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Graphene Nanoribbons Under Mechanical Strain Changxin Chen,* Justin Zachary Wu, Kai Tak Lam, Guosong Hong, Ming Gong, Bo Zhang, Yang Lu, Alexander L. Antaris, Shuo Diao, Jing Guo,* and Hongjie Dai* Graphene has led to intense investigation of both experimental[1–4] and theoretical work[5] in recent years, owing to attractive material properties including high mobility,[6,7] thermal conductivity,[8] Young’s modulus,[9] zero effective carrier mass,[10] and long mean free path for carrier transport at room temperature.[11] One of the most important potential applications of graphene is as a building block for next-generation electronics and photonics,[10,12,13] but a major obstacle is the zero bandgap of semi-metallic two-dimensional (2D) graphene. One possible solution is to form one-dimensional graphene nanoribbons (GNRs) with 1–2 nm width, opening up sizable bandgaps.[14,15] Unfortunately, high-quality, long and ultra-narrow GNRs (ca. 2 nm) are difficult to be prepared, particularly ones with smooth edges throughout the ribbon length, and it has been shown that GNRs with large degree of edge roughness exhibit low mobility and conductivity due to scattering effects at the edges.[16] Wider GNRs (>15 nm) have a higher tolerance of edge roughness and show higher mobility and conductivity but much smaller bandgaps. It is therefore desirable to tune the bandgaps in GNRs for high-performance electronics and photonics applications. Theoretical and experimental studies have suggested that strain have a substantial effect on the vibrational and electronic band structure of carbon nanotube (CNT),[17–19] 2D graphene[20,21] and GNR.[22,23] Both ab initio calculations and tightbinding modeling show no bandgap opening for 2D graphene
Dr. C. X. Chen,[+] Dr. J. Z. Wu,[+] Dr. G. S. Hong, M. Gong, B. Zhang, A. L. Antaris, S. Diao, Prof. H. J. Dai Department of Chemistry and Laboratory for Advanced Materials Stanford University Stanford, California 94305, USA E-mail: [email protected]; [email protected] Dr. C. X. Chen Key Laboratory for Thin Film and Micro fabrication of the Ministry of Education National Key Laboratory of Science and Technology on Micro/Nano Fabrication Department of Micro/Nano Electronics School of Electronic Information and Electrical Engineering Shanghai Jiao Tong University Shanghai 200240, PR China Dr. K. T. Lam,[+] Dr. Y. Lu, Prof. J. Guo Department of Electrical and Computer Engineering University of Florida Gainesville, FL 32611–6130, USA E-mail: [email protected] [+]
These authors contributed equally to this work.
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even at uniaxial strains up to 20% as strain only causes the Dirac point to move away from the high symmetry K point in the Brillouin zone.[24–26] In contrast, theoretical studies advise a GNR could have sizable bandgap changes under uniaxial strain,[22] which could be useful for implementing graphene technology. Uniaxial strain modulates the bandgap of GNRs by shifting the Dirac point relative to the allowed wavevector lines (k-lines) in armchair GNRs, and by modifying the magnitude of spin polarization at the edges in zigzag GNRs. There has been a lack of reported experimental investigations into creating mechanical strains in GNRs, as well as into its effects on their material properties. In this work, uniaxial strains (0–6%) were applied to individual GNRs with highly smooth edges by atomic force microscopy (AFM) manipulation and the strain effects on the Raman spectroscopic and electrical properties of GNRs were investigated experimentally for the first time. We demonstrated that the Raman G-band frequency of GNRs showed an approximate linear dependence on uniaxial strain with downshifts under strain at a rate of about −10 cm−1 per 1% strain (/%) for GNRs with a width of ca. 20 nm. Uniaxial strain was found to tune the bandgap of GNRs significantly in a non-monotonic manner, with the bandgap varied between ca. 25 meV and ca. 62 meV under strain for a 19-nmwide GNR. These results were in good agreement with theoretical modeling carried out. The GNRs used in this work were ca. 20 nm in width and exhibited highly smooth edges, prepared by sonochemical unzipping of high quality arc-discharge grown multiwalled carbon nanotubes (MWCNTs)[27–29] (see Experimental Section for preparation details). The resulting GNR solution was spun onto silicon chips with 300-nm-thick thermally oxidized SiO2 at 3000 rpm to obtain well dispersed individual GNRs. The asdeposited GNRs on the SiO2/Si substrate had a PmPV polymer coating on the surface[27] (about 0.5 nm thick), which facilitated AFM manipulations and deformation due to the lack of direct GNR-SiO2 interactions. Without the polymer coating (i.e., after calcination to burn off the PmPV), we found that the AFM manipulation of GNRs was much more challenging due to the flatness of GNRs with a lower height and the stronger Van der Waals forces between GNRs and substrate. The PmPV coating was van der Waals adhesion in nature and would not have a significant effect on the mechanical property of GNRs. PmPV could be removed by calcination at 350 °C for 20 min after GNR manipulation. We manipulated and stretched GNRs on the SiO2/Si substrate with an AFM tip by pushing the middle of the GNR to form a bend and introduce tensile strain in the GNR (see Figure 1 and Experimental Section for AFM manipulation details). Due to the large radius of curvature of the bend relative to the small width of the GNR, the dominant strain induced in the GNR was uniaxial strain along the GNR length
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Figure 1. Strained individual GNR by AFM manipulation. a) An AFM image of GNR 1 with PmPV coating before AFM manipulation. b) An AFM image of GNR 1 after AFM manipulation and then calcination to remove the PmPV coating; the arrow shows the direction of AFM tip pushing GNR. The GNR is ca. 26 nm in width and ca. 1.2 nm in apparent height.
direction from the elongation of the GNR after the manipulation. AFM data also showed no obvious torsional deformation along the length of the manipulated GNRs. By changing the pushing/bending motion range of the AFM tip, we were able to obtain different displacements and different uniaxial strains in GNRs up to ca. 6%. Strain was introduced into various GNRs with different widths and layer numbers in our experiment (Figure 1 and Figure S1, Supporting Information), among which GNR 1 was 26 nm in width and 1.2 nm in apparent height and estimated to be a double-layer GNR.[27] After AFM manipulation, we observed that GNR 1 was dragged out along the scanning direction of the AFM tip (Figure 1b). Due to friction, the GNR was stretched along its axis. A monolayer GNR (GNR 2), 19 nm wide and 0.9 nm in apparent height, was also investigated (Figure S1, Supporting Information). The average tensile strain in the GNR was determined by the ratio of the apparent elongation measured and the unstrained length, estimated to be 0.33% and 0.29% respectively for GNR 1 and 2. The strain in our manipulated GNRs was in the elastic deformation range of GNRs.[30] The GNRs were pinned and kept strained by frictional
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forces between GNRs and the underlying substrate after AFM manipulation. Spatially resolved Raman imaging/spectroscopic mappings were performed for the strained GNRs to investigate the effect of the uniaxial strain on the Raman spectra. Raman spectroscopic mapping was done with a 532 nm laser excitation with a spot size of about 0.6 µm (see Experimental Section). Raman spectroscopic images generated from the obtained Raman spectra could be overlaid well with the AFM image of the strained GNRs (Figure 2a, 2d and Figure S2, Supporting Information). The GNR exhibited a higher intensity ratio of Raman D- and G-band than the MWCNT due to the existence of the edges in GNR (see Figure 2b). Also, the Raman G band of the GNR showed slight upshift in frequencies than that of MWCNTs due to the lack of curvature caused by rolling.[28] The Raman spectra taken along the strained GNR 1 (Figure 2c) showed a gradual downshift of the G band from the end (position 6) to the central manipulated position (position 3), with a shift of −6.5 cm−1. For GNR2, a shift of −4.9 cm−1 in the G band was observed progressively from 1589.1 cm−1 at the end (position 5) to 1584.2 cm−1 at the manipulated position (position 3) (Figure 2e). In a manipulated GNR, strain propagated from the center and decreased towards the GNR ends from the manipulated position. In addition to observing the gradual upshift of the G band from the manipulated position to the two ends of the strained GNRs, examination of AFM images found that the ends of the GNRs often had very small displacements in position after the manipulation in our experiments (see Figure S3, S1a, and S1b, Supporting Information and Figure 1), indicating that the strain had propagated to the ends. The tensile strain on the flexible graphene hexagonal lattice was anticipated to be able to spread to a much longer distance[31] than the length (2.5–3.5 µm) of the GNRs used in our experiment. Assuming the friction coefficient between the GNR and substrate was constant and the lack of sharp kinks due to manipulation, we approximated that the uniaxial strain in the strained GNR linearly decreased from the manipulated position to the ends (where the strain was relaxed to zero) along the GNR length direction (see Figure 3a), corresponding to the gradual shift seen in the Raman data. Within this simplified model of strain distribution, local uniaxial strains along the GNRs were estimated and correlated with the shift of the G bands as a function of the strain. The tensile strain linearly decreased from 0.65% and 0.58% to zero (from the manipulated position to the end) for GNR 1 and 2 respectively. It was found that the shift of the GNR’s G bands had an approximately linear dependence on the uniaxial strain (Figure 3b), with shift rates estimated to be −10.3 cm−1/% and −8.7 cm−1/% for strained GNR 1 and GNR 2, respectively. The downshift of the G band as a result of tensile strain was also observed for 2D graphene in previous studies.[32,33] The downshift of G band could be attributed to the elongation of the carbon–carbon bonds under uniaxial strain, weakening the bonds and lowering the vibrational frequency. We investigated theoretically the G band’s shift as a function of uniaxial strain for GNRs of various widths. The shift of Raman G band of strained graphene was due to shifting of the optical phonon (OP) mode,[34–37] i.e., the doubly degenerate zone center E2g mode.[37] The phonon spectra of graphene
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COMMUNICATION Figure 2. Raman spectroscopic mapping of individual strained GNRs. a) An overlay of a Raman image and an AFM image for strained GNR 1. The Raman image was generated from the intensity integral total of the D-band 1324–1360 cm−1 region (represented in red) and the G-band 1559–1592 cm−1 region (represented in green). The GNR and MWCNTs show as different colors in the figure due to the different dominance of D and G band intensities. b) Raman spectra at the positions 1 and 7 in (a), showing typical Raman spectra for GNRs and CNTs respectively. c) Raman spectra taken at positions 1 to 6 in (a) along the strained GNR 1. The spectra were fitted with Lorentzians (red and green fitting lines) to obtain the positions of the G band peak, showing a gradual downshift of the G band from the end position to the manipulated position in the GNR; The spectra at position 1 to 4 were fitted with single peak and the spectra at position 5, 6 were fitted with two peaks due to signal from the MWCNT nearby. The dashed line is a guide for the eyes. d) An overlay of a Raman image and an AFM image for strained GNR 2. The Raman image was generated from the intensity integral of the D band in the 1339–1366 cm−1 region (represented in red). e) Raman spectra taken at positions 1 to 5 in (d) along the strained GNR 2. The spectra are fitted with Lorentzians (red fitting lines) to obtain the G-band peak positions. The dashed line is a guide for the eyes.
and GNRs were calculated using local density approximation in density functional theory with a projector augmented wave pseudopotential supplied by the Vienna Ab Initio Simulation Package[38,39] to calculate the force constants at different uniaxial strains (see Experimental Section, Supplementary Note 1 and Figure S4 in the Supporting Information) and the corresponding OP mode responsible for the G band was identified from the eigenvector resembling the E2g mode. The shift of the G band under uniaxial strain for different widths of armchair GNRs (denoted with the number of dimer lines Na across the ribbon with Na = 7, 10, 22 and 28) and 2D graphene was then extracted (Figure 3c). It was observed that the theoretical G band’s shift increased linearly with the increase of the uniaxial strain for various widths of GNRs, consistent with the experimental result. Calculations showed that the layer number and edge chirality of the GNR did not have an obvious effect on the shift rate of the G band under uniaxial strain. We found that the shift rate of the G band decreased with the width of the GNR (inset in Figure 3c), and the smaller shift rates for narrower GNRs were due to the effect of GNR edges which modified the force constant of GNRs (Table S1, Supporting
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Information). As the ribbon width increased, the effect of the edges was reduced and the shift rate of the strained wide GNR approached that of strained 2D graphene (about −18.0 cm−1/%). For the ca. 26 and ca. 19 nm wide GNRs, the theoretical shift rates of the G band were about −17.5 cm−1/% and -17.1 cm−1/% respectively, which were a little larger than the experimental measured rates (ca. 9–10 cm−1/%). The difference could be due to the isolated GNR considered in the first-principle calculations without including environmental effects such as the presence of strong substrate interactions. The van der Waals interaction between the carbon atoms and the substrate surface would result in additional spring constant terms to the vibrational energy that could decrease the effect of uniaxial strain on the overall dynamical matrix, which would in turn reduce the shift rate of the G band. Another effect could be due to the laser spot size of the Raman system, which could shift the measured frequency of G band at the end and the maximum-strain position of the GNR to a lower and higher value respectively due to asymmetric distribution of strain around these two positions and thereby lowering the measured shift rate.
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Figure 3. Raman shift of strained GNRs. a) A schematic illustration of the distribution of uniaxial strain along the length direction of a manipulated GNR. b) The frequency shift of G band as a function of uniaxial strain at position 1 to 6 in GNR 1 (red) and at position 1 to 5 in GNR 2 (black). The linear least-squares-fits shows shift rates for these two GNRs. Error bars show possible strain errors from the overlay deviation of the Raman image and the AFM image. c) Theoretical frequency shift of the G band for the Na = 7, 10, 22 and 28 armchair GNRs and the 2D graphene as a function of uniaxial strain. The insert shows shift rate of the G band against GNR width, approaching that of 2D graphene for wide GNR; The dash line in the insert corresponds to the shift rate of the 2D graphene at −18.0 cm−1/%.
To investigate the electrical properties of strained GNRs, field-effect transistors (FETs) were made on individual strained GNRs by e-beam lithography and lift-off with palladium (Pd) used as the source and drain contacts (see Experimental Section). For GNRFETs fabricated on a strained 19-nm-wide monolayer GNR (GNR 3) (Figure 4a), the strains of the three GNR segments (labeled 1–3 in Figure 4a) were about 4.04%, 3.07% and 1.60% respectively estimated from the midpoint of the segments. Room-temperature electrical characteristics and temperature-dependent measurements (Figure 4b and 4c respectively, see Experimental Section for details) for these GNRFETs showed an increase in the on/off current ratio in the transfer
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characteristic curves at lower temperatures, with a decrease in the minimum conductance by more than 2 orders of magnitude from 295 K to 45 K for the FET 2 as shown in Figure 4c. A plot of the minimum conductance (Goff) as a function of inverse temperature, ln (Goff ) ∝ T −1 (Figure 4d) showed a linear relation in the temperature range of 295 K to 105 K, corresponding to conductance primarily through thermally activated carriers at the point of minimum conductance. The asymmetric electron and hole conductance of the devices shown in Figure 4b and 4c is likely due to the Fermi level alignment at the contacts, and so we performed non-equilibrium Green’s function (NEGF) simulation to fit the asymmetric transfer characteristics and extracted the bandgap of GNRs (see Experimental Section, Figure S5 and Supplementary Note 2, Supporting Information). As a result, bandgaps (Eg) of ca. 35, 62, and 25 meV were extracted for segments 1, 2, and 3 of the strained GNR (with strains of about 4.04%, 3.07% and 1.60%) respectively (see Figure 4e). It was shown that the uniaxial tensile strain could effectively modulate the GNR bandgap, which was altered by about 2.5 times from 25 meV to 62 meV that was measured at the different segment with different strain. A similar non-monotonic varying trend of the bandgaps was observed for all of our 8 measured strained GNRs with widths ranging from ca. 17 to ca. 26 nm (see Figure S6 and Supplementary Note 3 in the Supporting Information for a 22-nmwidth strained GNR), varying in amplitude by dozens of meV. We simulated the bandgap dependence on uniaxial strain for various chiralities of GNRs using the pz orbital tight-binding model (see Experimental Section). Given that the GNRs prepared by our method had random chiral edges from near armchair to zigzag,[28,29] a chiral GNR was picked to calculate the bandgap changes under uniaxial strain (for the first time) and compared with the experimentally observed trend. For a calculated 19-nm-wide (9,6) GNR, a non-monotonic fluctuating bandgap change was observed, with a similar period and amplitude of the bandgap variation under uniaxial strain as seen in the experimental result (Figure 4e). The further calculations showed that the bandgap of a similar width of armchair GNR as a function of uniaxial strain had an oscillatory dependence while that of the similar width of zigzag GNR displayed minute monotonic increase under uniaxial strain. Since chiral ribbons can be considered as a combination of armchair and zigzag regions according to the chiral angle, represented in (n,m) notation where the ratio of armchair to zigzag region is m:(n −m),[40] the bandgap variation under uniaxial strain for chiral GNRs can be attributed to the dominant bandgap change of the armchair portion in chiral GNRs. Simulation of armchair GNRs showed that the bandgap will be increased from ca. 215 meV to ca. 400 meV when the uniaxial strain varies from 0% to 2.0% for a 4.3-nm-wide ribbon (Figure 5). A bandgap of 400 meV could afford an on/off ratio of 106 to 107 for a Pd-contacted p-type unipolar GNRFET,[41,42] which could be used in complementary metal-oxide-semiconductor (CMOS) logic devices.[43] As a reference, a 2.0-nmwide unstrained GNR would exhibit a similar bandgap of ca. 410 meV. Therefore, with a suitable uniaxial strain applied to armchair GNRs, the GNR’s width restriction for logic application can be relaxed to a larger range up to ca. 5 nm rather than sub-2 nm. Theoretical simulations had predicted that
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COMMUNICATION Figure 4. Electrical characteristics of strained GNRs. a) An AFM image of three three-terminal FET devices on SiO2/Si (with Si back gate) fabricated along strained 19-nm-wide GNR 3. The three GNR segments labeled as 1, 2 and 3 have strains of 4.04 ± 0.41%, 3.07 ± 0.31% and 1.60 ± 0.25% respectively, as estimated from the midpoint of the segments and the variation in strain along the segments. b) Room-temperature conductance as a function of gate bias (GDS–VGS) of the three GNR segments. c) Temperature-dependent GDS–VGS curves of FET 2 at drain bias VDS = −1.0 mV. d) The minimum conductance of GDS–VGS curves for the three devices as a function of the inverse of temperature from 295 K to 105 K at intervals of 10 K. The red lines are the linear fit to the experimental data. e) Extracted experimental bandgaps under each uniaxial strain of the three segments. Horizontal error bars cover the range of strain in each channel; Vertical error bars show the fitting error of the bandgap extraction. The dash line in the figure shows the theoretical bandgap of a 19-nm-wide (9,6) chiral GNR, to show the expected bandgap change and strain modulation behavior for similar width of GNR.
the impact of the scattering induced by line-edge roughness (LER) rapidly degraded mobility for ribbon widths less than 5 nm.[44,45] Toward this direction, a chemical synthesis method that can reliably produce high-quality GNRs with controlled width ca. 5 nm will be expected for future high-performance strained-GNR logic device application. In summary, uniaxial strain has been successfully introduced into individual GNRs for the first time by AFM manipulation to investigate effects of strain on the Raman spectroscopic and electrical properties of GNRs. It was found that the Raman G-band frequency of GNRs downshifted linearly under uniaxial strain at a shift rate of about −10 cm−1/% for GNRs with a width of around 20 nm. The bandgap of GNRs could be tuned significantly by uniaxial strain in a non-monotonic fluctuating way, varying from 25 to 62 meV for a 19-nm-wide GNR under strain. Theoretical modeling on the Raman G-band shift and bandgap variation of GNRs under uniaxial strains was also performed, showing good agreement with the experimental results. Strain engineering of GNRs opens a path to tune the bandgap of graphene and is promising for tailoring the properties of GNRs towards versatile electronics and photonics applications.
Experimental Section Preparation of GNRs: MWCNTs (30 mg, Aldrich, 406074–500MG) were calcined in air at 550 °C in a 1-inch tube furnace for 2 h, which formed etching pits on the sidewall by oxidation reactions at pre-existing defects on nanotubes without destroying pristine sidewalls. After that, calcined MWCNTs (15 mg) and poly(m-phenylenevinylene-co-2,
Adv. Mater. 2014, DOI: 10.1002/adma.201403750
5-dioctoxy-p-phenylenevinylene) (PmPV) (7.5 mg, Aldrich, 555169– 1G) were dissolved in 1,2-dichloroethane (DCE) (4 mL) and then sonicated (Cole Palmer sonicator, Model 08849–00) for 1 h to unzip MWCNTs into GNRs. Afterward, the solution was ultracentrifuged at 50 000 rpm (revolutions per minute) for 2 h to remove most of residual MWCNTs. The GNR-rich supernatant was extracted from the obtained solution. AFM Manipulation of GNRs: The MultiMode scanning probe microscope and commercial AFM tips (model: ACST, force constant k = 7 N m−1 and resonance frequency f0 = 150 kHz) from the APPNano company were used in the manipulation. The tapping AFM mode was used. Firstly, the scanning direction of the AFM tip was set to be perpendicular to the GNR axis. Then the drive amplitude and scan rate of the AFM were set as a typical value of 200–700 mV and 1.0–1.6 Hz respectively, while keeping the target amplitude, proportional gain and integral gain as 0.5 V, 2, and 0.2 respectively. The aspect ratio (the width/height ratio of the AFM scanning) was changed into 16:1 to make the AFM tip scan within a very short GNR segment where the manipulation was to be performed. Afterwards, the setpoint of the AFM was decreased at a small step size carefully, increasing the force applied on the GNR by the AFM tip gradually. When the setpoint was decreased to a typical value of 0.010–0.050 V, the GNR could be pushed by the AFM tip to cause a displacement. Different displacement amplitudes can be acquired by changing the scan size of the AFM tip (typically in a range of 150–280 nm). Raman Measurements of Individual Strained GNRs: The positions of individual strained GNRs on the SiO2/silicon chips were located relative to pre-fabricated alignment markers by AFM. The Horiba–Jobin–Yvon LabRAM HR confocal Raman system was used for the Raman mapping. The sample was first observed under Raman microscope to determine the location of the strained GNR by the marker and set the region of Raman mapping. And then the micro-area Raman mapping with a typical scanning area of about 4.5 µm by 4.5 µm was performed for strained GNR. The 532-nm He–Ne laser with a power of ca. 1 mW µm−2 was used. A confocal hole diameter of 150 µm, a slit width of 100 µm,
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www.MaterialsViews.com and drain electrodes on the strained GNRs. The devices were then annealed in vacuum at 200 °C for 20 min to improve the contacts. In addition, electrical annealing was also done to further clean the ribbons and improve the electrical contact. An Agilent 4156C semiconductor parameter analyzer was used to measure the devices. The devices were measured in vacuum at ca. 5 × 10−6 Torr. A Janis closed cycle He cryostat was used to cool down the devices to low temperatures for the temperature-dependent electrical measurement. Device Simulator in the NEGF Simulation: The NEGF formulism was used to construct the ballistic device simulator, using a tight-binding Hamiltonian for the GNR.[49] The surface potential in the device was solved self-consistently with a three dimension Poisson solver coupled with the charge calculation via the NEGF formulism. The transmission spectrum was calculated and the conductance at different gate biases is obtained using the Landauer formula. Bandgap Calculation of GNRs under Uniaxial Strain: The band structures for different chiralities of GNRs were calculated by using a pz orbital tight-binding model method, whose binding parameters were extracted from ab initio calculations as in previous studies.[50,51] Edge bond relaxation and Hubbard term in the Hamiltonian were added to take care of the armchair and zigzag regions of the ribbon, respectively. The binding parameters under different uniaxial strain were modified according to the Harrison binding parameter relation. Detailed description of the Hamiltonian is included in Supplementary Note 4 in the Supporting Information.
Supporting Information Supporting Information is available from the Wiley Online Library or from the author.
Acknowledgements
Figure 5. Theoretical bandgap dependence on uniaxial strain and GNR width. a) A calculated three-dimensional plot of GNR bandgap as a function of ribbon width and uniaxial strain for the family of Na = 3p armchair GNRs, beginning at width 3.9 nm. The black line in the plot corresponds to a 19.0-nm-wide ribbon. b) The bandgap variation with uniaxial strain for specific ribbon widths. a 100x objective and a typical exposure integration time of ca. 60 s per spot were used in the Raman measurement. Calculation of Phonon Spectrum: The phonon spectrum of GNR was calculated via density functional theory with software packages Phonopy[46] and Vienna Ab Initio Simulation Package (VASP).[38,39] Atomic structures of GNRs with different width and strain was obtained using the local density approximation[47] and the projector augmentedwave pseudopotential[48] supplied in VASP, with hydrogen terminated edges. A space of more than 1.2 nm was left between ribbons. The force constant up to the fifth nearest neighbor was calculated using the supercell method in Phonopy. Further details were described in Supplementary Note 1 in the Supporting Information. Fabrication and Electrical Measurements of GNRFETs: The strained GNRs were calcined at 350 °C for 20 min to remove the coated PmPV. The electron-beam lithography followed by electron-beam evaporation of palladium (thickness: ca. 20 nm) were used to fabricate source
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This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DOE DE-SC0008684, the U.S. National Science Foundation (NSF) Postdoctoral Award Project (Award No. CHE1137395- 1), the Foundation for the Author of National Excellent Doctoral Dissertation of China (FANEDD) (Award No. 201154), the National Natural Science Foundation of China (Award No. 61177052, No. 60807008), the Program for New Century Excellent Talents in University (Award No. NCET-11–0319), and the Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (Award No. 131064). Received: August 16, 2014 Revised: September 15, 2014 Published online:
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Graphene Nanoribbons Under Mechanical Strain Changxin Chen,* Justin Zachary Wu, Kai Tak Lam, Guosong Hong, Ming Gong, Bo Zhang, Yang Lu, Alexander L. Antaris, Shuo Diao, Jing Guo,* and Hongjie Dai* Graphene has led to intense investigation of both experimental[1–4] and theoretical work[5] in recent years, owing to attractive material properties including high mobility,[6,7] thermal conductivity,[8] Young’s modulus,[9] zero effective carrier mass,[10] and long mean free path for carrier transport at room temperature.[11] One of the most important potential applications of graphene is as a building block for next-generation electronics and photonics,[10,12,13] but a major obstacle is the zero bandgap of semi-metallic two-dimensional (2D) graphene. One possible solution is to form one-dimensional graphene nanoribbons (GNRs) with 1–2 nm width, opening up sizable bandgaps.[14,15] Unfortunately, high-quality, long and ultra-narrow GNRs (ca. 2 nm) are difficult to be prepared, particularly ones with smooth edges throughout the ribbon length, and it has been shown that GNRs with large degree of edge roughness exhibit low mobility and conductivity due to scattering effects at the edges.[16] Wider GNRs (>15 nm) have a higher tolerance of edge roughness and show higher mobility and conductivity but much smaller bandgaps. It is therefore desirable to tune the bandgaps in GNRs for high-performance electronics and photonics applications. Theoretical and experimental studies have suggested that strain have a substantial effect on the vibrational and electronic band structure of carbon nanotube (CNT),[17–19] 2D graphene[20,21] and GNR.[22,23] Both ab initio calculations and tightbinding modeling show no bandgap opening for 2D graphene
Dr. C. X. Chen,[+] Dr. J. Z. Wu,[+] Dr. G. S. Hong, M. Gong, B. Zhang, A. L. Antaris, S. Diao, Prof. H. J. Dai Department of Chemistry and Laboratory for Advanced Materials Stanford University Stanford, California 94305, USA E-mail: [email protected]; [email protected] Dr. C. X. Chen Key Laboratory for Thin Film and Micro fabrication of the Ministry of Education National Key Laboratory of Science and Technology on Micro/Nano Fabrication Department of Micro/Nano Electronics School of Electronic Information and Electrical Engineering Shanghai Jiao Tong University Shanghai 200240, PR China Dr. K. T. Lam,[+] Dr. Y. Lu, Prof. J. Guo Department of Electrical and Computer Engineering University of Florida Gainesville, FL 32611–6130, USA E-mail: [email protected] [+]
These authors contributed equally to this work.
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even at uniaxial strains up to 20% as strain only causes the Dirac point to move away from the high symmetry K point in the Brillouin zone.[24–26] In contrast, theoretical studies advise a GNR could have sizable bandgap changes under uniaxial strain,[22] which could be useful for implementing graphene technology. Uniaxial strain modulates the bandgap of GNRs by shifting the Dirac point relative to the allowed wavevector lines (k-lines) in armchair GNRs, and by modifying the magnitude of spin polarization at the edges in zigzag GNRs. There has been a lack of reported experimental investigations into creating mechanical strains in GNRs, as well as into its effects on their material properties. In this work, uniaxial strains (0–6%) were applied to individual GNRs with highly smooth edges by atomic force microscopy (AFM) manipulation and the strain effects on the Raman spectroscopic and electrical properties of GNRs were investigated experimentally for the first time. We demonstrated that the Raman G-band frequency of GNRs showed an approximate linear dependence on uniaxial strain with downshifts under strain at a rate of about −10 cm−1 per 1% strain (/%) for GNRs with a width of ca. 20 nm. Uniaxial strain was found to tune the bandgap of GNRs significantly in a non-monotonic manner, with the bandgap varied between ca. 25 meV and ca. 62 meV under strain for a 19-nmwide GNR. These results were in good agreement with theoretical modeling carried out. The GNRs used in this work were ca. 20 nm in width and exhibited highly smooth edges, prepared by sonochemical unzipping of high quality arc-discharge grown multiwalled carbon nanotubes (MWCNTs)[27–29] (see Experimental Section for preparation details). The resulting GNR solution was spun onto silicon chips with 300-nm-thick thermally oxidized SiO2 at 3000 rpm to obtain well dispersed individual GNRs. The asdeposited GNRs on the SiO2/Si substrate had a PmPV polymer coating on the surface[27] (about 0.5 nm thick), which facilitated AFM manipulations and deformation due to the lack of direct GNR-SiO2 interactions. Without the polymer coating (i.e., after calcination to burn off the PmPV), we found that the AFM manipulation of GNRs was much more challenging due to the flatness of GNRs with a lower height and the stronger Van der Waals forces between GNRs and substrate. The PmPV coating was van der Waals adhesion in nature and would not have a significant effect on the mechanical property of GNRs. PmPV could be removed by calcination at 350 °C for 20 min after GNR manipulation. We manipulated and stretched GNRs on the SiO2/Si substrate with an AFM tip by pushing the middle of the GNR to form a bend and introduce tensile strain in the GNR (see Figure 1 and Experimental Section for AFM manipulation details). Due to the large radius of curvature of the bend relative to the small width of the GNR, the dominant strain induced in the GNR was uniaxial strain along the GNR length
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Figure 1. Strained individual GNR by AFM manipulation. a) An AFM image of GNR 1 with PmPV coating before AFM manipulation. b) An AFM image of GNR 1 after AFM manipulation and then calcination to remove the PmPV coating; the arrow shows the direction of AFM tip pushing GNR. The GNR is ca. 26 nm in width and ca. 1.2 nm in apparent height.
direction from the elongation of the GNR after the manipulation. AFM data also showed no obvious torsional deformation along the length of the manipulated GNRs. By changing the pushing/bending motion range of the AFM tip, we were able to obtain different displacements and different uniaxial strains in GNRs up to ca. 6%. Strain was introduced into various GNRs with different widths and layer numbers in our experiment (Figure 1 and Figure S1, Supporting Information), among which GNR 1 was 26 nm in width and 1.2 nm in apparent height and estimated to be a double-layer GNR.[27] After AFM manipulation, we observed that GNR 1 was dragged out along the scanning direction of the AFM tip (Figure 1b). Due to friction, the GNR was stretched along its axis. A monolayer GNR (GNR 2), 19 nm wide and 0.9 nm in apparent height, was also investigated (Figure S1, Supporting Information). The average tensile strain in the GNR was determined by the ratio of the apparent elongation measured and the unstrained length, estimated to be 0.33% and 0.29% respectively for GNR 1 and 2. The strain in our manipulated GNRs was in the elastic deformation range of GNRs.[30] The GNRs were pinned and kept strained by frictional
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forces between GNRs and the underlying substrate after AFM manipulation. Spatially resolved Raman imaging/spectroscopic mappings were performed for the strained GNRs to investigate the effect of the uniaxial strain on the Raman spectra. Raman spectroscopic mapping was done with a 532 nm laser excitation with a spot size of about 0.6 µm (see Experimental Section). Raman spectroscopic images generated from the obtained Raman spectra could be overlaid well with the AFM image of the strained GNRs (Figure 2a, 2d and Figure S2, Supporting Information). The GNR exhibited a higher intensity ratio of Raman D- and G-band than the MWCNT due to the existence of the edges in GNR (see Figure 2b). Also, the Raman G band of the GNR showed slight upshift in frequencies than that of MWCNTs due to the lack of curvature caused by rolling.[28] The Raman spectra taken along the strained GNR 1 (Figure 2c) showed a gradual downshift of the G band from the end (position 6) to the central manipulated position (position 3), with a shift of −6.5 cm−1. For GNR2, a shift of −4.9 cm−1 in the G band was observed progressively from 1589.1 cm−1 at the end (position 5) to 1584.2 cm−1 at the manipulated position (position 3) (Figure 2e). In a manipulated GNR, strain propagated from the center and decreased towards the GNR ends from the manipulated position. In addition to observing the gradual upshift of the G band from the manipulated position to the two ends of the strained GNRs, examination of AFM images found that the ends of the GNRs often had very small displacements in position after the manipulation in our experiments (see Figure S3, S1a, and S1b, Supporting Information and Figure 1), indicating that the strain had propagated to the ends. The tensile strain on the flexible graphene hexagonal lattice was anticipated to be able to spread to a much longer distance[31] than the length (2.5–3.5 µm) of the GNRs used in our experiment. Assuming the friction coefficient between the GNR and substrate was constant and the lack of sharp kinks due to manipulation, we approximated that the uniaxial strain in the strained GNR linearly decreased from the manipulated position to the ends (where the strain was relaxed to zero) along the GNR length direction (see Figure 3a), corresponding to the gradual shift seen in the Raman data. Within this simplified model of strain distribution, local uniaxial strains along the GNRs were estimated and correlated with the shift of the G bands as a function of the strain. The tensile strain linearly decreased from 0.65% and 0.58% to zero (from the manipulated position to the end) for GNR 1 and 2 respectively. It was found that the shift of the GNR’s G bands had an approximately linear dependence on the uniaxial strain (Figure 3b), with shift rates estimated to be −10.3 cm−1/% and −8.7 cm−1/% for strained GNR 1 and GNR 2, respectively. The downshift of the G band as a result of tensile strain was also observed for 2D graphene in previous studies.[32,33] The downshift of G band could be attributed to the elongation of the carbon–carbon bonds under uniaxial strain, weakening the bonds and lowering the vibrational frequency. We investigated theoretically the G band’s shift as a function of uniaxial strain for GNRs of various widths. The shift of Raman G band of strained graphene was due to shifting of the optical phonon (OP) mode,[34–37] i.e., the doubly degenerate zone center E2g mode.[37] The phonon spectra of graphene
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COMMUNICATION Figure 2. Raman spectroscopic mapping of individual strained GNRs. a) An overlay of a Raman image and an AFM image for strained GNR 1. The Raman image was generated from the intensity integral total of the D-band 1324–1360 cm−1 region (represented in red) and the G-band 1559–1592 cm−1 region (represented in green). The GNR and MWCNTs show as different colors in the figure due to the different dominance of D and G band intensities. b) Raman spectra at the positions 1 and 7 in (a), showing typical Raman spectra for GNRs and CNTs respectively. c) Raman spectra taken at positions 1 to 6 in (a) along the strained GNR 1. The spectra were fitted with Lorentzians (red and green fitting lines) to obtain the positions of the G band peak, showing a gradual downshift of the G band from the end position to the manipulated position in the GNR; The spectra at position 1 to 4 were fitted with single peak and the spectra at position 5, 6 were fitted with two peaks due to signal from the MWCNT nearby. The dashed line is a guide for the eyes. d) An overlay of a Raman image and an AFM image for strained GNR 2. The Raman image was generated from the intensity integral of the D band in the 1339–1366 cm−1 region (represented in red). e) Raman spectra taken at positions 1 to 5 in (d) along the strained GNR 2. The spectra are fitted with Lorentzians (red fitting lines) to obtain the G-band peak positions. The dashed line is a guide for the eyes.
and GNRs were calculated using local density approximation in density functional theory with a projector augmented wave pseudopotential supplied by the Vienna Ab Initio Simulation Package[38,39] to calculate the force constants at different uniaxial strains (see Experimental Section, Supplementary Note 1 and Figure S4 in the Supporting Information) and the corresponding OP mode responsible for the G band was identified from the eigenvector resembling the E2g mode. The shift of the G band under uniaxial strain for different widths of armchair GNRs (denoted with the number of dimer lines Na across the ribbon with Na = 7, 10, 22 and 28) and 2D graphene was then extracted (Figure 3c). It was observed that the theoretical G band’s shift increased linearly with the increase of the uniaxial strain for various widths of GNRs, consistent with the experimental result. Calculations showed that the layer number and edge chirality of the GNR did not have an obvious effect on the shift rate of the G band under uniaxial strain. We found that the shift rate of the G band decreased with the width of the GNR (inset in Figure 3c), and the smaller shift rates for narrower GNRs were due to the effect of GNR edges which modified the force constant of GNRs (Table S1, Supporting
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Information). As the ribbon width increased, the effect of the edges was reduced and the shift rate of the strained wide GNR approached that of strained 2D graphene (about −18.0 cm−1/%). For the ca. 26 and ca. 19 nm wide GNRs, the theoretical shift rates of the G band were about −17.5 cm−1/% and -17.1 cm−1/% respectively, which were a little larger than the experimental measured rates (ca. 9–10 cm−1/%). The difference could be due to the isolated GNR considered in the first-principle calculations without including environmental effects such as the presence of strong substrate interactions. The van der Waals interaction between the carbon atoms and the substrate surface would result in additional spring constant terms to the vibrational energy that could decrease the effect of uniaxial strain on the overall dynamical matrix, which would in turn reduce the shift rate of the G band. Another effect could be due to the laser spot size of the Raman system, which could shift the measured frequency of G band at the end and the maximum-strain position of the GNR to a lower and higher value respectively due to asymmetric distribution of strain around these two positions and thereby lowering the measured shift rate.
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Figure 3. Raman shift of strained GNRs. a) A schematic illustration of the distribution of uniaxial strain along the length direction of a manipulated GNR. b) The frequency shift of G band as a function of uniaxial strain at position 1 to 6 in GNR 1 (red) and at position 1 to 5 in GNR 2 (black). The linear least-squares-fits shows shift rates for these two GNRs. Error bars show possible strain errors from the overlay deviation of the Raman image and the AFM image. c) Theoretical frequency shift of the G band for the Na = 7, 10, 22 and 28 armchair GNRs and the 2D graphene as a function of uniaxial strain. The insert shows shift rate of the G band against GNR width, approaching that of 2D graphene for wide GNR; The dash line in the insert corresponds to the shift rate of the 2D graphene at −18.0 cm−1/%.
To investigate the electrical properties of strained GNRs, field-effect transistors (FETs) were made on individual strained GNRs by e-beam lithography and lift-off with palladium (Pd) used as the source and drain contacts (see Experimental Section). For GNRFETs fabricated on a strained 19-nm-wide monolayer GNR (GNR 3) (Figure 4a), the strains of the three GNR segments (labeled 1–3 in Figure 4a) were about 4.04%, 3.07% and 1.60% respectively estimated from the midpoint of the segments. Room-temperature electrical characteristics and temperature-dependent measurements (Figure 4b and 4c respectively, see Experimental Section for details) for these GNRFETs showed an increase in the on/off current ratio in the transfer
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characteristic curves at lower temperatures, with a decrease in the minimum conductance by more than 2 orders of magnitude from 295 K to 45 K for the FET 2 as shown in Figure 4c. A plot of the minimum conductance (Goff) as a function of inverse temperature, ln (Goff ) ∝ T −1 (Figure 4d) showed a linear relation in the temperature range of 295 K to 105 K, corresponding to conductance primarily through thermally activated carriers at the point of minimum conductance. The asymmetric electron and hole conductance of the devices shown in Figure 4b and 4c is likely due to the Fermi level alignment at the contacts, and so we performed non-equilibrium Green’s function (NEGF) simulation to fit the asymmetric transfer characteristics and extracted the bandgap of GNRs (see Experimental Section, Figure S5 and Supplementary Note 2, Supporting Information). As a result, bandgaps (Eg) of ca. 35, 62, and 25 meV were extracted for segments 1, 2, and 3 of the strained GNR (with strains of about 4.04%, 3.07% and 1.60%) respectively (see Figure 4e). It was shown that the uniaxial tensile strain could effectively modulate the GNR bandgap, which was altered by about 2.5 times from 25 meV to 62 meV that was measured at the different segment with different strain. A similar non-monotonic varying trend of the bandgaps was observed for all of our 8 measured strained GNRs with widths ranging from ca. 17 to ca. 26 nm (see Figure S6 and Supplementary Note 3 in the Supporting Information for a 22-nmwidth strained GNR), varying in amplitude by dozens of meV. We simulated the bandgap dependence on uniaxial strain for various chiralities of GNRs using the pz orbital tight-binding model (see Experimental Section). Given that the GNRs prepared by our method had random chiral edges from near armchair to zigzag,[28,29] a chiral GNR was picked to calculate the bandgap changes under uniaxial strain (for the first time) and compared with the experimentally observed trend. For a calculated 19-nm-wide (9,6) GNR, a non-monotonic fluctuating bandgap change was observed, with a similar period and amplitude of the bandgap variation under uniaxial strain as seen in the experimental result (Figure 4e). The further calculations showed that the bandgap of a similar width of armchair GNR as a function of uniaxial strain had an oscillatory dependence while that of the similar width of zigzag GNR displayed minute monotonic increase under uniaxial strain. Since chiral ribbons can be considered as a combination of armchair and zigzag regions according to the chiral angle, represented in (n,m) notation where the ratio of armchair to zigzag region is m:(n −m),[40] the bandgap variation under uniaxial strain for chiral GNRs can be attributed to the dominant bandgap change of the armchair portion in chiral GNRs. Simulation of armchair GNRs showed that the bandgap will be increased from ca. 215 meV to ca. 400 meV when the uniaxial strain varies from 0% to 2.0% for a 4.3-nm-wide ribbon (Figure 5). A bandgap of 400 meV could afford an on/off ratio of 106 to 107 for a Pd-contacted p-type unipolar GNRFET,[41,42] which could be used in complementary metal-oxide-semiconductor (CMOS) logic devices.[43] As a reference, a 2.0-nmwide unstrained GNR would exhibit a similar bandgap of ca. 410 meV. Therefore, with a suitable uniaxial strain applied to armchair GNRs, the GNR’s width restriction for logic application can be relaxed to a larger range up to ca. 5 nm rather than sub-2 nm. Theoretical simulations had predicted that
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COMMUNICATION Figure 4. Electrical characteristics of strained GNRs. a) An AFM image of three three-terminal FET devices on SiO2/Si (with Si back gate) fabricated along strained 19-nm-wide GNR 3. The three GNR segments labeled as 1, 2 and 3 have strains of 4.04 ± 0.41%, 3.07 ± 0.31% and 1.60 ± 0.25% respectively, as estimated from the midpoint of the segments and the variation in strain along the segments. b) Room-temperature conductance as a function of gate bias (GDS–VGS) of the three GNR segments. c) Temperature-dependent GDS–VGS curves of FET 2 at drain bias VDS = −1.0 mV. d) The minimum conductance of GDS–VGS curves for the three devices as a function of the inverse of temperature from 295 K to 105 K at intervals of 10 K. The red lines are the linear fit to the experimental data. e) Extracted experimental bandgaps under each uniaxial strain of the three segments. Horizontal error bars cover the range of strain in each channel; Vertical error bars show the fitting error of the bandgap extraction. The dash line in the figure shows the theoretical bandgap of a 19-nm-wide (9,6) chiral GNR, to show the expected bandgap change and strain modulation behavior for similar width of GNR.
the impact of the scattering induced by line-edge roughness (LER) rapidly degraded mobility for ribbon widths less than 5 nm.[44,45] Toward this direction, a chemical synthesis method that can reliably produce high-quality GNRs with controlled width ca. 5 nm will be expected for future high-performance strained-GNR logic device application. In summary, uniaxial strain has been successfully introduced into individual GNRs for the first time by AFM manipulation to investigate effects of strain on the Raman spectroscopic and electrical properties of GNRs. It was found that the Raman G-band frequency of GNRs downshifted linearly under uniaxial strain at a shift rate of about −10 cm−1/% for GNRs with a width of around 20 nm. The bandgap of GNRs could be tuned significantly by uniaxial strain in a non-monotonic fluctuating way, varying from 25 to 62 meV for a 19-nm-wide GNR under strain. Theoretical modeling on the Raman G-band shift and bandgap variation of GNRs under uniaxial strains was also performed, showing good agreement with the experimental results. Strain engineering of GNRs opens a path to tune the bandgap of graphene and is promising for tailoring the properties of GNRs towards versatile electronics and photonics applications.
Experimental Section Preparation of GNRs: MWCNTs (30 mg, Aldrich, 406074–500MG) were calcined in air at 550 °C in a 1-inch tube furnace for 2 h, which formed etching pits on the sidewall by oxidation reactions at pre-existing defects on nanotubes without destroying pristine sidewalls. After that, calcined MWCNTs (15 mg) and poly(m-phenylenevinylene-co-2,
Adv. Mater. 2014, DOI: 10.1002/adma.201403750
5-dioctoxy-p-phenylenevinylene) (PmPV) (7.5 mg, Aldrich, 555169– 1G) were dissolved in 1,2-dichloroethane (DCE) (4 mL) and then sonicated (Cole Palmer sonicator, Model 08849–00) for 1 h to unzip MWCNTs into GNRs. Afterward, the solution was ultracentrifuged at 50 000 rpm (revolutions per minute) for 2 h to remove most of residual MWCNTs. The GNR-rich supernatant was extracted from the obtained solution. AFM Manipulation of GNRs: The MultiMode scanning probe microscope and commercial AFM tips (model: ACST, force constant k = 7 N m−1 and resonance frequency f0 = 150 kHz) from the APPNano company were used in the manipulation. The tapping AFM mode was used. Firstly, the scanning direction of the AFM tip was set to be perpendicular to the GNR axis. Then the drive amplitude and scan rate of the AFM were set as a typical value of 200–700 mV and 1.0–1.6 Hz respectively, while keeping the target amplitude, proportional gain and integral gain as 0.5 V, 2, and 0.2 respectively. The aspect ratio (the width/height ratio of the AFM scanning) was changed into 16:1 to make the AFM tip scan within a very short GNR segment where the manipulation was to be performed. Afterwards, the setpoint of the AFM was decreased at a small step size carefully, increasing the force applied on the GNR by the AFM tip gradually. When the setpoint was decreased to a typical value of 0.010–0.050 V, the GNR could be pushed by the AFM tip to cause a displacement. Different displacement amplitudes can be acquired by changing the scan size of the AFM tip (typically in a range of 150–280 nm). Raman Measurements of Individual Strained GNRs: The positions of individual strained GNRs on the SiO2/silicon chips were located relative to pre-fabricated alignment markers by AFM. The Horiba–Jobin–Yvon LabRAM HR confocal Raman system was used for the Raman mapping. The sample was first observed under Raman microscope to determine the location of the strained GNR by the marker and set the region of Raman mapping. And then the micro-area Raman mapping with a typical scanning area of about 4.5 µm by 4.5 µm was performed for strained GNR. The 532-nm He–Ne laser with a power of ca. 1 mW µm−2 was used. A confocal hole diameter of 150 µm, a slit width of 100 µm,
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www.MaterialsViews.com and drain electrodes on the strained GNRs. The devices were then annealed in vacuum at 200 °C for 20 min to improve the contacts. In addition, electrical annealing was also done to further clean the ribbons and improve the electrical contact. An Agilent 4156C semiconductor parameter analyzer was used to measure the devices. The devices were measured in vacuum at ca. 5 × 10−6 Torr. A Janis closed cycle He cryostat was used to cool down the devices to low temperatures for the temperature-dependent electrical measurement. Device Simulator in the NEGF Simulation: The NEGF formulism was used to construct the ballistic device simulator, using a tight-binding Hamiltonian for the GNR.[49] The surface potential in the device was solved self-consistently with a three dimension Poisson solver coupled with the charge calculation via the NEGF formulism. The transmission spectrum was calculated and the conductance at different gate biases is obtained using the Landauer formula. Bandgap Calculation of GNRs under Uniaxial Strain: The band structures for different chiralities of GNRs were calculated by using a pz orbital tight-binding model method, whose binding parameters were extracted from ab initio calculations as in previous studies.[50,51] Edge bond relaxation and Hubbard term in the Hamiltonian were added to take care of the armchair and zigzag regions of the ribbon, respectively. The binding parameters under different uniaxial strain were modified according to the Harrison binding parameter relation. Detailed description of the Hamiltonian is included in Supplementary Note 4 in the Supporting Information.
Supporting Information Supporting Information is available from the Wiley Online Library or from the author.
Acknowledgements
Figure 5. Theoretical bandgap dependence on uniaxial strain and GNR width. a) A calculated three-dimensional plot of GNR bandgap as a function of ribbon width and uniaxial strain for the family of Na = 3p armchair GNRs, beginning at width 3.9 nm. The black line in the plot corresponds to a 19.0-nm-wide ribbon. b) The bandgap variation with uniaxial strain for specific ribbon widths. a 100x objective and a typical exposure integration time of ca. 60 s per spot were used in the Raman measurement. Calculation of Phonon Spectrum: The phonon spectrum of GNR was calculated via density functional theory with software packages Phonopy[46] and Vienna Ab Initio Simulation Package (VASP).[38,39] Atomic structures of GNRs with different width and strain was obtained using the local density approximation[47] and the projector augmentedwave pseudopotential[48] supplied in VASP, with hydrogen terminated edges. A space of more than 1.2 nm was left between ribbons. The force constant up to the fifth nearest neighbor was calculated using the supercell method in Phonopy. Further details were described in Supplementary Note 1 in the Supporting Information. Fabrication and Electrical Measurements of GNRFETs: The strained GNRs were calcined at 350 °C for 20 min to remove the coated PmPV. The electron-beam lithography followed by electron-beam evaporation of palladium (thickness: ca. 20 nm) were used to fabricate source
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This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DOE DE-SC0008684, the U.S. National Science Foundation (NSF) Postdoctoral Award Project (Award No. CHE1137395- 1), the Foundation for the Author of National Excellent Doctoral Dissertation of China (FANEDD) (Award No. 201154), the National Natural Science Foundation of China (Award No. 61177052, No. 60807008), the Program for New Century Excellent Talents in University (Award No. NCET-11–0319), and the Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (Award No. 131064). Received: August 16, 2014 Revised: September 15, 2014 Published online:
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