A new type-II lepidocrocite-type TiO2/GaSe heterostructure: Electronic and optical properties, bandgap engineering, interaction with ultrafast laser pulses
AA new type-II lepidocrocite-type TiO /GaSe heterostructure: Electronic and opticalproperties, bandgap engineering, interaction with ultrafast laser pulses Yilin Zhao ,Hong Zhang ∗ College of Physics, Sichuan University,Chengdu 610065, PR China
Xinlun Cheng Key Laboratory of High Energy Density Physics and Technology of Ministry of Education,Sichuan University, Chengdu 610065, PR China
Recently, van der Waals heterostructure has attracted interest both theoretically and experi-mentally for their potential applications in photoelectronic devices, photovoltaic devices, plasmonicdevices and photocatalysis. Inspired by this, we design a lepidocrocite-type TiO /GaSe heterostruc-ture. Via first-principles simulations, we show that such a heterostructure is a direct bandgapsemiconductor with a strong and broad optical absorption, ranging from visible light to UV region,exhibiting its potential application in photoelectronic and photovoltaic devices. With the planar-averaged electron density difference and Bader charge analysis, the heterostructure shows a strongcapacity of enhancing the charge redistribution especially at the interface, prolonging the lifetime ofexcitons, and hence improving photocatalytic performance. By applying biaxial strain and interlayercoupling, the heterostructure exhibits a direct-indirect bandgap transition and shows a potential formechanical sensors due to the smooth and linear variation of bandgaps. Furthermore, our resultindicates that a lower interlayer distance leads to a stronger charge redistribution. The calculation ofirradiating ultrafast on the heterostructure further reveals a semiconductor-metal transition for theheterostructure. Moreover, we find an enhanced induced plasmonic current in the heterostructureunder both x-polarized and z-polarized laser, which is beneficial to plasmonic devices designs. Ourresearch provides valuable insight in applying the lepidocrocite-type TiO /GaSe heterostructure inphotoelectronic, photovoltaic, photocatalytic, mechanical sensing and plasmonic realms. I. INTRODUCTION
Recent years, two-dimensional (2D) materials havecome into notice for their unusual properties, whichmainly arise from the quantum confinement and the orig-inal structure characteristics. Assembling 2D materialsinto van der Waals heterostructures is one of the mostefficient and achievable ways to take advantage of allkinds of 2d materials, yielding a range of applications intunneling devices[1–3], optoelectronic devices[4–7], pho-tovoltaic devices[8–12], plasmonic devices[13–16], light-emitting diodes[12, 17, 18], etcetera.Gallium selenide (GaSe) is a layered semiconductingmaterial, composed of four sublayers stacking in the se-quence of Se-Ga-Ga-Se. The monolayer GaSe sheetshave been successfully synthesized in experiment[19–22],which is widely used in optoelectronics[23, 24], nonlin-ear optics[25], terahertz experiments[26], solar energyconversion[27], field-effect transistors (FETs)[21], and soon.Titanium dioxide (TiO ), due to its unique prop-erties, such as environment-friendly, photo and chem-ical stability and low production cost[28, 29], is oneof the most prominent semiconductors with a large ∗ [email protected] range of applications in photocatalysis[30–32], photo-voltaic cells[33–36], and so forth. However, the largebandgap limits its light absorption window to ultravi-olet (UV) range. Besides, the fast recombination ofphoto generated electron and hole pairs makes TiO less efficient in photocatalysis[37]. Compared with otherconfigurations of TiO , a lepidocrocite-type TiO hasbeen experimentally synthesized with a larger bandgap(about 3.80eV) and stronger redox power[38–40]. The-oretical and experimental efforts have been carried outto seek ways to improve the photocatalytic activities oflepidocrocite-type TiO [30, 31, 41, 42]. Coupling TiO with other 2D monolayers into heterostructure is one ofthe effective approaches. However, to the best of ourknowledge, among these TiO heterostructures, little isknown about the electronic properties of lepidocrocite-type TiO /GaSe heterostructure.In this work, we theoretically studied the structural,electronic and optical properties of the lepidocrocite-typeTiO /GaSe heterostructure. The direct bandgap, type-II band alignment, strong and wide optical absorptionsuggest its potential application in photovoltaic and pho-toelectronic devices. To further explore the charge trans-ference of the heterostructure, the planar-averaged elec-tron density difference and Bader charge analysis wascarried out to reveal its merit in intensifying the chargeredistribution and serving as photocatalyzer. We also in-vestigated how the biaxial strain and interlayer distance a r X i v : . [ c ond - m a t . m t r l - s c i ] F e b can be applied to tune the band structure of the het-erostructure, increasing the possibility for a wider rangeof application. Finally, we studied the ultrafast laser act-ing on the heterostructure, further revealing its potentialapplication in plasmonic devices.The paper is organized as follows. In Sec.II, we de-scribe the computational details employed in this pa-per. In Sec.III A, we investigate the band structures,electronic properties of GaSe and TiO monolayers. InSec.III B and III C, we study the electronic and opti-cal properties of the TiO /GaSe heterostructure. InSec.III D, we explore the approaches to modulate theband structure with biaxial strain and interlayer cou-pling. In Sec.III E, we have a deep study on ultrafastlasers acting on the heterostructure. In Sec.IV, we sum-marize our results. II. COMPUTATIONAL DETAILS
Our calculations were mainly based on the first-principles density functional theory (DFT). Theprojector-augmented wave (PAW) method was implantedin the Vienna ab initio simulation package (VASP)[43,44]. The Perdew-Burke-Ernzerhof (PBE) version ofthe generalized gradient approximation (GGA) wasemployed[45]. The Van der Waals (vdW) interactionbetween TiO and GaSe layers was corrected with theDFT-D3 method of Grimme[46, 47]. As we all know, theDFT method is not quite accurate when dealing withtransition-metals systems with localized electrons (d orf). As a result, the DFT+U method was applied to de-scribe the localized Ti 3d electrons in the following equa-tion: E U = U (cid:88) I,σ Tr (cid:2) n Iσ (cid:0) − n lσ (cid:1)(cid:3) (1) E P BE + U − E P BE + U − J (cid:88) σ Tr [ ρ σ − ρ σ ρ σ ] (2)Where n Iσ denotes the occupation of the relevant lo-calized manifold at site I with spin σ , U denotesthe effective on-site Coulomb interaction[48]. With aself-consistent DFT+U approach[49, 50] performing onQuantum Espresso (QE), an open source first principlescode, the value of U was determined to be 4.75eV for theTi 3d electrons. The vacuum region along z direction wasset to be 20 and the energy cutoff was set to be 700eVthrough all calculations. For the structure relaxations,the k-points sampling with Γ centered MonkhorstPackScheme was chosen to be 8 × × × × × × re-spectively. All structures are fully relaxed until the forceswere less than 0.01eV/ and the energy tolerances weresmaller than 1 × − α ( ω ) was derived from the following formula, α ( ω ) = √ ω (cid:20)(cid:113) ε ( ω ) + ε ( ω ) − ε ( ω ) (cid:21) (3)Where (cid:15) ( ω ) and (cid:15) ( ω ) are the real and imaginary partof the complex dielectric function. For the calculation ofthe planar-averaged charge density, a fully relaxed 2x2unit cells of TiO /GaSe heterostructure was chosen, andthe k-points sampling was set to be 4 × ×
1. Moreover,the planar-averaged electron density difference ∆ ρ ( z ) isdefined as:∆ ρ (z) = (cid:90) Σ( z ) [ ρ ( T iO / GaSe ) − ρ ( T iO ) − ρ ( GaSe )]= (cid:88) ij ∆ ρ ij ∆ x i ∆ x j (4)In which, ρ ( T iO /GaSe ), ρ ( T iO ), ρ ( GaSe ) are the elec-tron density of TiO /GaSe heterostructure, TiO , GaSe,respectively. In addition, the interaction between theheterostructure and laser were calculated with the real-space and real-time TDDFT code OCTOPUS[51]. Tocalculate the nonlinear optical response of the system,we solved the time-dependent Schrodinger equation: − i ∂∂ t Ψ i ( r , t ) = Ψ i ( r , t ) × (cid:20) − ∇ υ ext ( r , t ) + υ Hartree ( r , t ) + υ xc ( r , t ) + υ laser ( r , t ) (cid:21) (5)Where ∇ denotes the kinetic energy, υ ext ( r , t ) is the ex-ternal potential, υ Hartree represents the electron-electroninteraction, υ xc ( r , t ) describes the exchange-correlationpotential, and υ laser ( r , t ) is the time-dependent electro-magnetic laser field. The initial state is given by solv-ing the ground-state Kohn-Sham equations. Then, theKohn-Sham orbitals propagate as:Ψ i ( r , t + ∆ t ) = e − i (cid:82) t +∆ tt dτ ˆ H KS ( r,t ) Ψ i ( r , t ) (6)As shown in Fig.1, the laser was simulated with theGaussian wave packet, which is defined as: f ( x ) cos[ ωt + φ ( t )] g ( t ) (7) g ( t ) = G exp (cid:104) − ( t − t ) / τ (cid:105) (8)In which f(x) denotes the laser polarization direction, ω represents the circular frequency, φ ( t ) defines the ini-tial phase, G is the amplitude of g(t) in units of eV/(1eV/ is equal to 1 . x W/cm , according to I = ecE , where e is the dielectric function, c is the lightvelocity in vacuum), t determines where g(t) centersaround, and τ is related to the full width at half maxi-mum (FWHM). The elements are described by the Pseu-doDojo Potentials[52]. The generalized gradient approx-imation (GGA) expressed by Perdew-Burke-Ernzerhof I n t e n s it y ( e V / ¯ ) t (fs)t G FIG. 1. Illustration of Gaussian laser oscillogram (PBE) functional is used both for the ground-state andexcited-state calculations. The simulation box is definedby adding a sphere of radius 8 around each atom witha uniform mesh grid of 0.3. For the time evolution, thetime-step is set to be 0 . (cid:126) eV − (around 0.0033fs). III. RESULTS AND DISCUSSIONA. Structures and electronic properties of GaSeand TiO monolayer SeTop view (a)
Se O2O1TiTop view (b) Se GaSide view (c)
O1 O2TiGa Side view (d)
FIG. 2. (a)Top and (c)side view of GaSe monolayer. Yellow,green stand for gallium, selenium, respectively. (b)Top and(d)side view of lepidocrocite-type TiO monolayer. Blue, redstands for titanium and oxygen. Before constructing the heterostructure, we first ana-lyzed geometric properties of the GaSe and TiO mono-layers. For GaSe monolayer, as shown in Fig.2, theoptimized lattice parameters are a=b=3.81 ; the Ga-Sebond length d Ga − Se and the Ga-Ga bond length d Ga − Ga are 2.40 and 2.497, respectively, which is in good agree-ment with previous studies (a=b=3.82, d Ga − Se =2.501, d Ga − Ga =2.470)[53]. For lepidocrocite-type TiO mono-layer, we can see from Fig.2(b, d) that the lattice param-eters are a=3.83 , b=3.05 . There are two inequivalent Oatoms that are 2-fold (O1) and 4-hold (O ) coordinatedto Ti atoms. The Ti-O1 bond length d T i − O is 1.860 ;The Ti-O bond length d T i − O is 2.014 ; The Ti to O in the next unit cell bond length d (cid:48) T i − O is 2.212 , whichalso consists with the values reported by other researchgroups (a=3.73 , b=3.03 , d T i − O =1.82 , d T i − O =2.23 , d (cid:48) T i − O =1.96 )[54].Meanwhile, we calculated the charge densities of theprimitive cells of GaSe and TiO monolayers. The Badercharge analysis suggests that 0.66 electron transfers fromeach Ga atom to per Se atom; each Ti atom lost 2.34electrons and each O atom at position 1 and 2 gains 1.07,1.17 of the electrons respectively. M K-3-2-10123 0 2 4 6X S Y-6.0-4.5-3.0-1.50.01.53.04.56.0 0 2 4 6 8 10 12 14 16 18 20 22 E n e r gy ( e V ) (a) PDOS(States/eV) total Ga-s Ga-p Se-s Se-p E n e r gy ( e V ) (b) PDOS(States/eV) total Ti-s Ti-p Ti-d O-s O-p
FIG. 3. The band structure and projected density of states(PDOS) of (a) GaSe monolayer and (b) lepidocrocite-typeTiO monolayer primitive cell. In Fig.3(a-b), we further computed the band structuresand projected density of states (PDOS) of the primitivecells of GaSe and TiO monolayers. Fig.3 shows thatGaSe possess an indirect band-gap of 1.796eV, which wellagrees with the value of previous study (1.82eV)[55]. Theconduction band minimum (CBM) locates at the Γ point,which is composed of 4s states of Ga atom and 4s, 4pstates of Se atom. The valence band maximum (VBM)lies on the ΓM line in the Brillouin zone (BZ), whichmainly contains the 4s, 4p states of Ga atom and 4pstates of Se atom. On the contrary, as shown in Fig.3(b),the TiO monolayer has a direct band gap of 3.633eV,locating at Γ point in the BZ, which is consistent withthe experiment value of 3.80eV2 due to the application ofDFT+U method. The CBM is contributed by 3d statesof Ti atom and 2p states of O atom, while VBM consistsof 2p states of O atom. B. Structures and electronic properties of TiO /GaSe heterostructure (a) (b) Se2
Se1Se2
Armchair direction Z i g za g d i r ec ti on (c) z d i r ec ti on (d) Se1
FIG. 4. Top view of (a) GaSe and (c) lepidocrocite-type TiO monolayer. (b)Top and (d) side view of the lepidocrocite-typeTiO /GaSe heterostructure. The black dash line rectanglesstand for the unit cells of each structure. The vacuum layeris not plotted. To start with, we cleaved a 1 × × slab. The van der Waals het-erostructure was constructed by stacking the GaSe (001)monolayer on the top of the TiO (001) monolayer. Thelattice mismatch is less than 4 . monolayer is 2.87 . Unlike theGaSe and TiO monolayer, the heterostructure is mono-clinic, with the space group of Pm. In the unit cell, theSe1 atom is on the top of the O atom and Se2 is on thetop of Ti atom; or equivalently, Se1 atom is on the top ofTi atom and Se2 is on the top of O atom. In order to an-alyze the stability of the heterostructure, we calculatedthe binding energy E b , which is defined in the formula: E b = E heterostructure − E Gase − E Tio (9)In which, E heterostructure , E GaSe , E T iO are the total en-ergy of the heterostructure, GaSe monolayer and TiO monolayer, respectively. By this definition, a more neg-ative E b indicates a more stable structure. The value of E b is calculated as -2.491eV, indicating a good stabilityof the heterostructure and a strong interaction of the twomonolayers.The band structure and partial density of states ofTiO /GaSe heterostructure are shown in Fig.5(a). As we can see, TiO /GaSe heterostructure is a semiconduc-tor with a direct band-gap of 0.963eV; the CBM andVBM both lie at the Γ point, which indicates that thelowest-energy electron-hole pairs can be spontaneouslyseparated, making TiO /GaSe heterostructure suitablefor applications in photovoltaic devices. The CBM aremainly composed of the 3d states of Ti atom, while theVBM is contributed by the 4p states of Ga, Se atoms.It is also clear that the CBM of TiO is lower thanthe CBM of GaSe; the VBM of TiO is also lower thanthe VBM of GaSe, which exhibits a type-II band align-ment. For further clarification, the band alignment withreference to the vacuum level ( E v acuum ) is shown inFig.5(b). The band offsets of the heterostructure are∆ E c =1.135eV and ∆ E v =2.643eV. For comparison, thenatural band offsets of individual TiO and GaSe mono-layer are ∆ E c =0.931eV and ∆ E v =2.773eV. The differ-ence in band offsets is mainly due to the charge redistri-bution when forming heterostructure. When light irra-diating, the photoexcited electrons can transfer from thevalence band (VB) to the conduction band (CB) bothin the TiO and GaSe monolayers. At the same time,photoexcited holes are left in the VBs. Due to the con-duction band offset ∆ E c , the photo-excited electrons onGaSe CB tend to flow to the CB of TiO nano sheet.Meanwhile, driven by the valence band offset ∆ E v , theleft holes shift from the VB of TiO surface to the VB ofGaSe surface. This kind of charge redistribution benefitsthe separation of photoexcited electrons and holes, pro-longing the lifetime of excitons, which accelerates the ox-idation and redox reactions on the surface and improvesthe efficiency of photocatalytic activity.To quantitatively investigate the charge redistributionactivity, we calculated the z-direction planar-averagedelectron density difference ∆ ρ ( z ) of the TiO /GaSe het-erostructure, as shown in Fig.6(a). The charge accumu-lation region is depicted in purple, while the charge de-pletion region is shown in cyan. The planar-averagedelectron density indicates that the charge redistributionmainly occurs at the interface of the heterostructure andthe electrons tend to flow from GaSe surface to TiO surface, which is in accordance with the band alignmentanalysis. To quantitively gain an insight of the chargetransference, we carried out the Bader charge analysis ofthe TiO /GaSe heterostructure. The result suggests that0.099 electrons transfers from GaSe layer to the TiO layer. The net charge accumulation leads to the for-mation of a built-in electric field at the interface of theTiO /GaSe heterostructure. The direction of the elec-tric field is from GaSe monolayer to the TiO monolayer,which in turn hinders the flow of the electrons and holes,and the system will finally achieve equilibrium as the dif-fusion force is balanced with the built-in electric field. X S Y-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.0 0 5 10 15 20 25 30 E n e r gy ( e V ) (a) PDOS (States/eV) total Ti-d O-p Ga-p Se-p (b) FIG. 5. (a) The band structure and projected density of states (PDOS) of TiO / GaSe heterostructure. (b) Illustration of theband alignment of the TiO /GaSe heterostructure with respect to the vacuum level. (c)(a) (b) Z direction
FIG. 6. (a) The planar-averaged electron density difference ∆ ρ ( z ) along z direction of the TiO /GaSe heterostructure. (b)Side and (c) top view of the charge density difference of the TiO /GaSe heterostructure. The purple and cyan denote electronaccumulation and depletion regions, respectively. A b s o r p ti on () ( c m - ) (nm) TiO /GaSe GaSe TiO (a) Armchair A b s o r p ti on () ( c m - ) (nm) TiO /GaSe GaSe TiO (b) Zigzag A b s o r p ti on () ( c m - ) (nm) TiO /GaSe GaSe TiO (c) Z-axis A b s o r p ti on () ( c m - ) (nm) Armchair Zigzag Z-axis (d) TiO /GaSe FIG. 7. The optical absorption coefficient α ( λ ) of TiO /GaSe heterostructure, GaSe monolayer, TiO monolayer along (a) arm-chair direction, (b) zigzag direction, (c) z-axis. (d) Comparison of the absorption coefficient of the TiO /GaSe heterostructurealong the armchair, zigzag and z direction. C. Optical properties of TiO /GaSeheterostructure and TiO , GaSe monolayers To further explore the photoelectronic properties ofTiO /GaSe, we calculated the optical absorption coef-ficient α ( ω ) of the heterostructure, GaSe slab and TiO slab along the armchair, zigzag and z directions, as ex-hibited in Fig.7(a-d). The absorption range of the het-erostructure extends broadly from visible light to theultraviolet (UV) region, and the absorption intensityreaches an order of 10 . Compared with TiO andGaSe monolayer, the heterostructure s absorption be-havior is clearly enhanced in UV region, which indicatesthat TiO /GaSe heterostructure can be used for develop-ing electro-photonic detectors. The absorption intensityalong armchair direction is stronger than those along thezigzag and z-axis directions in 120 220nm, and the ab-sorption intensity along z axis is weaker than those alongthe armchair and zigzag directions in 220 320nm. Theanisotropic behavior makes TiO heterostructure suit-able for serving as polarized optical sensors. D. Tuning band structures of heterostructure withbiaxial strain and interlayer coupling
For the application of 2D materials in real systems,the modulation of electronic structure has always beenan important question. It has been clarified in many ex-perimental and theoretical studies that the mechanicalstrain and interlayer coupling play an important role inmodulating band structures and electronic properties ofmaterials[56–60]. In this case, we first studied the changein the bandgaps and band edges of the TiO /GaSe het-erostructure when applying biaxial tensile and compres-sive strains in the xy-plane. The biaxial strain alongx and y direction can be characterized by the degreein which the lattice constant differs from its optimizedvalue: ε = ( a − a ) /a , where a denotes the optimizedlattice parameter. The tensile and compressive strainis characterized by the positive and negative value of ε ,respectively. The evolution of bandgaps of TiO /GaSeheterostructure under a strain ranging from −
5% to %5with a spacing of 1% along zigzag and armchair directionsis shown in Fig.8(a).From Fig.8(a), we can see that as the lattice constantsincrease along the armchair direction, the bandgap de-creases. However, as the lattice parameters augmentalong the zigzag direction, the bandgap increases. Mean-while, for the strain along the armchair direction, the -5 -4 -3 -2 -1 0 1 2 3 4 50.650.700.750.800.850.900.951.00 -5 -4 -3 -2 -1 0 1 2 3 4 5-6.0-5.8-5.6-5.4-5.2-5.0-4.8-4.62.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.00.950.960.970.980.991.001.011.021.03 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0-6.0-5.8-5.6-5.4-5.2-5.0-4.8-4.6 B a nd g a p ( e V ) (%) Armchair Zigzag (a) E n e r gy l e v e l ( e V ) (%) Armchair Zigzag (c) B a nd g a p ( e V ) d i (¯) (b) E n e r gy l e v e l ( e V ) d i (¯) (d) FIG. 8. (a) Bandgap, (b) CBM and VBM of the TiO /GaSe heterostructure as a function of strain ε along the armchair andzigzag direction, respectively. (b) Bandgap, (d)CBM and VBM of the TiO /GaSe heterostructure as a function of interlayerdistance di. bandgap of the heterostructure is more sensitive to thetensile strain than compressive strain. On the con-trary, when it comes to the zigzag direction, the bandgapchanges more rapidly with compressive strain than ten-sile strain. In addition, the bandgap changes linearlywhen applying tensile strain along armchair direction orcompressive strain along zigzag direction, which indicatessuch heterostructure may be developed as a mechanicalsensor.For better revealing the change of the band structureunder biaxial strain, we studied in detail the variations ofband edges of the heterostructure. As Fig.8(c) indicatess,along armchair direction, strain has more influence on theCBM than VBM, while strain almost equally affects theCBM and VBM along zigzag direction, which explainswhy bandgap changes more rapidly with strain alongarmchair direction than along zigzag direction. Mean-while, with the increase of compressive strain along arm-chair direction, the CBM and VBM varies almost at thesame gradient, which accounts for the insensibility for thebandgap to compressive along armchair direction. How-ever, the inertia for bandgap to tensile strain along zigzagdirection is due to the fact that tensile strain along zigzagdirection nearly has no effect on the band edges of theheterostructure.In the case of interlayer coupling, the bandgap andband edges as a function of the interlayer distance d i is shown in Fig.8(c, d). A lower d i than the equilibriumvalue denotes a compressive strain along the directionperpendicular to the surface, while a larger interlayerthan the optimized value stands for a tensile strain. Itindicates that as d i increases, the bandgap of the het-erostructure first decreases rapidly, and then reaches athreshold of around 0.95eV. This is for the fact that theCBM of the heterostructure hardly changes with different d i , while the VBM gradually increases with the increaseof d i . Comparing Fig.8(a) with Fig.8(b), it can also beseen that to changing bandgap with biaxial strain is moreeffective than interlayer coupling.Such phenomena are mainly due to the fact that theapplied tensile and compressive strain changes the dis-tance between the atoms, leading to a different superpo-sition of the atomic orbitals which result in the shift ofthe energy of the states.Then, we further investigated the detailed band struc-tures with different strains, as shown in Fig.9(a-l). It ex-hibits an obvious transition for the heterostructure fromdirect bandgap to indirect bandgap in all cases. Thebandgap becomes indirect as long as the biaxial strainis applied, while for the interlayer coupling, the transi-tion occurred when d i is less than 2.6. For biaxial strain,comparing with the optimized heterostructure, the com-pressive strain along the armchair direction drives theCBM from Γ to Y. On the contrary, the tensile along X S Y-2.0-1.5-1.0-0.50.00.51.01.52.0 X S Y X S Y X S YX S Y-2.0-1.5-1.0-0.50.00.51.01.52.0 X S Y X S Y X S YX S Y-2.0-1.5-1.0-0.50.00.51.01.52.0 X S Y X S Y X S Y E n e r gy ( e V ) Armchair -4% (a)
Armchair -1% (b)
Armchair +1% (c)
Armchair +4% (d) E n e r gy ( e V ) Zigzag -5% (e)
Zigzag -2% (f)
Zigzag +2% (g)
Zigzag +5% (h) E n e r gy ( e V ) (i) (j) (k) (l) FIG. 9. Band structures of the TiO /GaSe heterostructure with (a-d) ε = ± ±
4% along the armchair direction and (e-h) ε = ± ±
5% along the zigzag direction. (i-l) Band structures of the TiO /GaSe heterostructure with interlayer distance d i =2.0, 2.6, 2.8, 4.0, respectively. VacuumGaSeTiO Vacuum ( - e / ¯ ) z (¯) (a) Vacuum ( - e / ¯ ) z (¯) Vacuum TiO GaSe (b)
VacuumGaSeTiO Vacuum ( - e / ¯ ) z (¯) (c) FIG. 10. The planar-averaged electron density difference ∆ ρ ( z ) along z direction of the heterostructure with the interlayerdistance di=2.4, 2.9 and 3.4, respectively. the armchair direction cause the VBM to shift along ΓXline. Similar phenomena are also found when applyingstrain along the zigzag direction. For interlayer coupling,when the interlayer distance d i varies from 2.0 to 2.6, theCBM of the heterostructure locates at the Y point and the VBM lies at the point on ΓX line. At the range of2.8 to 4.0, the CBM and VBM both lie at the Γ point.Essentially, such phenomena are mainly due to the factthat for the equilibrium heterostructure, the energy dif-ference between the conduction band at the Γ and Y isso small that a slight change in the distance between theatoms under the strain is sufficient to alter the energystates, leading to a transformation from direct bandgapto indirect bandgap. This is also true for the valenceband at Γ and the point on ΓX line.Finally, we investigated how interlayer distance affectsthe charge redistribution. The Bader charge analysis in-dicates that about 0.193 electrons transfer from GaSemonolayer to TiO surface when d i =2.4. When d i =3.4,the transferred electron number is 0.054, while for theoptimized structure ( d i =2.9), the value was 0.099. Theplanar-averaged electron density difference of the het-erostructure with different d i are plotted in Fig.10(a-c).As the figures suggest, with the decrease of the inter-layer distance, the amount of the accumulated net chargeon the interface increases, which manifests that chargeredistribution can be enhanced by decreasing interlayerdistance. This is for the fact that as the interlayer dis-tance decrease, the interaction between the monolayerswill increase, enhancing the charge redistribution at theinterface. E. Ultrafast laser induced semiconductor-metaltransition in TiO /GaSe heterostructure To explore the potential application for the TiO /GaSeheterostructure in developing optoelectronic devices, wefinally calculated the electronic properties of the het-erostructure under the illumination of ultrafast laserswith different intensities and different frequencies, re-spectively. The Fermi level is assumed to be determinedby the external voltage bias and is immune to the elec-tronic dynamics in the heterostructure. By investigat-ing the intrinsic density of states (DOS) of TiO /GaSe,as shown in Fig.11, the change of the electron occu-pied states is characterized by the highest electron state(HES), as well as the number of electrons across theFermi level ( N F ).
1. Ultrafast laser with different intensity irradiating on theTiO /GaSe heterostructure For the study of intensity of the ultrafast lasers influ-ence on the heterostructure, we studied two cases. In thefirst case, the intensity of the incident x-axis polarizedlaser with 358nm wavelength alter from 3.5 eV/ to 4.5eV/, with a spacing of 0.25 eV/. As shown in Fig.12(b,c), at first, the HES of the heterostructure just fluctu-ates with the propagation of the laser pulse. At 3fs,for the whole range of laser intensity, the HES starts tocross the Fermi level, which indicates a transition fromsemiconductor to metal. In addition, after 4fs, the HESstops fluctuates with the laser pulse and maintains themetallic electronic state afterwards. Why does such phe-nomenon occur? As aforementioned, the heterostructurecan enhance the charge redistribution at the interface, -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 502468101214161820 DO S ( S t a t e s / e V ) Energy (eV)
FIG. 11. Intrinsic density of states (DOS) of the TiO /GaSeheterostructure. and at equilibrium, the electrons diffusion is balancedwith the built-in electric field which arises from the netcharge accumulation. When the intense ultrafast laserwas applied, this balance will be temporarily broken. Byabsorbing energy from the incident laser, more and moreelectrons are excited, enhancing the diffusion of electronsand holes, as well as the interaction between monolayers,which essentially leads to the semiconductor-metal tran-sition. Meanwhile, with the increase of the number ofaccumulated charges at the interface, the built-in elec-tric field gradually augments, too. However, since thelaser varies very fast, the new balance between the built-in electric field and the diffusion of excitons cannot beachieved temporarily. As a result, the highest electronstates (HES) fluctuate as the laser intensity changes, cor-responding to the trend of HES in Fig.12(b) from 0fs to4fs. Nevertheless, the intensity of the laser is damping.After 4fs, the value of the intensity is not more than1eV/. With such a low intensity, no more electrons willbe excited from the heterostructure. Consequently, thenew equilibrium between the built-in electric field andthe diffusion of excitons is reached, which explains whythe HES still maintains the relatively high energy leveland the heterostructure maintains the metal state since4fs.To further elucidate the charge redistribution in theprocess, we calculated the photo-induced charge den-sity distribution in real-time propagation, as exhibitedin Fig.12(d-i). It suggests that at 0.5fs, the inducedelectron density and the hole density are still localizedunder the weaker laser intensity, which manifests thatthe heterostructure is still a semiconductor. On the con-trary, at 5fs, the more enhanced induced electron densityand hole density becomes continuous and forms photo-induced currents, which suggests a semiconductor-metaltransition.In the other case, the incident laser was chosen to be z-axis polarized with 694nm wavelength, and the intensity0 I n t e n s it y ( e V / ¯ ) t (fs) 3.50 3.75 4.00 4.25 4.50 (a) H E S ( e V ) t (fs) 3.5 3.75 4.0 4.25 4.5 (b) N F t (fs) 3.5 3.75 4.0 4.25 4.5 (c) (d) (e) (f) (g) (h) (i) x=0 (j) y=0 (k) z=0 (l) FIG. 12. (a) Laser oscillogram. (b) The highest electron state (HES) and (c) the number of electrons across the Fermi level ofTiO /GaSe as a function of time. Induced charge density distribution of TiO /GaSe at (d-f) 5fs and (g-i) 0.5fs with x-polarizedlaser intensity equals to 4.25 eV/. Electron accumulation and depletion are denoted as red and blue, respectively. (j) Frontview, (k) side view and (l)top view of TiO /GaSe corresponding to induced charge density distribution. also varies from 3.5 eV/ to 4.5 eV/, with a spacing of 0.25eV/. Similar phenomena have been found for the trendof HES and N F from Fig.13(b, c). The different pointis that under high intensity laser, the photo-induced cur-rent is more intense than that in the case where laser isx-polarized, as shown in Fig.13(d-i), which means thatthe heterostructure is more sensitive to the laser alongz direction. In addition, the photo-induced current is mainly at the interface of the heterostructure, which cor-responds to the aforementioned conclusion that the het-erostructure can enhance the charge redistribution at theinterface, which causes the polarization of electrons andholes, leading to the formation of interface dipole. Thebehaviors of the plasmon resonance manifests that thecoupling of TiO /GaSe and ultrafast laser has potentialapplication in nanoscale plasmonic devices.1 I n t e n s it y ( e V / ¯ ) t (fs) 3.50 3.75 4.00 4.25 4.50 (a) H E S ( e V ) t (fs) 3.5 3.75 4 4.25 4.5 (b) N F t (fs) 3.5 3.75 4 4.25 4.5 (c) (d) (e) (f) (g) (h) (i) x=0 (j) y=0 (k) z=0 (l) FIG. 13. (a) Laser oscillogram. (b) HES and (c) N F of TiO /GaSe as a function of time. Induced charge density distributionof TiO /GaSe at (d-f) 2fs and (g-i) 0.5fs with z-polarized laser intensity equals to 4.25 eV/. Electron accumulation and depletionare denoted as red and blue, respectively. (j) Front view, (k) side view and (l)top view of TiO /GaSe corresponding to inducedcharge density distribution.
2. Ultrafast laser with different frequency acting on theTiO /GaSe heterostructure Various wavelength lasers have always been applied ininvestigating the optical properties of all kinds of mate-rials. To simulate lasers acting on TiO /GaSe in ex-periment, the laser wavelengths are set to be 694nm,633nm, 543nm, 488nm, 358nm, corresponding to the ruby laser, Helium-Neon gas laser (red), Helium-Neongas laser (green), Argon ion laser and Nitrogen laser, re-spectively. The intensity of the laser is chosen to be 4.5eV/. As shown in Fig.14(b, c), the trends of the HES and N F are similar to these we discussed in Sec.III E 1. Whatis new is that although the laser with other wavelengthcan also raise the HES of the system, only 358nm wave-length laser can transfer the system from semiconductor2 I n t e n s it y ( e V / ¯ ) t (fs) 3.50 3.75 4.00 4.25 4.50 (a) H E S ( e V ) t (fs) 694nm 633nm 543nm 488nm 358nm (b) N F t (fs) 694nm 633nm 543nm 488nm 358nm (c) (d) (e) z=0 -0.030-0.022-0.015-0.00750.00.00750.0150.0220.030 (f) -0.030-0.022-0.015-0.00750.00.00750.0150.0220.030 (g) -0.030-0.022-0.015-0.00750.00.00750.0150.0220.030 (h) -0.030-0.022-0.015-0.00750.00.00750.0150.0220.030 (i) x=0 (j) y=0 (k) z=0 (l) FIG. 14. (a) Laser oscillogram. (b) HES and (c) N F of TiO /GaSe as a function of time. Induced charge density distributionof TiO /GaSe at (d-f) 5fs and (g-i) 0.5fs with x-polarized laser frequency equals to 358nm. Electron accumulation and depletionare denoted as red and blue, respectively. (j) Front view, (k) side view and (l)top view of TiO /GaSe corresponding to inducedcharge density distribution. to metal, which indicates that the semiconductor-metaltransition can be induced by tuning the wavelength of theincident laser. One reason for explaining the transitionis that the eigenfrequency of the TiO /GaSe heterostruc-ture is close to 358nm, which makes the electrons gainmore resonance energy. Another reason is that 358nm isin the UV region, which is stronger in energy than theothers. Consequently, the electrons may absorb more en- ergy and are more likely to be excited.In the case of laser along z direction, as exhibitedin Fig.15(b, c), the trend of HES and N F also resem-bles the aforementioned ones, but unlike the case ofx-direction laser, all of the wavelength can induce asemiconductor-metal transition for the system. This isalso indicates that the heterostructure is more sensitiveto the z-polarized laser. Moreover, the distribution of3 I n t e n s it y ( e V / ¯ ) t (fs) 694nm 633nm 543nm 488nm 358nm (a) H E S ( e V ) t (fs) (b) N F t (fs) (c) (d) (e) (f) (g) (h) (i)(j) x=0 y=0 (k) z=0 (l) FIG. 15. (a) Laser oscillogram. (b) HES and (c) N F of TiO /GaSe as a function of time. Induced charge density distribution ofTiO /GaSe at (d-f) 1.5fs and (g-i) 0.5fs with z-polarized laser frequency equals to 488nm. Electron accumulation and depletionare denoted as red and blue, respectively. (j) Front view, (k) side view and (l)top view of TiO /GaSe corresponding to inducedcharge density distribution. induced charge density, as shown in Fig.15(d-i), suggeststhat under the ultrafst laser, the electrons and holes atthe interface are polarized and the interface dipole is for-matted. IV. CONCLUSIONS
In summary, we have systematically studied the prop-erties of the lepidocrocite-type TiO /GaSe heterostruc-ture based on first-principle calculations. From the anal-ysis of the band structure and PDOS as well as the op-tical absorption spectrum, we find that the TiO /GaSehas a direct bandgap at the value of 0.963eV. It exhibits4a type-II band alignment, a strong and broad optical ab-sorption, ranging from visible light to UV region, whichis beneficial to photovoltaic and photoelectronic devices.The planar-averaged electron density and Bader chargeanalysis further confirm its advantage in enhancing theseparation of the electrons and holes, which is benefitialto photocatalysis. Through the investigation of bandgapmodulation with biaxial strain and interlayer coupling,we find a direct-bandgap to indirect-bandgap transitionboth for biaxial strain and interlayer coupling. The lin-ear change of bandgap with biaxial strain manifests itspotential application in mechanical sensors. Finally, thecalculation of ultrafast laser acting on TiO /GaSe fur-ther indicates that laser with specific wavelength and in-tensity can induce a semiconductor-metal transition forthe heterostructure. Furthermore, the enhanced induced plasmonic current implys that TiO /GaSe coupling withultrafast laser may be a good candidate in plasmonic de-vices. Our calculations provide valuable guidance for ap-plying the lepidocrocite-type TiO /GaSe heterostructurein photovoltaic devices, photoelectronic devices, photo-catalysis, mechanical sensors and plasmonic devices. ACKNOWLEDGMENTS
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