Engineering Defect Transition-Levels through the van der Waals

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C: Physical Processes in Nanomaterials and Nanostructures

Engineering Defect Transition-Levels through van der Waals Heterostructure Akash Singh, Aaditya Manjanath, and Abhishek K. Singh J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b08082 • Publication Date (Web): 04 Oct 2018 Downloaded from http://pubs.acs.org on October 9, 2018

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The Journal of Physical Chemistry

Engineering Defect Transition-Levels through van der Waals Heterostructure Akash Singh, Aaditya Manjanath, and Abhishek Kumar Singh∗ Materials Research Centre, Indian Institute of Science, Bangalore 560012, India E-mail: [email protected]

Abstract

istic transition level in a host material, which can not be changed without adversely affecting the integrity of the material. Hence, in spite of numerous materials either synthesized or theoretically predicted, only few have found applications in the electronic devices. 2D materials have been emerging as a possible replacement for silicon in miniaturized devices. 13–17 Among them, due to direct band gap and relatively large carrier mobilities, monolayer MoS2 is considered as a front-runner . 18–20 The success of the MoS2 in 2D electronics will critically depend on the ease of modulation of the electronic transport via doping. As grown MoS2 exhibits unintentional n-type conductivity, whose origin is still being debated and is mostly attributed to S vacancy . 19,21–24 On the other hand, a cation vacancy in MoS2 acts as deep acceptor, 25,26 which makes the device development even more challenging. Another promising material in the same family WS2 , suffers from the same problem, where W-vacancy 15,27 gives rise to a deep acceptor level. 28 Tuning these deep defect levels in MoS2 and WS2 to shallow remains an open challenge and must be overcome to develop the electronic devices based on these materials. In order to make these defect levels shallower, it was proposed to have an alloy of two different metal atoms (Mo and W) or of two different chalcogens (S and Se). 29 However, alloying offers its own sets of challenges such as controlling its exact composition, segregation versus solid solutions, ordered vs disordered alloys etc, which are extremely difficult to con-

Tuning defect levels in 2D semiconductors without significantly altering the integrity of the materials remains one of the most difficult challenges, which critically restricts their usage in electronic and optoelectronic devices. In this work, we demonstrate that the deep levels created by a cation vacancy in a monolayer of MoS2 , can be tuned to a shallow level by heterostructuring it with a monolayer of WS2 , while maintaining their structural and compositional integrity intact. The overall change in dielectric constant rescales the defect transition levels in a heterostructure. In result, the deep defect levels are shallowed by nearly 4(V−1 Mo ) and 2(V−1 ) times, respectively, compared to their W monolayer counterparts. Our finding has potential to revolutionize the doping strategy of the 2D materials and could pave the way for 2D electronics.

Introduction Point defects are inherently present in materials and play a central role in tuning the electronic and optoelectronic properties of semiconductors. 1–5 Based on the position of charge transition levels of a defect–position of Fermi level at which defect changes the charge states–with respect to the band edges, a defect can be shallow or deep . 6–8 Intrinsic or extrinsic shallow defects in a material provide the charge carriers that are necessary for electronic devices . 9–12 However, every defect has its character-

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trol in experiments . 30–33 Recent advancement in transfer technology of monolayers of the 2D materials on substrates or another monolayers 34–37 has made it possible to develop a range of heterostructures, having properties better than their constituent layers. With the advent of van-der-Waals (vdW) heterostructure, where two monolayers are stacked vertically, most of the challenges associated with the alloying are automatically taken care . 34,38–40 Heterostructuring could also be applied to tune the position of defect transition levels in the 2D materials. Here, using first-principles density functional theory, we show that the cation vacancy in a monolayer MoS2 , which is a deep acceptor becomes a shallow acceptor in a MoS2 /WS2 vdW heterostructure. Similarly, within the same heterostructure, the deep cation vacancy in WS2 , turns into a shallow acceptor. Compared to their monolayer counterparts, in MoS2 /WS2 vdW heterostructure, defect transition levels corresponding to VW and VMo become nearly 2 and 4 times shallower. This dramatic shift of defect transition levels is found to be directly proportional to the changes in effective dielectric constant by heterostrcuturing, and hence this approach can be extended to tune the defect transition levels across the various class of 2D materials.

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sufficient vacuum of more than 15 Å was used in the z-direction. The vdW interactions were included through the semi-empirical Grimme’s formalism of the DFT-D2 . 47 Relaxed lattice parameters of MoS2 and WS2 are found to be in good agreement with the reported values . 48 The MoS2 (3.178 Å) and WS2 (3.176 Å) have negligible lattice mismatch ( 0.06% ) and are ideal for the vdW heterostructure. The interlayer distance between the W and Mo layers is found to be 6.22 Å which in excellent agreement with the reported value. 49 A search for minimum energy stacking carried out, shown in supplementary information (SI) in Fig. S2, and AB stacking of the layers found to be energetically most favorable (Fig. 1(c)). The defect [X] formation energy 50 in charge state q is given by X pristine defect E f [X q ] = Etot − Etot − ni µi (1) i q +qEF + ∆ , pristine defect and Etot are total energies of where Etot defective and pristine supercells, respectively, ni is the number of atoms of ith species (i = Mo, W), either added to (ni > 0) or removed (ni < 0) from pristine supercell to form isolated defect. The chemical potentials µMo(W) are referenced to the total energy of a Mo(W) atom in crystalline (bcc) Mo(W) metal. EF is the position of Fermi-level, referenced to the valence-band maximum (VBM), ∆q is alignment of average electrostatic potential of supercell containing neutral defect with respect to the bulk and to account for spurious electrostatic interaction among the periodic images of the charged defects. In order to correct the spurious Coloumbic interaction, we calculate the formation energies of these defects as a function of uniformly scaled (Lxx = Lyy = Lzz ) supercell sizes. The formation energy converges at a supercell size of 8 × 8 × 8 (Lzz ≈ 26 Å), as shown in Fig. S4 in the SI. This supercell was used for all subsequent calculations. The Fermi-level position at which, stable defect changes its charge state from q to q 0 , known as defect charge transition level (q/q 0 ) and can be derived from the formation energies:

Methodology The calculations were performed using density functional theory (DFT) implemented with the projector-augmented wave method in the Vienna ab initio simulation package (VASP). 41,42 Electronic exchange and correlation were approximated by the Perdew-Burke-Ernzerhof (PBE) form of the generalized gradient approximation (GGA) . 43–45 Kinetic energy cutoff for the plane wave expansion was set to 350 eV. All the structures were completely relaxed until the component of the Hellmann-Feynman forces is less than 0.005 eV/Å. A MonkhorstPack k-point mesh 46 of 19 × 19 × 1 was used for the relaxation of unit cell of MoS2 , WS2 and MoS2 /WS2 . To avoid the spurious interactions among the periodic images of the 2D sheets,


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the previous report . 51 Unlike the monolayers, MoS2 /WS2 vdW heterostructure has an indirect band gap of 1.16 eV between the Γ and K-points (Fig. 1(f)). The defect formation energy (E f ) provides key information about defect concentration, its stability in the material, and charge transition levels. GGA functional 52 is known to underestimate the band gap and hence could give incorrect defect transition levels. The parametrized screened hybrid functional of Heyd Scuseria Ernzerhof (HSE) 53 or the quasi-particle approach of G0 W0 are required to overcome this problem. The G0 W0 approach becomes computationally prohibitively expensive for large supercell calculations. The calculated HSE band gaps of monolayers MoS2 , WS2 , and MoS2 /WS2 are 1.89 eV, 2.0 eV and 1.3 eV, respectively (agreeing well with experimental values 20,38,54 ) are also very close to PBE values. The HSE(PBE) (0/ − 1) levels for VMo in −1 charge state occurs 1.25(1.16) eV and 0.27(0.21) eV (above the VBM), respectively, for monolayer MoS2 and MoS2 /WS2 vdW heterostructure. Overall no qualitative change was observed between HSE and PBE(GGA) calculations, therefore, all the defect transition levels, presented in this work, are calculated using the PBE level. The E f of cation vacancies in monolayers and heterostructure in their respective possible charge states are calculated and have been shown in Fig. 2. In Fig. 2 (a) and (b), magenta and blue lines indicate the stable charge state of VMo and VW in monolayer MoS2 and WS2 , respectively. The vertical green dashed line indicates the CBM of MoS2 /WS2 vdW heterostructure. The solid green lines indicate the stable charge states of VMo(W) in heterostructure. In the monolayers, the formation energy of VMo (VW ) in neutral charge state is 4.87 eV (4.4 eV) in S-rich condition. The electronegativity difference between Mo and S is larger than that between W and S. Therefore, irrespective of the growth condition, the formation energy of VW is lower than that of VMo . The (0/−1) and (−1/−2) levels for VMo in MoS2 , occurs at 1.16 eV and 1.61 eV above the VBM. In the case of WS2 , (0/−1) and (−1/−2) lev-

0

(q/q 0 ) =

E f (X q ) − E f (X q ) |EF =0 , (q 0 − q)

(2)

where E f (X q ; EF = 0) is the formation energy of defect X in charge state q . The thermodynamic transition level implies that for Fermilevel positions below (above) (q/q 0 ), charge state q (q 0 ) is stable. (a)

(d) 3 S

1 2.4

2 Mo

S

Energy (eV)

0

3.13 A0

A

1 0

Mo S

1.70 eV

−1 −2 Γ

Μ

Κ

Γ

3.14 A0

2.4

S W S

(e) 3 2 Energy (eV)

1A0

(b)

(c)

1 0

W S

1.83 eV

−1 −2 Γ

S

Μ

Κ

Γ

(f) 3

W 3.09 A0

S

Energy (eV)

2

S 6.22 A0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1 0

W S Mo

1.16 eV

−1

Mo

S

−2 Γ

Μ

Κ

Γ

Figure 1: Side views (left) of (a) monolayer MoS2 , (b) monolayer WS2 , and (c) vdW heterostructure (MoS2 /WS2 ). (d), (e) and (f) are their corresponding band structure (right). The dotted lines on the left indicate the unit cells of these crystal structures. The Fermi level (red dotted line on the right) is set to 0 eV.

Result and Discussion Monolayer MoS2 and WS2 have hexagonal symmetry and they are comprise of three stacked sublayers in a chalcogen-metal-chalcogen (X-MX) formation (Figs. 1(a) and (b)). Monolayers MoS2 and WS2 have a direct band gaps at the K-point in Brillouin zone with values of 1.70 eV (Fig. 1(d)) and 1.83 eV (Fig. 1(e)), respectively and are in good agreement with


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els for VW occurs at 1.02 eV and 1.6 eV above the VBM. Both types of cation vacancies are very deep acceptors and are more favourable to form under the n-type conditions. These vacancies can pin the Fermi level near the conduction band and will act as electron trap centers. Therefore, the cation vacancy in MoS2 and WS2 , will act as scattering or charge recombination centers, which are highly undesirable for electronic devices. Furtheremore, we also considered the effect of spin orbit coupling (SOC) on VW in monolayer WS2 and found a negligible effect on defect transition level (Fig. S5 in SI). Similarly, in MoS2 , the SOC effect will be very low due to Mo being lighter than W. (a) Formation energy (eV)

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monolayer to heterostructure are 0.95 eV and 1.13 eV, respectively, whereas for VW the shifts are 0.68 eV and 0.94 eV, respectively. The resulting levels are shallowed by nearly 4 (V−1 Mo ) −1 and 2 (VW ) times, moving them very close to the VBM compared to their monolayer counterparts. This unprecedented change arises from the reduction in the bound−carrier−charged interaction resulting from increased screening in heterostructures, 55 compared to individual layer. Therefore, by forming the heterostructure of two appropriate monolayers, we obtain a powerful means by which the defect levels can be tuned. A knowledge about the character of the low energy states is necessary to understand the behavior of different defects. We calculated the electronic structure of these materials by using Crystal Orbital Hamiltonian Population (COHP) 56 and the results are summarized in Fig. S1 in SI. COHP plot shows that in both monolayers and vdW heterostructure, the frontier occupied band (near the Fermi level) is an antibonding type, denoted by a negative value in Fig. S1, while the remaining occupied orbitals are bonding orbitals. On the other hand, the unoccupied orbitals forming the conduction bands, are all antibonding. To further investigate the participating orbitals in the states near the Fermi level, we plot the molecular orbital (MO) diagram based on the projected density of states, as shown in Fig. S3 in SI. In monolayers, Mo(W) d xy and d x2 −y2 are the highest occupied (VBM) antibonding orbitals, while in MoS2 /WS2 vdW heterostructure, they are (Mo+W)-d z2 with a small contributions from S-p z . In monolayers, the lowest unoccupied (CBM) antibonding states originates from Mo(W)-d z2 and S-(p x ,p y ), while in the heterostructure they originate from Mo-d z2 + S-(p x ,p y ). Upon creating a cation vacancy in monolayers, the point group symmetry reduces to C1h . Six uncoordinated bonds are present in its vicinity and the net atomic relaxation is approximately 0.12 Å inwards (outwards) for the neutral (−1) charge state. The density of states (DOS) and Kohn-Sham defect levels within the band gap, with respect to vac-

(b) 0

MoS2/WS2

MoS2

WS2

−1

5 0

0

−1

−2

0

4

VMo

−3

−2

−1 VW

−2

−1 −3 −2

3

0

0.5

1

1.5 0 0.5 Fermi level (eV)

1

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1.5

Figure 2: Defect formation energy of the cation vacancies, as a function of Fermi level, for the S-rich ((a) and (b)), condition for monolayer MoS2 (magenta), monolayer WS2 (blue), and MoS2 /WS2 (green). The magenta, blue and green-dashed line signifies the CBM position of monolayer MoS2 , monolayer WS2 and the MoS2 /WS2 vdW heterostructure. Next, in the MoS2 /WS2 vdW heterostructure, E f of VMo(W) is higher than the corresponding E f values in their respective monolayers by about ∼0.2-0.4 eV. Most interestingly, in the MoS2 /WS2 vdW heterostructure, the defect transition levels of the cation vacancies move significantly, closer to VBM, turning them into shallow acceptors. For VMo the (0/ − 1) and (−1/ − 2) levels are at 0.21 eV and 0.48 eV, respectively above the VBM. Similarly, for VW the (0/ − 1) and (−1/ − 2) levels move to 0.34 eV and 0.66 eV, respectively above the VBM. Therefore, the overall shift in the defect transition levels (0/ − 1) and (−1/ − 2) of VMo from


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0 −2

MoS2

MoS2/WS2

0

Total S(p) W(d) Mo(d)

MoS2/WS2 0

0

0

VMo −4

WS2

VMo

VW

VW

CBM

Mo(d ,d 2 ,d 2 2 ) xy z x −y + S(py,pz)

S(pz) +Mo(dyz)

−6

VBM

Figure 3: Kohn-Sham levels of cation vacancy (neutral charge state) near the Fermi level (red-dashed lines) in monolayers MoS2 , WS2 and MoS2 /WS2 vdW heterostructure. Black filled and open circles are representing occupied and unoccupied defect states, respectively.The single cation vacancy produces occupied S-pz (less contribution of Mo(W)-dyz ) and unoccupied Mo(W)(dxy ,dz2 ,dx2 −y2 ) + S-(py ,pz ) defect states near the Fermi level. These defect states are similar in monolayers and in the heterostructure. uum, are shown in Fig. 3. All the defect KohnSham levels are similar in character for both monolayers and MoS2 /WS2 vdW heterostructure, however, the positions get significantly shifted in the heterostructure. In monolayers and vdW heterostructure, VMo(W) creates five defect states, with two below and three above the Fermi level. Among these five, one is non-degenerate and two are doubly degenerate. However, the occupied defect state in MoS2 /WS2 vdW heterostructure is in resonance with the VBM. The unoccupied defect states are strongly contributed by Mo(W)-d orbitals with negligible contributions from S-p, while the occupied defect state arises from the S-p orbitals (Fig. 3). The VBM of MoS2 /WS2 vdW 2 heterostructure shifts up by 0.69 eV (∆MoS VBM ) WS2 and 0.53 eV (∆VBM ) with respect to monolayers MoS2 and WS2 , respectively. Likewise, the defect Kohn- Sham levels shift (∆DKS ) up in MoS2 /WS2 vdW heterostructure, by 0.18 WS2 2 eV (∆MoS DKS ) and 0.21 eV (∆DKS ) for VMo and VW , respectively (Fig. 3). Since the position of the VBM of MoS2 /WS2 vdW heterostructure is higher compared to the monolayer MoS2 and WS2 , therefore the positions of defected Kohn-Sham levels of VMo and VW are closer to the VBM in the vdW heterostructure. Furthermore the VBM of WS2 is higher than VBM of

2

Defect transition level

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


WS2 MoS2

CBM CBM

1.5 CBM

1

VMo@ MoS2

MoS2/WS2

VW@ WS2

0.5 VW@ MoS2/WS2 VMo@ MoS2/WS2

0 VBM 3

3.5 4

4.5 5

5.5 6

6.5 7

Dielectric constant Figure 4: Defect transition level (0/ − 1) and (−1/ − 2), in monolayers MoS2 , WS2 and in MoS2 /WS2 vdW heterostructure, as a function of dielectric constant. Black dotted line is indicates VBM (set to zero). Red filled square and circle signifies the transition levels of VMo and VW , respectively. The color dotted lines; blue, magenta and green are indicating CBM of monolayers and MoS2 /WS2 vdW heterostructure, respectively.


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MoS2 , hence, VMo is closest to the VBM of vdW heterostructure. Therefore, in MoS2 /WS2 vdW heterostructure the deep defect levels of VMo(W) becomes shallower. The dielectric screening will change in the heterostructure compared with the monolayers. Therefore, next, we analyze the variation of the defect transition level as a function of the dielectric constant. The dielectric constants of these structures were calculated using the density functional perturbation theory (DFPT). 57 Fig. 4 shows the variation of transition levels of the cation vacancies as a function of dielectric constant. The direction-dependent dielectric constants of monolayer MoS2 (εxx = εyy = 4.18, εzz =1.23), which is higher than monolayer WS2 (εxx = εyy = 3.87, εzz =1.23), arising from the higher electronegativity difference between the cation and S atoms in monolayer MoS2 . However, MoS2 /WS2 vdW heterostructure has higher dielectric constants (εxx = εyy = 6.98, εzz =1.61) compared to the constituent monolayers. This increases the screening and thus, reduces the hole−charged−impurity interaction. This delocalizes the strongly localized defect states observed in the monolayers, thereby reducing the defect charge density at the vacancy site. 55,58 As a result, defect transition levelsDTL ∝ 1/εhost , where εhost is the representative dielectric constant of the host, 55 leading to the shallowing of the defect levels in the heterostructure.

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which keeps the integrity of the materials, can be extended to tune the defect levels for targeted applications in a very large class of 2D materials.

ASSOCIATED CONTENT Supporting Information Available: Additional information including the thermodynamics of formation energy, Crystal Orbital Hamiltonian Population (COHP) and molecular orbital picture plots of monolayers MoS2 , WS2 and the MoS2 /WS2 vdW heterostructure. This material is available free of charge via the Internet at http://pubs.acs.org/.

AUTHOR INFORMATION Corresponding Author ∗ Email: [email protected] Notes The authors declare no competing financial interests. Acknowledgement The authors thank Materials Research Centre and Supercomputer Education and Research Centre, Indian Institute of Science for the computational facilities. This work was supported by the India-Korea project. Akash Singh acknowledges the DST-Inspire fellowship (1F150954).

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Page 10 of 11

Page 11 of 11

Graphical TOC Entry W

Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2 1.5

VMo

VW

CBM VMo

−1

0.5 0

Mo

MoS2

VW

−1

CBM MoS2/WS2 −1

0

0

1 0

W

CBM

−1 WS2 0

VBM

Mo


11

Engineering Defect Transition-Levels through the van der Waals

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