KAgSe: A New 2D Efficient Photovoltaic Material with Layer

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Functional Nanostructured Materials (including low-D carbon)

KAgSe: A New 2D Efficient Photovoltaic Material with Layer-independent Behaviors Qiang Wang, Jianwei Li, Yan Liang, Yihang Nie, and Bin Wang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b16505 • Publication Date (Web): 02 Nov 2018 Downloaded from http://pubs.acs.org on November 2, 2018

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ACS Applied Materials & Interfaces

KAgSe: A New 2D Efficient Photovoltaic Material with Layer-independent Behaviors Qiang Wang,†,‡ Jianwei Li,† Yan Liang,¶ Yihang Nie,‡ and Bin Wang∗,† †Shenzhen Key Laboratory of Advanced Thin Films and Applications, College of Physics and Energy, College of Electronic Science and Technology, Shenzhen University, Shenzhen, 518060, People’s Republic of China ‡Institute of Theoretical Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, People’s Republic of China ¶School of Physics, State Key Laboratory of Crystal Materials, Shandong University, 250100 Jinan, People’s Republic of China E-mail: [email protected]

Abstract Recent advances in the development of two-dimensional (2D) materials have stimulated people’s interest and enthusiasm to discover new kinds of low dimensinal functional materials. In this paper, we propose a novel 2D layered semiconductor KAgSe using the first principles calculation method, which displays excellent photovoltaic properties with proper direct band gap and significant carrier mobility. By evaluating the cohesive energy, vibrational phonon spectrum and temporal evolution of the total energy at a high temperature of 500K, the KAgSe monolayer is proved to be existence stably. Finite cleavage energy comparable to that of black phosphorus implies the feasibility of mechanical exfoliation of KAgSe monolayer from the bulk. Layered KAgSe

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shows a ∼1.5 eV direct band gap, which is roughly independent of the number of layers. Remarkable optical absorption coefficients in visible light region and significant carrier mobilities reveal a favorable application prospect of layered KAgSe in photovoltaic devices. Especially, the layer-independent optical absorption provides enormous convenience and less difficulty in experimental fabrication of photoelectronic devices which are based on finite layers KAgSe. To further explore the photovoltaic behaviors, the polarization angle related photocurrent is evaluated for the KAgSe monolayer based nano-device by irradiating a beam of linearly polarized light to the scattering region. Moreover, large photon responsivity and external quantum efficiency are also obtained for KAgSe monolayer.

Keywords 2D KAgSe, first principles calculation, layer-independent behaviors, high carrier mobility, optical absorption, photocurrent

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Introduction

Since the experimental fabrication of graphene by Giem et al. in 2004, 1 the investigations of two-dimensional (2D) materials have attracted increasing interests in many fields of frontier science. Many researches of 2D materials, such as graphene, h-BN, transition metal dichalcogenides (TMDC), black phosphorus (BP), etc., have been performed to investigate the electronic, thermal, optical, magnetic, and mechanical properties. 2–12 A great deal of related ideal performances and favorable applications of these 2D materials have also been proposed and predicted, 13–16 which further arouse people’s interests to explore new families of 2D functional materials. Especially, searching 2D materials possessing ideal direct band gaps and high carrier mobilities becomes significative in view of the essential requirements in building nanoscale electronic devices, where some new emerging layered 2D materials are on

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the way including SnS2 , SnSe2 , 17 T iN X(X = F, Cl, Br), 18 CaP3 , 19 GeP3 20,21 and so forth. Owing to the unique electronic properties of these 2D materials, many novel applications have been explored in electronics, photonics, energy storage and energy conversion. In addition, the investigation on the 2D Dirac materials is also a growing field currently, such as AsO, 22 Nb2 O3 , 23 PbX, (X=H, F, Cl, Br and I) 24 and SnC2 H, 25 and a series of applications and representations have been reported. These 2D Dirac materials appear novel properties on quantum spin Hall and quantum anomalous Hall effect, which maybe provide promising platforms for designing topological quantum devices operating even at high temperature. PbFCl-type structure is one of the three main layered types of rare-earth and transitionelement compounds. 26 Recent advances in developing 2D PbFCl-type materials are mainly devoted to their synthesis, characterizations and applications in different aspects. Chen et al. prepared 2D BiOCl via a new sonochemical method for the first time, which had been proved to be a convenient and efficient experimental route. 27 Using an ab initio evolutionary methodology structure search method, Zhou et al. investigated the pressure-induced variation of the electronic structures and phase transition mechanisms of 2D layered BiOF. 28 Ali et al. observed an unusual ”butterfly” shaped titanic angular magnetoresistance in quasi2D nonmagnetic Dirac material ZrSiS. 29 Based on the first principles calculation, Xu et al. found that the monolayer ZrSiO can be a long-sought-after 2D oxide topological insulator, which has similar crystal structure as the well-known iron-based superconductor LiFeAs, and thus predicted a new material composed by superconductor and topological insulator. 30 By synthesizing the WO3 /BiOCl layered heterojunction, Shamaila et al. indicated that the catalytic performance and dispersibility of the BiOCl were largely enhanced in the visible light region due to the photosensitive property of WO3 . 31 KAgSe is one of the representative members of PbFCl-type tetragonal materials with space group P 4/nmm, whose bulk phase has been synthesized and characterized experimentally for a long time. 32 The bulk KAgSe has a proper direct band gap and processes potential applications in semiconductor industry. However, no investigation about 2D layered KAgSe

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has been reported to best of our knowledge. In this regard, it is significant to research the stability and electronic behaviors and further explore the feasible applications of 2D layered KAgSe. In this paper, we systematically investigated the crystal structure, stability, electronic properties and optoelectronic performances of 2D layered KAgSe, and further calculated the photocurrent of a KAgSe monolayer based nano-device using the first principles calculation method. Numerical results show that layered KAgSe is easy to be exfoliated from the bulk and is structurally stable to be existence. Layered KAgSe has a moderate direct band gap and high carrier mobility, which is roughly independent of the number of layers. The superior optical absorption, photon responsivity and the external quantum effect (EQE) in the visible light region represent that layered KAgSe is a promising candidate for photovoltaic devices and components of 2D solar cell systems. In addition, the layer-number independent behaviors of band gap and optical absorption are nearly derived from weak coupling between adjacent layers, which provides enormous convenience and less difficulty in experimental fabrication of finite layers KAgSe based photoelectronic devices. The rest of this paper is organized as follows. In Section II, the computational methods used in this investigation are briefly introduced. In Section III, the numerical results including dynamic stability, electric properties, and optical response of 2D layered KAgSe are presented. In addition, the photoelectric transport properties of 2D monolayer KAgSe nano-device are shown based on the first principles calculation method. In section IV, a brief summary is given to this investigation.

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Computational Methods

The DFT code VASP was employed to research the stability and electric properties of 2D KAgSe. 33 In our calculation, the exchange-correlation potential was dealt with hybrid functionals at both PBE 34 and HSE06 35 levels, and the cut-off energy was set 450 eV. A vacuum

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Figure 1: (color online) (a) Side view of bulk KAgSe with K, Ag and Se atoms indicated by large violet, medium silver and small green spheres, respectively. The unit cell is outlined by a box in the lower left of top view panel. (b) Side view of three different structures of KAgSe monolayer. The two outside layers of each structure are K and K layers (Structure I), K and Se layers (Structure II), and Se and Ag layers (Structure III) in sequence. (c) Cleavage energies Ecl versus separation distance for KAgSe monolayers of the three different structures from the bulk. (d) Top view and side view of 2D KAgSe monolayer with The unit cell is outlined by a box in the lower left of top view panel. (e) Isosurface plot of charge density difference between KAgSe monolayer and individual K, Ag and Se atoms with isosurface −3 value 0.6 e˚ A . The spheres with yellow color indicate electron donors, while the spheres with blue color mean electron acceptor.

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of 20 angstrom perpendicular to the 2D plane was used to demonstrate finite layers, and 15 × 15 k-meshed grid was employed to describe the periodic properties of 2D KAgSe. Convergence criteria was restricted less than 10−5 eV in energy and 0.01 eV per angstrom in force. In addition, Phonopy code 36 was adopted to calculate the phonon spectrum, and molecular dynamics simulations was performed at 500K as long as 3000 fs to verify the thermal stability of 2D KAgSe. The photovoltaic transport of 2D KAgSe nano-device was performed using Nanodcal, which is based on the state-of-the-art NEGF-DFT method. 37 In this calculation, the normconserving nonlocal pseudo-potential 38 and atomic orbital basis set were employed, and the exchange-correlation potential was handled at PBE 39 and PBE+U 40 levels. K-mesh grid was set 24 × 1 perpendicular to the transport direction, and self-consistence was restricted less than 10−5 eV. Here, the PBE+U type exchange-correlation potential was used to model the identical band gap as that obtained from the HSE06 calculation in view of the absence of HSE06 type hybrid functional in Nanodcal.

Figure 2: (color online) (a) Phonon band dispersion curves of the 2D KAgSe monolayer (b) The variation of total energy as a function of time under T = 500K (c) Top and side views of a snapshot of monolayer KAgSe after 3 picosecond in ab initio MD simulation.

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3

Numerical Results and Discussions

3.1

Crystal structure and stability

Fig. 1(a) shows the side view of the schematic structure of bulk KAgSe, which is a stratified material with alternating atomic layers of K-Se-Ag-Se-K along (001) direction. There are two K atoms, two Ag atoms and two Se atoms in each unit cell as indicated by the small box in the lower left of Fig. 1(a). Firstly, we examined the feasibility of mechanical exfoliation of KAgSe monolayer from the bulk. There exist three different exfoliating candidates of monolayer in view of the difference of two outside atomic layers, which are K and K layers (Structure I), K and Se layers (Structure II), and Se and Ag layers (Structure III) as presented in Fig. 1(b) in sequence. By calculating the cleavage energy Ecl , we verified the feasibility of each structure in mechanical exfoliation from the bulk. In our calculation, a KAgSe supercell with four layers was used to avoid the neighboring fractures. As represented in Fig. 1(c), Ecl of KAgSe monolayer are 0.53 J/m2 , 2.48 J/m2 and 2.64 J/m2 for Structure I, Structure II and Structure III, respectively. Obviously, Structure I is much easier to be exfoliated than Structure II and Structure III. For Structure I, Ecl is a little larger than that of graphene (0.37 J/m2 ), 41 MoS2 (0.421 J/m2 ) 42 and black phosphorus (0.367 J/m2 ), 43 but smaller than that of GeP3 (1.14 J/m2 ), 20 CaN2 (1.09 J/m2 ) 44 ”homogeneic” BiOBr (0.584 J/m2 ) and BiOI (0.614 J/m2 ). 45 The finite value of Ecl implies the feasibility to exfoliate monolayer KAgSe from the bulk. Thus, we only focus on the Structure I in the rest of this manuscript, and call it monolayer KAgSe directly. The optimized atomic structure of monolayer KAgSe is shown in Fig. 1(d), where the small box in the lower left indicates a unit cell including two K, two Ag and two Se atoms. Lattice constants and inter-layer distances of the entirely optimized 2D KAgSe from monolayer to multi-layer are listed in Table 1, where the lattice constants of the bulk (a = b = 4.574˚ A) is very close to the experimental values (4.52˚ A). An obvious feature is that the lattice parameters a from bilayer to multi-layers are very close, whereas larger than

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that of monolayer. To get more insight into the chemical bonds between atoms of monolayer KAgSe, the charge density differences between KAgSe and individual K, Ag and Se atoms are calculated. Numerical results are shown in Fig. 1(e), where the yellow spheres and blue spheres indicate electron donors and electron acceptors, respectively, with sphere size describing the magnitude of charge transfer. Obviously, charge transfer occurs mainly from Ag to K and Ag to Se among the neighbor atoms. Then we examine the stability of 2D KAgSe by evaluating the cohesive energy, vibrational phonon spectrum and temporal evolution of the total energy. The cohesive energy is calculated to examine the structural stability, which is defined as Ecoh = (2EK + 2EAg + 2ESe − EKAgSe )/6. Here EK , EAg , and ESe are the total energy of single K, Ag and Se atoms, respectively, and EKAgSe is the total energy of the unit cell of monolayer KAgSe. Numerical result indicates that Ecoh of KAgSe monolayer is equal to 2.61 eV per atom. Although smaller than those of graphene (7.46 eV per atom), 46 BP (3.45 eV per atom) 47 and MoS2 (4.98 eV per atom), 48 it is larger than those of other PbFCl-type 2D materials. For instance, Ecoh of CaFX (X=Cl, Br and I) 49 are 2.22, 2.12 and 2.02 eV per atom, respectively. The large cohesive energy demonstrates the structural robustness of KAgSe monolayer. Next, the vibrational phonon spectrum is calculated to verify the dynamic stability of KAgSe monolayer. As presented in Fig. 2(a), the phonon spectrum curves show one quadratic and two linear acoustic branches as the typical characteristics of 2D crystals. The absence of imaginary phonon mode in the entire Brillouin suggests that the structure is stable minima on the potential energy surface, which indicates that the KAgSe monolayer is dynamically stable. 50 The temporal evolution of the total energy is also calculated to inspect the thermal stability of KAgSe monolayer by using the first principles molecular dynamics simulation. The simulation is carried out for a 4 × 4 × 1 supercell at 500 K and the evolutionary time reaches 3 ps with time step of 1 fs. As shown in Fig. 2(b), the total energy of the system fluctuates around constant value -294 eV with considerably small fluctuation magnitude. The fully relaxed structure after 3 ps is plotted in Fig. 2(c), where no bonding broken or

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Figure 3: (a)-(b): Band structures and PDOS for (a) monolayer and (b) bilayer KAgSe at PBE level (the blue solid curves) and HSE06 level (the red circle curves). In each panel, the Fermi level is set equal to zero. (c) Band gaps of layered KAgSe versus the number of atomic layers by using PBE and HSE06 functionals (d) Real space distribution of local density of states at VBM and CBM for bilayer KAgSe.

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obvious geometry reconstruction appears implying the thermal stability of KAgSe monolayer during the temporal evolution.

3.2

Electric properties of 2D KAgSe

Fig. 3(a) and (b) show the electric band structures of 2D monolayer and bilayer KAgSe, respectively, at PBE level (the blue solid curves) and HSE06 level (the red circle curves). A direct band gap appears in monolayer KAgSe with the value being about 0.59 eV at PBE level and 1.35 eV at HSE06 level. At both levels, the valence band maximum (VBM) and the conduction band minimum (CBM) are located at Γ point. The projected density of states (PDOS) and the projected band structures (Fig. S1) show that the VBM is dominated by p orbitals of Se and d orbitals of Ag, while the CBM is roughly contributed by all the atomic orbitals with the contributions from p orbitals of Se and s orbitals of Ag being a little larger. Moreover, in view of necessity of the substrate to practical applications, 51,52 we also calculated the band structure of monolayer KAgSe on monolayer BN substrate whose lattice mismatch is less than 3%. As shown in Fig. S2(a) and (b), the relaxed minimum distance between KAgSe and BN is 3.61 ˚ A. More importantly, the BN substrate almost does not affect the intrinsic properties of KAgSe monolayer as showed in Fig. S2(c). Similar properties has also been found for monolayer KAgSe with bilayer BN substrate. For bilayer KAgSe, the profiles of band structure and PDOS are very close to those of monolayer KAgSe. The band gaps are 0.68 eV at PBE level and 1.53 eV at HSE level, which are a litter larger than those of monolayer. In order to further explore the layer-number dependent properties of 2D KAgSe, the Table 1: Numerical results of lattice constant a (a = b) and inter-layer distance d of the unit cell of fully optimized KAgSe with monolayer (1L), bilayer (2L), trilayer (3L), and four-layer (4L). The parameters of bulk KAgSe is also listed in the last column. Structures 1L 2L 3L 4L Bulk ˚ a (A) 4.485 4.562 4.567 4.581 4.574 ˚ d (A) 2.476 2.483 2.415 2.544

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band gaps versus number of layers are calculated at both PBE and HSE06 levels. As shown in Fig. 3(c), the band gap of monolayer is slightly smaller than that of bilayer. While, the band gap roughly does not change with further increase of number of layers. The layernumber independent band gap of KAgSe is very different from some familiar 2D materials, such as TMDCs 17 and BP, 43 whose band gaps decrease versus the increasing number of layers showing obvious quantum size effect. To further explore the underlying physics of the layer-number independent behavior, the real space projection of local density of states at Γ point for CBM and VBM of the bilayer KAgSe are presented in Fig. 3(d). For both CBM and VBM, the charge is mainly accumulated around Ag and Se atoms, while barely around K atoms. Because the outside surface in each layer are K atoms, the inter-layer interactions are rather weak and hardly can the band gap be tuned by changing the number of layers. Thus, the difference of band gaps between monolayer and multi-layers can only be attributed to the variation of lattice constants as shown in Table 1. The lattice constant of KAgSe monolayer is smaller than those of multi-layers, which may induce trivial variations of the band gap.

3.3

Optical absorption and carrier mobility

The roughly 1.4∼1.5 eV band gaps (at HSE06 level) imply a potential application of layered KAgSe as a component of 2D solar cell in view of the optimum band gap about 1.2∼1.6 eV of excitonic solar cells. 18 To measure the optical harvesting ability, the optical absorption coefficients a(ω) are evaluated at both PBE and HSE06 levels for 2D KAgSe with different layers according to the expression 53 √ a(ω) =

2ω c

rq

21 (ω) + 22 (ω) − 1 (ω),

(1)

where ω is the frequency of incident light and c is light velocity. 1 and 2 are the real part and imaginary part of frequency-dependent dielectric function, respectively. 2 is calculated

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by summation over empty states, and 1 can be obtained according to the usual KramersKronig transformation. 54 Fig. 4(a)-(d) show the absorption coefficients versus the energy of incident photons for 2D monolayer, bilayer, trilayer and four-layer KAgSe, respectively, where the polarization vector is set parallel (Rk ) or perpendicular (R⊥ ) to the plane. For each panel, the optical absorptions from HSE06 calculation can be roughly recognized as right moving of those from PBE calculation with qualitative agreement of detailed behaviors for both Rk and R⊥ . When the light energy increases larger than the band gap, the optical absorption is firstly governed by Rk and then by R⊥ . Obviously, layered KAgSe possesses high absorption over a wide range of visible light (∼ 1.6-3.2 eV) behaving an ideal solar absorbing component of excitonic solar cells. More importantly, we find that the optical absorption shows very similar behaviors for 2D KAgSe with different layers, which gives accordant information with that shown in Fig.3(c). The layer-number independent optical absorption provides enormous convenience and less difficulty in experimental fabrication of finite layers KAgSe based photoelectronic devices. Table 2: Effective mass (m∗ /m0 ), elastic module (C), deformation potential constant (E1 ), and carrier mobility (µ) of KAgSe monolayer for electron, light hole and heavy hole Carrier Type Electron Light Hole Heavy Hole

m∗ /m0 0.208 0.185 2.164

C2D (N m−1 ) E1 (eV ) µ(cm2 V −1 s−1 ) 39.426 1.437 6257.516 39.426 2.226 3280.915 39.426 2.226 24.108

Carrier mobility is another crucial factor effecting the efficiency of photovoltaic conversion. We have also predicted the carrier mobilities based on the deformation potential (DP) theory, 55 whose reliability has been widely examined theoretically in 2D atomic structures. According to the DP theory, carrier mobility µ2D can be calculated by 56

µ2D =

e¯h3 C2D , kB T |m∗e/h |(E1 )2

(2)

2

where kB is the Boltzmann constant; T is the temperature; m∗e/h = ±¯ h2 ( ddkE2k )2 is the effective 12


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Figure 4: (color online) Optical absorption coefficients versus the energy of incident light for 2D (a) monolayer, (b) bilayer, (c) trilayer and (d) four-layer KAgSe. The polarization vector is set parallel (Rk ) or perpendicular (R⊥ ) to the plane, and the exchange-correlation functional is treated at PBE and HSE06 levels. The two vertical dash lines in each panel indicate the region of visible light. mass of electrons or holes alone the Γ → X direction; C2D is the elastic modulus and E1 is the deformation potential. As summarized in Table 2, the obtained carrier mobilities of KAgSe monolayer are 6.26 × 103 cm2 V −1 s−1 for electrons, 3.28 × 103 cm2 V −1 s−1 for light holes and 0.24 × 103 cm2 V −1 s−1 for heavy holes. Although the carrier mobility of KAgSe monolayer is smaller than that of graphene 57 and black phosphorene (∼ 1 − 2 × 104 cm2 V −1 s−1 ), 58 but much larger than those of Si ( ∼ 480−1300 cm2 V −1 s−1 ), 59 MoS2 (∼ 200−500 cm2 V −1 s−1 ) 10 and chalcogenides (∼ 300 − 2000 cm2 V s−1 ). 60 The high carrier mobilities of layered KAgSe make it a promising material for photoelectronic devices.

3.4

Photocurrent in KAgSe monolayer nano-device

In view of the favorable optical absorption of 2D KAgSe, we build a KAgSe monolayer based nano-device and calculate the photocurrent by using the first principles calculation method. For a two-probe system with optical excitation in the scattering region, electrons can absorb photons and jump from valence bands to conduction bands accompanied with generation 13



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Figure 5: (color online) Schematic structure of 2D KAgSe monolayer two-probe device. The left blue region and right red region represent the drain and source, respectively. The yellow zone in the center scattering region stands for lighting area. of electron-hole pairs when the photon energies are larger than the band gap. Then the electron-hole pairs will be re-separated into electrons and holes, which flow along opposite directions owing to the bias voltage and contribute to a photocurrent. At the first level Born approximation, the photocurrent flowing into the left probe can be expressed as 61–63 JLph

ie = h

Z

Tr ΓL {G(ph)

KAgSe: A New 2D Efficient Photovoltaic Material with Layer

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