Layer-dependent bandgap and electrical engineering of molybdenum disulfide

Journal Pre-proof Layer-dependent bandgap and electrical engineering of molybdenum disulfide Haixia Li, Aiming Ji, Canyan Zhu, Lei Cui, Ling-Feng Mao PII:

S0022-3697(18)32816-6

DOI:

https://doi.org/10.1016/j.jpcs.2020.109331

Reference:

PCS 109331

To appear in:

Journal of Physics and Chemistry of Solids

Received Date: 19 October 2018 Revised Date:

31 December 2019

Accepted Date: 2 January 2020

Please cite this article as: H. Li, A. Ji, C. Zhu, L. Cui, L.-F. Mao, Layer-dependent bandgap and electrical engineering of molybdenum disulfide, Journal of Physics and Chemistry of Solids (2020), doi: https:// doi.org/10.1016/j.jpcs.2020.109331. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

Author Statement Haixia Li: Methodology, Software, Writing- Reviewing and Editing. Aiming Ji: Data curation, Writing- Original draft preparation. Canyan Zhu: Investigation, Resources. Lei Cui: Validation. Ling--Feng Mao: Conceptualization, Methodology, Writing- Reviewing and Editing. Ling

Layer-dependent bandgap and electrical engineering of molybdenum disulfide Haixia Li1,2, Aiming Ji1,*, Canyan Zhu1, Lei Cui2, Ling-Feng Mao3,* 1

Institute of Intelligent Structure and System, Soochow University, Suzhou 215006, P.R. China

2

3

School of Information Engineering, Suqian College, Suqian 223800, P.R. China School of Computer & Communication Engineering, University of Science &

Technology Beijing, Beijing 100083, P.R. China

*

Corresponding authors. [email protected], [email protected]

Notes The authors declare no competing financial interest.

ABSTRACT Exploring the state of MoS2 with different layers is a matter of interest in band gap and electrical engineering. In this paper, metal-oxide-semiconductor field-effect transistors based on MoS2 are studied, with respect to the number of MoS2 layers in the channel. The residual stress changes from 0.4568 to 1.9234 GPa with number of MoS2 layers increasing from one to five. At the same time, the band gap of the MoS2 decreases by 45.4% from 1.727 to 0.943 eV. Our simulations show that when residual stress increases, the Schottky barrier height and the MoS2/H–SiO2 interface barrier height can significantly decrease and the drain-source and direct tunneling currents will inevitably increase. The results in this paper provide a theoretical basis for the fabrication of strained MoS2 devices..

Keywords: MoS2/H–SiO2, layer number, residual stress, drain-source current, direct tunneling current

1. Introduction Traditional semiconductors are based on silicon (Si). It is believed that this material is reaching its limits for aggressively scaled devices due to a series of small size effects [1,2]. The transition metal dichalcogenides (TMDs) [3–5] are considered as alternative materials to replace Si in the transistor channel. Molybdenum disulfide (MoS2) is one of the most stable layered materials of this class [6–9] due to high on– off current ratio and good electrical performance. Its electronic structure is sensitive to the number of layers and stacking orientation [10–14], and the application of external pressure or strain to modify its physical properties is a clean tool to tune

device performance [15]. Much research has been performed in the areas mentioned above [11,16–40]. Notable physical effects such as strain-induced direct-to-indirect band gap transition and semiconductor-to-metal transition have been predicted [18,20,28,29,34,36]. As the number of MoS2 layers is reduced, a significant increase of the luminescence quantum efficiency [11,37], device performances [38] and the outstanding mechanical properties [40] in metal-oxide-semiconductor field-effect transistors (FETs) based on MoS2 are observed. By applying uniaxial tensile strain (in-plane) experimentally, monolayer and bilayer MoS2 normally show red shifts [31–33]. Additionally, trilayer MoS2 shows a blue shift when an in-plane compressive biaxial strain is applied [34]. Both direct and indirect interband transitions of monolayer and multilayer MoS2 can be efficiently tuned using hydrostatic pressure [35,39]. Theoretical work [21] predicts a band gap reduction under uniaxial compressive strain across the c-axis of the crystal structure of MoS2. Thus, by varying the thickness and applying uniaxial strain, the photonic [39], mechanical [40] and electrical [34,41–45] properties can be effectively tuned. However, the quantitative relationship between MoS2 layers and stress/strain has been seldom studied, and neither has the influence of stress/strain on electrical characteristics. In this paper, the quantitative relationship between MoS2 layers and stress/strain is revealed, and their influences on electrical characteristics are studied.

2. Methods We chose H-passivated MoS2/SiO2 structure (denoted MoS2/H–SiO2) as our

study system since this is widely used for MoS2 FETs [45] (Fig. 1). The Mo–S bond length is 2.4 Å, the crystal lattice constant is 3.2 Å and the distance between the upper and lower sulfur atoms is 3.2 Å [7,46].

Fig. 1. The geometric structure of MoS2 FET.

The studied MoS2/H–SiO2 with one, two, three, four and five S–Mo–S sheets (denoted 1L, 2L, 3L, 4L and 5L, respectively) is constructed to reveal the relationship between MoS2 layers and stress/strain. To reduce the lattice mismatch, an interface model is created by placing a (3 × 3) MoS2 monolayer onto a (2 × 2) SiO2 (111) surface [47] (Fig. 2).

Fig. 2. Side view of the structural model of MoS2/H–SiO2 with four-layer MoS2.

The article uses a specific computer code, CASTEP (Cambridge Serial Total Energy Package) [48,49]. The Vanderbilt ultra-soft pseudo potential is used. The structures are optimized using the convergence criteria for self-consistent field energy at 5 × 10-7 eV/atom, cutoff energy for plane wave at Ecut = 320 eV with k-point grid size of 10 × 10 × 1. We use the same vacuum (15 Å) in calculation.

Results

3.

The band structures of MoS2 with different layers without substrate are plotted in Fig. 3(a–e), corresponding to 1L, 2L, 3L, 4L and 5L, respectively. 3

(b) 3

2

2

1

Energy(eV)

Energy(eV)

(a)

1L

band gap=1.727eV

0

1 0

-1

-1

-2 GA 3

HK

G

ML

H

(c)

(d)

-2 GA 3

HK

G

ML

H

2 Energy(eV)

Energy(eV)

2 1 3L

band gap=1.094eV

0 -1

(e)

2L

band gap=1.210eV

1 4L

band gap=0.984eV

0 -1

-2 GA 3

HK

G

ML

H

ML

H

-2 GA

HK

G

ML

H

Energy(eV)

2 1 5L

band gap=0.943eV

0 -1 -2 GA

HK

G

Fig. 3. Electronic band structures of different layers of MoS2 with one (a), two (b), three (c), four (d) and five layers (e). The valence band maximum is set to 0 eV.

The band gap shifts to lower energies with the increasing of layers (Fig. 3) and can be seen more clearly in Fig. 4. The conduction band minimum (CBM) and valence band maximum (VBM) with different MoS2 layers clearly show that the CBM shifts to lower energies with increasing layers (Fig. 4a). The bandgap decreases with the increasing number of

layers (Fig. 4b). Our results are consistent with those of previous reports [10,28,50– 53]. Previous results [38,53] are compared with our results in Fig. 4b. The direct band gap for 1L computed by us (1.727 eV) is in reasonable agreement with that of Han et al. [51] of 1.7 eV for 1 L using the GGA of Perdew et al. [49] within the FP-LAPW scheme.

(b)1.8

(a)

Band gap(eV)

Energry(eV)

2 1L 2L 3L 4L 5L

1 0 -1

1.6 1.4 1.2 1.0 0.8

GA

HK

G

ML

H

Our results Ref.[54] Ref.[38]

1

2

3 Layers

4

5

Fig. 4. (a) The CBM and VBM with different layers of MoS2. (b) Band gap as a function of layers. Ref. [38]: calculations with Quantum Espresso software package. Ref. [53]: first principles calculations with the PWscf package.

The plotted band structures show that the curvature at the edges of both the VB and CB at the high symmetry points of the Brillouin zone is markedly different (Fig. 4a). We use its curvature to calculate the effective mass for holes and electrons (Fig. 5). The effective masses for holes and electrons are calculated at the bottom of CB and the top of VB, respectively. The electrons and holes show the lowest effective mass for 1L. Our results are comparable to recent theoretical work [38], shown in hollow squares and circles in Fig. 5, and are compared in Table 1.

0.9

1.2 Electron Eff. mass Ref.[38]

1.0

0.7

0.8

0.6

0.6

mh*/m0

me*/m0

0.8

Hole Eff. mass Ref.[38]

0.5 0.4 0.4

1

2

3 4 5 Layers Fig. 5. The electrons (square, left axis) and holes (circle, right axis) effective mass of MoS2 with different layers. The results of ref. [38] are shown in the form of hollow squares and circles. Table 1. Comparison of our results and previous results as a function of the number of layers. The calculated band gap, hole and electron effective mass m* in unit of electron mass m0 are presented. Band gap (eV)

Effective mass hole *

*

(mh /m0) Number of MoS2 layers

Our

Ref. [38]

results

Ref.

Our

[53]

results

electron (me /m0) Ref. [38]

Our

1.727

1.80

1.81

0.54

0.56

0.45

2

1.210

1.26

1.23

0.68

0.95

0.49

3

1.094

1.17

0.97

0.72

0.73

0.60

4

0.984

0.99

0.88

0.73

0.66

0.69

5

0.943

0.95

0.74

0.59

0.79

2.0

Ref. [38]

results

1

0.45 0.73 0.58 0.57 0.55

1.8

(b)

(a)

1.6 Band gap(eV)

1.6 Pressure(GPa)

Effective mass

1.2 0.8

1.4 1.2 1.0

0.4 1

2

3 Layers

4

5

0.8

0.6

0.9 1.2 1.5 Pressure(GPa)

1.8

Fig. 6. The relationship between layers and stress/strain: (a) residual stress as a function of MoS2 layers and (b) bandgap as a function of tensile stress.

Changes in the number of layers will cause changes in the residual stress inside the lattice. The Pulay scheme of density mixing is applied for the evaluation of energy and stress [55,56]. Through the calculation of stress in the CASTEP module, we

obtain the residual stress in different MoS2 layers, which clearly shows that the residual stress increases from 0.4568 to 1.9234 GPa with the number of layers increasing from one to five (Fig. 6a). The residual stress follows the direction of layer growth, which is perpendicular to MoS2 layers. Combining Fig. 4b and Fig. 6a, we obtain the quantitative relationship between MoS2 layers and residual stress (Fig. 6b). The band gap clearly decreases from 1.727 to 0.943 eV with pressure increasing from 0.4568 to 1.9234 GPa. The same trend was also observed in previous experiments [27,34,54]. We conclude that the change of residual stress caused by increasing the layers of MoS2 has the same effect on the tuning of the band gap as using pressure engineering.

(b)

electron eff. mass hole eff. mass

(a)

16

0.44

10

0.5

10

-3

m*/m0

14

0.6

ni(cm )

10

0.7

12

φΒ(eV)

0.8

0.43

ni

0.4

10

0.4

0.8

1.2

1.6

2.0

10

0.4

0.8

Pressure(GPa)

1.2 1.6 Pressure(GPa)

2.0

Fig. 7. (a) Effective mass and intrinsic concentrations as a function of tensile stress. (b) Schottky barrier height (ϕB) vs tensile stress.

From the effective mass (Fig. 5) and the stress–strain (Fig. 6a), we obtain the relationship between effective mass and tensile stress (Fig. 7a, left axis). We also calculate the intrinsic carrier concentrations (ni) (Fig. 7a, right axis). We investigate Schottky contacts to MoS2 with low work-function metal Cu (ϕm = 4.7 eV) electrodes. The Schottky barrier heights (ϕB) are calculated as follows [57]:

φB = φm +

Eg 2

− φ f , φ f = kT ln

ND ni

(1)

where ND is the substrate dopant concentration. The extracted ϕB for the different layers shows values of 0.444, 0.438, 0.433, 0.431 and 0.427 eV for different tensile stress (Fig. 7b), with a reduction (3.8%) of ϕB from 0.444 to 0.427 eV. Next we turn our attention to the impact of ϕB on the device characteristics. We use the 2D thermionic emission equation to describe the electrical transport behavior of Schottky-contacted MoS2 devices according to Kawakami [58]:  q I DS = WA2*DT 3 2 exp  −  kT

qVDS     φB − n    

(2)

where W is the contact width of the MoS2 electrode junction and W = 1 µm, A2*D is the two-dimensional equivalent Richardson constant and A2*D = q ( 8π k 3 me* ) / h 2 , T is the 12

absolute temperature, q is the magnitude of the electron charge, k is the Boltzmann constant and n is the ideality factor. The output characteristics (drain-source current IDS vs drain-source voltage VDS) are shown in Fig. 8a. An increase in the current with increased tensile stress (corresponding to the increasing number of MoS2 layers) due to the fact that the metal contact fails to connect to all the layers [38,58]. Similar phenomena were also observed experimentally by Kang [59] and theoretically by Quereda [60]. There is a small drop in current for four-layer MoS2 FETs, consistent with a previous result [38]. The higher is VDS, the more obvious is the tensile stress effect (Fig. 8b). The relative change for different VDS also increases with increasing tensile stress. The threshold voltage changes from 1.6 to 0.8 V with the increasing layer number.

600

200

500

150

46

0.06

0 0.0

0.1

VDS=0.10V VDS=0.15V

44

45

0.04

50

0.46 GPa 1.07 GPa 1.34 GPa 1.75 GPa 1.92 GPa

(I3-I1)/I1

100

300

100

Relative change

IDS(µA)

IDS(µA)

400

200

(b)

IDS(µΑ)

(a)

0.40

0.41

0.42

VDS(V)

0.02

VDS=0.20V

0.2 0.3 VDS(V)

0.00 0.4

0.4

0.8

1.2 1.6 Pressure(GPa)

43 2.0

Fig. 8. Device characteristics of MoS2 FETs when VGS = 0 V. (a) Typical output (IDS–VDS) of the MoS2 FETs with different tensile stress. Inset: zoom-in plot of IDS–VDS characteristics. (b) Output current (left axis) and relative change (right axis, I1 and I3 represent the current at VDS = 0.1 and 0.2 V, respectively) as a function of tensile stress at different VDS.

Further, the valence band profiles are calculated using the average potential method [61]. The electrostatic potential for the MoS2/SiO2 supercell is averaged in the x–y plane; then, a planar microscopic potential is calculated in the z direction:

Potential(eV)

(a)24

1 z +t 2 V ( z ' )dz ' ∫ z − t 2 t 0.46 GPa 1.07 GPa 1.34 GPa 1.75 GPa 1.92 GPa

16 8 0

10

20

Å

-8 0

30 40 Z( )

50

60

(3)

5.2

(b) Barrier Height(eV)

V ( z) =

4.8 4.4 4.0 0.4

0.8

1.2 1.6 Pressure(GPa)

2.0

Fig. 9. (a) Planar microscopic potential along the z direction. (b) Barrier heights with different tensile stress.

At the MoS2/H–SiO2 interface, the band changes continuously from MoS2 to SiO2 (Fig. 9a). The barrier heights calculated from Fig. 9a clearly show a downward trend (Fig. 9b). It is clear that the tunneling current will increase with the increasing of tensile stress due to the reduction of barrier height.

Ando and Itoh [62] presented a numerical calculation method for gate leakage current: J DT =

B

  V 1 2  1 − 1 − ox     φ   

2

Eox

2

 C exp  −  Eox 

  V 3 2   × 1 − 1 − ox      φ     

(4)

where Vox is the voltage added to the barrier layer, the electric field in the oxide is Eox = Vox/Tox, Tox is oxide thickness and B and C are given respectively by

B=

C=

q3me* ∗ 16π 2 hmox φ ∗ 3 ( 2mox )

1

(5)

2

×φ

3

2 (6) 4 qh where ϕ is the potential barrier height (eV) at the metal–oxide interface neglecting the

* effect of image potential, h is the reduced Plank’s constant, me is the free electron ∗ mass and mox is the effective mass of electrons in the conduction band in oxide and ∗ mox = 0.5m .

The direct tunneling current will increase with increasing tensile stress; however, as pressure increases to 1.34 GPa and above, the relative change becomes weak (Fig. 10a). The increasing trend and the relative change of direct tunneling current under the influence of residual stress is shown in Fig. 10b (right axis). Because the metal contact fails to connect to all layers, the barrier height will increase as the number of layers of MoS2 increases to five (Fig. 9). So, for pressure greater than 1.6 GPa, the direct tunneling current will decrease. Similar phenomena were also observed experimentally by Kang [59] and theoretically by Lu [38]. The relative change is reduced; in other words, with reduction of residual stress (corresponding to

decreases in the number of MoS2 layers), the influence of stress will be greater. 6

(J4-J1)/J1

2

JDT(Α/cm )

10

2

10

0.46 GPa 1.07 GPa 1.34 GPa 1.75 GPa 1.92 GPa

0

10

-2

0

1

2 Vox(V)

3

4

VOX=0.5V VOX=1.0V

25

4

10

TOX=1nm

VOX=1.5V VOX=2.0V

20

4000 3000 2000

15 Relative change

10 0.4

5000 2

(b)30

TOX=1nm

0.8

1.2 1.6 Pressure(GPa)

JDT(A/cm )

(a)

10

1000 0 2.0

Fig. 10. (a) Direct tunneling current as a function of the applied voltage across gate oxide for different tensile stress. (b) Direct tunneling current (right axis) and relative change (left axis, J1 and J4 represent the current at Vox = 0.5 and 2.0 V, respectively) vs tensile stress at different Vox.

4. Conclusion A study of the bandgap and electrical engineering in 1L, 2L, 3L, 4L and 5L MoS2 on SiO2 substrate has been presented. Our calculations well explain the effect of the number of MoS2 layers and pressure changes on the electronic structure of MoS2/H–SiO2. The residual stress increases as the number of MoS2 layers increases. At the same time the drain-source current and direct tunneling current will increase with increasing tensile stress. Its effect on direct tunneling current becomes greater as the number of layers decreases. Our results are consistent with existing results, indicating that the quantitative relationship between stress and the number of layers disclosed in this paper is correct. We demonstrate that its characteristics can be controlled by changing the number of MoS2 layers. The conclusions in this paper are also applicable to other 2D TMDs.

Acknowledgements The authors acknowledge financial support from the National Natural Science Foundation of China under Grant No. 61774014, the Postgraduate Research &

Practice Innovation Program of Jiangsu Province No. KYZZ15_0331 and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China No. 19KJB510060.

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Highlights: A novel approach to the number of layers and stress-strain in MoS2/SiO2 Relationship between layer numbers and stress/strain is revealed The effect of layers on tunneling current is explained Tunability of characteristics of MoS2 devices by changing the number of MoS2 layers