Significant Enhancement of the Stark Effect in Rippled Monolayer Blue

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Significant Enhancement of the Stark Effect in Rippled Monolayer Blue Phosphorous Shantanu Agnihotri, Priyank Rastogi, Yogesh Singh Chauhan, Amit Agarwal, and Somnath Bhowmick J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00022 • Publication Date (Web): 09 Feb 2018 Downloaded from http://pubs.acs.org on February 11, 2018

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The Journal of Physical Chemistry

Significant Enhancement of the Stark Effect in Rippled Monolayer Blue Phosphorous Shantanu Agnihotri,† Priyank Rastogi,† Yogesh Singh Chauhan,† Amit Agarwal,‡ and Somnath Bhowmick∗,¶ †Department of Electrical Engineering, Indian Institute of Technology Kanpur, Kanpur, U.P., 208016, India ‡Department of Physics, Indian Institute of Technology Kanpur, Kanpur, U.P., 208016, India ¶Department of Material Science & Engineering, Indian Institute of Technology Kanpur, Kanpur, U.P., 208016, India E-mail: [email protected] Phone: +91-512-2597161

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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

Abstract We explore the impact of a vertical electric field on the electronic properties of rippled monolayer blue phosphorus (blue-P). Based on density functional theory (DFT) calculations, we demonstrate electric field induced splitting and shifting of the energy levels of rippled blue-P, similar to the Stark effect in atomic energy levels. The bandgap of rippled blue-P is found to decrease linearly either with increasing electric field strength for a fixed ripple height or with increasing ripple height for a fixed electric field strength. The application of a transverse electric field also leads to a spatial separation of the conduction and valance band states near the bottom and the top of the ripple, respectively. The demonstrated Stark effect in rippled blue-P offers a potent bandgap engineering tool, and it may open a gateway for possible electronic and optoelectronic applications.

1

Introduction

In spite of having exceptionally large charge carrier mobility, usage of graphene 1 is often limited by its lack of an intrinsic bandgap. In this regard, recently developed or predicted two dimensional (2D) materials based on group-V elements like phosphorus and arsenic, seem to be promising on account of a unique combination of sizeable bandgap and reasonably good charge carrier mobility. 2–7 Several stable allotrope of atomically thin group-V elements have been predicted so far. 8–11 Among them, layered black phosphorus has been synthesized and characterized via different spectroscopic and microscopic methods. It has a huge potential for several optoelectronic and electronic applications, like field effect transistors, ultrafast photonics etc. 2,12–15 Among other allotrope of 2D phosphorus, blue-P was found to be very similar to black-P in terms of cohesive energy and also predicted to be dynamically stable. 9 Recently, blueP has also been experimentally synthesized on top of Au(111) substrate and it’s growth thermodynamics has been studied using ab initio simulations. 16–18 Unlike black-P, which has 2


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a puckered honeycomb structure, monolayer blue-P has a silicene/germanene like buckled honeycomb structure. 11,19,20 According to DFT calculations, free standing blue-P is predicted to have a relatively large bandgap of 1.9 eV [2.7 eV, if hybrid functional is used instead of generalized gradient approximation, for more accurate bandgap prediction]. 9–11 Clearly, the bandgap is more than ideal (ranging from 1 to 1.6 eV) for solar energy harvesting and other optoelectronic applications. 21,22 An effective way to modulate the bandgap of 2D materials, is by applying external perturbations like strain, electric field and doping, as demonstrated in case of group-V materials like black phosphorus, 23–29 blue phosphorus, 30–34 arsenic 7 and other 2D semiconductors. 35–40 Under the influence of an external electric field, energy levels of the semiconductors shift, leading to bandgap modulation. This is similar to the splitting and shifting of the atomic energy levels in the presence of an applied electric field, which is known as the Stark effect. Due to poor dielectric screening, manifestation of the Stark effect can be significantly enhanced in 2D materials, which is termed as the giant Stark effect (GSE) in the literature. 36 In recent studies, the bandgap modulation via GSE has also been experimentally demonstrated in potassium doped 41 and electrostatically gated black phosphorus. 42 In case of blue-P, electric field strength required for bandgap modulation is Ez > 0.5 V/˚ A, as predicted by ab initio calculations, 30 which is possibly beyond the reach of current experimental capabilities. However, the number is calculated based on a pristine structure of blue-P, which is “flat” (i.e., no undulations present). 30 But it is well known that, an external electric field tunes the bandgap of 2D materials more effectively in presence of ripples (when compared to “flat” layers), as shown in case of MoS2 43 and black phosphorus. 44 As a matter of fact, 2D materials are always rippled and this is what lends them stability and allows them to exist. 45–47 Otherwise, presence of any long range crystalline order in 2D is forbidden, according to the Mermin-Wagner theorem. 48 At room temperature, up to ≈ 1 nm height fluctuations in the form of ripples are commonly reported in the literature. Experimentally, the ripple formation can also be controlled by using anisotropic surface curvature during the

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synthesis or transfer process - as demonstrated for graphene 49 and strain engineering - as shown for black phosphorus. 50 Motivated by this, we study the bandgap modulation of rippled blue-P by applying a transverse electric field. We find that, there is a remarkable bandgap decrease in rippled blue-P, from 1.9 eV to approximately 1/4th of this value at Ez = 0.4 V/˚ A. More importantly, significant bandgap reduction (15–25% of the pristine value, depending on the ripple height) is observed even for smaller electric field like 0.1 V/˚ A, which lies within the range of existing experimental capabilities. We find the bandgap modulation to be directly proportional to the electric field strength and the ripple height. We uncover an interesting correlation between bandgap reduction and spatial separation of the highest occupied and lowest unoccupied molecular orbital at the top and the bottom of the ripple, respectively. This spatial separation of the different carries is also expected to reduce the possibility of electron-hole recombination. The article is organized as follows: computational details are presented in Sec. 2. This is followed by a description of crystal structure and electronic band structure of pristine blue-P in Sec. 3 and rippled blue-P in Sec. 4. The impact of a vertical electric field is presented in Sec. 5, and we summarize our findings in Sec. 6.

2

Method

The structural optimizations and electronic band structure calculations are evaluated within density functional theory (DFT) framework, as implemented in the QUANTUM ESPRESSO package. 51 We use a plane-wave basis set with a 30 Ry kinetic energy cutoff and projector augmented wave (PAW) method based pseudopotential. Electron exchange-correlation is treated with a generalized gradient approximation (GGA), as proposed by Perdew-BurkeErnzerhof (PBE). 52 Dispersion forces are taken into account by using a DFT-D type of van der Waals correction, as prescribed by Román-Pérez and Soler. 53 A vacuum region of 20 ˚ A is

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3.0

r

y

θ

2.0

b a

x arm ch a ir

(a)

Y

S

E-EE-E F (eV) F

zig zag

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


1.0 0.0

CBM VBM

-1.0 -2.0

Γ

X

(b)

-3.0 (c) Y

Γ

X

S

Figure 1: (a) Top and side view of monolayer blue phosphorus. The rectangular unit cell is chosen, as opposed to the smaller hexagonal unit cell, to facilitate the formation of ripples. (b) First Brillouin zone, corresponding to the rectangular unit cell shown in panel (a), along with the high symmetry points. (c) The electronic band structure of pristine blue-P, along various high symmetry directions. The VBM and CBM of monolayer blue phosphorus (indirect bandgap of magnitude 1.9 eV) is located near the Y and X valley, respectively. used normal to the monolayers to avoid any interaction among spurious facsimile images. All the structures are fully relaxed until the force on each atom (total energy change due to ionic relaxation between two successive steps) is less than 10−3 Ry/au (10−4 Ry). In case of pristine monolayer blue phosphorus [see Fig. 1], Brillouin zone integrations are carried out using a 14 × 24 × 1 Monkhorst pack k-point grid, while a 2 × 18 × 1 grid is chosen for ripples [see Fig. 2].

3

Pristine Blue-P

The crystal structure [top and side view, prepared by XCrysDen 54,55 ], along with the rectangular unit cell and the first Brillouin zone of planar blue-P is shown in Fig. 1(a) and Fig. 1(b), respectively. We have chosen a rectangular supercell (with 4 atoms per unit cell), over a smaller hexagonal one (2 atoms per unit cell), as the former contains both zigzag and armchair segment - made of two and four atoms, respectively. Thus, it is straightforward to 5



repeat the rectangular unit cell along the x and y axis, for the purpose of generating ripples in the armchair and zigzag direction, respectively. After relaxing the structure, the equilibrium lattice parameters are found to be a = 5.69 ˚ A and b = 3.28 ˚ A, along the armchair and zigzag direction, respectively and the bond length and bond angle are measured to be r = 2.26 ˚ A and θ = 93.03◦ , respectively. The corresponding electronic band structure, plotted along various high symmetry directions, is shown in Fig. 1(c). The valence band maximum (VBM) and the conduction band minimum (CBM) of the indirect bandgap (magnitude Eg = 1.9 eV) semiconductor is located near the Y and X valley, respectively. The equilibrium structural parameters and the electronic band structure obtained by us are in good agreement with the values reported in the literature. 9,10,30 This also validates the choice of the energy cutoff and density of k-point grid used in the DFT calculations.

4

Rippled Blue-P

Having validated the structural properties and the electronic band structure of pristine monolayer blue phosphorus, we now proceed to study rippled blue-P. Instead of generating the ripples thermally in a random manner (via molecular dynamics simulations), we create them in a controlled way, such that the ripple height can be regulated easily, enabling a systematic study. The ripples are created separately along the armchair and the zigzag direction in a manner such that they are periodic and sinusoidal in shape, with wavelength L and height h [see Fig. 2 (a) and Fig. 2 (b)]. The ripples are created by first repeating the unit cell n times, either along the armchair (n = 12) or zigzag direction (n = 20) to get an elongated supercell of aspect ratio of

12a b

or

20b , a

respectively. Then, the wavelength L of the ripples is chosen

such that, L < (n × a) and L < (n × b) along the armchair and zigzag direction, respectively. Finally, an initial sinusoidal disturbance is added to the atomic positions, followed by a complete relaxation (barring the ripple wave-length L, which is kept constant) to minimize the

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(c) 2

(a) armchair 2h

L

0

∆AC

-2 Y 2 (d) (d)

(b) zigzag

E-EF (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


E-EF (eV)

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0

-2 X

Γ

∆ZZ

Γ

˚, h = 7.64 A ˚) and (b) zigzag Figure 2: Ripple of blue-P along the (a) armchair (L=60.86 A ˚ ˚ (L=59.62 A, h = 6.86 A) direction. The corresponding electronic band structures are shown in panel (c) and (d), respectively. The highest occupied and lowest unoccupied energy levels are marked by red lines.

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forces on the constituent atoms. Since the atoms move in the vertical direction to minimize the forces (arising due to the compression applied along the length of the supercell), the smaller the value of wave-length (L), the larger is the height (h) of the ripple. The electronic band structures of the relaxed armchair and zigzag ripples are shown in Fig. 2 (c) and Fig. 2(d), respectively. Since the ripples shown in Fig. 2 have a large aspect ratio, the corresponding first Brillouin zone appears to be ‘pseudo one dimensional’. For example, the structure shown in Fig. 2 (a) is approximately 21 times longer in the armchair direction than that of zigzag and as a consequence, ΓX line (parallel to the armchair side) is negligible in length than compared to the ΓY line (parallel to the zigzag side). Thus we focus on the band structure along the ΓY direction for an armchair ripple, and in the ΓX direction for a ripple in the zigzag direction. The corresponding energy gaps are also marked separately by ∆AC (for armchair) and ∆ZZ (for zigzag), as shown in Fig. 2 (c) and Fig. 2 (d), respectively. In the following section, we investigate in detail the evolution of the band structure of rippled blue-P on application of a vertical electric field.

5

Impact of Vertical Electric Field on Rippled Blue-P

The effect of an external electric field, acting perpendicular to the rippled blue phosphorus monolayer, is simulated by applying a sawtooth like potential in the z direction. 56 The evolution of the valence and conduction bands, with increasing electric field strength (Ez ) is shown in Fig. 3 (a) and Fig. 3 (b), for a zigzag (h = 7.82 ˚ A) and armchair (h = 7.64 ˚ A) ripple, respectively. Evidently, the energy gap between the valence and conduction bands decreases with increasing electric field. Also note that in general the conduction band curvature increases with increasing electric field, and this will reflect in decreased effective mass, as we show later. Further investigation reveals that, in the presence of an external electric field, the molecular orbitals corresponding to the VBM and CBM are localized near the crest and trough of

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Ez Ez Ez Ez

Figure 3: Shift of the highest valence and the lowest conduction band due to the vertical electric field is illustrated for wrinkled blue-P for (a) zigzag (h = 7.82 ˚ A) and (b) armchair ˚ (h = 7.64 A) ripple, respectively. The bandgap decreases due to the Stark effect, although its indirect nature remains unchanged. Also the conduction band curvature increases with increasing Ez , leading to the reduction of effective mass of electrons.

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the ripple, respectively. As shown in Fig. 4(a), there is no overlap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). Such a spatial separation of the conduction (LUMO) and valence states (HOMO) does not happen in pristine blue-P or in the absence of Ez in rippled blue-P and this can be very effective for reducing the possibility of electron-hole recombination.

HOMO

Top

(a) (a)

Electric Field

Bottom

Eg HOMO

2

LUMO

LUMO

} Δ2

E-EF (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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(b) (b)

E0g

Δ2

Eg = E0 g - (Δ1+Δ2)

0

Δ1

} Δ1 -2

10

08

PDOS

(d)

Figure 4: (a) Charge density distribution corresponding to HOMO and LUMO for an armchair ripple [h = 9.22 ˚ A, E = 0.25 V/˚ A ], showing clear evidence of spatial localization of the conduction and valence states. Origin of bandgap [Eg = ∆ZZ /∆AC for zigzag/armchair ripple] reduction is shown by a schematic diagram, where solid and dotted lines represent energy levels at finite and zero electric field, respectively. (b) DOS of the topmost and bottommost atom of the armchair ripple at finite (solid line) and zero external electric field (dotted line and blue shade). Corresponding energy levels are also marked by horizontal lines. Clearly, an upward (downward) shift of the energy levels corresponding to the topmost (bottommost) atom by an amount of ∆1 (∆2 ) reduces the zero field energy gap (Eg0 ) by an amount equal to ∆1 + ∆2 . Variation of ∆1 and ∆2 as a function of external electric field is mostly linear for both zigzag and armchair ripples [see Fig. 5]. The spatial separation of the conduction and valence states can be understood as follows. The atoms near crest and trough of the ripple experience different potential in the presence of a vertical electric field. As a result, the energies of the constituent atoms are expected to shift (with respect to the levels observed in the zero field) according to their heights. As 10


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shown schematically in the lower half of Fig. 4(a), the energy of the valence states ‘localized’ near the ripple peak increases, while the energy of the conduction states ‘localized’ near the valley decreases, leading to an overall decrease in the bandgap. This observation is substantiated further by comparing the zero and finite electric field density of states (DOS) of the highest and lowest atom present in an armchair ripple. As shown in Fig. 4(b), in zero electric field, the DOS curve of the topmost and bottommost atom coincide, implying that the electronic states corresponding to them are at the same energy level. When a vertical electric field is applied, the energy levels corresponding to the topmost (bottommost) atom are shifted upward (downward) by an amount ∆1 (∆2 ) with respect to their zero field values. As a result, the energy gap Eg (equal to ∆ZZ /∆AC ) at a finite electric field reduces by an amount of ∆1 +∆2 from it’s value of Eg0 (equal to ∆0ZZ /∆0AC ) at zero electric field, i.e., Eg = Eg0 − (∆1 + ∆2 ). After identifying the mechanism of bandgap closing, we now focus on the bandgap variation with varying ripple height, and the applied electric field. We consider ripple heights up to ≈ 1 nm, consistent with the ripple height found in other 2D materials like graphene and black phosphorus, at room temperature, via experimental and molecular dynamics studies. 45–47 Strength of the vertical electric field Ez is varied from 0.1 to 0.4 V/˚ A. Such an electric field can be applied in a electrostatically gated blue-P device, as shown in a recent experimental study on black-P. 42 The vertical electric field can also be emulated via potassium doping as shown in 41 for black phosphorus. However, it’s effectiveness for rippled blue-P needs to be investigated separately, because the doping locations are likely to be determined by the curvature of ripple. The variation of ∆1 and ∆2 with increasing strength of the external electric field is shown in Fig. 5 (a) and Fig. 5 (b) for zigzag and armchair ripples, respectively. We find that the magnitude of ∆1 is always higher than that of the ∆2 . This implies that the occupied valence band states shift by a larger amount on application of Ez . We also find that the bandgap modulation is more for larger ripple height. Since the bandgap of a rippled blue-P is much

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Δ1 & Δ2 (eV)

0.8 0.6

0.8

(a) (c)

Δ1, ZZ R.H. =3.67 Å Δ2, ZZ R.H. =3.67 Å

0.6

Δ1, ZZ R.H. =8.4 Å Δ2, ZZ R.H. =8.4 Å

Δ1, AC R.H. =9.22 Å Δ2, AC R.H. =9.22 Å

0.4

0.4

0.2

0.2 0.0 0.0

(b) (d)

Δ1, AC R.H. =3.67 Å Δ2, AC R.H. =3.67 Å

Δ1 & Δ2 (eV)

1.0

0.1

0.2

0.3

0.0 0.0

0.4

Electric Field (V/Å)

0.1

0.2

0.3

0.4

Electric Field (V/Å)

(c) (a)

(d) (b) ∆AC (eV)

∆ZZ (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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Figure 5: Variation of ∆1 and ∆2 as a function of external electric field is mostly linear for both (a) zigzag and (b) armchair ripples. Reduction in the bandgap of monolayer blue phosphorus with increasing strength of vertical electric field for ripples (c) along the zigzag direction and (d) along the armchair direction. Note that, bandgap of the pristine structure, without any ripples, is found to be unaffected for Ez ≤ 0.4 V/˚ A. The bandgap reduction with the electric field strength is mostly linear as indicated by the linear fit based on Eq. 1 and shown by the dotted line.

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more tunable on application of Ez (as compared to pristine blue-P), presence of wrinkles is important for manifestation of Stark effect within experimentally accessible electric field value. The electric field induced variation of the bandgap of rippled blue-P is shown in Fig. 5 (c) for zigzag ripples and in Fig. 5 (d) for armchair ripples, for different ripple heights. Note that, in the absence of an external electric field, the bandgap of zigzag ripple does not change with height as opposed to the case of armchair ripples. We also find that the bandgap of pristine blue phosphorus monolayer remains completely unaffected upto Ez = 0.4 V/˚ A and then decrease rapidly and vanish at ≈ 0.5 V/˚ A electric field, which is in good agreement with Ghosh et al. 30 However, bandgap closing happens on account of a higher conduction band (not the actual conduction band at zero electric field) decreasing in energy very rapidly on application of fields larger than 0.4 V/˚ A. Bandgap modulation has also been shown in monolayer black phosphorous, 28,57 as well as in an allotrope of monolayer arsenic having the same crystal structure as black phosphorous. 7 On the other hand, the energy gap between the valence and conduction band of rippled blue-P reduces on application of Ez , starting from very small field strength [see Fig. 5 (c) and (d)]. Predominantly, the dependence of the bandgap (Eg ) value of the zigzag (Eg = ∆ZZ ) and armchair (Eg = ∆AC ) ripples with increasing electric field (E) is linear and it can be expressed by, Eg − Eg0 = −|e|SE .

(1)

Here the linear coefficient S, which captures the impact of the transverse field on the bandgap, is the giant Stark effect (GSE) coefficient, and e is the charge of an electron. Value of S is obtained for each of the ripples by fitting the energy gap vs. electric field data [see Fig. 5 (c) and Fig. 5 (d)]. The giant Stark effect is also expected to depend on the ripple height. This follows from the simple fact that potential difference between the localized valence band states at the top of the ripple and the conduction band states at the bottom of the ripple is proportional to the 13



ripple height (h). Thus larger ripple height leads to increased potential difference between the crest and trough atoms, and this leads to faster decrease of the bandgap with Ez . This trend can clearly be observed both in the case of zigzag, as well as armchair ripples as shown in Fig. 5(c) and Fig. 5(d), respectively. Accordingly the giant Stark coefficient S [see Eq. (1)] is found to be proportional to the ripple height; expressed as S = αh, with α laying in a narrow range of 0.4-0.44 [for both types of ripples]. A similar study on rippled MoS2 revealed the ratio of S/h to be approximately equal to 0.23. 43 Note that, some fluctuations from the linear dependence of the bandgap on Ez and h are observed in case of armchair ripples [see Fig. 5 (d)].

-1

e

*

(% )

0

R e la tiv e d e c r e a s e in 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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-2 -3

F la R .H R .H R .H R .H R .H

-4 -5 0 .0

t . = 3 . = 6 . = 7 . = 8 . = 9

.6 7 .7 Å .6 4 .4 8 .2 2

Å Å Å Å

a r m c h a ir

0 .1

0 .2

0 .3

E le c tr ic F ie ld ( V /Å ) Figure 6: Relative decrease of effective mass of electron (m∗e , expressed in the units of the rest mass of an electron) in the Γ-Y direction (calculated for an armchair ripple), with respect to the effective mass at the zero electric field. Other than the flat monolayer blue phosphorus, m∗e decreases as the field gets stronger and the rate of the decay becomes more rapid with increasing ripple height. In addition to the bandgap modulation, the band curvature in vicinity of the CBM also changes significantly, on application of a transverse field in rippled blue-P [see Fig. 3].

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This leads to a change in the effective mass (m∗e ) of blue-P, which along with the bandgap modulation has a significant impact on the transport properties of rippled blue-P. As shown in Fig. 3(a), for the zigzag ripples, the conduction band in the Γ-X direction is very flat, which implies that the corresponding effective mass is very large. Thus we focus only on the m∗e for armchair ripples only, in the Γ-Y direction. The effective mass were extracted under parabolic approximation, where the norm of residuals were in the range of 0.0015 - 0.0017. The variation of m∗e , with the applied electric field, for different ripple heights is shown in Fig. 6. Other than the flat monolayer blue phosphorus, m∗e decreases with respect to the effective mass calculated for the zero electric field. Depending on the ripple height, nearly A. Similar 2.5-4.5% decrease of m∗e is observed as the electric field is increased to 0.3 V/˚ to the case of bandgap variation with ripple height, larger h leads to more decrease in the effective mass with increasing electric field strength. Note that all the calculations presented in this paper are based on the use of GGA-PBE functional for approximating the exchange correlation effects. Generally, GGA-PBE underestimates the bandgap by 30–40%, which can be improved by using a hybrid functional based on a screened Coulomb potential. 58 However, GGA-PBE calculations generally predict the qualitative trends accurately. Interestingly, hybrid functional predicted bandgap of blue-P monolayer is 2.7 eV, 30 but experimentally reported bandgap value of blue-P on Au (111) surface is equal to 1.1 eV, 16 which is even smaller than that of GGA-PBE prediction (1.9 eV). This is likely to be a consequence of the substrate-blue phosphorus interactions. Due to relatively large bandgap of freestanding monolayer blue-P (according to DFT calculations), the effective bandgap modulation in “flat” structures, requires electric field strength of the order 0.5 V/˚ A (or even higher if we consider the HSE06 bandgap), which is possibly beyond the limits of current technology. 42 However, magnitude of the electric field reduces significantly by considering presence of ripples in a monolayer, as shown in this work. Since the bandgap decreases further in multilayers and blue-P grown on Au substrate, we believe that they are the ideal candidates to be experimentally probed based on our computational pre-

15



dictions, because the mechanism of bandgap tuning remains qualitatively same, as predicted in this paper.

6

Conclusion

To summarize, we have shown that the combination of ripples and perpendicular electric field offer a unique way for tuning the bandgap of rippled monolayer blue-P - similar to the case of MoS2 43 and black-P. 44 Unlike the flat monolayer blue-P, for which the bandgap remains unchanged for Ez < 0.5 V/˚ A and then sharply drops to zero, 30 we observe a continuous decrease of bandgap with increasing electric field in the presence of ripples. We find that in rippled blue-P, the decrease in the bandgap is directly proportional to the electric field strength, as well as to the height of the ripple. In case of the largest ripple considered in this work, magnitude of bandgap at Ez = 0.4 V/˚ A drops to almost 1/4th of its initial value at the zero electric field. This is a consequence of the fact that the energy levels associated with the HOMO and LUMO gets shifted in presence of the vertical electric field, leading to the bandgap closing in rippled blue-P. This effective band structure modulation opens up the possibility of using rippled blue-P for electronic and optoelectronic applications. Interestingly, we find that the highest occupied and the lowest unoccupied molecular orbitals are spatially separated in the ripple for non-zero vertical electric field. While the former is localized near the crest, the latter is centered around the trough of the ripple. This spatial separation of HOMO and LUMO is likely to reduce the possibility of electron-hole recombination in blue-P and improve it’s transport properties.

7

Acknowledgment

SB acknowledges funding from SERB Fast Track Scheme for Young Scientist (SB/FTP/ETA0036/2014). The authors acknowledge funding from Ramanujan fellowship research grant 16


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and DST Nanomission project. The authors also thank computer center IIT Kanpur for providing HPC facility.

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