Distinct electronic and transport properties between 1T-HfSe2 and 1T-PtSe2

Distinct Electronic and Transport Properties between 1T-HfSe2 and 1T-PtSe2

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Distinct Electronic and Transport Properties between 1T-HfSe2 and 1T-PtSe2 Icuk Setiyawati, K. -R. Chiang, H. -M. Ho, Y. -H. Tang PII: DOI: Reference:

S0577-9073(19)30935-9 https://doi.org/10.1016/j.cjph.2019.09.029 CJPH 958

To appear in:

Chinese Journal of Physics

Received date: Revised date: Accepted date:

1 August 2019 19 September 2019 27 September 2019

Please cite this article as: Icuk Setiyawati, K. -R. Chiang, H. -M. Ho, Y. -H. Tang, Distinct Electronic and Transport Properties between 1T-HfSe2 and 1T-PtSe2 , Chinese Journal of Physics (2019), doi: https://doi.org/10.1016/j.cjph.2019.09.029

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Highlights • Different electronic and transport properties between 1T-HfSe2 and 1T-PtSe2 . • Distinct interlayer bond ionicity and number of 5d electrons between Hf and Pt. • Robust two-dimensional characteristic of 1T-HfSe2 . • Strong layer dependence of metal-to-semiconductor transition in 1T-PtSe2 .

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Distinct Electronic and Transport Properties between 1T-HfSe2 and 1T-PtSe2 Icuk Setiyawatia , K. -R. Chianga , H. -M. Hoa , Y. -H. Tanga,∗ a

Department of Physics, National Central University, Jung-Li 32001, Taiwan

Abstract In this study, we employed the first-principles calculation to investigate the structural, electronic and transport properties of 1T-HfSe2 and 1T-PtSe2 transition metal dichalcogenides, and further explain why they share the same 1T (octahedral) layered structure but exhibit very different electronic and transport properties. There are two underlying concepts: the degree of interlayer bond ionicity and the number of 5d valence electrons of transition metal. The high degree of Hf-Se bond ionicity not only gives rise to the indirect energy gap of HfSe2 bulk and thin films, but also results in the weak Se-Se vdW interlayer coupling to further restrict the electron transport only within a HfSe2 layer. On the other hand, the modulation of metallic/semiconducting property of PtSe2 bulk and thin films can be understood by the significant vdW interlayer coupling, which induces charge redistribution of Se atom and allows electrons to transport within a PtSe2 layer as well as cross neighboring layers. Finally, our transport calculation for 1T-HfSe2 /1T-PtSe2 bulks and monolayers suggests the great electron transport within Hf-Se/Pt-Se layer but suppresses/allows electron from neighboring layers. The robust two-dimensional characteristic of 1T-HfSe2 and the metalto-semiconductor transition of 1T-PtSe2 may provide more knowledge for future application in nanoelectronic and optoelectronic devices. Keywords: first-principles calculation, transport calculation, transition metal dichalcogenides

1. Introduction The transition metal dichalcogenides (TMDs) MX2 , where M is a transition metal and X is a chalcogen, exhibit a covalent/ionic intra-layer M-X bond a X-X van der Waals (vdW) interlayer coupling. The coordination environment of the transition metal (M) and its d orbital counts form the layered structures and further lead to the strong anisotropy in their chemical, mechanical, and electrical properties. The replacement of M from Groups 4−10 transition metals [1] not only gives rise to the different coordination types, i.e. 1T (octahedral), 2H (trigonal prismatic), and 3R (rhombohedral) with different stacking polytypes, ∗

Corresponding author Email address: [email protected] (Y. -H. Tang)

Preprint submitted to Chinese Journal of Physics

October 9, 2019

but also results in the great tunability of the conduction band minimum (CBM), valance band maximum (VBM), and direct/indirect energy gaps. The 2H-(Mo,W)X2 Group 6 TMDs have been extensively studied for nanoelectronic and optoelectronic devices, including the field-effect transistors (FETs)[2, 3, 4, 5], resonators[6], amplifiers[7], and phototransistos[8]. However, their carrier mobilities (∼340 cm2 /Vs) are too low for practical applications. The 1T-(Hf,Zr)X2 Group 4 TMDs have been predicted to exhibit higher carrier mobility [9, 10], where the HfSe2 (above 2000 cm2 /Vs) is one promising choice for potential applications in FET [11, 12] and phototransistor [13]. The finite energy gap combined with high two-dimensional (2D) carrier mobilities of semiconducting TMDs may overcome the leakage current operation in graphene-based devices due to the lack of band gap [14], and has already attracted much attention for enormous exciting possibilities in nanoelectronic devices applications. Early theoretical works [15, 16, 17, 18] have employed the linear combination of atomic orbitals (LCAO) approach and the tight-binding (TB) model to demonstrate the structural stability and semiconducting/metallic properties of groups 4-10 based MX2 TMD bulks, which are dominated not only by the featuring d0 -d6 transition metal centres but also by the ionic/covalent intralayer M-X bonds [1]. Moreover, the recent development of firstprinciples calculation provides more understandings in energy dispersion and band splitting to explain the semiconducting 1T-HfSe2 with an indirect band gap ranging from 0.9 eV to 1.2 eV [19, 20, 21, 22], indirect-to-direct energy gap variation of 2H-MoS2 from bulk to monolayer [23, 24], and the metal-to-semiconductor transition for the reduction of 1T-PtSe2 film thickness [25]. In this study, we employed the first-principles calculation to comprehensively investigate the structural, electronic and transport properties of HfSe2 and PtSe2 TMDs with 1T (octahedral) layered structures. Regardless of the reduced film thickness, the weak vdW interlayer interaction of 1T-HfSe2 is supported by the nearly unchanged lattice parameters, slightly varied indirect energy gap, the absence of interlayer differential charge density, and the vanish of interlayer transport channel. This is in sharp contrast to the strong vdW interlayer coupling of 1T-PtSe2 , due to its strong layer dependence of metal-to-semiconductor transition and vdW interlayer distance, along with the great transmission probabilities not only within a PtSe2 layer but also across neighboring layers. 2. Calculation Details The 1T-MSe2 (M=Hf,Pt) layered structure with space group D3d can be represented by a hexagonal unit cell containing one M and two Se ions, forming the in-plane M-Se bond and Se-Se interlayer vdW interaction. Figs. 1(a) and (b) show the top and side views of 1T-MSe2 2L case, respectively, where a vacuum (dvac ) of 12 ˚ A along the z-direction is considered within a unit cell to construct a 1T-MSe2 N-layered (NL) thin film. The structural relaxation and electronic properties were performed by the Vienna ab initio simulation package (VASP) with Density functional theory (DFT) based on projector augmented wave (PAW) pseudopotential method [26, 27, 28] for Hf (6s and 5d), Pt (6s and 5d), Se (4s, and 4p) and Generalized Gradient Approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) 3

(a)

(b)

z M

dvac

y

x

Se

y

Δc x

c

Unit cell

a

(c) y x

ǥ

ǥ Left Electrode

Scattering region

a

Right Electrode

Figure 1: (a) Top and (b) side views of 1T-MSe2 (M=Hf,Pt) 2L thin film. (c) Two probe model, consisting of a central scattering region sandwiched between left and right electrodes, where the enlarged 1x4x1 orthogonal scattering region is chosen for the transport calculation along y-direction.

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exchange-correlation functional [29]. The collinear spin polarized and van der Waals (vdW) correction were considered at vdW-DF level with the optB86b-vdW[30, 31] for geometry optimizations. The hybrid fock exchange (HSE06) functional[32, 33] and the noncollinear spin orbital coupling (SOC) were applied for the band structure calculations. The structure was fully relaxed until the energy and the residual force per atom were less than 1×10−6 eV and 0.005 eV/˚ A, respectively. The energy cut-off for plane-wave basis is set to 500 eV for bulk (NL), and the Monkhorst-Pack k-point sampling in the Brillouin zone (BZ) is Γ centered with 12×12×9 (12×12×1), 12×12×9 (12×12×1), and 32×32×24 (32×32×1) meshes for geometry optimizations, self-consistent calculation, and projected density of states, respectively. The electron transport was calculated by the Nanodcal transport package [34, 35] implemented by a two-probe model with DFT and non-equilibrium Green’s function (NEGF) formalism [36]. As shown in Fig. 1(c), the enlarged 1×4×1 orthogonal scattering region is chosen for the transport calculation along the y direction. The double-ζ double-polarized basis sets of linear combination of atomic orbitals (LCAO) with GGA-PBE exchange-correlation functional and noncollinear SOC are applied. The k-point samplings are 32×20×20 and 30×20×1 for bulk and NL films, respectively. The transmission coefficient is expressed in the form of T = T r(ΓL GrC ΓR GaC ) ,

(1)

ΓL,R = t[ΣrL,R − ΣaL,R ] .

(2)

where

r(a)

Here GC is the retarded (advanced) Green’s function of central scattering region, t is the r(a) hopping matrix, and ΣL[R] is the retarded (advanced) self-energy of left [right] electrode. Due to the different size of scattering region for transport calculation along x, y, and z directions, we normalized the transmission coefficient to nanometer for better comparison. 3. Results and Discussions 3.1. Structural and Electronic Properties of 1T-HfSe2 For 1T-HfSe2 bulk, the optimized lattice constants and van der Waals (vdW) interlayer distance are a=3.727 ˚ A, c=6.177 ˚ A, and ∆c=3.013 ˚ A, which are in agreement with experimental results [19, 37]. As the number of HfSe2 layers (N) is reduced from its bulk counterpart to form a few-layered film (NL), there are nearly no changes in the lattice constants, ∆c, and the intra Hf-Se bond length. Moreover, we present in Figs. 2(a)-(c) the local density of states (LDOS), band structure, and projected density of states (PDOS) for 1T-HfSe2 bulk, 3L, and 1L cases, respectively. The valance band maximum (VBM) is always located at Γ point, which is mainly contributed by the Se-p orbital. The conduction band minimum (CBM) is shifted from L to M points with the decrease of film thickness, which are both dominated by the Hf-d orbital. Due to the ligand field of 1T (octahedral) symmetry, 5

HfSe2 - Bulk

L (CB)

Energy (eV)

(a)

Γ (VB)

Hf_eg Hf_t2g

ડ (VB)

‫( ۻ‬CB) ડ (VB)

Hf Se

z y

Energy (eV)

(c)

5 4 3 2 1 0 -1 -2 -3 -4 -5

5 4 3 2 1 0 -1 -2 -3 -4 -5

L(CB)

Γ(VB)

Se_px+py Se_pz

G

M K

M (CB)

Energy (eV)

(b)

5 4 3 2 1 0 -1 -2 -3 -4 -5

G A

L

H

A

0

1 2 PDOS (States/eV)

3

HfSe2 – 3L

Hf_eg Hf_t2g Γ(VB)

M(CB)

Se_px+py Se_pz

M

G

K

G

0

3 6 PDOS (States/eV)

9

HfSe2 – 1L

Hf_eg Hf_t2g M(CB) Γ(VB)

Se_px+py Se_pz

G

M

K

G

0

1 2 PDOS (States/eV)

3

Figure 2: Local density of states (LDOS), band structure, and projected density of states (PDOS) for 1T-HfSe2 (a)bulk, (b) 3L, and (c) 1L cases.

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two groups of unoccupied Hf-d orbital are formed. As shown in PDOS’s of Fig. 2, the t2g orbital, composed of dz2 , dxy , and dx2 −y2 , has lower energy and the eg orbital, made up of dxz and dyz , locates at higher energy. This leads to an indirect energy gap evolution from bulk to NL film as summarized in Fig. 3(a), where Eg =0.79 eV (Γ-L) for bulk and Eg =0.98 eV (Γ-M) for 1L. The downsizing of film thickness results in nearly no change in structural properties along with the slightly variation of indirect band gap. The underlying mechanism is described below. The electronic configuration of the transition metal Hf is 5d2 6s2 and that of the chalcogen Se is 4s2 4p4 , respectively. Due to the large electronegativity difference of 1.25 between Hf (1.3) and Se (2.55) [38], the relatively ionic Hf-Se bond not only forces the four valence electrons of Hf atom to transfer to the two Se atoms to fully fill their valence shell, which is favorable to form Se-Se vdW interlayer coupling, but also creates an empty d0 configuration of Hf atom as the conduction band shown in Fig. 2. In addition, we present in Fig. 3(b) the differential charge density, ρdif f = ρ2L − ρtop − ρbottom , with the isosurfaces of ±0.0002 e/Bohr3 (yellow/blue) for 1T-HfSe2 2L thin films, where ρ2L is the charge density of 2L case and ρtop(bottom) is the charge density of top (bottom) layer only. It is clear to see that the change of stacking layers along z-direction only weakly induces the charge redistribution around Se atom and hence causes slight shift of Se-pz and Hf-dz2 shown in Fig. 2 and the minor variation of energy gap from bulk to monolayer shown in Fig. 3(a). This leads to the robust 2D property of 1T-HfSe2 thin films and may be promising for potential applications in nanoelectronic and optoelectronic devices. 3.2. Structural and Electronic Properties of 1T-PtSe2 In sharp contrast to the 2D characteristics of 1T-HfSe2 , as presented in Fig. 3(c), 1TPtSe2 exhibits a semimetal-to-semiconductor transition when N≤3, along with the notable thickness dependence of both in-plane lattice constant, a, and vdW interlayer distance, ∆c. Moreover, we display in Fig. 3(d) the differential charge density with the isosurfaces of ±0.0007 e/Bohr3 (yellow/blue) for 1T-PtSe2 between 2L and 1L films. This reveals that vdW interlayer coupling significantly generates charge redistribution around Se atom and simultaneously influences intra-layer Pt-Se bonding deeply. Now an intriguing question arises: Why PtSe2 and HfSe2 share the same 1T (octahedral) layered structure but perform very distinct structural and electronic properties? This can be better elucidated by two crucial characteristics of Pt atom (Group 10). First, Pt has more 5d valance electrons so that the Pt-d orbitals are partially filled. Secondly, the relatively covalent Pt-Se intra-layer bond becomes easily influenced by the vdW interlayer coupling via the charge redistribution around Se atom, according to the small electronegativity difference of 0.35 between Pt (2.2) and Se (2.55) [38]. These render PtSe2 bulk to be semi-metallic shown in Fig. 4(a), where the CB at K-point, which is composed of Pt-d and Se-px , py , and the VM at Γ-point, which is dominated by Se-pz orbital are overlapped near Fermi energy. On the other hand, for the PtSe2 thin films (N≤3), the outmost Se atoms, which are free of the vdW interlayer coupling, become decisive and in turn efficiently reduce the vdW-induced charge redistribution around Se atom. When the number of layer decreases, as shown in Figs. 4(b) and (c), the separation between VBM (Se-pz ) and the CBM (Pt-d 7

(a)

(c)

HfSe2

PtSe2

1.00

1.2 2.52 3.78

2.48

0.90

0.85

0.8

1

2

3

2.46 3.74

2.44

0.6 3.70

2.42

a Dc

3.72

1

2

3

2.40 4

5 Bulk

Number of Layers (NL)

0.4

G-M for film G-L for bulk

0.80

a (Å)

Energy Gap (eV)

3.76

Dc (Å)

0.95

Energy Gap (eV)

2.50

1.0

0.2

4

5

0.0

Bulk

Number of Layers (NL)

1

2

3

4

5

Bulk

Number of Layers (NL)

(b)

(d)

οܿ ൌ ʹǤͷʹ%

οܿ ൌ ͵ǤͲͳ%

z

y

Figure 3: (a) Energy gap evolution for the indirect energy gap of (a) 1T-HfSe2 (Γ-L for bulk and Γ-M for NL thin films). (b) Differential charge density with the isosurfaces of ±0.0002 e/Bohr3 (yellow/blue) for 1T-HfSe2 between 2L and 1L films.(c) Energy gap evolution for the metal-semiconductor transition of 1TPtSe2 . The inset shows layer dependence of lattice constant, a, [left-hand coordinate] and of vdW interlayer distance, ∆c, [right-hand coordinate]. (d) Differential charge density with the isosurfaces of ±0.0007 e/Bohr3 (yellow/blue) for 1T-PtSe2 between 2L and 1L films.

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PtSe2 - Bulk

K (CB)

Energy (eV)

(a)

Γ (VB)

5 4 3 2 1 0 -1 -2 -3 -4 -5

Pt_eg

K(CB)

Energy (eV)

ડ‫( ۻ‬C)

ડ‫( ۻ‬V)

5 4 3 2 1 0 -1 -2 -3 -4 -5

M K

ડ‫( ۻ‬V)

Pt

Se

z y

Energy (eV)

ડ‫( ۻ‬C)

5 4 3 2 1 0 -1 -2 -3 -4 -5

L H

G A

A 0

1 2 PDOS (states/eV)

3

PtSe2 – 3L

Pt_eg Pt_t2g ΓM(VB) ΓM(CB)

Se_px+py Se_pz

G

(c)

Se_px+py Se_pz

G

(b)

Pt_t2g

Γ(VB)

M

G 0

K

1 2 PDOS (states/eV)

3

PtSe2 – 1L

Pt_eg Pt_t2g

ΓM(CB) ΓM(VB)

Se_px+py Se_pz

G

M

G 0

K

1 2 PDOS (states/eV)

3

Figure 4: Local density of states (LDOS), band structure, and projected density of states (PDOS) for 1T-PtSe2 (a)bulk, (b) 3L, and (c) 1L cases.

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and Se-px , py ) becomes larger and thus leads to the increase of indirect energy gap about 1.16 eV of monolayer (1L) case, which agrees with previous theoretical work [25]. Originated from the competition between intra-layer Pt-Se bond and vdW interlayer coupling simply via the charge redistribution around Se atom, such strong thickness dependent energy gap of 1T-PtSe2 not only attracts fundamental interests but also pave a promising path to novel nanoelectronic devices. 3.3. Transport Properties Finally, we investigate the transport properties for both TMDs. For 1T-HfSe2 bulk and monolayer, the transmission spectra in (x,y,z) and (x,y) directions and the DOS’s of Hf and Se atoms are shown in Figs. 5(a) and 7(a), respectively, which are in consistent with the separated Se-p dominated VB’s and Hf-d dominated CB’s presented in Figs. 2(a) and (c). Note that the LCAO approach and the absence of HSE06 correction in transport calculation simply causes the rigid shift of CB’s and the reduction of energy gap, but doesn’t affect the energy dispersion in both cases. Here the same transmission spectra along x and y directions originates from the octahedral symmetry of 1T layered structure. We further display in Figs. 5(b) and (c) the density of scattering stats (DOSS) at ±0.5eV for transport in y and z directions, respectively. Whether electron transport along y or z direction, the transmission channels are mostly near the Se atom for VB at -0.5eV and around the Hf-Se intra-layer bonding for CB at +0.5eV. This suggests that the valid transmission probabilities are restricted within a Hf-Se layer, which is beneficial to the electron transport along y (x) direction but significantly suppresses electron from neighboring HfSe2 layers. Such anisotropic transport properties cause the notable 2D characteristic of 1T-HfSe2 stated in Section 3.1. On the contrary, for 1T-PtSe2 bulk and monolayer shown in Figs. 6(a) and 7(b), the high transmission probability can be observed along all (x,y,z) and (x,y) directions, respectively. As we’ve discussed in Section 3.2, the mixture of Pt-d and Se-p orbitals near the Fermi energy (0eV) renders great transmission probabilities not only within a PtSe2 layer along y direction but also crossing neighboring layer along z direction. 4. Conclusion In conclusion, we provide three theoretical evidences to explain why 1T-HfSe2 and 1TPtSe2 share the same 1T (octahedral) layered structure but perform very distinct electronic and transport properties. First, the structural parameters, including the lattice constants, vdW interlayer distance, and Hf-Se (Pt-Se) intra-layer bond lengths, are nearly independent (greatly dependent) on the film thickness. Second, from bulk to monolayer, the indirect energy gap of 1T-HfSe2 can be well preserved due to the empty d0 configuration of Hf atom and fully filled Se valance shell, while a metal-to-semiconductor transition of 1T-PtSe2 results from the significant charge redistribution around Se atoms. Finally, our transport calculation for 1T-HfSe2 /1T-PtSe2 bulks and monolayers suggests the great electron transport within Hf-Se/Pt-Se layer but prevents/allows electron from neighboring layers. These theoretical findings provide insights into the prominent 2D characteristic of 1T-HfSe2 and the widely tunable electronic properties of 1T-PtSe2 . 10

(a)

HfSe2 - Bulk

Transmission Coefficient

Transmission - X Transmission - Y Transmission - Z

200

Hf - DOS Se - DOS

10

150 100 5

DOS ( states/eV )

250

15

50 0

0 -3

-2

-1

0

Energy (eV)

1

2

3

(c) E=-0.5eV E=+0.5eV

(b) y

E=-0.5eV

y

E=+0.5eV

x

x z y

Transport in z direction

Transport in y direction

Figure 5: For 1T-HfSe2 bulk, (a) transmission spectra along x, y, z directions are represented by black, red, and blue solid lines, respectively, and the density of states for Hf and Se are denoted by the magenta and blue shaded areas, respectively. The density of scattering stats (DOSS) at ±0.5eV for the transport in (b) y (isosurface of 0.03 e/Bohr3 ) and (c) z (isosurface of 0.02 e/Bohr3 ) directions.

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(a)

PtSe2 - Bulk 250 Transmission - X Transmission - Y Transmission - Z

200

Pt - DOS Se - DOS

10

150 100 5

DOS ( states/eV )

Transmission Coefficient

15

50 0

0 -3

-2

-1

0

Energy (eV)

1

2

3

Fermi energy (E=0eV)

(b)

y

Fermi energy (E=0eV)

x

Transport in y direction

Transport in z direction

Figure 6: For 1T-PtSe2 bulk, (a) transmission spectra along x, y, z directions are represented by black, red, and blue solid lines, respectively, and the density of states for Hf (Pt) and Se are denoted by the magenta and blue shaded areas, respectively. (b) The density of scattering stats (DOSS) at Fermi energy (0eV) for the transport in y (isosurface of 0.03 e/Bohr3 ) and z (isosurface of 0.02 e/Bohr3 ) directions.

12

HftSe2 - monolayer 15

250

Transmission - X Transmission - Y

200

Hf - DOS Se - DOS

10

150 100

5

DOS ( states/eV )

Transmission Coefficient

(a)

50 0

0 -3

-2

-1

0

1

2

3

Energy (eV)

PtSe2 - monolayer 15

250

Transmission - X Transmission - Y

200

Pt - DOS Se - DOS

10

150 100

5

DOS ( states/eV )

Transmission Coefficient

(b)

50 0

0 -3

-2

-1

0

1

2

3

Energy (eV) Figure 7: The transmission spectrum of (a) 1T-HfSe2 and (b) 1T-PtSe2 monolayers along x and y directions are represented by black and red solid lines, respectively. The density of states for Hf (Pt) and Se are denoted by the magenta and blue shaded areas, respectively.

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