film solar cells due to its direct bandgap, high optical absorption coefficient, suitable bandgap (1.39–1.52 eV), and abundance of constituent elements. However, the power conversion efficiency (PCE) of CZTS-based solar cells currently lags behind that of Cu(In,Ga)Se₂ (CIGS) cells, mainly due to insufficient open-circuit voltage caused by a large number of disordered cations and defect clusters, resulting in non-radiative recombination and band-tail states.To address these challenges, partial or complete cation substitution has become a viable strategy for altering the harmful defects in CZTS. This study proposes a heterovalent substitution of Zn in CZTS and explores the potential of novel quaternary chalcogenide compound A₂M₂M'Q₄ (A = Na, K, Rb, Cs, In, Tl; M = Cu, Ag, Au; M' = Ti, Zr, Hf, Ge, Sn; Q = S, Se, Te) as absorbers for solar cells. By substituting elements in five prototype structures, a comprehensive material database comprising 1350 A₂M₂M'Q₄ compounds is established.High-throughput screening and first-principles calculations are used to evaluate the thermodynamic stabilities, band gaps, spectroscopic limited maximum efficiencies (SLMEs), and phonon dispersions of these compounds. Our research results indicate that 543 compounds exhibit thermodynamic stability (E_hull < 0.01 eV/atom), 202 compounds possess suitable band gaps (1.0–1.5 eV), and 10 compounds meet all the criteria for thermodynamic and dynamic stability, suitable band gaps, and high optical absorption performance (10⁴–10⁶ cm^–1), with theoretical SLME values exceeding 30%.Notably, Ibam-Rb₂Ag₂GeTe₄ exhibits the highest SLME (31.8%) in these candidates, featuring a band gap of 1.27 eV and a small carrier effective mass (< m₀). The electronic structures and optical properties of these compounds are comparable to those of CZTS, which makes them suitable for highly efficient single-junction thin-film solar cells.All the data presented in this work can be found at https://www.doi.org/10.57760/sciencedb.j00213.00006.

Keywords:

PACS:

74.25.Jb	(Electronic structure (photoemission, etc.))
74.55.+v	(Tunneling phenomena: single particle tunneling and STM)
74.62.En	(Effects of disorder)

作者及机构信息

1.
上海大学理学院, 上海市高温超导重点实验室, 上海　200444

2.
华南师范大学, 华南先进光电子研究院, 广州　510006

3.
复旦大学物理系, 应用表面物理国家重点实验室, 上海　200433

通信作者: 徐飞, feixu@shu.edu.cn ; 洪峰, fenghong@shu.edu.cn

基金项目: 国家自然科学基金(批准号: 62350054, 12175131, 12374379)资助的课题.

Authors and contacts

1.
Shanghai Key Laboratory of High Temperature Superconductors, College of Sciences, Shanghai University, Shanghai 200444, China

2.
South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, China

3.
State Key Laboratory of Surface Physics, Department of Physics, Fudan University, Shanghai 200433, China

Corresponding author: Xu Fei, feixu@shu.edu.cn ; Hong Feng, fenghong@shu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62350054, 12175131, 12374379).

文章全文

1. 配对密度波与拆对散射的对立与统一

超导是一种神奇的宏观量子态, 超导材料表现有零电阻和完全抗磁性. 一般认为形成这种量子态, 首要的微观机理是要使得材料费米能处的电子形成两两配对, 配对电子的动量相反, 即配对电子的波矢为零^[1]. 这种情况下, 配对序参量不会呈现出波动特性, 衡量配对电子束缚能的超导能隙在空间中呈现均匀分布. 20世纪60年代初, 理论学家Fulde P, Ferrell R A和Larkin A I, Ovchinnikov Y N预言在磁场作用下, 配对电子的总动量不为零, 呈现出有限波矢^[2,3]. 这种超导态就会呈现出波动的特性, 称为配对密度波态或者 “FFLO”态. 在“FFLO”态中, 超导能隙在空间中会呈现出周期为2π/Q的振荡(), 其中, FF态是平面波形式的配对密度波, $\varDelta \left(\boldsymbol{r}\right)={\varDelta }_{0}{{\mathrm{e}}}^{{\mathrm{i}}\boldsymbol{Q}\cdot \boldsymbol{r}}$ , 而LO是驻波形式的配对密度波, $\varDelta \left(\boldsymbol{r}\right)={\varDelta }_{0}{\mathrm{cos}}\left(\boldsymbol{Q}\cdot \boldsymbol{r}\right)$ . 近十几年间, 随着扫描隧道显微技术的发展与测量精度的提高, 学者们逐渐在多种超导量子材料中观测到了超导能隙在空间中的微弱振荡行为(振荡幅度占能隙平均值的5%左右)^[4–12], 并指认为类比于“FFLO”态的配对密度波.

$图 1 配对密度波(a)与拆对杂质散射(b)造成的超导能隙振荡\r\nFig. 1. Superconducting gap modulations induced by pair density waves (a) and pair-breaking scatterings (b).$

图 1 配对密度波(a)与拆对杂质散射(b)造成的超导能隙振荡

Fig. 1. Superconducting gap modulations induced by pair density waves (a) and pair-breaking scatterings (b).

下载: 全尺寸图片幻灯片

同样在20世纪60年代初, 我国理论学者于渌在国内有限的科研条件下发现了超导体内磁性杂质的拆对行为, 即超导能隙内形成局域束缚态^[13]. 这项工作在国际上被广泛认为是超导领域内的经典之作. 于渌先生的论文附录中详细推导了能隙在杂质周围的周期性振荡行为(图1(b)), 并指出了这种变化的量级在1/15(图2). 这在当时来看确实是一个可以忽略的小量, 然而却与当前实验观测到的能隙振荡幅度的数量级吻合. 近期, 李东海等^[14]则进一步指出了在多种情况下(包括磁性杂质、非磁性杂质、相位变化的超导序参量、磁性超导体等), 多个杂质的拆对散射形成干涉后可以形成全局的能隙的周期性振荡. 这样的振荡行为可能不涉及相位调制, 并区别于配对密度波.

$图 2 于渌对磁性杂质周围能隙振荡的推导与量级估算, 节选自文献[13]\r\nFig. 2. Results on superconducting gap modulations near the magnetic impurities by Lu Yu from Ref. [13].$

图 2 于渌对磁性杂质周围能隙振荡的推导与量级估算, 节选自文献[13]

Fig. 2. Results on superconducting gap modulations near the magnetic impurities by Lu Yu from Ref. [13].

下载: 全尺寸图片幻灯片

量子世界中, 对立往往隐喻着统一. 上述两种振荡机制的确又有着深刻的联系. 例如, “FFLO”态中引入的磁场是明确破缺时间反演对称性的^[2,3]; 磁性杂质也是因为明确破坏了时间反演对称性, 从而破坏超导电性, 并产生局域束缚态和能隙振荡^[13]; 当超导材料存在自发性的时间反演对称性破缺时, 非磁性杂质也可破坏超导并激发出能隙振荡^[14]. 因此, 配对密度波与拆对散射似乎都与时间反演对称性破缺有着统一的内禀联系. 进一步, 二者在关联体系内甚至可能存在着混合: 当杂质拆对散射在某个特定波矢特别强且呈现发散趋势时, 往往也意味着此处费米面的失稳, 有可能在相同波矢涌现出丰富的密度波态.

2. 实验上的区分

目前发表的大多数论文把已有的实验数据都解释成配对密度波. 如此是否准确, 成为领域内值得深思的问题. 我们从扫描隧道显微谱学技术和理论层面对这个难题进行一些抛砖引玉的剖析. 在实验中, 扫描隧道显微镜一般是对超导样品的某一个小的区域进行能隙的谱学成像, 对实空间数据傅里叶变换后得到能隙振荡的波矢. 另一种测量方法是利用超导针尖与超导样品实现约瑟夫森隧道结, 对约瑟夫森电流或者是约瑟夫森零能电导峰进行空间成像, 再对实空间数据进行傅里叶变换后得到所谓配对电子密度振荡的波矢. 值得注意的是, 这里配对电子密度并不直接对应于超流密度, 而是一个唯象局域波函数的密度, 实则经过严格推导后对应于超导能隙的一个复杂函数^[15], 近似与能隙大小的平方值成比例. 这样, 约瑟夫森扫描隧道显微镜测量到的信号仍然是超导能隙的空间振荡行为, 并不能被夸大认为是通常意义上的配对电子超流密度的波动. 这样, 两种实验方法实则都是测量超导能隙振荡行为, 我们也无法用后者严格区分配对密度波和拆对杂质散射.

拆对杂质散射机理一般要求存在杂质或者晶体缺陷, 而配对密度波则是发生在不依赖杂质的纯洁晶格中电子结构的行为. 因此, 实验中如果在没有杂质或缺陷的干净区域测量到能隙振荡, 则很大可能是来自配对密度波. 实验中如果只在杂质或缺陷附近测量到能隙振荡, 而在干净区域振荡消失, 则很大可能是拆对散射; 在这种情况下, 振荡信号在倒空间中一般呈现弧形或者圆形结构, 部分反映出费米面的几何. 当测量到的能隙振荡在杂质附近出现, 且在倒空间结构呈现为点状信号时, 则既可能来自配对密度波, 又可能来自能带结构中态密度比较大的点状区域(hot spot)间的散射(杂质拆对散射), 亦或是二者的混合.

在这种最难的情况下, 如果信号真的是来自纯净的配对密度波, 在理论上有可能利用博戈留波夫(Bogoliubov)费米面(如文献[16])对配对密度波的存在进行确认. 在有限动量配对下, 超导能隙并不严格在所有费米波矢打开在费米能, 在某些动量位置, 超导能隙打开在费米能旁边, 这样会有残留的费米面形成博戈留波夫费米面. 博戈留波夫费米面在动量空间的几何形状应当与配对电子的波动波矢有着严格的倒空间-实空间对应关系. 如果探测到这样的对应关系, 则可以锁定配对密度波起源. 值得注意的是, “FFLO”意义下的配对密度波都是针对可以局部定义的配对序参量而言的. 在许多强关联系统中, 由于局域库仑排斥, 配对更可能发生在近邻键上. 这种情况下, 配对密度波与谱学能隙或约瑟夫森电流的关系更为复杂, 值得在理论和实验上进一步厘清. 但这种复杂性不影响利用博戈留波夫费米面来判断配对密度波的准确性, 因此后者具有更好的通用性优势. 近期, 我们利用以上原则在笼目超导材料KV₃Sb₅和CsV₃Sb₅中用(约瑟夫森)扫描隧道显微镜对两种类型的能隙振荡进行了初步的区分, 并尝试把来自配对密度波的振荡和可能存在的博戈留波夫费米面进行联系^[17], 希望能对深刻理解两种机制的区别和联系起到推动作用.

补充材料

17-20240795Suppl.pdf

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图 1 5种四元硫族化合物A₂M₂M'Q₄原型的晶体结构

Fig. 1. Five prototypes of A₂M₂M'Q₄.

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图 2 使用高通量第一性原理计算筛选新材料的工作流程示意图

Fig. 2. Schematic workflow of novel materials’ discovery with high-throughput first principle calculations.

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图 3 (a) 1350种A₂M₂M'Q₄化合物的E_hull和 ${{E}}_{\text{g}}^{\text{PBE}}$ 的散点图和直方图; (b) 202种化合物的ΔE_g直方图

(a) The scatter plot and histograms of E_hull and ${{E}}_{\text{g}}^{\text{PBE}}$ for 1350 A₂M₂M'Q₄ compounds; (b) histogram of ΔE_g for 202 compounds.

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(a) 72种化合物在薄膜厚度为2 μm时的SLME与 ${{E}}_{\text{g}}^{\text{HSE}}$ 的关系图, 蓝线为Shockley-Queisser极限; (b) Ibam-Rb₂Ag₂SnTe₄的声子色散谱; 4种SLME超过31%的候选材料, CZTS和CZTSe的(c) SLME与薄膜厚度的关系和(d) 光吸收系数

(a) SLME at 2 μm vs. the HSE bandgap ${{E}}_{\text{g}}^{\text{HSE}}$ for the 72 compounds, the blue curve represents the Shockley-Queisser limit; (b) phonon dispersion of Ibam-Rb₂Ag₂SnTe₄; (c) thickness dependent SLME values and (d) optical absorption spectra of the top 4 compounds (SLME > 31%), CZTS and CZTSe.

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图 5 (a) Ibam-Rb₂Ag₂GeTe₄; (b) P2/c-Rb₂Cu₂GeTe₄的能带结构、分态密度、晶体结构和载流子有效质量

Fig. 5. Band structure, partial density of states (PDOS), structure and effective mass of (a) Ibam-Rb₂Ag₂GeTe₄; (b) P2/c-Rb₂Cu₂GeTe₄.

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表 1 四元硫族化合物A₂M₂M'Q₄实验报道的带隙和结构与本工作的对比

Table 1. Reported structures and bandgap for A₂M₂M'Q₄ systems.

Compounds	E_hull/(eV·atom^–1)	Stable phase		E_g/eV
Compounds	E_hull/(eV·atom^–1)	Experiment	This work	Experiment	HSE06
Na₂Cu₂ZrS₄^[43]	0.129	C2/m	Ibam	—	0.07
Cs₂Ag₂ZrTe₄^[44]	0	C222	C222	—	2.08
Rb₂Cu₂SnS₄^[38]	0.012	Ibam	Ibam	2.08	2.02
K₂Ag₂SnSe₄^[41]	0	P2/c	P2/c	1.8	1.69
Cs₂Ag₂TiS₄^[45]	0.001	P4₂/mcm	P4₂/mcm	2.44	2.44
Cs₂Cu₂TiS₄^[45]	0	P4₂/mcm	P4₂/mcm	—	2.56
K₂Cu₂TiS₄^[45]	0.002	P4₂/mcm	P4₂/mcm	2.04	2.62
Rb₂Ag₂TiS₄^[45]	0.002	P4₂/mcm	P4₂/mcm	2.33	2.45
Rb₂Cu₂TiS₄^[45]	0.001	P4₂/mcm	P4₂/mcm	2.19	2.63

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