A new promising semiconductor material (phosphorene) is studied using theoretical simulation. The possibilities of changing the magnitude and nature of interband transitions under the action of compressive and tensile stresses on the phosphorene crystal lattice are determined. It is found that phosphorene can be both direct-gap and indirect-gap semiconductors, depending on the magnitude and direction of stress action. Phosphorene can be used in new generation nanoelectronic devices with controlled movement of charge carriers

Krivosheeva, A. V.

Shaposhnikov, V. L.

Štich, I.

Кривошеева, А. В.

Шапошников, В. Л.

Belarusian State University of Informatics and Radioelectronics Repository

ISSN 1063-7834, Physics of the Solid State, 2021. © Pleiades Publishing, Ltd., 2021.Russian Text © The Author(s), 2021, published in Fizika Tverdogo Tela, 2021, Vol. 63, No. 10, pp. 1663–1667.LOW-DIMENSIONALSYSTEMSThe Effect of Compressive and Tensile Strainson the Electron Structure of PhosphoreneA. V. Krivosheevaa, b, *, V. L. Shaposhnikova, and I. Štichba Belarusian State University of Informatics and Radioelectronics (BSUIR), Minsk, 220013 Belarusb Center for Computational Material Science, Institute of Physics of the Slovak Academy of Sciences,Bratislava, 84511 Slovakia*e-mail: krivosheeva@bsuir.byReceived May 13, 2021; revised May 13, 2021; accepted May 13, 2021Abstract—A new promising semiconductor material (phosphorene) is studied using theoretical simulation.The possibilities of changing the magnitude and nature of interband transitions under the action of compres-sive and tensile stresses on the phosphorene crystal lattice are determined. It is found that phosphorene canbe both direct-gap and indirect-gap semiconductors, depending on the magnitude and direction of stressaction. Phosphorene can be used in new generation nanoelectronic devices with controlled movement ofcharge carriers.Keywords: phosphorene, monolayer, band structure, band gap, deformation, stressesDOI: 10.1134/S1063783421100188INTRODUCTIONThe discovery of the possibilities for graphene [1]has caused a surge of interest in materials consisting ofmonoatomic layers interconnected by means ofvan der Waals forces. The unique properties of two-dimensional materials such as binary transition metalchalcogenides and materials of one type of atoms, forexample, phosphorene, make it possible to design newtype of nanoelectronic devices on their basis [2, 3].Such compounds have structural stability and highmobility of charge carriers at room temperature andcan be used to create field-effect transistors [4]. Thereare papers on the successful creation of structuresfrom individual layers of refractory metal dichalco-genides [5, 6] and studies of their optical absorptionand photoconductivity spectra [7]. Samples of low-power field-effect transistors, logic circuits, pho-totransistors [4, 8, 9] are made on the basis of MoS2,one of the most stable and best studied layered dichal-cogenides [2]. A study of the strains of the crystal lat-tice of MoS2 showed that biaxial stress leads to adecrease in its band gap, and the MoS2 monolayer,which is a direct-gap semiconductor, transforms intoan indirect-gap semiconductor already at 2% defor-mation [10].A new promising semiconductor material for opto-electronics and nanoelectronics is phosphorene (atwo-dimensional modification of black phosphorus).The experimental production of phosphorene by sep-arating black phosphorus into layers of monoatomicthickness has increased the attention to this material[3, 11–13]. Unlike graphene, the atoms in phos-phorene do not lie in the same plane, but form acurved structure [11]. Phosphorene is a direct-gapsemiconductor with a band gap of about 2 eV [12].There is information about the manufacture of field-effect transistor based on phosphorene [3]. Theauthors of [13] proposed to use phosphorene in medi-cine as a carrier agent for a targeted drug delivery sys-tem (chlorambucil) in the treatment of oncologicaldiseases.The development of new devices based on layeredmaterials requires a detailed study of their propertiesand the conditions for changing their physical charac-teristics under various influencing factors. The influ-ence of impurities, vacancies, and ways of differentarrangement of dichalcogenide layers on their proper-ties is studied in [14–16]. Another possibility of mod-ifying properties is the strain of the crystal lattice of thematerial due to the compressive or tensile stresses, as aresult of which magnetic properties can appear in non-magnetic materials, and the nature of direct and indi-rect transitions also changes [10, 17–23]. The numberof publications describing the possibility of engineer-ing the band gap of two-dimensional materials usingapplied stresses is increasing. Such stresses can be pro-duced by bending or tension of the substrate, on whichthe material layer is located, or by the inhomogeneitiesin the material [24]. The described engineering is usedto design a new class of straintronic devices based ontwo-dimensional crystals, in which the electrical andoptical parameters of the devices are controlled by12 KRIVOSHEEVA et al.Fig. 1. 1 × 1 cell of phosphoren. The solid line shows theunit cell without taking into account the vacuum.xybaYyyzZ1 23 4applying controlled levels of uniaxial and biaxialstresses [24]. The possibility of increasing the Seebeckcoefficient and the electrical conductivity of phos-phorene due to the application of uniaxial stresses hasbeen theoretically confirmed. This fact indicates thatthis material is promising for thermoelectric applica-tions [25, 26]. However, the effect of strain of thephosphorene crystal lattice on its physical propertieshas not been studied.This work presents the results of theoretical simu-lation of the effect of compressive and tensile stressesin the crystal lattice of phosphorene on the change inits band gap and the nature of interband transitions.These data are necessary to determine the possibilitiesof targeted modification of the properties of two-dimensional materials.EXPERIMENTALPhosphorene has an orthorhombic crystal lattice(space group is Cmca) [27]; the arrangement of phos-phorus atoms in it is shown in Fig. 1. Here Z denotes aparameter, the value of which was varied to realize theeffect of compressive or tensile stress.In the process of modeling, a translational cell witha size of 1 × 1 in the xy plane corresponding to a prim-itive cell was used. In the z direction, a vacuum layerwith a thickness of 15 Å was added to exclude the inter-action between the layers during translation. Whenmodeling deformation in phosphorene, two parame-ters (Z parameter corresponds to the distance betweenatoms of 2 and 3 and Y parameter corresponds to thedistance between atoms of 1 and 2) were controlled bychanging the projection parameter Δy with a step of0.01 Å.The atomic positions in the crystal lattice wereoptimized in the context of the density functional the-ory using the PAW-PBE approximation [28] imple-mented in the VASP program code [29]. The cutoffenergy given by the ENCUT parameter was 340 eV.Integration over the Brillouin zone was performed bythe method of linear tetrahedra over a grid of 12 × 12 ×1 points centered at the Γ point. The change in atomicpositions stopped when the forces acting on the atomsreached a value of 1 meV Å–1.RESULTS AND DISCUSSIONFirst, we calculated the values of the lattice con-stants a and b, at which the total energy of the systemis minimum, which corresponds to an unstressed crys-tal lattice. For this, parameters a and b were changedsequentially with a step of 0.01 Å. The optimized lat-tice parameters of phosphorene are a = 3.30 Å and b =4.62 Å; the minimum values are Z = 2.26 Å and Y =2.22 Å. Then, in order to model the effect of stress inthe lattice at the optimized values of a and b, theparameters Z and Y were changed in the range selectedfor each particular case with a step of 0.01 Å. We con-sidered two types of impacts (only the parameter Z isvaried in the range from 2.20 to 2.32 Å; both parameterZ (in the same range of values) and Y (from 2.17 to2.28 Å) varied simultaneously).According to calculations, the band gap of phos-phorene with an undeformed crystal lattice is 0.89 eV(Fig. 2a); the material is a direct-gap semiconductorwith the first direct transition at Γ point. The band gapand structural parameters of the material are in goodagreement with the results of other theoretical calcula-tions for phosphorene (Eg = 0.9 eV [30], a = 3.30 Å,and b = 4.624 Å [31]). The distance between phospho-rus atoms in the plane of the layer (between atoms of 1and 2, 3 and 4) is 2.22 Å; the distance between phos-phorus atoms in the direction perpendicular to thelayer (between atoms of 2 and 3, Fig. 1) is 2.26 Å.The electronic band structures of phosphorenewith parameters corresponding to the unstressed lat-tice in comparison with the spectra of phosphoreneunder the action of compressive and tensile stresses areshown in Fig. 2. It is obvious that the application ofstresses changes the structural symmetry and leads toa shift in the band extrema from high symmetry points:a decrease in the Z  parameter relative to its equilib-rium value leads to a shift in the minimum of the con-duction band from the Γ point in the Γ–X direction(Γ ' point), the semiconductor becomes indirect-gapsemiconductor. In addition, a region of f lat bandsappears in the valence band in the vicinity of the Γ pointwith increasing Z parameter (Fig. 2b), which shouldPHYSICS OF THE SOLID STATE  2021PHYSICS OF THE SOLID STATE  2021THE EFFECT OF COMPRESSIVE AND TENSILE STRAINS 3Fig. 2. The electronic band structure of phosphorene with an undeformed crystal lattice (a) under the effect of compressive(Z = 2.20 Å) and tensile (Z = 2.32 Å) stresses (along the Z direction) (b) and under the effect of stresses that change distancesalong Z and Y directions (c). Zero on the energy scale corresponds to the position of the maximum of the valence band.X S YΓ ΓΓ' X S YΓ ΓΓ' X S YΓ ΓΓ'Energy, eVEnergy, eVEnergy, eV0 0 0–2 –2 –22 2 2–4 –4 –44 4 4Y = 2.22 Å, Z = 2.26 Å, Eg = 0.89 eV Y = 2.22 Å, Z = 2.32 Å, Eg = 0.55 eVY = 2.22 Å, Z = 2.20 Å, Eg = 1.15 eVY = 2.16 Å, Z = 2.32 Å, Eg = 0.58 eVY = 2.27 Å, Z = 2.20 Å, Eg = 0.99 eV(c)(b)(a)Fig. 3. Total and partial densities of electronic states of phosphorene with an undeformed crystal lattice (a) under the effect ofcompressive (Z = 2.20 Å) and tensile (Z = 2.32 Å) stresses (along the Z direction) (b) and under the effect of stresses that changedistances along the Z and Y directions (c). Zero on the energy scale corresponds to the position of the Fermi level.20.6610.44000DOS, states/eVDOS, states/eVDOS, states/eV−4 −2 420(a)Energy, eV−4 −2 420Energy, eV−4 −2 420Energy, eVp-states p-statess-statesTotal DOSs-statesTotal DOSp-statess-statesTotal DOSPristine structure0.228210(b)Z = 2.20 ÅZ = 2.32 ÅY = 2.27 Å, Z = 2.20 ÅY = 2.16 Å, Z = 2.32 Å0.660.44000.228210(c)60.44000.2284 KRIVOSHEEVA et al.Fig. 4. Changes in the magnitude and nature of electron transitions in phosphorene under the influence of deformation of its crys-tal lattice (a) when changing the Z parameter and (b) when changing the Z and Y parameters. The dashed line corresponds to theparameters of the unstressed lattice.0.80.71.00.61.1a = 3.30 Åb = 4.62 Å0.91.2Eg, eVEg, eV2.20 2.22 2.24 2.26 2.28 2.30 2.32Z, Å Y, Å 0.80.71.00.61.10.91.22.16 2.18 2.20Γ−ΓΓ−Γ'2.22 2.24 2.26 2.281.30.5(a) (b)lead to an increase in the corresponding componentsof effective hole masses. This affects the mobility ofcharge carriers and other physical parameters. Theposition of the band peaks shifts in a similar way witha simultaneous decrease in the Z parameter and anincrease in the Y parameter (Fig. 2c). In its turn, anincrease in the Z parameter with a simultaneouschange in the Y parameter leads to a decrease in theband gap, the semiconductor remains direct-gapsemiconductor.Figure 3 shows the total and partial densities ofelectronic states of phosphorene with an undeformedcrystal lattice (a) and upon application of compressiveand tensile stresses (b, c). The states near the Fermilevel are formed due to the hybridization of the s andp states of phosphorus. The impact of stresses pre-dominantly leads to a redistribution of the peaks of thes and p states in the conduction band; the displace-ment of the peaks leads to a change in the band gap:it decreases for Z tension and increases for Z com-pression.The dependences of the change in the band gap ofphosphorene on the direction and magnitude of theapplied stresses are shown in Fig. 4. They can beextrapolated by linear polynomials such as Eg(Z) =12.34 – 5.06Z (for Γ–Γ transition), Eg(Z) = 0.053 +0.47Z (for Γ–Γ ' transition) (Fig. 4a), Eg(Y) = –11.16 +5.43Y (for Γ–Γ transition), and Eg(Y) = 6.78 – 2.55Y(for Γ–Γ ' transition) (Fig. 4b). The data indicate thatthe direction of movement of charge carriers in thecrystal lattice of phosphorene can be controlled byadjusting the magnitude and direction of appliedstresses that change the Z and Y parameters due to thedisplacement of the position of the minima and max-ima of the bands and the corresponding transforma-tion of a direct-gap semiconductor into an indirect-gap semiconductor. This makes it possible to designnew types of electronic devices.CONCLUSIONSThe influence of deformation of the crystal latticeof phosphorene on the structure of its electronic bandsis determined by computer simulation from first prin-ciples. It is found that both compressive and tensilestresses arising in semiconductor crystal lattice canlead to the transformation of such a direct-gap semi-conductor into an indirect-gap semiconductor andvice versa. The determined conditions for such transi-tions expand the possibilities of designing new elec-tronic devices based on the materials.ACKNOWLEDGMENTSWe are grateful to colleagues K. Tokár and J. Brndiar fortheir help in performing calculations and participation indiscussions of the results, as well as to Professor V. E. Bori-senko for helpful remarks when writing this article.FUNDINGThis work was supported by an international grant underthe scholarship program of the Slovak Academy of Sciencesand a state assignment of the Republic of Belarus “PhysicalMaterials Science, New Materials and Technologies”(Fizmattech).PHYSICS OF THE SOLID STATE  2021THE EFFECT OF COMPRESSIVE AND TENSILE STRAINS 5CONFLICT OF INTERESTThe authors declare that they have no conflicts of interest.REFERENCES1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang,Y. Zhang, S. V. Dubonos, I. V. Grigorieva, andA. A. Firsov, Science (Washington, DC, U. S.) 306,666 (2004).2. K. S. Novoselov, D. Jiang, F. Schedin, T. J. 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The Effect of Compressive and Tensile Strains on the Electron Structure of Phosphorene

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The Effect of Compressive and Tensile Strains on the Electron Structure of Phosphorene

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