Monolayered Silicon and Germanium Monopnictide Semiconductors

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Monolayered Silicon and Germanium Monopnictide Semiconductors: Excellent Stability, High Absorbance, and Strain Engineering of Electronic Properties Ai-Qiang Cheng, Zi He, Jun Zhao, Hui Zeng, and Ru-Shan Chen ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b17560 • Publication Date (Web): 29 Jan 2018 Downloaded from http://pubs.acs.org on January 30, 2018

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ACS Applied Materials & Interfaces

Monolayered Silicon and Germanium Monopnictide Semiconductors: Excellent Stability, High Absorbance, and Strain Engineering of Electronic Properties Ai-Qiang Cheng,†,§ Zi He,†,§ Jun Zhao,‡,¶ Hui Zeng,∗,† and Ru-Shan Chen∗,† School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China, School of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210023, China, and School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, China E-mail: [email protected]; [email protected]

Abstract The discovery of stable two-dimensional (2D) semiconductors with exotic electronic properties is crucial to the future electronic technologies. Using the first principles calculations, we predict the monolayered Silicon- and Germanium-monopnictides as a new class of semiconductors owning excellent dynamical and thermal stabilities, prominent anisotropy, and high possibility of experimental exfoliation. These semiconductors, including the monolayered SiP, SiAs, GeP, and GeAs, possess wide bandgaps of 2.08∼2.64 ∗

To whom correspondence should be addressed School of Electronic and Optical Engineering, Nanjing University of Science and Technology ‡ School of Science, Nanjing University of Posts and Telecommunications ¶ School of Chemistry and Chemical Engineering, Nanjing University § These authors contributed equally to this work. †

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eV obtained by hybrid functional calculation. Under small uniaxial strains (-2%∼3%), dramatic modulations of their band structures are observed, and furthermore, all the 2D monolayers (MLs) can be transformed between indirect and direct semiconductors. The monolayered GeAs and SiP exhibits extraordinary optical absorption in the range of visible and ultraviolet (UV) light spectra, respectively. The exfoliation energies of these monolayers are comparable to graphene, implying a strong probability of successful fabrication by mechanical exfoliation. These intriguing properties of the monolayered Silicon- and Germanium-monopnictides, combined with their highly stable structures, offer tremendous opportunities for electronic and optoelectronic devices working under UV-visible spectrum.

Keywords: monolayered monopnictide, strain engineering, optical absorbance, exfoliation energy, indirect-to-direct transition. The rising of graphene has sparked tremendous interests in various two-dimensional (2D) materials consisting of atomically thin sheets, 1–3 such as Group-IV elemental analogues, 4 transition metal dichalcogenides, 5 III-VI layered materials, 6 monolayer MXenes, 7 which are promising semiconductor candidates for nanoelectronics and optoelectronics due to their suitable bandgaps. Among them, the monolayered MoS2 and phosphorene, possessing both appreciated fundamental bandgap and moderate intrinsic carrier mobility, have attracted considerable attentions more recently. 8–10 Experimental studies have demonstrated intriguing electrical performance in the MoS2 - and phosphorene-based nanoelectronic and optoelectronic devices. 11 However, few-layered phosphorene is chemically unstable, which hinder its practical applications in semiconductor device. 12 Meanwhile, the presence of various defects in the fabrication of monolayered MoS2 is considered to be inevitable, which significantly deteriorate the carrier mobility and thus impede its device applications. 13 In this sense, searching for stable 2D semiconductors with novel electronic properties becomes a challenging problem. More recently, bulk crystals of four IV-V layered materials, i.e. SiP, SiAs, GeP, and

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GeAs, have been experimentally fabricated by using self-flux under high pressure and seeded flux growth. 14,15 Experimental characterizations have shown that they crystallize with orthorhombic phase for SiP and monoclinic phase for the others. Moreover, the atoms in each 2D layer are covalently bonded and different layers are stacked by weak van der Waals (vdW) interactions, in analogy to the transition metal dichalcogenides. 16 All these IV-V binary compound crystals are semiconductors with bandgaps of 0.52∼1.69 eV. 17–20 The anisotropic structures of these monolayered binary compound AB (A=Si, Ge; B= P, As) give rise to highly anisotropic transport properties and high-temperature thermoelectric character. 21,22 Previous density functional theory (DFT) calculations revealed that the monoclinic phase is energetically more favorable than the orthorhombic phase, 23–25 and the electronic properties of several free-standing MLs have been investigated. 25–28 However, the fundamental physical properties related to these MLs are not yet clear, and their potential applications in nanoelectronic and optoelectronic are still lacking. For instance, what about the optical adsorption properties of these 2D IV-V binary monolayers (MLs), which is of great importance to their applications in the field of optoelectronic. How are the electronic properties of these MLs modulated by stain engineering ? Furthermore, is it possible to experimentally fabricate these monolayered binary compounds and what is the effective synthesis route ? Motivated by the successful fabrication of few-layered IV-V binary compound in experiments, 14,20 in the following part, we perform DFT calculations to systematically study the structures, electronic and optical properties, and stabilities of the monolayered SiP, SiAs, GeP, and GeAs semiconductors. It will be shown that these semiconductors exhibit excellent dynamical and thermal stabilities, and the dramatic modulations of band structures can be obtained by small uniaxial strains. Moreover, the excellent optical absorbance ranging from visible to UV light and the feasibly experimental route to fabricate these 2D MLs from bulk crystal will also be addressed. In this work, we have carried out the first-principles calculations based on DFT within the generalized gradient approximation (GGA) to study the electronic structures. All calcula-

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tions are implemented in the Vienna ab initio simulation package (VASP). 29,30 For structural optimizations, the exchange-correlation potential is described by GGA with Perdew-BurkeErnzerhof (PBE) version. 31 We have adopted the DFT-D3 approach proposed by Grimme et al to correctly describe the vdW interactions. 32 The cutoff energy for plane-wave basis is 500 eV. For the ionic relaxation, the convergence criteria are 0.01 eV/Å for the remnant force and 10−6 eV/atom for the energy. The Brillouin zone (BZ) is sampled by using the MonkhorstPack scheme, 33 and we adopt the k-grid of 30×6×1 for geometry optimization and 40×8×1 for the computation of density of states. To minimize the interlayer interactions, the vacuum spacing of 25 Å was employed for the monolayers. To correct the well-known bandgap underestimation reported by GGA-PBE, we also performed band structure calculations based on screened hybrid functional in the form of Heyd-Scuseria-Ernzerhof (HSE06). 34,35 The phonon dispersion spectra are calculated by using density functional perturbation theory utilized in the CASTEP code. 36,37 To study the thermal stability, we have carried out ab initio molecular dynamics (AIMD) simulations in the canonical ensemble. The 6 × 1 × 1 ML supercell consisting of 144 atoms is used in simulation, and the temperature is controlled by the Nosé-Hoover algorithm at 1000 K and 1500 K. 38 To evaluate the optical properties of these monolayered semiconductors, we computated the frequency-dependent dielectric function ϵ(ω) as well as the absorption coefficient α(ω). 39 The imaginary part ϵ2 (ω) is calculated by using the formula:

ϵ2 (ω) =

1 4π 2 e2 lim 2 Σc,v,k 2Wk δ(ϵck − ϵvk − ω) × ⟨uck+eα q |uvk ⟩⟨uck+eβ q |uvk ⟩∗ Ω q→0 q

(1)

where c and v are associated with the conduction and valence band states, respectively. The real part ϵ1 (ω) is calculated by using the Kramer-Kroning transformation. 40 Furthermore, it is noteworthy to mention that the light incidence along the Z axis, as indicated in Figure 1, and the polarization along X/Y direction. Hence, the frequency-dependent absorption coefficient A(ω) is derived from the dielectric functions:

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A(ω) =

√ √ 1 2ω[ ϵ21 (ω) + ϵ22 (ω) − ϵ1 (ω)] 2

(2)

Among the four IV-V bulk crystals, only SiP has the orthorhombic phase with space group Cmc21 (No. 36), while the other three (SiAs, GeP, GeAs) possess the monoclinic C2/m (No. 12) symmetry. The preferred exfoliation orientation (cleavage planes) for the SiP is [0, 0, 1], while the other three crystals is [2, 0, −1]. The primitive cells of the monolayered binary IV-V semiconductors are rectangular, and each primitive cell consist of 12 Group-IV atoms and 12 Group-V atoms. The optimized lattice parameters of each primitive cell are listed in Table 1, which is found to be well consistent with the experimental characterizations. 17–19,21 For these four monopnictides, every Group-V (denoted as B in Figure 1) atom is coordinated to three Group-IV (denoted as A) atoms, and each A atom is coordinated to three B atoms and one other A atom. There is negligible difference in bond length between AA1 bond and AA2 bond. However, the bond length is slightly increased from AB1 to AB4 . Additionally, the buckling distance δ is also increased as the atomic number is increasing. Table 1: Structural parameters of the monolayered binary compound AB (A=Si, Ge; B= P, As). The parameters are corresponding to the representation shown in Figure 1. MLs SiP SiAs GeP GeAs

a (Å) 3.519 3.682 3.648 3.803

b (Å) 20.449 21.246 21.393 22.129

β (◦ ) 90.00 106.56 100.18 100.38

AA1 (Å) AB1 (Å) AB4 (Å) 2.351 2.271 2.300 2.346 2.394 2.422 2.479 2.360 2.395 2.479 2.471 2.504

δ (Å) 4.732 4.856 4.982 5.099

The thermal and dynamical stabilities of the monolayered semiconductors are evaluated in terms of total energy variation and phonon dispersion, respectively. As shown in Figure 2, the time-dependent evolutions of the total energies are oscillating within a very narrow range, suggesting that these MLs are thermally stable. Hence, the AIMD snapshots have clearly shown that the puckered monoclinic monolayers are well maintained, demonstrating that all 2D MLs are stable at 1000 K. In particular, the SiP and SiAs have superior stabilities and are found to be stable under 1500 K, which is in consistence with the experimental measure5



Figure 1: Ball-and-stick model of the monolayered IV-V semiconductors. Top: top view of 2 × 1 monolayered supercell from the Z-axis, and the primitive cell is marked by black rectangle. Bottom: side view of the 2 × 1 supercell from the X-axis. Some bond lengths (A=Si, Ge; B= P, As) are shown and the corresponding values are listed in Table 1. ment. 14 The calculated phonon dispersions shown in Figure S1 have clearly demonstrated that there is no imaginary phonon mode, ensuring the dynamical stability of these MLs. Furthermore, the highest frequency obtained for the monolayered SiP is about 400 cm−1 , and this value is decreased to about 300 cm−1 for both SiAs and GeP, and 220 cm−1 for the GeAs. This is attributed to the differently elemental IV-V bonds. Thus, these monolayered monopnictide semiconductors exhibit excellent dynamical and thermal stabilities. The electronic structures of the monolayered IV-V semiconductors are shown in Figure 3. All 2D MLs possess suitable bandgaps (Eg ), which decrease with the increasing of atomic number. The band structures of each 2D monolayered semiconductor calculated at HSE is generally 0.65 eV larger than the level are shown in Figure S2. It is found that EHSE g and EgGGA lie in the visible light region, which is greater value reported by PBE. Both EHSE g than the corresponding value for the germanane (1.53 eV) as well as phosphorene (1.65 eV)

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Total Energy (eV/atom)

-5.36

-4.92

-5.38

-4.94

SiP

SiAs 1500K

1500K -5.40

-4.96

-5.42

-4.98

-5.44

-5.00

(b)

(a) -5.46

-5.02

-4.80 -4.48 Total Energy (eV/atom)

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


GeP

-4.82

GeAs

1000K

1000K

-4.50

-4.84 -4.52 -4.86 -4.54 -4.88

(c)

(d)

-4.56

-4.90 0

1

2

3

4

5

0

1

Time (ps)

2

3

4

5

Time (ps)

Figure 2: The evolution of total energies and snapshots of the 2D monolayered (a) SiP, (b) SiAs, (c) GeP, and (d) GeAs from AIMD simulations at the end of 5ps. and comparable with MoS2 (2.13 eV). 16,40–42 As demonstrated in Figure 4a, the valence band maxmium (VBM) is originated from the hybridization of p-orbitals of A and B atoms. In contrast, the s- and p-orbital of A and B atoms almost have equal contributions to the conducting band minimum (CBM). Thus, except for the GeP, the other three MLs are direct bandgap semiconductors. It is noted that the CBM of GeP is located at 4/5 along Γ → X, in striking contrast to the SiP case. It is attributed to the fact that CBM of the former is governed by the s-orbital of the Ge atom, as confirmed by its PDOS result shown in Figure 4b. To estimate the transport properties of these MLs, we have calculated the effective mass 2

E(k) −1 (m∗ ) of charge carriers by using the expression m∗ = h ¯ 2 ( ∂ ∂k , and the calculated results 2 )

are listed in Table 2. As shown in Figure 3, the CBM significantly disperse along x direction, indicating small effective mass mxe in the four MLs. The value of mxe is smaller than that of monolayered phosphorene (0.17 m0 ) 43 and antimonene. 44 The effective mass along y direction

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3

3

2

2

E (eV)

1

E (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

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(a) SiP

1

(b) SiAs

0

0

-1

-1

-2

-2

3

3

2

2

1

1

(d) GeAs

(c) GeP 0

0

-1

-1

-2

G

X S

Y

X S

G G

Y

-2

G

Figure 3: The calculated electronic band structures from GGA-PBE for the monolayered (a) SiP, (b) SiAs, (c) GeP, and (d) GeAs. The dashed line indicates the Fermi level. mye is much lighter than the corresponding mxe value, implying strong anisotropy in electron transport and high mobility along y direction. For the hole carrier, the mxh value is between 0.137 ∼ 0.351 m0 , which are also smaller than that of most 2D materials. 45,46 Hence, the hole carrier along y direction is lowered to 0.002 m0 . Overall, these monolayered IV-V semiconductors are anticipated to have excellent and highly anisotropic transport properties, leading to a very promising perspective for future nanoelectronics. Table 2: Electronic structure parameters of the IV-V binary monopnictide MLs. EgGGA (eV) and EgHSE (eV) are the bandgap calculated by GGA and HSE, respectively; Φ is the work function. The effective masses of electron (me ) and hole (mh ) along x and y directions, and m0 is the rest mass of electron. MLs SiP SiAs GeP GeAs

Type EgGGA (eV) EgHSE (eV) Φ (eV) Direct 1.899 2.641 4.783 Direct 1.694 2.353 4.496 Indirect 1.610 2.309 4.752 Direct 1.423 2.077 4.457

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mxe (m0 ) 0.111 0.050 0.053 0.118


mye (m0 ) 0.062 0.003 0.004 0.004

mxh (m0 ) -0.351 -0.137 -0.175 -0.152

myh (m0 ) -0.050 -0.002 -0.004 -0.002

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(a) SiP

Partial Density of States (arb.unit)

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


(b) GeP

Total

Total

Si

Ge

Si -s

Ge -s

Si -p

Ge -p

P

P

P -s

P -s

P -p

-2

-1

0

1

P -p

2

-2

-1

E (eV)

0

1

2

E (eV)

Figure 4: The partial density of states (PDOS) for the monolayered (a) SiP and (b) GeP. The Fermi level is set to zero. Recent investigations show that dramatic modulation of electronic properties in 2D semiconductors has been realized experimentally by using strain engineering. 47 We thus studied the influence of a uniaxial strain (εy ) along the y axis on the electronic structures of monolayered binary compounds, as presented in Figure 5. The uniaxial strain εy is defined by εy =

b−b0 , b0

where b0 and b are the unstrained- and strained-lattice constants along y direc-

tion, respectively. The stain-driven direct(indirect)-to-indirect(direct) bandgap transition is observed for all 2D MLs. More importantly, such bandgap transition is achievable for experimental realization because the critical tensile strain is only 1%, 3%, 1% for the monolayered SiP, SiAs, GeAs, respectively. Hence, 2% compressive strain allows indirect-to-diect bandgap transition for the monolayered GeP, which is crucial for its optoelectronic applications. It is interesting to find that the direct bandgap of SiAs could be effectively modulated from 1.3∼1.9 eV by the uniaxial strain εy , which is similar to the cases in SmSe and GeSe. 48,49

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2.0

2.0 0.3

0.3

Eg (eV)

1.8 0.2

1.8

1.6

1.7

Eg

Eg 1.6

0.2

(a)

0.1

Toal Energy

0.1

Toal Energy

(b) 1.4

Direct

1.5

Indirect

Direct

0.0

Indirect

Total Energy (eV)

1.9

0.0

1.2 0.3

1.4

0.2 1.5

Eg

0.2 Eg

1.3

Toal Energy

1.4

Total Energy

(c)

0.1

0.1

(d) 1.2

1.3

Indirect

Direct

Direct

0.0

Indirect

ToTal Energy (eV)

0.3 1.6

Eg (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

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0.0

1.1 -4

-2

0 y

2

4

-4

-2

(%)

0 y

2

4

(%)

Figure 5: The electronic bandgaps and total energies of the monolayered binary compound AB (A=Si, Ge; B= P, As) varied with respect to the strain along y axis. (a)-(d) show sequently the monolayered SiP, SiAs, GeP, and GeAs. Hence, the bandgaps of the monolayered SiP and SiAs are linearly decreased with respect to the compressive strain. The uniaxial stain, which can be imposed to the 2D nanomaterials by different substrates in practice, allow us to tailoring the band structures of these MLs for potential applications in electronics. 50 The photon energy absorption spectra of these MLs are shown in Figure 6. For the SiP, SiAs, and GeP monolayers, these semiconductors exhibit significant absorbance starting at approximately 2.0 eV, which is explicitly presented in the zoomed inset. In contrast, the optical absorbance for the GeAs is about 1.5 eV. This is because significant absorbance takes place as h ¯ ω > Eg . Therefore, the monolayered GeAs has prior visible light absorption to the other three MLs, especially in the energy range of 1.5∼3.6 eV. In general, the calculated absorbance spectra are in accordance with their corresponding bandgaps shown in Figure 3. In addition, the monolayered SiP exhibit strong ultraviolet absorption, and its absorbance peak is located at 5.0 eV. Thus, the vdW heterostructure consisting of SiP and GeAs could be promising 2D semiconductor candidate for photovoltaics as well as optoelectronics. 51

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6

SiP

16

SiAs 4

GeP GeAs

Absorbance (a.u.)

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

12

SiP SiAs

0 1.5

8

2.0

2.5

3.0

GeP

Photon Energy (eV)

GeAs

4

0 0

2

4

6

Photon Energy (eV)

Figure 6: The calculated absorbance of these monolayered semiconductors as a function of photon energy. The magnified inset shows the light absorption at the region of solar spectrum. To investigate the possibility of exfoliating these 2D MLs from the surface of its layered crystal, we have examined the exfoliation process and calculated the exfoliation energy varied with respect to the separation, as exhibited in Figure 7. The exfoliation energy is only 0.26 J/m2 for the SiP and increased to 0.37 J/m2 for the GeAs. It is worthy to mention that the exfoliation energy of graphite is 0.32 J/m2 , which is higher than that of Silicon monopnictides (i.e. SiP and SiAs) and comparable with Germanium monopnictides (i.e. GeP and GeAs). 52,53 Therefore, the monolayered Silicon and Germanium monopnictides could be experimentally fabricated from its bulk crystal by mechanical cleavage. Moreover, compared to those of MoS2 and phosphorene, the exfoliation energy of the IV-V monopnictide monolayers is fairly favorable, implying their great potentials in constructing 2D nanoelectronic devices. 54 In summary, we have studied the structures, electronic properties, stability, and possible exfoliation of the monolayered SiP, SiAs, GeP, and GeAs semiconductors. These monolayered

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0.4

SiP SiAs

2

Exfoliation Energy (J/m )

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

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GeP

0.3

GeAs

0.2

0.1 d-d0

0.0 0

2

4

6 d-d

0

(

Å

8

10

12

)

Figure 7: Calculated exfoliation energies as a function of separation distance d, where d0 is the vdW distance between adjacent layers in bulk crystal. monopnictide semiconductors are found to have excellent dynamical and thermal stabilities, and their bandgaps are 1.42∼1.90 eV calculated by GGA-PBE functional and are increased to 2.08∼2.64 eV according to accurate hybrid HSE06 functional. The semiconductors of the IV-V MLs exhibit high anisotropy in the effective mass of the charge carriers, suggesting strongly anisotropic electrical transport properties. These 2D monolayers can transformed between indirect and direct semiconductors and their bandgaps can be effectively tuned by applying an achievable uniaxial strain. The exfoliation energy of the IV-V monopnictide monolayers is found be be energetically favorable, therefore these semiconductor MLs are expected to be experimentally fabricated by using mechanical cleavage in the near future. The monolayered SiP, SiAs, GeP, and GeAs semiconductors can enrich the family of 2D nanomaterials and could have promising potentials for novel electronic and optoelectronic devices.

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ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Calculated phonon dispersion spectra of the monolayered semiconductors; The electronic band structures obtained from HSE for the monolayered semiconductors (PDF)

AUTHOR INFORMATION Corresponding Authors ∗ E-mail: [email protected]. (H.Z.). ∗ E-mail: [email protected]. (R.C.). ORCID Jun Zhao: 0000-0001-7118-4992 Hui Zeng: 0000-0002-7657-6714 Author Contributions § These authors contributed equally to this work. Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS We are grateful to Dr. N. Xu for electronic structure simulations as well as inspirational discussions. We thank L. Zhang, Y. Sun, and Q.-Z. Tian for analyzing the simulation data. This work is financially supported by National Natural Science Foundation of China (Grant Nos. 11404037, 61701232, and 11304022).

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Optical Absorbance and exfoliation energies of the Monolayered Silicon and Germanium Monopnictide Semiconductors 702x303mm (144 x 144 DPI)


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Monolayered Silicon and Germanium Monopnictide Semiconductors

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