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A New Family of Two-Dimensional Ternary Photoelectric Materials Wang-Ping Xu, Rui Wang, Baobing Zheng, Xiaozhi Wu, and Hu Xu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 26 Mar 2019 Downloaded from http://pubs.acs.org on March 26, 2019

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ACS Applied Materials & Interfaces

A New Family of Two-Dimensional Ternary Photoelectric Materials Wangping Xu1,2, Rui Wang1, Baobing Zheng2,3*, Xiaozhi Wu1,*, Hu Xu2,* 1 Department

of Physics, Chongqing University, Chongqing, 401331, China. Department of Physics & Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China 3 College of Physics and Optoelectronic Technology & Advanced Titanium Alloys and Functional Coatings Cooperative Innovation Center, Baoji University of Arts and Sciences, Baoji, 721016, China. 2

*Corresponding Authors: [email protected]; [email protected]; [email protected]

Abstract Screening unique two-dimensional (2D) materials with high mobility and applicable band gap is motivated by not only the interest in basic science but also the practical applications for photoelectric materials. In this work, we have systematically studied a new family of 2D ternary quintuple layers (QLs), named ABC (A= Na, K, Rb; B=Cu, Ag, Au; C=S, Se, Te). Our results indicate that the QLs of KCuTe, KAgS, KAgSe, KAuTe, RbCuTe, RbAgSe and RbAgTe host direct band gaps. Moreover, KCuTe, RbCuTe and RbAgTe QLs show extremely high mobilities of ~104 cm2V1s1. Interestingly, the linear scaling between exciton binding energy and quasi-particle band gap for ABC QLs exhibits unexpected deviation with the 1/4 law. In addition, KAgSe, KAgS, RbAgSe and RbAgTe show outstanding power energy conversion efficiencies up to 21.5%，suggesting that they are good potential donor materials. Our results provide many potential candidates for utilizing in photoelectric materials and may be realized in experiments due to the possible exfoliation from their parent compounds.

Keywords: 2D photoelectric materials; carrier mobility; exciton binding energy;

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power conversion efficiency; first-principles calculations 1. Introduction 2D materials, possessing unique crystal structures and intriguing electronic properties that are highly desirable in nanosized electronic and optoelectronic devices, have attracted much scientific interest during the last decade, particularly for the field-effect transistors (FETs).1-7 It is well known that the high-performance FETs should possess suitable band gap and high in-plane carrier mobility. However, the hitherto exfoliated or synthesized 2D materials, such as graphene,8 transition-metal dichalcogenides (TMDs),4,

7, 9

h-BN10 and phosphorene,11 may exhibit some

shortcomings more or less when they are considered as the candidates for fabricating FETs. For example, despite owning the highest carrier mobility, graphene has the zero band gap, which hinders their potential applications in electronic devices, especially for FETs; TMDs with tunable band gaps are confined within their comparatively low carrier mobilities (several hundred cm2V1s1). By contrast, black phosphorene with band gap and large carrier mobility is an applicable material for FET application.11-14 To complement experiment, first-principles calculations are employed to predict novel 2D materials that possess applicable band gaps and high carrier mobilities. Group-VA monolayers, such as black arsenic-phoshporus,15 blue phosphorous,16 arsenicene,17 and binary compounds (AsSb, BiAs),18,19 are predicted to have moderate direct band gaps and excellent mobilities (up to ~104 cm2V1s1). Group-(IV-VI) monolayers (Sn(S,Se)2)20 and group-(IV-V) monolayers (SnP3)21 with tunable band gaps and high carrier mobilities are also explored. In addition, the titanium trisulfide (TiS3) monolayer22 with a favorable direct band gap (1.02 eV) and the high in-plane electron mobility (~104 cm2V1s1) is reported recently. Lu et al. proposed a new 2D monolayer material (CaP3) with desirable band gap (1.15 eV) and ultrahigh carrier mobility (~2.0104 cm2V1s1).23 All of these theoretical studies significantly broaden the potential candidates of 2D materials that may be utilized in future photoelectric devices. However, so far the reported 2D materials are mainly restricted to binary compounds, and there are few investigations on 2D ternary compounds.24,25 Therefore, it is highly desirable to design or explore novel 2D ternary compounds,


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especially for those possessing moderate direct band gaps and high carrier mobilities. Recently, high-throughput calculations demonstrate that KAgSe QL can be easily exfoliated from its bulk phase in experiment.26,27 Furthermore, KAgSe QL is theoretically proposed to be an efficient photovoltaic material very recently.28 In this work, based on the structure of KAgSe QL, we report a family of ABC (A= Na, K, Rb; B=Cu, Ag, Au; C=S, Se, Te) ternary compounds that host promising photoelectric properties. Importantly, most of 2D ABC materials exhibit moderate direct band gaps and high carrier mobility larger than TMDs. In addition, the exciton binding energies and the power conversion efficiencies (PCEs) have been investigated in these 2D ABC compounds. 2. Methods First-principles calculations were implemented in the Vienna Ab initio Simulation Package (VASP)29-30 based on density functional theory (DFT). The ion-electron interactions were described by the projector augmented wave method31. We set 500 eV as the plane-wave basis cutoff energy, and employed a 10×10×1 and 20×20×1 k-point meshes for structural relaxations and quasi-particle (QP) band structures, respectively. The atomic positions were fully relaxed until the Hellmann-Feynman forces acting on each atom were less than 102 eV/Å. The Perdew-Burke-Ernzerhof functional32 combined with the one-shot G0W033 correction was employed, and the excitonic effects were considered by using Bethe-Salpeter equation (BSE)34-35 method. To obtain the QP band structures, the wave function was expanded using maximally localized Wannier36 functions basis. For G0W0-BSE calculations, the cutoff energy for the response functions parameter (ENCUTGW) was set to 200 eV. The vacuum layers of 25 Å were used for QP band structures and BSE calculations. The semi-empirical DFT-D337 correction was included to evaluate the van der Waals (vdW) interactions.

3. Results and discussions

Bulk KAgSe crystallizes in a tetragonal layered structure stacked along the z



direction,26 which can be experimentally exfoliated to KAgSe QL.27-28 Motived by this progress, we systematically investigated all of the possible ABC (A=Na, K and Rb; B= Cu, Ag and Au; C=S, Se and Te) ternary QLs, within the framework of the lattice of KAgSe QL. The structures of ABC QLs and the corresponding Brillouin zone are shown in Fig. 1. Clearly, the ABC QLs host the square lattices [see Fig. 1(a)] due to their tetragonal parent compounds. As shown in Fig. 1(b), A atoms and C atoms are separated by the central B atoms, thus forming the five atomic layers structure.

Figure 1. Top (a) and side (b) views of the structures for ABC ternary compounds, the violet atoms represent Na, K and Rb, the gray atoms represent Cu, Ag and Au, and the yellow atoms represent S, Se and Te, respectively. (c) Schematic diagram of Brillouin zone for ABC.


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Figure 2. The phonon spectra of KCuTe (a), KAgS (b), KAuTe (c), RbCuTe (d), RbAgSe (e) and RbAgTe (f).

The vibrational phonon spectra of our proposed ABC QLs are calculated and shown in Figs. 2 (a)-(f). We can find that there are no imaginary frequencies found for these ABC QLs, indicating that all of the proposed QLs are dynamically stable. Moreover, the results of ab initio molecular dynamics (AIMD) simulations at 300 K, as shown in Figure S1 of Supporting Information (SI), further confirm the stabilities of our proposed QLs. To further assess the stabilities of ABC QLs, we also calculate the formation energy of KCuTe as an example. The obtained formation energy of 1.303 eV/atom for KCuTe is comparable of typical MoS2 monolayer, implying that our proposed 2D ABC materials are stable and supposed to be synthesized experimentally. In addition, we establish the effective metal substrates for these QLs to facilitate their experimental syntheses. Here, we take the KAgSe and RbCuTe as examples. The calculated adsorption energies per unit cell for KAgSe and RbCuTe deposited on the Cu(111) substrate [see Figs. 3(a) and (b)] are 0.54 eV and 1.43 eV, respectively. These results indicate that it is possible to synthesize these QLs on the suitable substrates. To show the oxidation resistance, we have studied the oxidation reaction of our predicted ABC QLs and take KAgSe as an example (see Figure S2 in SI). The obtained energy barrier of 1.48 eV for O2 dissociation suggests that oxidation resistance of our predicted ABC QLs are much stronger than common



2D materials.

Figure 3. The QL structures of KAgSe (a) and RbCuTe (b) are deposited on Cu(111) metal substrates, respectively.

Since the applicable direct band gap is highly desirable for photoelectric materials. Therefore, we calculated the electronic properties of all possible ABC QLs. To obtain the accurate band gap, we employ G0W0 method38 to calculate the band gaps of our proposed ABC QLs. The results indicated that KCuTe, KAgS, KAgSe, KAuTe, RbCuTe, RbAgSe and RbAgTe QLs are direct band gap semiconductors. The calculated G0W0 band gap of KAgSe QL is 1.49 eV, which show excellent consistency with the reported value of ∼1.5 eV28. The other band gaps of ABC QLs are also given in the corresponding band structures of Fig. 4. Note that despite lacking experimental results, the high-precision G0W0 method usually gives accurate band gaps for these ternary QLs. As shown in upper panels of Fig. 4, both the conduction-band minimum (CBM) and valence-band maximum (VBM) are located at the Г point. The G0W0 band gaps range from 0.85 eV to 1.54 eV, which are located at the favorable range for solar light adsorption. Moreover, taking KAgSe as an example [see Fig. 4(c)], we can find that the CBMs of ABC QLs are mainly dominated by the s orbitals of A atoms, while the VBMs are mainly contributed from the px and py orbitals of C atoms.


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Figure 4. The QP band structures (upper panels) and the corresponding BSE optical spectra (bottom panels) of the KCuTe (a), KAgS (b), KAgSe (c), KAuTe (d), RbCuTe (e), RbAgSe (f) and RbAgTe (g). The charge distribution of the VBM and CBM of KAgSe are shown in (c), and the isosurface values are set to 0.08 e/Å3.

The exciton binding energy (EBE) plays a more important role in 2D photoelectric materials. Physically, EBE (Eb) is defined as the energy difference between the QP band gap (Eg) and BSE optical gap.39 The calculated BSE optical gaps are shown in bottom panels of Fig. 4, and the EBE values of these QLs range from 0.45 eV to 1.02 eV, suggesting that we can manipulate the EBEs by changing the chemical composition of these ternary QLs. The relationship between EBEs and QP band gaps of these QLs is shown in Fig. 5. It is clear that the EBEs show a linear dependence on the QP band gaps, and our results reveal that the slope of linear scaling law is approximately 1/3 in these square QLs, which drastically deviates from the previously reported 1/4 law for 2D materials.40,41 We can make the following arguments for this deviation. Firstly, the deduction of 1/4 linear scaling law employs a two-band k  p model that omits the contributions from the other bands,41 thus resulting in the overestimation of Eg and underestimation of Eb/Eg. Secondly, the numbers of band gaps (Ng) depend on the crystal symmetry, and the 1/4 law is deduced according to the hexagonal symmetry, i.e, Ng=6. In our ABC QLs, the tetragonal symmetry leads to Ng=4, which also can cause the deviation from 1/4 law. Therefore, for ABC QLs with square lattices, the actual linear scaling may be larger than 1/4, and the obtained linear scaling 1/3 is thus reasonable. Note that the large EBEs for ABC QLs can effectively prevent the rapid recombination of electron-hole pairs and be more stable at high



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temperatures.

Figure 5. EBEs as a function of QP band gaps. The blue squares denote the calculated values, and the purple line is fitted by the calculated values.

High carrier mobility is an important factor for improving the carrier transport ability of photoelectric materials. Therefore, the carrier mobilities of these 2D ABC QLs are investigated using the deformation potential method at room temperature (300 K).22 The calculated results and the corresponding parameters are summarized in Table 1. It is worth noting that we only need to consider the carrier mobility of one direction in views of the square lattices for these QLs. The obtained electrons mobilities are completely larger than 103 cm2V1s1. In particular, the electrons mobilities of KCuTe, RbCuTe and RbAgTe are extremely high (over 104 cm2V1s1), which are not only larger than that of typical MoS2 monolayer,42 but also comparable of that of black phosphorene.12-13 Interestingly, we find that the electron mobilities are almost 200 times higher than the hole mobilities for these QLs. This is because that the curvatures of CBMs and VBMs in band structures show large differences, which lead to the fact that the effective masses of electron are much smaller than those of hole, even ten times smaller. In addition, the small deformation potentials of electron for these structures also can result in high carrier mobilities. Therefore，these ABC QLs are promising candidates for fabricating high-performance FETs due to their larger carrier motilities.

Table 1. The carrier mobilities (µ) at 300 K for electrons and holes in different ternary compounds. Carrier typea

Structure

effective masses

deformation potential (eV)

2D elastic modulus


(Jm2)

mobilities (103 cm2V1s1)

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e

h

m*/m0

E1

C_2D

μ_2D

KAgS

0.29

1.46

37.33

4.43

KCuTe

0.25

1.02

42.99

13.53

KAgSe

0.22

1.61

41.60

6.93

RbCuTe

0.22

0.57

32.30

43.75

KAuTe

0.16

1.74

23.38

6.04

RbAgSe

0.20

3.24

42.73

2.06

RbAgTe

0.22

0.98

28.95

12.68

KAgS

2.39

2.45

37.33

0.02

KCuTe

1.82

2.44

42.99

0.05

KAgSe

2.13

2.52

41.60

0.03

RbCuTe

1.57

2.28

32.30

0.05

KAuTe

1.55

2.65

23.38

0.03

RbAgSe

1.75

3.25

42.73

0.03

RbAgTe

1.44

2.44

28.95

0.05

Figure 6. (a) Band alignments for KAgSe, KAgS, RbAgSe, RbAgTe QLs and Ca(OH)2 monolayers. (b) PCEs as a function of the donor bandgap and conduction band offset.

The direct band gaps (0.9~1.5 eV) of KAgSe, KAgS, RbAgSe and RbCuTe imply that these QLs are highly favorable to be applied as solar cell donor materials.43 In order to realize the possible applications for solar cell, it is necessary to find out the appropriate acceptor materials for these materials. To facilitate the conduction of electron and improve the cell efficiency, the CBMs and VBMs of these materials should be lower than those of donor materials. Our G0W0 calculations using band-gap-center approximation 44 indicate that the vacuum level corrected CBMs and VBMs are 1.15 eV and 2.65 eV for KAgSe, 1.01 eV and 2.48 eV for KAgS, 1.05 eV and 2.31 eV for RbAgSe, and 1.05 eV and 2.59 eV for RbAgTe, respectively. After careful examination of various 2D materials, we have found that



the optimal acceptor materials are monolayer Ca(OH)2 with CBM of 1.20 eV and VBM of 4.85 eV by G0W0 band-gap-center approximation, which matches well with those QLs. Clearly, all of them have a type-II heterojunction alignment, as shown in Fig. 6(a). According to the approach that can be found elsewhere,43, 46-47 we obtain the corresponding PCEs, as shown in Fig. 6(b). We find the upper limit of PCEs for these four heterojunctions to be 21.5%, 19.4%, 19.8% and 19.5%. Note that the PCEs of our proposed heterojunctions are not only much larger than that of experimental reported MoS2/p-Si heterojunction and graphene-based solar cells,48-50 but also comparable of the GaS/ Ca(OH)2 trilayer system.45 Therefore, we can conclude that our proposed ABC compounds (KAgSe, KAgS, RbAgSe and RbAgTe) are competitive donor materials for solar cell. 4. Conclusion In summary, a new family of high-performance and feasible exfoliated 2D photoelectric materials are proposed. The stabilities of these QLs have been verified by the phonon spectra calculations, and the effective metal substrates are established. Most of proposed QLs have moderate direct band gaps (0.9 ~ 1.5 eV) and unexpected EBEs. Moreover, they show extremely large electron mobilities, comparable to that of black phosphorene, which indicates that these QLs are promising for photoelectric materials. In addition, our calculations indicated that the (KAgSe, KAgS, RbAgSe and RbAgTe)/Ca(OH)2 systems are type-II heterojunction alignment with the highest PCE up to 21.5%. Our finding show that these 2D ternary QLs are promising candidates for solar energy industry. Supporting Information. The AIMD simulations of KAgS and KAgTe monolayers at 300 K and reaction pathways of O2 dissociation on the KAgSe surface. Corresponding Authors: *E-mail: [email protected] *E-mail: [email protected] *E-mail: [email protected]


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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grant Nos. 11674148, 11334003 and 11847301), the Guangdong Natural Science Funds for Distinguished Young Scholars (No. 2017B030306008), the Fundamental Research Funds for the Central Universities (2018CDXYWU0025), the Natural Science Basic Research plan in Shaanxi Province of China (Grant Nos. 2018JQ1083 and 2018ZDXMGY119), the Scientific Research Program Funded by Shaanxi Provincial Education Department (Grant Nos. 17JK0041 and 18JC001), the Baoji University of Arts and Sciences Key Research (Grant No.: ZK2017009), the Science, Technology

and

Innovation

Commission

of

Shenzhen

Municipality

(No.

ZDSYS20170303165926217), and the Center for Computational Science and Engineering of Southern University of Science and Technology.

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