Thickness-Dependent Phase Stability and Electronic Properties of

Subscriber access provided by OPEN UNIV OF HONG KONG

C: Physical Processes in Nanomaterials and Nanostructures

Thickness-Dependent Phase Stability and Electronic Properties of GaN Nanosheets and MoS/GaN van der Waals Heterostructures 2

Jun Wang, Haibo Shu, Pei Liang, Ning Wang, Dan Cao, and Xiaoshuang Chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10915 • Publication Date (Web): 23 Jan 2019 Downloaded from http://pubs.acs.org on January 25, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 16 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

The Journal of Physical Chemistry

Thickness-Dependent Phase Stability and Electronic Properties of GaN Nanosheets and MoS2/GaN van der Waals Heterostructures Jun Wang,† Haibo Shu,†,* Pei Liang,† Ning Wang, ‡ Dan Cao, ‡ and Xiaoshuang Chen§ †

College of Optical and Electronic Technology and ‡College of Science, China Jiliang University, 310018 Hangzhou, China § National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Science, 200083 Shanghai, China  Corresponding author. Haibo Shu, Phone: +86-0571-86875622, E-mail: [email protected] ABSTRACT: The formation of GaN-based heterostructures is essential for optoelectronic applications, but it is greatly limited by the traditional heteroepitaxial method due to the impact of lattice mismatch. Integrating two-dimensional layered semiconductors (e.g., MoS2) on GaN surface into van der Waals (vdW) heterostructures can effectively overcome the constraint of lattice mismatch but also create the possibility to induce novel electronic and optical properties due to size and interface effects. Here we report the thickness effect on the structural, electronic, and optical properties of GaN nanosheets and MoS2/GaN van der Waals heterostructures based on the hybrid density-functional theory calculations. Our results demonstrate the thickness-driven structural transitions of GaN nanosheets from the wurtzite, haeckelite, to graphitic phase, which is accompanied by a direct-to-indirect band gap transition. The integration of a MoS2 monolayer on GaN nanosheets into MoS2/GaN vdW heterostructures exhibits the strong thickness dependence of band gap, band alignment, and optical absorption coefficient. Overall, two-dimensional MoS2/GaN vdW heterostructures possess moderate band gaps (1.35~1.7 eV), type-II band alignment, and large visible-light absorption coefficient, which makes them potential candidate for photovoltaic and photocatalytic applications.

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 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

Page 2 of 16

1. INTRODUCTION Group-III nitride semiconductors have drawn considerable attention in the past few decades because of their outstanding properties that lead to a variety of applications in electronics and optoelectronics1-3. Among these semiconductor materials, gallium nitride (GaN) is the most studied target since it possesses many advantages of properties including of high room-temperature electron mobility (~103 cm2V-1s-1), wide band gap (~3.4 eV), and large short-wavelength absorption coefficient, which makes it an important semiconductor for device applications in the light emitting diodes, field effect transistors, solar cells, laser, photodetectors, and high-speed optoelectronic devices4-6. With the development trend of device minimization and integration, low-dimensional GaN nanomaterials such as nanowires, nanotubes, and nanosheets have attracted more and more interests due to the advantages of their structures and potential properties with respect to their bulk counterpart7-10. In particular, twodimensional (2D) GaN materials are expected to be realized for optoelectronic applications since the success of atomically thin graphene and transition metal dichalcogenides (TMDs)11-13. Hence, great efforts are devoted to the synthesis of 2D GaN materials, and they have been synthesized experimentally with the thickness from dozens of nanometers to several atomic layers10,14-16. However, the structure of 2D GaN is still under debate. It is widely acceptable that the ultrathin GaN nanosheets with the wurtzite (WZ) phase are unstable and tend to transform into a graphitic (GP) phase17,18. The recent theoretical studies have found that few-layer GaN nanosheets can reconstruct into a haeckelite (HK) phase with alternating octagonal and square rings19,20. Therefore, the understanding of size effect on fundamental structural and electronic properties of GaN nanosheets is essential for their device applications. In addition to the consideration of intrinsic electronic structures, the realization of high-quality GaN-based heterostructures is also particular importance for the practical optoelectronic applications. This stems from that heterostructures can not only take advantage of properties from the constituent materials but also create the carrier confinement21. However, these are a large lattice mismatch between GaN and the commonly used substrates and semiconductor materials (e.g., Si, SiC, and sapphire)

22-24

,

which easily produce a number of interfacial defects that degrade the device performance25. Hence, it is strongly desired to develop the new-type GaN-based heterostructures to avoid the impact of interfacial defects. Two-dimensional TMD materials, such as MoS2, WS2, and MoSe2,26-28 emerge as a new class of semiconductor systems which possess strong in-plane chemical bonding and weak interlayer interaction via van der Waals (vdW) force. The integration of these 2D semiconductor materials on GaN surfaces can create vdW heterostructures without the constraints of lattice matching29. Moreover, these GaN-based vdW heterostructures can utilize the advantages of both 2D TMDs and GaN, which enables them with tunable electronic and optoelectronic properties30. Recently, some representative GaN-based 2


Page 3 of 16 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


vdW heterostructures, such as MoS2/GaN,31,32 MoSe2/GaN,33 and WS2/GaN,34 have been successfully demonstrated in experiment. From these previous studies, GaN-based heterostructures consisted of GaN and atomically thin TMDs exhibit excellent electronic and optoelectronic properties and great potential in optoelectronics and photovoltaics. Despite of these preliminary achievements, the details on the fundamental electronic and optical properties of these vdW heterostructures remain unclear. For example, the epitaxial growth of GaN thin layer on monolayer MoS 2 leads to the formation of GaN/MoS2 heterojuction with a type-II band alignment31. However, the synthesis of atomically thin TMDs including MoS2, MoSe2, and WS2 on GaN substrates makes the produced 2D/3D TMD/GaN vdW heterojunctions with the type-I band-alignment32-34. Meanwhile, the size and interfacial effects play the important role in determining the properties of heterojunctions35. Considering the potential thickness-dependent structural stability of GaN, the integration of atomically thin TMDs on GaN nanosheets may bring novel electronic and optical properties. To clarify above issues, a deep understanding of thickness effect on the structural, electronic, and optical properties of TMD/GaN vdW heterostructures is strongly desired. In this work, we investigate the thickness effect on the structural, electronic and optical properties of two-dimensional GaN nanosheets and MoS2/GaN vdW heterostructures based on the hybrid density functional theory (DFT) calculations. Our results demonstrate that the 2D GaN nanosheets undergo a two-step phase transition from GP, HK, to WZ phase with increasing sheet thickness, resulting in an indirect-to-direct band gap transition. The integration of a monolayer MoS2 on GaN nanosheets and bulk leads to the formation of MoS2/GaN vdW heterostructures which exhibit the strong thicknessdependent electronic and optical properties. Furthermore, the 2D MoS2/GaN vdW heterostructures with a type-II band alignment exhibit superior visible-light absorption efficiency as compared to the independent GaN and MoS2 nanosheets, which renders them as promising candidates for photovoltaic and photocatalytic applications.

2. COMPUTATIONAL DETAILS All DFT calculations were performed by using projector augmented wave (PAW) pseudopotential36 as implemented in the Vienna ab initio Simulation Package (VASP)37,38. The generalized-gradient approximation of Perdew-Burke-Ernzerh (GGA-PBE)39 was used to describe the electronic exchangecorrelation energy. The interfacial interaction of MoS2/GaN vdW heterostructures was treated by using the PBE functional with the vdW correction (DFT-D2)40. A kinetic cutoff energy of 400 eV was used for the plane-wave expansion set. The k-point sampling in the Brillouin zone was implemented by the Monkhorst-Pack scheme with the grid of 8×8×1 for these 2D systems. In order to avoid the spurious interaction between neighboring slabs, a vacuum layer of ~20 Å was included in the supercell models. 3



Page 4 of 16

For the geometry optimization of all considered structures, the convergence criteria of energy and forces acting on each atom were 10-3 eV and 10-2 eV/Å, respectively. To investigate the kinetic structural stability of GaN nanosheets, their phonon band structures were calculated using the density functional perturbation theory (DFPT) as implemented in the Phonopy program41,42. Owing to the band-gap underestimation of semiconductors with the GGA-PBE functional, the Heyd-Scuseria-Ernzerhof hybrid functional (HSE06)43 was used to compute the electronic and optical properties of GaN and MoS2/GaN heterostructures. In the HSE06 calculations, the atomic positions of all these 2D structures were further relaxed on the basis of the GGA-optimized structural parameters and the k-point mesh was set to 4×4×1.

3. RESULTS AND DISCUSSION We first address the structural stability and electronic properties of GaN nanosheets with different layer thicknesses, which is crucial for the understanding of electronic and optical properties of MoS 2/GaN heterostructures. For the pristine GaN nanosheets, there are three potential phase structures: WZ, GP, and HK phases, as shown in Figure 1a-c. GaN(0001) nanosheets in WZ phase has a hexagonal buckled configuration with the AB stacking sequence along the out-of-plane direction (Figure 1a). Owing to the existence of intrinsic polar field induced by alternating positive and negative charges layers, ultrathin GaN nanosheets in WZ phase are unstable. There are three ways to stabilize GaN nanosheets: (i) the depolarization of GaN nanosheets into the planar GP phase (Figure 1b), (ii) the reconstruction of GaN nanosheets into HK phase (Figure 1c), and (iii) the surface passivation. Considering that the surface passivation requires the participant of extra atoms/molecules, thus it has not been considered in the present study. To understand the potential structural transition, the stability of GaN nanosheets in three crystal phases (i.e., WZ, GP, and HK) is evaluated by the energy comparison. Figure 1d presents the energies of Ga-N pair (EGa-N) in three crystal phases as a function of layer number N. Here the data points are directly from DFT calculations, and the fitting curves are obtained by the following equations, EGa-N(WZ) = (NEB(WZ)+AES(WZ))/N

(1)

EGa-N(HK) = (4NEB(HK)+AES(HK))/4N

(2)

EGa-N(GP) = (NEM(GP)+(N-1)EVDW(GP))/N

(3)

where EB(WZ), EB(HK), and EM(GP) are the energy of Ga-N pair in WZ bulk, HK bulk, and GP monolayer, respectively. ES(WZ) and ES(HK) are the surface energy of WZ-phase and HK-phase GaN nanosheets, respectively, EVDW(GP) is interlayer vdW energy of GaN nanosheets in GP phase, and A is the surface area of nanosheets. The lattice and energy parameters of GaN nanosheets and bulks are listed in Table S1 of Supporting Information (SI). The layer number N is equal to the number of Ga-N pair in WZ- and GP-phase nanosheets, and a N-layer nanosheet in HK phase contains 4N Ga-N pairs. It is seen from Figure 1d that the structure of GaN nanosheets undergoes a two-step phase transition with 4


Page 5 of 16

the change of nanosheet thickness. The GP phase is the most stable structure for monolayer and bilayer GaN nanosheets, and the HK phase becomes the most one when the layer number N increases to 3. When the layer number is beyond 19, the WZ-phase nanosheets are the most energetically favorable. The phase stability of GaN nanosheets originates from the competition between surface energies and bulk energies. The WZ-phase GaN nanosheets have the lowest bulk energies but the largest surface energies, while the GP-phase nanosheets are just reversed. Therefore, the reduction of sheet thickness can lead to the phase transition of GaN nanosheets from WZ, HK, to GP phase.

(a)

(b)

(d)

(c)

-11.0

WZ GP HK

-11.2

EGa-N (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


-11.4 -11.6 -11.8 -12.0 -12.2

GP 0

HK 5

10

WZ 15

20

25

Layer number N

Figure 1 Side view of atomic structure of GaN nanosheet with (a) wurtzite structure (WZ), (b) graphitic structure (GP), and (c) haeckelite structure (HK). The orange and blue balls denote Ga and N atoms, respectively. (d) The energies of Ga-N pair (EGa-N) in GaN nanosheets with three phases (i.e., WZ, GP, and HK) as a function of layer number N. The DFT calculated data of GaN nanosheets with WZ, GP, and HK phases are indicated by triangles, rectangles, and balls, respectively. The solid lines are the fitting curves obtained by eq. 1-3.

To further examine the phase stability of GaN nanosheets, the phonon dispersion curves of bilayer and trilayer nanosheets in both GP and HK phases have been investigated. We find that there are no any imaginary frequency modes in the phonon spectrum of GP- and HK-phase bilayer GaN nanosheets (Figure S1a and b), suggesting that both of them are kinetically stable. For the trilayer GaN nanosheet, only the HK phase is kinetically stable and the phonon spectrum of GP phase include a large number of imaginary frequency modes (Figure S1c and d). These imaginary modes are related to the change of GaN bond lengths and elastic instability of GaN sheets along the out-of-plane direction. The result supports the phase transition of ultrathin GaN nanosheets from the GP to HK phase with increasing layer number. Figure 2 shows electronic band structures of GaN nanosheets with different thicknesses calculated by the HSE06 method. For a given nanosheet thickness, here only the most stable phase structures were considered. We find that GaN nanosheet in its monolayer and bilayer structures is an indirect band-gap 5



semiconductor with the valence band maximum (VBM) at K point and conduction band minimum (CBM) at Γ point (Figure 2a and b), which is in good agreement with previous theoretical studies18,19. When the nanosheet thickness is beyond 3 atomic layers, GaN nanosheets become the direct band-gap semiconductors with both the VBM and CBM at Γ point (Figure 2c-f). Therefore, the thickness-induced phase transition also causes an indirect-to-direct band-gap transition in ultrathin GaN nanosheets (Figure 2g). As shown in Figure 2h, the band gap (Eg) of GaN nanosheets gradually decreases with increasing nanosheet thickness. However, the band-gap change is very small (< 0.1 eV) when the nanosheet thickness is larger than 4 atomic layers. Moreover, Eg of HK-phase GaN nanosheets is still lower than that of wurtzite GaN bulk film (3.07 eV). It needs to be mentioned that the GaN bulk film in WZ phase is modelled by using the slab geometry with six GaN bilayers, and its surfaces are terminated hydrogen atoms with fractional charges to eliminate the impact of surface dangling bonds. (a) 4

(b) 4

(c) 4

2

2

2

(g)

0 -2

Energy (eV)

Energy (eV)

Energy (eV)

GP 0 -2

Indirect band gap 0 -2

HK -4

-4

M K

(d) 4

(e)

Γ

M K

-4

Γ

4

(f)

Γ

M K

4

Γ

Direct band gap (h)

GP HK

-2 -4

Γ

M K

Γ

0 -2 -4

Γ

M K

Γ

2 0

Eg (eV)

0

2

Energy (eV)

Energy (eV)

Energy (eV)

3.2 2

Increasing layer thickness

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

Page 6 of 16

3.0

-2

2.8

-4

2.6 1

2 3 4 5 6 Layer number N

Figure 2 Band structures of GaN nanosheet in (a) monolayer, (b) bilayer, (c) trilayer, (d) tetralayer, (e) six layer, and (f) bulk calculated by the HSE06 functional. The insets in (c)-(e) indicate the calculated partial charge densities of surface states located at the top valence bands. The dash lines denote the position of Fermi level. (g) Schematic illustration for demonstrating the phase transition induced an indirect-to-direct band gap transition in ultrathin GaN nanosheets. (h) Band gap (Eg) of GaN nanosheets as a function of layer number N. The position of dash line corresponds to the band gap of wurtzite GaN bulk film.

The above results originates from that the band gap of GaN nanosheets is determined by two competition mechanisms: one is the quantum size effect that leads to the increase of Eg with the reduction of nanosheet thickness,44 and the other one is the effect of surface states that causes the Eg reduction with increasing surface states. For the layer number N ≤ 3, the band gap of GaN nanosheets is mainly affected by the quantum size effect, resulting in the reduction of band gap with the increase of 6


Page 7 of 16

nanosheet thickness. For the layer number N lies between 3 and 6, the calculated partial charge-densities indicate that top valence bands of GaN nanosheets are dominated by N-2p states at two surfaces of nanosheets (see the insets of Figure 2c-e). Moreover, the position of surface states almost does not change with the increase of nanosheet thickness, which is responsible for relatively smaller Eg of HKphase GaN nanosheets (2.7~2.8 eV) as compared to the wurtzite GaN bulk. For the optoelectronic and photovoltaic applications, the realization of carrier confinement in GaNbased devices is of particular importance. The formation of MoS2/GaN heterostructures is a feasible way to create the spatial confinement of carriers without the impact of lattice mismatch, which can be realized by integrating of a monolayer MoS2 on GaN nanosheets or bulk films. To evaluate the carrier confinement of MoS2/GaN heterostructures, the absolute band-edge positions of their constituent materials (MoS2 and GaN) are an important parameter. Figure 3 plots the band-edge energies of MoS2 and GaN nanosheets with respect to the vacuum level. It can be seen that both the CBM and VBM positions of GaN indicate a downshift trend with the thickness change from the monolayer (1L), few layers (2L~6L), to bulk (b-GaN). Moreover, the CBM and VBM positions of these GaN materials are different from that of 1L-MoS2, which creates the carrier confinement in MoS2/GaN heterostructures. Based on the calculated band-edge positions, there is a type-I band alignment for integrating 1L-MoS2 on 3D GaN bulk films and type-II band alignment for 2D MoS2/GaN heterostructures, suggesting the thickness-dependent band alignment of MoS2/GaN heterostructures. In addition, we find that the CBM positions of all considered MoS2 and GaN structures are higher than the water redox potential (-4.44 eV) and their VBM positions are lower than the water oxidation potential (-5.67 eV), implying a large potential for the photocatalytic water splitting.

-2 -2.84 -3.13

-3

-3.45

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


-4

-3.55

-3.56

-3.64

-4.24

+

H /H2

-5 H2O/O2

-6

-6.04

-6.08

-6.38

-6.24

-6.26

-6.27 -6.71

-7

MoS2

GaN

-8 1L

2L

3L

4L

6L

bulk

Figure 3 Band-edge positions of MoS2 monolayer and GaN nanosheets with respect to the vacuum level from the HSE06 method. Here GaN include its monolayer (1L), bilayer (2L), trilayer (3L), tetralayer (4L), six-layer (6L) and bulk structures. The dash lines indicate the standard water redox and oxidation potentials.

7


Energy (eV)

2 0 -2 -4

(d)

(b)



M K

2 0 -2 -4



M K



4 2

0 -2



(e)

(c)

2

-4



4

4

M K

4

(f)

2 0 -2 -4



M

K

0 -2 -4



Energy (eV)

4

Energy (eV)

Energy (eV)

(a)

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

Page 8 of 16

Energy (eV)






M

K





M

K



4 2 0 -2 -4

Figure 4 Projected band structures of MoS2/GaN vdW heterostructures with GaN in its (a) monolayer, (b) bilayer, (c) trilayer, (d) tetralayer, (e) six layer, and (f) bulk structures. Blue and red lines represent the band contribution from GaN and MoS2, respectively. The horizontal dash lines denote the position of Fermi level.

In order to further verify the band alignment of MoS2/GaN vdW heterostructures, their electronic structures were calculated by using the HSE06 functional. Figure 4 presents projected band structures of six MoS2/GaN heterostructures. The heterointerface structures are obtained by the energy comparison among various possible stacking configurations (Figure S2). It needs to be emphasized that integrating MoS2 on GaN bilayer causes a spontaneous phase transition of GaN nanosheet from GP phase to HK phase due to the compression strain induced by the interfacial coupling. The comparison of total energies shows that the HK-phase GaN bilayer is more stable than its GP phase under the compressionstrain condition (see Figure S3). It can be found that all heterostructures present relatively smaller band gaps (1.35~1.70 eV) than MoS2 (2.14 eV) and GaN nanosheets (2.72~ 3.20 eV), which contributes to the enhancement of visible-light absorption. For the 2D MoS2/GaN heterostructures (Figure 4a-e), their top valence bands and bottom conduction bands are contributed by MoS2 and GaN, respectively, indicating a type-II band alignment. More specifically, their CBM states originate from Mo-dZ2 orbitals and VBM states are mainly from N-2p orbitals based on the partial charge-density isosurface distributions (Figure 5a-c). Hence, the type-II band alignment of 2D MoS2/GaN vdW heterostructures contributes to the separation of photogenerated electrons and holes, which is crucial for the application of solar cells and photocatalysts. For the 2D/3D MoS2/GaN heterostructure, both CBM and VBM states are contributed by Mo-dZ2 orbital of MoS2 layer (see Figure 4f and Figure 5d), resulting in a type-I band alignment. Therefore, the thickness change of GaN layer can cause the band-alignment transition of MoS2/GaN heterostructures. The result can be applied to explain the experimental controversy on the 8 ACS Paragon Plus Environment

Page 9 of 16 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


band alignment of MoS2/GaN heterostructures where the epitaxial thin-layer GaN on MoS2 monolayer indicates a type-II band alignment31 and the growth of GaN monolayer on GaN substrate has a type-I band alignment32. The optical absorption of MoS2/GaN vdW heterostructures are studied by computing the complex dielectric function ε(ω) = ε1(ω) +ε2(ω), where the imaginary part ε2(ω) is related to the absorption at a given frequency ω and the real part ε1(ω) is obtained from ε2(ω) by Kramers-Kronig relation. The absorption spectrum can be calculated by the following formula,

 ( ) 

1 2 2 2 1   2  1 2 ( ) ch 2

(4)

where c represents the speed of light in vacuum and ω is in energy unit. Figure 6 presents the optical absorption spectrum of MoS2/GaN heterostructures with different GaN-layer thicknesses as a function of photon energy. For the comparison, the absorption spectrum of monolayer MoS2 and GaN bulk films has been also calculated. The absorption spectrum α(ω) of all structures exhibit strong anisotropy along two polarization directions. Overall,shows an obvious blue shift as compared to(see Figure 6a,b), which makes these materials with the relatively weak visible-light absorption along the out-of-plane direction. Therefore, MoS2/GaN vdW heterostructures paralleled to the light source can obtain higher absorption efficiency for using them as the optical absorber of solar cells, photodetectors, and photocatalysts. (a)

(c)

(d)

CBM

CBM

VBM

(b)

CBM

CBM VBM

VBM

Mo S

Ga N

VBM

Figure 5 The charge-density isosurface distributions of CBM and VBM states of MoS2/GaN heterostructures with (a) GP-phase GaN monolayer, (b) HK-phase GaN bilayer, (c) HK-phase GaN tetralayer, and (d) six-layer WZ-phase GaN film.

9



Compared to the freestanding MoS2 monolayer and GaN bulk, MoS2/GaN heterostructures exhibit superior visible-light absorption in two polarization directions, in particular for 2D MoS2/GaN vdW heterostructures (Figure 6). For example, the absorption coefficient of 2D MoS2/GaN heterostructures arrives at ~105 cm-1 when the photon energy is beyond 2.5 eV, which is comparable to the conventional optical-absorber materials, such as GaAs, CdTe, CIGS, and hybrid halide perovskites45,46. Such as result can be understood as follows, (i) 2D MoS2/GaN heterostructures possess moderate band gaps (1.35~1.70 eV) that match well with the distribution of solar spectrum. (ii) The achievement of p-d electron transitions. The CBM and VBM states of 2D heterostructures are mainly contributed by the Mo-dZ2 and N-2p orbitals, respectively (Figure 5). In contrast, the band-edge states of GaN nanosheets and bulk are dominated by Ga-4s,4p and N-2p orbitals. Owing to the larger dispersion of d electrons than s and p electrons, the p-d transitions in 2D MoS2/GaN heterostructures contributes to their higher visible-light absorption efficiency as compared to the pristine GaN materials. Although the optical absorption of MoS2 monolayer is dominated by the larger dispersion d-d transitions, its absorption depth is insufficient due to the atomic-layer thickness.

6 GaN Thickness 1L 2L 3L MoS2/GaN 4L 6L bulk

-1

// (10 cm )

(a)

4

5

(b)

2

0 Infrared 4

MoS2

Ultraviolet

Visible

5

-1

(10 cm )

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

Page 10 of 16

2

0 0

1

2

3

4

5

6

Photon energy (eV) Figure 6 Optical absorption spectra of MoS2/GaN heterostructures with different GaN thicknesses along the (a) inplane (α//) and (b) out-of-plane (α⊥) directions calculated by the HSE06 method. For the comparison, the absorption spectra of monolayer MoS2 (in green) and GaN bulk (in blue) are also indicated here. The shadow regions represent the range of visible light with the wavelength from 360 to 780 nm.

10


Page 11 of 16 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


4. CONCLUSIONS In summary, we revealed the thickness-dependent structural stability, electronic and optical properties of 2D GaN nanosheets and MoS2/GaN vdW heterostructures based on the DFT calculations. Our results demonstrate that the reduction of thickness leads to the phase transition of GaN nanosheets from WZ, HK, to GP phase, which is accompanied by a direct-to-indirect band-gap transition. Integrating a MoS2 monolayer on these GaN nanosheets makes the formation of MoS2/GaN vdW heterostructures, and their band gaps, band alignment, and optical absorption strongly depend on the phase structure and thickness of GaN layer. For the 2D MoS2/GaN vdW heterostructures, they possess suitable band gaps (1.35~1.70 eV), type-II band alignment, and large visible-light absorption coefficient, which make them great potential for the application of photovoltaic and photocatalytic devices.  ASSOCIATED CONTENT  Supporting Information Lattice and energetic parameters of GaN with different structures, phonon band structures of GaN nanosheets, interface configurations of MoS2/GaN vdw heterostructures, and in-plane strain effect on the phase stability of GaN bilayer. This material is available free of charge via the internet at http://pubs.acs.org.  AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] Notes The authors declare no competing financial interest.  ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (Grant no. 61775201 and 11404309), and in part by Zhejiang Provincial Natural Science Foundation of China (Grant no. LY18A040006) and the Fund of Shanghai Science and Technology Foundation of China (Grant no. 13JC1408800). Computational resources from Shanghai Supercomputer Centre are acknowledged.

REFERENCES AND NOTES

11



Page 12 of 16

(1) Waltereit, P.; Brandt, O.; Trampert, A.; Grahn, H. T.; Menniger, J.; Ramsteiner, M.; Reiche, M.; Ploog, K. H. Nitride Semiconductors Free of Electrostatic Fields for Efficient White Light-Emitting Diodes. Nature 2000, 406, 865-868. (2) Yan, Q.; Rinke, P.; Janotti, A.; Scheffler, M.; Walle, G. C. Effects of Strain on the Band Structure of GroupIII Nitrides. Phys. Rev. B 2014, 90, 125118. (3) Khan, A.; Balakrishnan, K.; Katona, T. Ultraviolet Light-Emitting Diodes Based on Group Three Nitrides. Nat. Photonics. 2008, 2, 77-84. (4) Molnar, R. J.; Lei, T.; Moustakas, T. D. Electron Transport Mechanism in Gallium Nitride. Appl. Phys. Lett. 1993, 62, 72-74. (5) Glavin, N. R.; Chabak, K. D.; Heller, E. R.; Moore, E. A.; Prusnick, T. A.; Maruyama, B.; Walker Jr., D. E.; Dorsey, D. L.; Paduano, Q.; Snure, M. Flexible Gallium Nitride: Flexible Gallium Nitride for HighPerformance, Strainable Radio-Frequency Devices. Adv. Mater. 2017, 29, 1701838. (6) Joh, J.; del Alamo, J. A. Critical Voltage for Electrical Degradation of GaN High-Electron Mobility Transistors. IEEE Electron Device Letters 2008, 29, 287-289. (7) Huang, Y.; Duan, X.; Cui, Y.; Lieber, M. C. Gallium Nitride Nanowire Nanodevices. Nano Lett. 2002, 2, 101-104. (8) Kuykendall, T. R.; Schwartzberg, A. M.; Aloni, S. Gallium Nitride Nanowires and Heterostructures: Toward Color-Tunable and White-Light Sources. Adv. Mater. 2015, 27, 5805-5812. (9) Li, C.; Liu, S.; Hurtado, A.; Wright, J. B.; Xu, H.; Luk, T. S.; Figiel, J. J.; Brener, I.; Brueck, S. R. J.; Wang, G. T. Annular-Shaped Emission from Gallium Nitride Nanotube Lasers. ACS Photonics 2015, 2, 1025-1029. (10)

Liu, B.; Yang, W.; Li, J.; Zhang, X.; Niu, P.; Jiang, X. Template Approach to Crystalline GaN Nanosheets.

Nano Lett. 2017, 17, 3195-3201. (11)

Geim, A. K. Graphene: Status and Prospects. Science 2009, 324, 1530-1534.

(12)

Li, H.; Zhang, Q. C.; Yap, C. R.; Tay, B. K.; Edwin, T. H.; Olivier, T.; Baillargeat, A. D. From Bulk to

Monolayer MoS2: Evolution of Raman Scattering. Adv. Mater. 2012, 22, 1385-1390. (13)

Novoselov, K. S.; Mishchenko, A.; Carvalho, A.; Castro Neto, A. H. 2D Materials and van der Waals

Heterostructures. Science 2016, 353, aac9439. (14)

Balushi, Z. Y. A.; Wang, K.; Ghosh, R. K.; Vilá, R. A.; Eichfeld, S. M.; Caldwell, J. D.; Qin, X.; Lin, Y. C.;

DeSario, P. A.; Stone, G.; et al. Two-Dimensional Gallium Nitride Realized via Graphene Encapsulation. Nat. Mater. 2016, 15, 1166-1171.

12


Page 13 of 16 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


(15)

Sun, C.; Yang, M.; Wang, T.; Shao, Y.; Wu, Y.; Hao, X. Defects Graphene-Oxide-Assisted Synthesis of

GaN Nanosheets as a New Anode Material for Lithium-Ion Battery. ACS Appl. Mater. Interfaces. 2017, 9, 26631-26636. (16)

Imaoka, T.; Okada, T.; Samukawa, S.; Yamamoto, K. Room-Temperature Synthesis of GaN Driven by

Kinetic Energy Beyond the Limit of Thermodynamics. ACS Appl. Mater. Interfaces. 2017, 9, 41629-41633. (17)

Freeman, C. L.; Claeyssens, F.; Allan, N. L.; Harding J. H. Graphitic Nanofilms as Precursors to

Wurtzite Films: Theory. Phys. Rev. Lett. 2006, 96, 066102. (18)

Sahin, H.; Cahangirov, S.; Topsakal, M.; Bekaroglu, E.; Akturk, E.; Senger, R. T.; Ciraci, S. Monolayer

Honeycomb Structures of Group IV Elements and III-V Binary Compounds. Phys. Rev. B 2009, 80, 155453. (19)

Kolobov, A. V.; Fons, P.; Tominaga, J.; Hyot, B.; André, B. Instability and Spontaneous Reconstruction

of Few-Monolayer Thick GaN Graphitic Structures. Nano Lett. 2016, 16, 4849-4856. (20)

Kolobov, A. V.; Fons, P.; Saito, Y.; Tominaga, J.; Hyot, B.; André, B. Strain Engineering of Atomic and

Electronic Structures of Few-Monolayer-Thick GaN. Phys. Rev. Mater. 2017, 1, 024003. (21)

Ambacher, O.; Smart, J.; Shealy, J. R.; Weimann, N. G.; Chu, K.; Murphy, M.; Schaff, W. J.; Eastman, L.

F. Two-Dimensional Electron Gases Induced by Spontaneous and Piezoelectric Polarization Charges in Nand Ga-Face AlGaN/GaN Heterostructures. J. Appl. Phys. 1999, 85, 3222-3233. (22)

Scholz, F. Semipolar GaN Grown on Foreign Substrates: a Review. Semicond. Sci. Tech. 2012, 27,

024002. (23)

Honda, Y.; Kuroiwa, Y.; Yamaguchi, M.; Sawaki, N. Growth of GaN Free from Cracks on a (111)Si

Substrate by Selective Metalorganic Vapor-Phase Epitaxy. Appl. Phys. Lett. 2002, 80, 222-224. (24)

Felbinger, J. G.; Chandra, M. V. S.; Sun, Y.; Eastman, L. F.; Wasserbauer, J.; Faili, F.; Babic, D.; Francis,

D.; Ejeckam, F. Comparison of GaN HEMTs on Diamond and SiC Substrates. IEEE Electron Device Letters 2007, 28, 948-950. (25)

Chien, F. R.; Ning, X. J.; Stemmer, S.; Pirouz P. Growth Defects in GaN Films on 6H-SiC Substrates.

Appl. Phys. Lett. 1996, 68, 2678-2680. (26)

Zhang, X.; Qiao, X. F.; Shi, W.; Wu, J. B.; Jiang, D. S.; Tan, P. H. Phonon and Raman Scattering of

Two-Dimensional Transition Metal Dichalcogenides from Monolayer, Multilayer to Bulk Material. Chem. Soc. Rev. 2015, 44, 2757-2785.

13



(27)

Page 14 of 16

Manzeli, S.; Ovchinnikov, D.; Pasquier, D.; Yazyev, O. V.; Kis, A. 2D Transition Metal Dichalcogenides.

Nat. Rev. Mater. 2017, 2, 17033.. (28)

Wang, J.; Shu, H.; Zhao, T.; Liang, P; Wang, N.; Cao, D.; Chen, X. Intriguing Electronic and Optical

Properties of Two-Dimensional Janus Transition Metal Dichalcogenides. Phys. Chem. Chem. Phys. 2018, 20, 18571-18578. (29)

Jariwala, D.; Marks, T. J.; Hersam, M. C. Mixed-Dimensional van der Waals Heterostructures. Nat.

Mater. 2017, 16, 170-181. (30)

Ouyang, B.; Ou, P.; Wang, Y.; Mi, Z.; Song, J. Phase Engineering of MoS2 through GaN/AlN Substrate

Coupling and Electron Doping. Phys. Chem. Chem. Phys. 2016, 18, 33351-33356. (31)

Tangi, M.; Mishra, P.; Ng, T. K.; Hedhili, M. N.; Janjua, B.; Alias, M. S.; Anjum, D. H.; Tseng, C. C.;

Shi, Y. H.; Joyce, J.; et al. Determination of Band Offsets at GaN/Single-Layer MoS2 Heterojunction. Appl. Phys. Lett. 2016, 109, 032104. (32)

Wan, Y.; Xiao, J.; Li, J.; Fang, X.; Zhang, K.; Fu, L.; Li, P.; Song, Z.; Zhang, H.; Wang, Y.; et al.

Epitaxial Single-Layer MoS2 on GaN with Enhanced Valley Helicity. Adv. Mater. 2018, 30, 1703888. (33)

Chen, Z.; Liu, H.; Chen, X.; Chu, G.; Chu, S.; Zhang, H. Wafer-Size and Single-Crystal MoSe2

Atomically Thin Films Grown on GaN Substrate for Light Emission and Harvesting. ACS Appl. Mater. Interfaces 2016, 8, 20267-20273. (34)

O’Regan, T. P.; Ruzmetov, D.; Neupane, M. R.; Burke, R. A.; Herzing, A. A.; Zhang, K.; Birdwell, A.

G.; Taylor, D. E.; Byrd, E. F. C.; Walck, S. D.; et al. Structural and Electrical Analysis of Epitaxial 2D/3D Vertical Heterojunctions of Monolayer MoS2 on GaN. Appl. Phys. Lett. 2017, 111, 051602. (35)

Wang, N.; Cao, D.; Wang, J.; Liang, P.; Chen, X.; Shu, H. Interface Effect on Electronic and Optical

Properties of Antimonene/GaAs van der Waals Heterostructures. J. Mater. Chem. C 2017, 5, 9687-9693. (36)

Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Waved Method.

Phys. Rev. B 1999, 59, 1758-1775. (37)

Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953-17979.

(38)

Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a

Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169-11185.

14


Page 15 of 16 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


(39)

Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T. A.; Joannopoulos, J. D. Iterative Minimization

Technologies for Ab Initio Total-Energy Calcualtions: Molecular Dynamics and Conjugate Gradients. Rev. Mod. Phys. 1992, 64, 1045-1097. (40)

Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion

Correction. J. Comput. Chem. 2006, 27, 1787-1799. (41)

Baroni, S.; De Gironcoli, S.; Dal Corso, A.; Giannozzi P. Phonons and Related Crystal Properties from

Density-Functional Perturbation Theory. Rev. Mod. Phys. 2001,73, 515. (42)

Togo, A.; Oba, F.; Tanaka, I. First-Principles Calculations of the Ferroelastic Transition between Rutile-

Type and CaCl2-type SiO2 at High Pressures. Phys. Rev. B 2008, 78, 134106. (43)

Paier, J.; Marsman, M.; Hummer, K.; Kresse, G.; Gerber, I. C.; Ángyán, J. G. Screened Hybrid Density

Functionals Applied to Solids. J. Chem. Phys. 2006, 124, 154709. (44)

Shu, H.; Chen, X.; Zhao, H.; Zhou, X.; Lu, W. Structural Stability and Electronic Properties of InAs

Nanowires and Nanotubes: Effects of Surface and Size. J. Phys. Chem. C 2010, 114, 17514-17518. (45)

Kim, M. R.; Ma, D. Quantum-Dot-Based Solar Cells: Recent Advances, Strategies, and Challenges. J.

Phys. Chem. Lett. 2015, 6, 85-99. (46)

Green, M. A.; Bremner, S. P. Energy Conversion Approaches and Materials for High-Efficiency

Photovoltaics. Nat. Mater. 2017, 16, 23-34.

15



TOC Graphic Bulk

Reduction of GaN Thickness

. ..

Monolayer

GP

GaN

HK

MoS2

Type-II MoS2

WZ

. ..

GaN

Type-I

16


Page 16 of 16

Thickness-Dependent Phase Stability and Electronic Properties of

Recommend Documents