Article pubs.acs.org/JPCC
Robust Electronic Properties of Sealed Graphene for Electronic Applications Liyan Zhu,†,‡ Jinlan Wang,*,‡ and Feng Ding*,† †
Institute of Textiles and Clothing, Hong Kong Polytechnic University, Kowloon, Hong Kong, People's Republic of China Department of Physics, Southeast University, Nanjing 211189, People's Republic of China
‡
ABSTRACT: In real device application, the sealing of graphene as that in the silicon microelectronic industry is required to ensure a stable local environment. In this work, through first-principles calculations, we demonstrate that single-atomic-thick graphene and graphene nanoribbons (GNRs) sealed between diamond layers maintain their intrinsic electronic properties. Furthermore, the study shows that the doping type and level and the conductivity of sealed graphene and GNRs can be tuned through the external pressure or the selection of the sealing material. This opens a door of using sealed graphene/GNR to replace the recently used freestanding or supported ones for robust electronic/ spintronic device synthesis.
I. INTRODUCTION Graphene, a monolayer of carbon atoms periodically arranged in the honeycomb lattice, exhibits many fascinating properties.1−3 The extraordinary linear energy-moment dependence around Dirac points results in massless Dirac fermions;1 electron mobility of graphene can be as high as 15 000 cm2 V−1 s−1 at room temperature.2,4 Outstanding electronic properties make graphene a promising candidate for postsilicon electronic devices. Recently, graphene-based field-effect transistors (FET), the fundamental component of modern electronic devices, have been successfully realized in several groups.5−11 For example, Novoselov et al. achieved an FET using few-layer graphene whose on−off ratio is about 30 at 300 K.6 Wang et al. greatly raised the on−off ratio up to 106 by using narrow single-layered graphene nanoribbons (GNRs).7 Very recently, Lin et al. reported a graphene FET with an operating frequency as high as 100 GHz.8 In experiments, supported graphene or suspended graphene with one or two sides exposed to the ambient environment are widely used. It is well known that the electronic states of graphene can be modulated by the physisorption of gas, the surface functionalization, or the interaction with a substrate. For instance, Novoselov et al.6 found that few-layer graphene was unintentionally doped when fabricating graphene-based devices. The few-layer graphene can be either n- or p-doped if exposed to water or NH3.6 That the NH3 functionalization induced n-doped graphene was confirmed by Guo et al.12 A similar phenomenon has been observed in GNRs. Wang et al.7 revealed that the physisorbed species (e.g., oxygen molecules) during the fabrication of FET usually makes the GNR p-doped. Summarizing these facts, one can expect that, with one or two sides exposed to the open environment, the electronic © 2012 American Chemical Society
properties of the graphene can be greatly changed by the surrounding gas, impurities (e.g., water, CO2), or contaminants (e.g., dust). Although the change of graphene’s properties can be utilized for device application, the variation of the environmental factors (e.g., humidity, impurities, gases, concentration of dusts) would result in an unpredictable performance change of the graphene devices. Therefore, in device application, the used graphene should be sealed to ensure a stable local environment. In the silicon microelectronic industry, the electronic packaging or sealing is a major step in chip manufacturing, and the function of the package includes signal and power distribution, heat dissipation, circuit support, and environmental protection.13 In the packaging of silicon-based chips, that the induced stress on silicon, which may reduce the performance or even cause chip cracking is a serious problem.14 This should be more serious in the sealing of graphene-based devices because the graphene is only one atom thick and its π electrons, which are crucial to its electronic properties, interact with the sealing materials directly. Would the sealing greatly change the electronic properties of graphene? Is it possible to maintain most prestigious electronic properties of freestanding graphene in the sealed ones? Can we use the sealing to tune the electronic properties of the sealed graphene for applications? So far, to our best knowledge, this kind of study is not available yet in the literature. Motivated by the above discussion, we have performed a systematic study on graphene and GNRs sealed between Received: October 19, 2011 Revised: March 17, 2012 Published: March 19, 2012 8027
dx.doi.org/10.1021/jp210058c | J. Phys. Chem. C 2012, 116, 8027−8033
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Figure 1. Side (a, b) and top (c, d) views of H-D-H/G/H-D-H and F-D-F/G/F-D-F. Red dashed rectangles in (a, b) and rhombuses in (c, d) represent the supercells adopted in the calculations. Note that the thickness of the vacuum layer is intentionally narrowed to shrink the sizes of the figures. Pressure (P, in GPa) as a function of the separation between graphene and neighboring H (e) or F (f) atoms of the diamond films, D, respectively. Solid red and blue lines correspond to the fitting curves using eq 2.
sealed graphene was modeled as single-layered graphene sandwiched between two three-layered diamond films (see Figure 1a−d). The dangling bonds on the outermost layers of the diamond films were saturated by hydrogen or fluorine atoms. The whole system is denoted as X-D-X/G/X-D-X, where X = H or F. A vacuum layer, of at least 15 Å, was adopted to separate the system from its periodic images. As shown in Figure 1a−d, the adopted supercells in calculations were represented by red dashed rectangles or rhombuses. To investigate the effect of external pressure on the electronic properties of graphene, the topmost and bottommost layers of hydrogen or fluorine atoms were fixed and all the rest of the atoms were fully relaxed in all calculations. In this study, diamond films are utilized as an example of sealing materials because the very small lattice mismatching between diamond and graphene makes the calculation with the periodic boundary condition (PBC) possible by imposing a small strain, ∼2.0%, into the sealing materials. Although a detailed theoretical study of graphene sealing in other materials
diamond films. We found that both sealed graphene and GNRs can well maintain their intrinsic electronic properties, although the sealing may make them either n- or p-doped. Furthermore, the study shows that the doping level can be tuned through the separation distance between the sealing substrates or the external pressure.
II. MODELING AND METHODS Diamond films were used to seal graphene and GNRs from the ambient environment, and their electronic properties under different sealing conditions (contact pressure) were calculated with the density functional theory (DFT) method. The reasons of choosing diamond are as follows: (i) it is a wide-band-gap semiconductor; (ii) it has an extreme high thermal conductivity, and thus the heat generated during the device operation can be dissipated efficiently; and (iii) it has very similar lattice constants to those of graphene. Two different surface passivations, hydrogen- or fluorine-passivated diamond (111) films, were considered to explore the doping effect. The 8028
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Figure 2. (a−d) Band structure and density of states of H-D-H/G/H-D-H (top panels) and F-D-F/G/F-D-F (bottom panels) with a separation of 1.7 (a), 1.9 (c), and 4.0 Å (b, d). Red and blue lines in band structures represent the bands mainly contributed from graphene and diamond films, respectively. The red and blue areas in the density of states correspond to the states that come from graphene and diamond films, respectively. (e−h) Charge density difference in H-D-H/G/H-D-H with separations of 4.0 (e) and 1.9 Å (f) and that in F-D-F/G/F-D-F with separations of 4.0 (g) and 1.9 Å (h). Red and blue areas represent electron accumulation and depletion, respectively. Isovalues are 0.15, 0.08, 0.15, and 1.44 e/Å3 in panels e−h, respectively.
is beyond the scope of this study, we expect that other inert substrates, such as poly(hydroxystyrene)8 and oxide,15 which have been exploited to fabricate high-speed graphene-based transistors, should have very similar effects. Sealed graphene between two inert substrates might be achieved through a multistep procedure, as described by Ponomarenko et al.16 As pressure can also be applied easily on the substrates, the pressure-dependent electronic properties of sealed graphene certainly can be easily used to design pressure sensors. All calculations were performed within the framework of DFT as implemented in the Vienna Ab initio Simulation Package (VASP).17,18 The exchange-correlation potential was approximated by the generalized gradient approximation (GGA) using the PBE functional. 19 The electron−ion interaction was described by the projector augmented wave (PAW) pseudopotential,20,21 in which the default maximal energy cutoffs (ENMAX) are 400, 250, and 400 eV for C, H, and F, respectively. The wavefunctions were expanded in terms of plane waves with an energy cutoff of 400 eV. The convergence criterion for energy was chosen as 10−4 eV, and the maximum force allowed on each atom was 0.01 eV/Å. The Brillouin zone was meshed by a 45 × 45 × 1 grid using the Monkhorst−Pack scheme.22 Convergence tests on the energy cutoff and k-point mesh indicate that the energy variation is less than 1 meV. The C−C bond length in graphene is calculated to test the method of calculation, and the optimized C−C bond length is 1.426 Å, which is in good agreement with experimental values. Both spin-polarized and spin-unpolarized DFT calculations were carried out. It was approved that both H-D-H/G/H-D-H and F-D-F/G/F-D-F are nonmagnetic. Hence, only results obtained by spin-unpolarized calculations were presented. Besides, the optimized lattice constants of freestanding graphene and the diamond film are 2.47 and 2.52 Å, respectively. The mismatch between lattice constants of graphene and the diamond film is only 2%. The matched structure, instead of a moiré pattern, is usually formed when the
mismatch between lattice constants is small, for example, epitaxial graphene grown on Ni(111) substrates.23 In this study, we have considered three different graphene− diamond configurations: namely, hollow, bridge, and top. Specifically, each hydrogen atom of the diamond films occupies a hollow site of a hexagon, a bridge site of a C−C bond, and the top of a carbon atom in graphene, respectively. Our calculation shows that the energy difference of the three configurations is small and the hollow configuration is slightly preferred when the separation between graphene and diamond films is large. However, the hollow configuration can be gratefully stabilized upon high pressure. For H-D-H/G/H-D-H, the energies of the bridge and top configurations are 0.004 and 0.005 eV per unit cell higher than that of the hollow configuration at a separation of 3.00 Å, respectively. However, the energy differences rise to 0.76 and 0.78 eV per unit cell, respectively, when the separation drops to 1.60 Å. Hence, the hollow configuration can be easily obtained by applying a moderated pressure.
III. RESULTS AND DISCUSSION A. Packaging of Two-Dimensional Graphene. Pressure (P) as a function of separation (D) between graphene and diamond films is presented in Figure 1e,f. The pressure on graphene is calculated as the first derivative of the energy P = (1/A)*d(E − E0)/dD
(1)
where A is the area of the unit cell, D is the distance between graphene and neighboring H/F layers, and E is the energy of the system with a separation of D, whereas E0 is the energy of the system at equilibrium distance. When the separation, D, is greater than 3.5 Å, the pressures on graphene for both H-D-H/ G/H-D-H and F-D-F/G/F-D-F are nearly zero, indicating that the equilibrium separation for both are ∼3.5 Å. Decreasing the separation from 3.5 Å leads to an exponential increase of the pressure. The pressure (in GPa) versus separation in H-D-H/ 8029
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Figure 3. Calculated shift of the conical point of graphene with respect to the Fermi level (a) and the vacuum level (c). VBM and CBM of free graphene, H-D-H, and F-D-F (b). Shift of the Fermi level with respect to the vacuum level (d).
2a). Comparing the CDDs of H-D-H/G/H-D-H at separations of 4.0 and 1.9 Å (Figure 2e,f), one can see that the density of π electrons in real space becomes larger upon compression and the overlap of π electrons between neighboring carbon atoms in graphene dramatically increases, which might enhance the conductivity of graphene. As for the F-D-F/G/F-D-F with a separation of 4.0 Å, the conical point of the Dirac cone exactly locates at the Fermi level (Figure 2d). The corresponding CDD (Figure 2g) reveals that there is almost no charge transfer between graphene and F-D-F. Only if the separation is reduced to 2.0 Å or less, can the vertex of the Dirac cone be slightly shifted above the Fermi level (Figure 2c), which demonstrates that the F-D-F gains charges from graphene or the graphene is doped with holes. This also can be seen in the CDD of F-D-F/G/F-D-F presented in Figure 2h, where electrons deplete from the periphery of the graphene surface, but accumulate around fluorine atoms. Similar to the H-D-H/G/H-D-H, the compression of π electrons in real space and the charge overlap enhancement between neighboring C atoms are also seen in the CDD of D = 1.9 Å. This indicates that, whether the graphene is electron- or hole-doped, its conductivity will be further enhanced upon high-pressure sealing. To understand the behaviors of the conical point shift versus the separation, the valence band maximum (VBM) and conduction band minimum (CBM) of graphene, H-D-H, and F-D-F with respect to the vacuum level are plotted in Figure 3b. The values of VBM and CBM of graphene are exactly the same and are lower than the VBM value of H-D-H by 0.62 eV. Thus, if the graphene is sandwiched between H-D-Hs, the electrons can be readily transferred from the valence bands of H-D-H to the conduction bands of graphene. Decreasing the separation, D, the enhanced attractive interaction between the electron in graphene and the hydrogen of H-D-H lowers the band energy
G/H-D-H and H-D-H/G/F-D-H can be well-fitted using the screened Coulomb (Yukawa) function P(D) = a*exp( −b*D)/D
(2)
The screened Coulomb (Yukawa) function describes the comprehensive interaction between graphene and diamond films, for example, repulsive interaction due to the compression of electron gas in graphene and attractive Coulomb interaction stemming from the electron transfer between graphene and diamond films during compression (see Figure 1e,f). Fitting curves for H-D-H/G/H-D-H and F-D-F/G/F-D-F are shown in Figure 1e,f. Coefficients a and b are 1656.0 Å GPa and 1.784 Å−1 (12260.0 Å GPa and 2.139 Å−1) for H-D-H/G/H-D-H (FD-F/G/F-D-F), respectively. Figure 2 presents the band structures and the local density of states (LDOS) of the sealed graphene at the separation distances of 4.0 Å (pressure P ∼ 0) and 1.7 Å (P ∼ 40 GPa) for H-D-H/G/H-D-H and 4.0 Å (P ∼ 0) and 1.9 Å (P ∼ 80 GPa) for F-D-F/G/F-D-F. It clearly shows that, for both cases, the electronic structure of the graphene near the Dirac point is very robust and graphene remains conducting at the pressure of 40− 80 GPa. This is expected since the symmetry of the graphene’s sublattices is not broken. The robustness of the graphene electronic structure ensures that supported or freestanding graphene-based electronic and spintronic devices can be potentially synthesized by using the sealed graphene. For H-D-H/G/H-D-H, the conical point of the Dirac cone of graphene is lower than the Fermi level by 0.36 eV when the separation is around 4.0 Å (Figure 2b). This implies that it is energetically favorable for electrons to transfer from H-D-H to graphene, which can be clearly seen from the charge density difference (CDD) of H-D-H/G/H-D-H (Figure 2e). Further decreasing the separation to 1.7 Å enhances the charge transfer and thus lowers the Dirac point notably to −0.89 eV (Figure 8030
dx.doi.org/10.1021/jp210058c | J. Phys. Chem. C 2012, 116, 8027−8033
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Figure 4. Cross-sectional views of the one-dimensional ac-GNR-6 sealed by H-D-H (a) and F-D-F (b), in which the red dashed rectangles represent the supercells adopted in the calculations. (c) Intrinsic band gap of ac-GNR-6 as a function of separation in H-D-H/ac-GNR-6/H-D-H and F-D-F/ ac-GNR-6/F-D-F. Dashed line indicates the band gap of free ac-GNR-6. Band structures and DOSs of H-D-H/ac-GNR-6/H-D-H with the separations of (d) 2.0, (e) 3.0, and (f) 4.0 Å, respectively. Band structures and DOSs of F-D-F/ac-GNR-6/F-D-F with the separations of (g) 1.7, (h) 1.8, and (i) 3.0 Å, respectively. Red and blue lines (areas) in these band structures (DOSs) correspond to those contributions from graphene and diamond films, respectively.
graphene. When the separation is less than 2 Å, the CBM of the F-D-F is slightly lower than the VBM of graphene. As a consequence, the electron transfer from graphene to the F-D-F occurs, manifested by the fact that the conical point of the Dirac cone of graphene becomes slightly higher than the Fermi level (see blue solid line in Figure 3a). In other words, graphene is p-type-doped when it is sandwiched between F-D-Fs with a very narrow separation. Most recently, an experimental study observed that the resistivity of graphene sandwiched between boron nitride layers is much larger than h/e2 near the neutrality point, indicating a metal−insulator transition (MIT) in graphene.16 However, such an MIT originates from Anderson localization instead of a gap opening.16 The MIT usually occurs at a lower carrier concentration (
