PHYSICAL REVIEW MATERIALS 3, 055201 (2019) Design of p-type transparent conductors from inverted band structure: The case of inorganic metal halide perovskites Peng Zhang, 1, 2 Shu Yu, 1 Xiuwen Zhang, 1 , * and Su-Huai Wei 2 , † 1 College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen, Guangdong 518060, China 2 Beijing Computational Science Research Center, Beijing 100193, China (Received 28 January 2019; published 15 May 2019) Transparent conductors (TCs), which bring two seemingly contraindicated properties, conductivity and transparency, together into one material, enable many critical technologies. Significant successes have been achieved for n-type TCs, such as Sn-doped In 2 O 3 , but developing their p-type counterparts has still encountered a big challenge, mainly due to the intrinsic band structure of conventional semiconductors. Here, we propose that a class of wide-gap inorganic metal halide perovskites have great potential as ideal p-type TCs, because of their inverted band structure compared to n-type TCs, i.e., they have s-like wave-function character at the top of the valence band, and p-like wave-function character at the lower valence bands and the bottom of the conduction band, which results in significantly improved p-type dopability, high hole mobility, and good optical transparency. This insight of designing p-type TCs from an inverted band structure opens an avenue for the future design of critical optoelectronic materials. DOI: 10.1103/PhysRevMaterials.3.055201 I. INTRODUCTION Transparent conductors (TCs) are essential for many mod- ern optoelectronic devices, such as transparent thin-film tran- sistors, touch-screen sensors, solar cells, flat-panel displays, and light-emitting diodes [1–7]. Currently, all the commer- cially available TCs are based on n-type oxides, such as Sn- doped In 2 O 3 and electron-doped ZnO, whereas the fabrication of their p-type counterparts has still been a big challenge, which seriously impedes the further exploration of transpar- ent electronics with novel functionalities. The difficulty in achieving p-type TCs in oxides (i.e., TCOs) roots mainly from two critical features of their band structures, as schematically illustrated in Fig. 1(a): (i) the valence-band maximum (VBM) of TCOs is usually dominated by the low-lying localized O 2 p orbitals, which based on the “doping limit rule” will even- tually lead to high acceptor formation energies, deep acceptor levels, poor hole mobility, and thus poor p-type conductivity [8–11]; (ii) the energy difference between the VBM and lower valence-band (VB) states in TCOs is relatively small, due to the degeneracy of O 2 p bands, which will trigger the intraband optical absorptions as the materials are heavily doped p type, and thus degrade the transparency [12–14]. On the contrary, the conduction- band minimum (CBM) of TCOs is predomi- nately derived from the low-lying delocalized cation s orbital, which ensures good n-type dopability, high electron mobility, and thus good n-type conductivity. Moreover, the large energy separation between the CBM and higher conduction-band (CB) states results in negligibly small intraband absorptions for visible light, which guarantees the transparency when the materials are doped n type [15–17]. * xiuwenzhang@szu.edu.cn † suhuaiwei@csrc.ac.cn This characteristic band structure of TCOs implies that it may be a formidable task to make oxides as p-type TCs; however, it meanwhile points out an important design strat- egy for realizing both the p-type conductivity and optical transparency in other materials: If one can find materials that have a band structure, where the VBM has a predominate s character and the CBM has a p character, as illustrated in Fig. 1(b), the good n-type conductivity in TCOs can then be transferred into good p-type conductivity in these materials. Meanwhile, the large energy separation between the s-like VBM and p-like lower VB states may be also obtained, which will retain the transparency as the materials are doped p type. This characteristic band structure for p-type TCs can be viewed as an exact “inverted band structure” of TCOs; nevertheless, the question is whether we can find promising candidates that satisfy this design strategy. Moreover, to be practical p-type TCs, additional criteria beside the p-type conductivity and transparency should also be satisfied, such as (i) high thermodynamic stability (ii) good defect tolerance ability, and (iii) ease to fabricate. In principle, for systems with an inverted band structure, the cation s orbital should form occupied bands with relatively low energy [see Fig. 1(b)], which can be achieved in com- pounds containing heavy elements with low valence states, such as Pb 2+ and Bi 3+ , because the large relativistic effect pushes down their occupied s orbital in energy. In oxides, one example of these systems is the Sn 2+ -based compounds, such as SnO and K 2 SnO 3 , which however exhibit either small optical band gaps or poor thermodynamic stability, preventing them from practical applications as p-type TCs [7,18,19]. More recently, a new class of inorganic metal halide perovskites (IMHPs) has emerged with superb optoelectronic properties [20–27]. Among them, CsPbCl 3 shows a short emission wavelength of ∼410 nm, corresponding to a band gap of ∼3.0 eV, guaranteeing the good transparency for most 2475-9953/2019/3(5)/055201(6) 055201-1 ©2019 American Physical Society