Features of Electronic, Mechanical, and Electromechanical Properties

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The Features of Electronic, Mechanical and Electromechanical Properties of Fluorinated Diamond Films of Nanometer Thickness Alexander G. Kvashnin, Pavel V Avramov, Dmitry G. Kvashnin, Leonid A. Chernozatonskii, and Pavel Sorokin J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b07946 • Publication Date (Web): 21 Nov 2017 Downloaded from http://pubs.acs.org on November 23, 2017

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The Journal of Physical Chemistry

The Features of Electronic, Mechanical and Electromechanical Properties of Fluorinated Diamond Films of Nanometer Thickness A.G. Kvashnin,1,2 P.V. Avramov,3 D.G. Kvashnin,4,5 L.A. Chernozatonskii,5 P.B. Sorokin4,5,6* 1

Skolkovo Institute of Science and Technology, Skolkovo Innovation Center 143026, 3 Nobel

Street, Moscow, Russian Federation 2

Moscow Institute of Physics and Technology, 141700, 9 Institutsky lane, Dolgoprudny,

Russian Federation 3

Department of Chemistry, Kyungpook National University, Daegu, Republic of Korea

4

National University of Science and Technology MISiS, 4 Leninskiy prospekt, Moscow,

119049, Russian Federation 5

Emanuel Institute of Biochemical Physics of RAS, 119334, 4 Kosygin Street, Moscow, Russian

Federation 6

Technological Institute for Superhard and Novel Carbon Materials, 7a Centralnaya Street,

Troitsk, Moscow, 108840, Russian Federation *

Corresponding author: [email protected]

ABSTRACT. Electronic, elastic and electromechanical properties of the quasi-two-dimensional diamond films of cubic and hexagonal symmetry with fluorinated surfaces were studied using 1

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electronic band structure calculations in the framework of DFT-PBE and self-consistent GW methods. Predicted 2D elastic constants and acoustic velocities of the films coincide well with available experimental data. It was found that both methods predict drastically different dependence of the band gaps, electromechanical responses and charge carrier effective masses upon the films’ thicknesses.

Introduction The rapidly growing family of two-dimensional films settled by isolation and investigation of graphene 1 currently includes dozens of materials, among which only graphene and h-BN are monolayers with a one-atom thickness, whereas other structures usually consist of several chemically and physically bounded atomic layers. 2 Fabrication of new 2D heterostructured films by combining layers of various compositions 3 opens a new way to create a wide range of various 2D films. The fabrication of such structures can be possible due to the nonchemical binding between different 2D fragments, whereas their chemical binding requires fine correspondence of their lattice parameters and specific thermodynamic conditions. Such requirements are perfect for producing new nanostructures based on multilayered graphene. A recently proposed chemically induced phase transition 4 allows one to assume that graphene layers can be chemically bounded to form thinnest diamond films (or diamanes 5) by adsorption of reference atoms. This effect is inherently nanoscale phenomenon, when the surface conditions directly affect thermodynamics. A careful choice of reference atomic types is the key to success in realization of such approach. Hydrogen, widely proposed for adsorption on graphene, in fact is not the best choice, mainly due to a complex hydrogenation mechanism that requires overcoming the nucleation barrier. 6 On the other hand, graphene fluorination is an energetically favorable endothermic process, which can be considered as a promising way for synthesizing such nanomaterials. 7,8 This suggestion is supported by a number of experimental results of graphite fluorination 9–12 among which 2


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formation of 2-layered diamond films in graphite was also observed. 9,10,13 The possibility of fabrication of nanometer-thickness multilayered diamond films with fluorinated surfaces rises an important question about their possible physical properties, since mostly only bilayered fluorinated diamond films have been predicted and studied theoretically. 14,15 The physical properties of such films, they dependence on the films atomic structure (e.g. surface type and thickness) and especially the value of impact will be in the scope of the presented paper.

In this work, physical properties of the diamond films with fluorinated surfaces of various symmetry and thickness were studied using electronic structure calculations. The elastic properties and acoustic velocities were analyzed, 2D elastic constants and acoustics velocities were calculated and compared with available reference data. Among studied structures lonsdaleite films display highest longitudinal stiffness and lowest Poisson ratio. The electronic properties were analyzed on GGA-PBE and GW levels. It was found that whereas PBE functional predicts nonlinear dependence of the band gaps width on the film thicknesses (which leads to the similar behavior of electromechanical properties, as well as electron and hole effective masses), the GW shift of bands leads to their usual monotonous behavior.

Computational details All calculations of the atomic structure and electronic properties were performed using the density functional theory (DFT) 16,17 in the generalized gradient approximation with the Perdew– Burke–Ernzerhof (PBE) exchange correlation functional, 18 as implemented into the VASP 19–21 package. The plane–wave energy cutoff energy was set to 500 eV, while the Brillouin zone was sampled using an 8×8×1 Monkhorst–Pack grid. 22 Atomic structure optimization was carried out until the maximum interatomic force became less than 0.01 eV/Å. The effective masses of both electrons and holes were determined using a k-point spacing smaller than 0.01 Å-1. To avoid interaction between the neighboring images of 2D diamond or fluorographene, the translation vector along c axis was set to be greater than 15 Å. 3



To evaluate the accuracy of the chosen approach, the atomic geometry, electronic and elastic properties of graphene and bulk diamond were calculated and compared with the corresponding experimental values. It was found that the DFT-PBE method predicts the structural parameters of the considered systems with an error less than 0.05 %: for diamond acalc = 3.566 Å, aexp = 3.568 Å, 23 for graphene: acalc = 2.469 Å, aexp = 2.459 Å. 24 At the DFT PBE level of theory, the band gap of diamond is equal to Eg = 4.5 eV, which is lower than the experimental value of 5.45 eV 25 due to a systematic underestimation of the band gap by the DFT-PBE approach. The elastic, electronic and transport properties of fluorographene were calculated and compared to available data as well. The elastic constants C11 = 230.2 N/m agrees with reference data of 260 N/m. 26 The calculated band gap of fluorographene is 3.1 eV compared to reference computational data of 3.1 eV 27 and 3.2 eV, 26 while the GW approach gives larger band gap of 7.2 eV comparable with 7.3 eV and 7.42 eV obtained in Refs. 27 and 26, respectively. The GW calculations of effective masses of fluorinated diamond films with different number of layers were performed on top of PBE wave functions at the relaxed geometry as implemented in the VASP code. 19–21 The plane–wave energy cutoff was set to 500 eV. The k-points mesh in the lateral directions was 8×8, while for the perpendicular direction the number of k-points was one.

Results and discussions High chemical activity of molecular fluorine leads to low-cost fluorination energy process. Even molecular fluorine can decompose and bind to graphene with energy barrier less than 1 eV. 8 Fluorographene can be considered as periodically connected dodecafluorocyclohexane carbon rings. It can be proposed that the conformers of dodecafluorocyclohexane dictate the conformers of fluorographene. The energy-favorable configuration of the fluorinated film is the “chair” conformer corresponding to fluorographene conformers “chair1” (also called as just “chair”) and “chair2” (“washboard”, 28 “stirrup“, 29 “zigzag” 26), whereas the “boat” conformer corresponds to 4


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conformers “boat1” (“bed”, 30 “boat“, 26,29) and “boat2” 31 (“armchair” 26). Increasing the thickness of the fluorographene films of the two former conformers leads to the cubic diamond films with (111) and (110) surfaces (see Fig. 1a,b), while the latter conformers relate with

(

)

hexagonal diamond (lonsdaleite) films with (101 0) (see Fig. 1c) and 2110 surfaces.

Fig. 1. Atomic structure of considered fluorinated films with the thickness of 10 layers with a) (111), b) (110) and (10 1 0) surfaces. Top view of the films shown in the insets. Black color is carbon, blue is fluorine. We studied the atomic and electronic structure and physical properties of the (111) and (110) oriented cubic diamond films, as well as a hexagonal diamond (lonsdaleite) film with (10 1 0) surface orientation with surface passivated by fluorine atoms. The only (10 1 0) lonsdaleite film was chosen (Fig. 1c), because it can be formed by fusing of the energetically favorable AA’ stacking of bilayer graphene, which is frequently found in experiment, 30,31 in contrast with the energetically unfavorable AA stacking, the connection of which leads to the ( 2 110) oriented lonsdaleite surface. The lattice parameters of the films with (111) surface change from a = 2.61 to 2.54 Å as the number of layers increases from 1 to10. For (110) surface lattice parameters change from a = 2.63 to 2.56 Å and for (10 1 0) they change from 4.56 to 4.23 Å.

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The dependencies of 2D elastic moduli Cij of the films upon the film thickness (Fig. 2a) were calculated from the linear part of stress-strain σ-η relation using the σ i = C ij η j formula. In order to neglect the 2D diamond film thickness, the definition of which is ambiguous, the stress and therefore the elastic moduli were expressed in N/m units. The stress-strain dependencies were calculated by applying the uniaxial strains in armchair and zigzag directions 34 to estimate the values of the elastic constants С11 and С12, respectively. A single-layered fluorographene film displays lower stiffness than graphene (C11 = 0.230 kN/m, C12 = 0.025 kN/m) due to the sp3 corrugation of carbon lattice which leads to higher elasticity. 35 The fluorinated diamond films with (10 1 0) surfaces display the highest longitudinal stiffness, because C11 and C12 constants of the film relate to C33 and C13 constants of the lonsdaleite crystal, respectively. 36 The predicted value of lonsdaleite C33 constant (1326.3 GPa 37) is higher than С11 constant for diamond, which could make lonsdaleite the stiffest crystal. Longitudinal and transverse acoustic velocities, presented in Fig. 2b, allow one to make a correct comparison of the elastic properties of the films with the data for bulk materials like diamond. It is clearly seen that velocities gradually grow with increasing of the film thickness due to the structure stiffness augmentation, and tend to the corresponding bulk values. The longitudinal and transverse acoustic velocities of (10 1 0) films become higher than the corresponding bulk diamond values when the film thickness exceeds 27 and 8 atomic layers, respectively (Fig. 2b, black line). The Poisson’s coefficients σ = C12/C11 for the cubic diamond (111) and (110) films are equal to 0.1 and 0.14, respectively, whereas the Poisson’s ratio of the lonsdaleite films varies in the vicinity of 0.01, which makes them unique materials with Poisson’s ratio close to zero.

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Fig. 2 The dependencies of a) elastic constants C11 (top) and C12 (bottom) and b) acoustic velocities of fluorinated diamond films with (111), (110), (10 1 0) surface orientations upon the number of layers and inverted number of layers, respectively. The electronic properties of considered films were calculated using both DFT-PBE and GW approaches. As DFT-PBE generally underestimates the band gap value due to an incorrect accounting of electron-electron interactions we calculated the band gap dependence on the thickness by using the one-particle Green’s function in combination with screened Coulomb interaction (GW). Obtained dependences for all types of films are shown in Fig. 3a by dashed lines. It could be seen that monolayers reveal similar band gap values of 7.1, 7.4 and 6.9 eV for films with (111), (110), (101 0) surfaces, which agrees well with reference data. 26,27 Twolayered films display slightly higher band gaps of 7.6, 7.4 and 7.1 eV compared to corresponding fluorographene conformers. Further increasing of thickness leads to monotonic decreasing of the band gap which tends to value of bulk material. This result stands in drastic contrast with our DFT-PBE predictions and reference calculations 38 which revealed nonlinear dependence of the 7



band gaps upon the film thickness (Fig. 3a). The band gap of diamond films displays the maximum at four layers with a sharp increase for 1-3 layers, and a monotonic decrease for thicker films. This result was obtained because films with a small number of layers (< 4) display a direct band gap, while increasing the number of layers leads to the lowering of the bands in ГM direction with transformation of a direct band-gap into an indirect one. In contrast, GW approach predicts the same behavior of bands in Г-M direction of films with more than 4 layers, compared to DFT-PBE. While for the thinner films the band structure significantly differs from DFT-PBE. All films except the fluorographene display indirect band gap. Increasing of the thickness leads to the decreasing of bands gap caused by the scissor shift of conduction and valence bands. However, this scissor shift is accompanied by the changing of the shape of the lowest conduction band, which can be observed in a case of DFT-PBE calculations. In the inset of Fig. 3a the conduction bands of 3-layered film is shown. Black curves represent the DFT-PBE results, while red ones are from GW. Bands obtained both from GW and DFT-PBE were shifted to one point for better view. The main difference is in the Г-M direction, where GW approach shows indirect band gap. Here we observed the unusual changes of behavior of the lowest conduction band calculated by GW compared to DFT-PBE results. Such effect can be connected with GW correction of the fluorographene (or thin fluorinated films) bands which leads to denser charge distribution near fluorine atoms and their pronounced electronegativity. Also it should be noted that self-energy corrections are usually more significant to those electronic states with a higher spatial density. This will influence the bands behavior and thus the band gap value. 39,40 The DFT-PBE also predicts lower band gaps of all cubic diamond films than the band gap of bulk diamond, which means that the band gap dependence on the film thickness should have minimum at a certain thickness after which it should tend to the bulk diamond value of 4.5 eV. 41 This behavior is similar to early predicted hydrogenated diamanes 42,43 and was associated with the dominant contribution of surface passivated atoms to the electronic properties of the whole film but GW data suggests the reconsideration of this conclusion. 8


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Fig. 3 a) Dependence of the band gap of the fluorinated cubic diamond films with (111) and (110) surfaces and hexagonal diamond film with (10 1 0) orientation upon the number of layers. Red horizontal lines are the band gap of single crystal diamond; blue lines are band gap for bulk lonsdaleite. The inset shows the lower conduction bands of 3-layered film, calculated by DFTPBE and GW approaches; b) The dependence of band gap of a 2-layered fluorinated film with (111) surface on the uniform strain in the range from -5% to 5% calculated by GW approach is presented. c) The incline a of the dependencies of band gap vs uniform strain upon the number of layers (the asymptotical incline values for diamond and lonsdaleite cases are vanished). The data calculated by DFT-PBE and GW is marked by solid and dashed lines, respectively. The electronic properties of diamond films (e.g. band gap values) depend on the mechanical deformations of the carbon lattice, like compression and tension. The band gap values of the films with different number of layers uniformly compressed or dilated in the range from -5% to 5% were calculated to find the rate of change in the electronic properties with deformation, ε. In

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the Fig. 3b, the band gap of a 2-layered fluorinated film with (111) surface as a function of mechanical deformation for a 2-layered fluorinated film with (111) surface is presented. It was found that mechanical strain leads to a linear dependence of the band gap Egap(ε) = a·ε + Egap(0) in the vicinity of the band gap of the unstrained structure Egap(0). The slope of the dependence is described by incline coefficient, a, which, therefore, is responsible for the rate of electromechanical properties of the film. The a coefficients of the bulk diamond and lonsdaleite were shifted to 0 in order to directly compare the behaviors of the electromechanical properties of diamond and lonsdaleite films in the same plot. As in the previous case the GW and PBE approaches display drastically different behavior (Fig. 3c). DFT-PBE predicts non-monotonic response to the mechanical strain for the films. The a coefficients for (110) and (10 1 0) films have a single minimum and single maximum, respectively. The a coefficient of the bulk diamond and lonsdaleite is equaled to 5.94 eV and 4.66 eV, respectively. In the case of (111) films, the a dependence has both maximum and minimum for 3 and 5 layers, respectively. The nonlinear behavior of the a coefficients reflects the direct-indirect transitions of the band gaps with increasing thickness of the films. The GW corrects the behavior of the bands. It was found that all studied films show similar monotonic behavior of the a coefficient on the number of layers. The dependence of a on the number of layers > 2 shows almost linear behavior. The points, corresponding to fluorographene with different fluorine termination do not obey linear law due to the difference in the band gap values shown in the Fig. 3a. For bulk diamond and lonsdaleite the a = 5.88 and 4.58, respectively. The dependencies of electron and hole effective masses at the band edges on the thickness of the films calculated by GW approach are presented in Fig. 4. It was found that the effective masses of electrons in thin (111) films increases monotonically with increasing of the thickness of the films and are smaller than the corresponding diamond values (see red line in Fig. 4a). For 10


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fluorographene monolayer electron effective mass is 0.42, which agrees well with reference data. 44 This fact allows better conductivity in few-layered diamond fluorinated films rather that for thick films. The effective masses of light holes of the multilayered (111) films are higher than the corresponding diamond value, and monotonically tend to the bulk value with increasing of thickness (green line in Fig. 4a). Similar behavior was observed in the case of heavy holes, where the heavy hole mass of fluorographene is 0.98. In the case of (110) diamond films (Fig. 4b), the behavior of the electron effective masses is different from (111) films. Thin films display higher effective masses compared to thick ones (see red line in Fig. 4b). However, both heavy and light holes display behavior similar to (111) films, where both effective masses are larger than the corresponding bulk values. The effective masses of heavy holes of lonsdaleite films with (10 1 0) surface monotonically decrease from 1.52, and tend to the bulk lonsdaleite value of 0.68 (Fig. 4c). For these films the electron effective masses decrease monotonically with increasing of the thickness as was observed for films with (110) surface.

Fig. 4 Dependence of electron and hole effective masses of the fluorinated diamond films with a) (111), b) (110) and c) (10 1 0) surface orientations on the number of layers (thickness).

Conclusions The elastic and electronic properties of quasi-two-dimensional cubic and hexagonal diamond films with fluorinated surfaces were studied using electronic structure calculations. It was found that both types of films display stiffness comparable with bulk diamond. The hexagonal diamond films display the most remarkable properties, combining the highest longitudinal stiffness with the smallest Poisson’s ration. It was shown that the electronic properties of the films predicted 11



with essential difference using DFT-PBE and GW approaches. Whereas PBE functional predicts nonmonotonic dependencies of the band gap value, effective electron and hole masses, as well as the rates of the band gap response to the mechanical strain upon the film thickness and GW approach display ordinary monotonous dependences (except for the monolayer, fluorographene case). Such sufficient difference between electronic structure of the films described in the framework of DFT-PBE and GW approaches can be connected denser charge distribution near fluorine atoms (and therefore their higher electronegativity) given by GW. The proposed films can be interesting in the many fields of nanotechnology. High mechanical stiffness can be useful for the application of diamond films as nanoscale elements in nanoelectronics. The wide band gap suggests application of the films as ultrathin insulating nanolayers whereas the presence of direct type of energy gap in thinnest films can be useful in nanophotonics.

Acknowledgments The authors are grateful to supercomputer cluster NUST "MISiS" provided by Materials Modeling and Development Laboratory (supported via the Grant from the Ministry of Education and Science of the Russian Federation No. 14.Y26.31.0005) and to the Joint Supercomputer Center of the Russian Academy of Sciences. D.G.K. acknowledges financial support of the Ministry of Education and Science of the Russian Federation in the framework of Increase Competitiveness Program of NUST «MISiS» (№ K2-2016-002) and grant of President of Russian Federation for government support of young PhD scientists (MK-3326.2017.2). P.B.S. gratefully acknowledges the financial support of the RFBR, according to the research project No. 16-32-60138 mol_а_dk.

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