Crossover point of the field effect transistor and interconnect applications in turbostratic multilayer graphene nanoribbon channel

The electrical transport properties of a turbostratic multilayer graphene nanoribbon (GNR) with various number of layers (1–8 layers) were investigated using a field effect transistor with a single GNR channel. In the turbostratic multilayer GNR with 5 layers or less, the carrier mobility and Ion/Ioff ratio in the FETs were improved by slightly increasing the conductance with increasing the number of layers, meaning that the excellent semiconducting characteristic. The improvement of the carrier transport properties promotes by the turbostratic stacking structure. In the turbostratic multilayer GNR with 6 layers or more, although the Ion/Ioff ratio degraded, the conductance extremely improved with increasing the number of layers. This indicates that the turbostratic multilayer GNR with thicker number of layers becomes the significantly lower resistivity wire as a metallic characteristic. We revealed that the crossover point of the physical properties between the semiconducting and metallic characteristics is determined by the strength to screen the surrounding environment effects such as charged impurity on the substrate. Our comprehensive investigation provides a design guidance for the various electrical device applications of GNR materials.

structure and GNR width in the ideal system treated in theory. What is the dominate factor that determines the conductive properties of the GNR material embedded in the device structure? The semiconducting and metallic characteristics tend to be mainly observed at a monolayer (or bilayer) GNR 6,24 and a multilayer GNR 28 , respectively. Therefore, we focus on the effect of the number of layers on the carrier transport properties of the GNR-FETs.
It is well known that the conductivity and carrier mobility of a monolayer graphene-FET extremely degrades on the SiO 2 /Si device substrate as a comparison with an intrinsic property of the monolayer graphene observed in a suspended structure 33 . Since the carrier concentration of the monolayer graphene with a linear dispersion is very low near the Dirac point, the carrier transport properties in the monolayer graphene-FETs are extremely sensitive to the surrounding environments such as the charged impurity and surface roughness 34 . On the other hand, in a multilayer graphene-FET, the carrier scattering induced by the surrounding environments is dramatically improved by the screening effect of the multi-stacking 35 . In the GNR system with a narrow width, the surrounding environment effect is considered to be extremely large compared with the graphene system.
In this study, to understand the surrounding environment effect on the carrier transport properties of the GNR, we investigated the transfer characteristics of the GNR-FETs with various number of layers (1-8 layers) on the SiO 2 /Si substrate. The turbostratic multilayer were synthesized by an overlayer growth of graphene on a GNR template prepared by unzipping from double-walled CNTs as previously reported 36 . We found that the carrier transport properties such as the semiconducting and metallic characteristics observed in the multilayer GNR with a narrow width (18-25 nm) are determined by strength to screen the charges of the impurity on the device substrate as a surrounding environment. This result indicates that the type of the device can be controlled by the number of layers in the multilayer GNR.

Results
Structural analysis of the multilayer GNRs. Figure 1a,b show the AFM images observed at the same location for the samples of the pristine and grown GNRs. Figure 1c is also the height profiles along L-L′, M-M′ and N-N′ lines, respectively. The height of the pristine GNR before the growth is ~ 1 nm. This value is obviously smaller than the diameter of the DWCNT (~ 3-15 nm) 22 used as the starting material, and is slightly higher than the interlayer distance (0.34 nm) in the bulk graphite. Considering that the height of the monolayer graphene on the SiO 2 /Si substrate is 0.6-0.8 nm due to a very weak interaction between the graphene and substrate 37 , this result means that the monolayer or bilayer GNRs are efficiently synthesized by unzipping from the DWCNTs. After the CVD growth, the height of the GNRs are increased by ~ 1 nm, meaning the formation of additional two or three layers of graphene on the pristine GNR template. Figure 1d,e show the enlarged images as indicated by the square in Fig. 1a,b, respectively. The root mean square (RMS) surface roughness of the grown GNR and substrate evaluated from the height profiles along R-R′, S-S′ and T-T′ lines in Fig. 1f is almost the same value (0.10-0.11 nm) among them, and the value is lower than a monolayer graphene step height. This indicates that the surface morphology in the grown graphene layers is atomically flat.
The Raman spectrum in the 2D-band region provides an evaluation method to distinguish the different number of layers and stacking structures in multilayer graphene system 38 . Figure 2 shows the 2D-band spectra observed from the pristine and grown GNR with different number of layers. The number of layers in the GNR is decided by the AFM observations. The dotted circles and thin solid lines indicate the experimental data and the fitting curves, respectively. The spectrum is normalized by the integrated intensities of the 2D-band region from 2600 to 2800 cm −1 . The spectrum observed from the pristine GNR can be fitted by a single Lorentzian peak, indicating that the pristine GNR is constructed by a monolayer structure. The stacking structures in the grown multilayer graphene are mainly divided into two types: the ordered stacking (e.g. AB stacking) and turbostratic stacking. In a multilayer graphene with the ordered stacking, the peak shape in the 2D-band spectrum is decomposed by two Lorentzian peaks at ~ 2680 and ~ 2720 cm −1 , respectively 39 . On the other hand, the peak shape observed from a turbostratic multilayer graphene, in which the stacking of the graphene layers is rotationally random in plane, shows a single Lorentzian at ~ 2700 cm −1 , just as in monolayer graphene 40 . Therefore, the turbostratic ratio (R′) in the multilayer graphene can be evaluated by the curve fitting analysis of the Raman spectrum in the 2D-band region using three Lorenz curves as the peak positions at ~ 2680, ~ 2700 and ~ 2720 cm −1 , as noted by I G'3DA , I G'2D and I G'3DB using the following equation 41 : where the R means the ordered stacking ratio. The ratios of turbostratic stacking in the pristine graphene and the grown multilayer graphene with 3 and 9 layers are about 100%, 71% and 68%, indicating that the grown graphene layer forms a turbostratic stacking at a high ratio.
Electrical transport properties of the turbostratic multilayer GNR. Figure 3 shows the transfer characteristics (conductance vs gate voltage) in the FETs using a single channel of the pristine GNR and the grown multilayer GNR with various number of layers measured at (a)-(d) 10 K and (e)-(h) 300 K, respectively. The conductance (σ) is defined as the inverse of the sheet resistance (R s ) as the following equation: where I sd and V sd are the source-drain current and source-drain voltage, respectively. L ch and W ch are also the length and width of the single GNR channel in the FET, respectively. Although the width of the GNR tends  Supplementary Fig. S1), the W ch measured in the transfer characteristics is almost the same value (18-25 nm) among them as indicated by the inset in Fig. 3. At the low temperature, the minimum value of conductance (σ min ) as an OFF state region reaches the detection limit value of current (~ 10 pA) in our source-measure unit, and the semiconducting characteristics are observed. The strong suppression of conductance in the OFF state region is caused by the formation of the transport gaps associated with the disordered structures 42 . On the other hand, at room temperature, the transfer characteristics measured at the grown multilayer GNR with 6 layers or more slightly depends on the temperature, resulting the degradation of I on /I off ratio. This means that the suppression effect in the grown multilayer GNR significantly reduces with increasing measurement temperature (the details of the carrier transport mechanism will be described in the section of "Discussion"). Next, we focus on the sheet resistance corresponding the maximum conductance (σ max ) value at the ON state region. Figure 4 is the change in the sheet resistance as a function of the number of layers. Note that the sheet resistance decreases with increasing the number of layers. We consider a simple resistance model in which the plane direction resistance of the layers is connected in parallel between the source and the drain electrodes, assuming that the conductance between graphene layers connected by van der Waals force can be ignored as shown in Fig. 4b. Then, the total sheet resistance ( R total ) of the multilayer GNR composed of n layers is described as where R n and R 1 are the sheet resistance of monolayer GNR in the n-th layer and pristine monolayer GNR as a growth template. Assuming that the sheet resistance of the grown monolayer GNR in each layer is equal to that of the pristine monolayer GNR as a growth template, the change in the sheet resistance with respect to the www.nature.com/scientificreports/ number of layers evaluated from the calculation becomes to be a curve as indicated by the solid line in Fig. 4a. However, the observed resistance value deviates from the calculated curve and show a lower resistance as indicated by arrows. The same behavior of the significant improvement in conductance with increasing the number of layers has been also observed in the turbostratic multilayer graphene 43,44 . The improvement is explained by reducing the carrier scattering due to the screening effect of the multi-stacking for the charges of the impurity on the SiO 2 /Si substrate (the detailed mechanism of the improvement in conductance will be described in the "Discussion" section). A notable difference between the multilayer graphene and multilayer GNR is the reduction rate of the sheet resistance as the number of layer increases. In the multilayer graphene, the sheet resistance of 7-layer graphene is ~ 0.7 times higher than that of single layer graphene 44 . In contrast, the sheet resistance of 6 or 8-layer GNR is ~ 0.3 times higher than that of single layer GNR (see Fig. 4a), indicating a larger reduction rate. The difference of the reduction rate of the sheet resistance between the graphene and GNR is thought to be caused by the structural dimensionality. In the multilayer GNR-FET, the channel width is extremely narrow due to a one-dimensional structure, and the effect of the carrier scattering by the charge impurities existed on the SiO 2 /Si substrate is significant. As a result, the conductance enhancement by the screening effect in the multilayer GNR is expected to be more pronounced than that in the multilayer graphene as a two-dimensional system. Figure 5 shows the carrier mobility of the GNR as a function of the number of layers measured at room temperature. The circles and dashed line are experiment data and eye guide, respectively. The pristine GNRs prepared by unzipping from the DWCNTs are composed of monolayer or bilayer. The carrier mobility observed from the pristine GNR is in good agreement with the value as previously reported 23 . Note that the carrier mobility significantly improves with increasing the number of layers. Usually, the carrier mobility observed from a few layer graphene composed of the AB (Bernal) stacking structure degrades with increasing the number of layers because the electrical band structure near the Dirac point approaches a parabolic dispersion 35,45 . It has been reported that the carrier mobility observed in a few layer graphene with the turbostratic stacking structure is higher than that of the monolayer graphene 46 because the electrical band structure keeps the linear dispersion due to a weak inter-layer coupling between the layers 40 . Therefore, it is considered that the anomalous carrier transport properties in the turbostratic multilayer GNR as a function of the number of layers is caused by the improvement of transfer conductance associated with keeping the linear dispersion and the screening effect.

Discussion
We discuss the carrier transport mechanism of the GNR under the gate bias region exhibiting a minimum conductance (σ min ) value as an OFF state. As shown in Fig. 3, the σ min of the multilayer GNR with 6 layers or more at the OFF state region depends on the measurement temperature. The analysis of temperature dependence in conductance is a convenient way to identify the dominate factors of such carrier scattering as phonons and charged impurities 47 . Figure 6 shows a plot of ln (σ min ) as a function of T −1 . The temperature dependence of ln (σ min ) measured from the grown multilayer GNRs with 6 and 8 layers is well fitted by the sum of the two-dimensional variable range hopping (2D-VRH) and thermal activation (TA) conductions 48 , expressed by where the σ VRH (T) and σ TA (T) are the temperature dependence of conductance based on the 2D-VRH and TA conduction models, respectively. In the 2D-VRH model, the σ VRH (T) has the following formula 49 where B is hopping parameter. The carriers in the 2D-VRH conduction thermally jump from one localized state to another between a large energy gap without going through a continuous electrical band structure. The www.nature.com/scientificreports/ phenomenon is frequently observed in reduced graphene oxide materials with many defects 50,51 . In the TA conduction model, the σ TA (T) is expressed by where the E a and k B are the thermal activation energy and the Boltzmann constant, respectively. The TA conduction means that the carriers flow via a continuous electrical band structure. When the measurement temperature rises at a boundary of around 40-100 K as indicated by the vertical dashed lines in Fig. 6, the conduction mechanism in the grown multilayer GNR with 6 and 8 layers changes from the 2D-VRH to the TA conductions. This means that the suppression effect of conduction significantly reduces due to increasing the measurement temperature. The σ min in the pristine GNR and the grown multilayer GNR with 5 layers or less is below the detection limit value at room temperature (see Fig. 3), meaning that the conduction mechanism is dominated by the 2D-VRH conduction due to the strong suppression of the carrier transport even at room temperature. We focus on the origin of reducing the suppression effect in the grown multilayer GNR with 6 and 8 layers. The suppression effect of the carrier transport is induced by the transport gap that arises from quantum confinement and edge effects 1,52 . The suppression is extremely enhanced at the Dirac point where the carrier concentration shows a minimum value due to the charge neutrality point. As a result, the conductance value of the monolayer GNR around the Dirac point sometimes exhibits zero-conductance as an OFF state 4 . The theoretical calculation predicts that a GNR with the width of 5 nm or less is required for the formation of the band gap energy larger than room temperature 53 although the band gap energy also depends on the edge structures. However, the transport gaps have been experimentally observed even with lager widths (~ 25 nm) 4,54 . Moreover, we observe that the strength of the suppression effect differs greatly between the pristine monolayer GNR and the grown multilayer GNR, despite the fact that the width is almost the same between them (see Supplementary  Fig. S2). These mean that the experimentally observed value of the transport gap associated with electron confinement in the GNR system is not determined only by the width and edge structures. Usually, there are many charged impurities (~ 10 12 cm −2 ) on the surface of the SiO 2 /Si device substrate. Since the amount of charged impurities on the device substrate is larger than a typical carrier concentration (~ 10 11 cm −2 ) of monolayer graphene near the Dirac point, the conductance and the carrier mobility significantly degrade on the device substrate due to the carrier scattering by the charged impurities 55,56 . The similar situation applies to the GNR system. Since the charged impurities induce the localized potential barriers in the GNR with a narrow width, it is considered that the transport gap is significantly induced by the charged impurities.
The appearance temperature of the TA conduction is expected to increase with increasing the number of layer. However, the opposite trend is observed as shown in Fig. 6. Both 6-and 8-layer GNR-FETs are thought to have efficiently screening effect, considering that the screening length in the multilayer graphene is to be ~ 1 nm 57 . Therefore, the temperature range of the TA conduction in the multilayer GNR with a thickness of more than 1 nm seems to be strongly dependent on the crystallinity of the synthesized GNR rather than the number of layers. In fact, a similar carrier transport mechanism with the combination of TA and VRH conductions has been observed in the reduced graphene oxide material 48 , and the appearance temperature of the TA conduction strongly depends on the crystallinity. In the synthesis of multilayer graphene grown on graphene template via our CVD process, since the crystallinity tends to decrease as the number of layer increases 43 , it seems that the appearance of the TA conduction is observed at higher temperature in the 6-layer GNR-FET than the 8-layer GNR-FET.
We discuss the effect of the charged impurities on the carrier transport in the turbostratic multilayer GNR. Figure 7a,b show the self-consistent potential profiles of the bottom layer and the top layer in the multilayer GNR with 8 layers on the SiO 2 substrate when the density of charged impurity is 2 × 10 11 cm −2 . The potential profile is calculated within the Thomas-Fermi approximation. In the bottom layer attached on the substrate, the surface potential is strongly modulated by the charged impurities, indicating that the electron-hole puddles as the localized states near the charge neutrality point are formed by the potential barrier of the charged impurities 58 . In this case, the carrier transport property is dominated by the 2D-VRH conduction via the localized states. On the other hand, the modulation of the surface potential due to the charged impurities dramatically reduces in the top layer because the charges on the substrate is screened in the interlayer of the multilayer GNR. Since the electrical band structure in the top layer of the multilayer GNR is not modulated by the charged impurities, the carrier transport is dominated by the TA conduction via a continuous band structure without any localized states as indicated by Fig. 6. The same screening effect are also observed at the multilayer graphene 35,57 . As a result, the significant improvement of the conductance in the turbostratic multilayer GNR is observed by the efficient screening effect as shown in Fig. 4a. Figure 7c shows the calculated carrier mobility in each layer of the turbostratic multilayer GNR with 4 layers (squares) and 8 layers (circles). The carrier mobility improves with increasing the number of layers due to the enhancement of the screening effect. The improvement of the mobility becomes apparent in the vicinity of 4th to 6th layer, and this trend is in good agreement with the experiment result as shown in Fig. 5. It has been reported that the screening length in multilayer graphene is ~ 1 nm 57, 59 . In the simulation, the mobility is asymptotic to the value calculated by a model considering only phonon scattering, as indicated by the dashed line. Figure 8 shows the temperature dependence of the maximum conductance (σ max (T)) in the pristine monolayer and the grown multilayer GNR-FET as the ON state region. The σ max (T) is normalized by the σ max (300 K) measured at room temperature. For the pristine monolayer GNR-FET, the σ max (T) is independent to the measurement temperature. It has been reported that the conductance observed from the monolayer graphene is independent to the measurement temperature because the density of the charged impurities on the substrate is larger than the thermally excited carriers around the Dirac point due to the linear dispersion 35 . The similar situation applies to the GNR system. As a result, the conductance of the pristine GNR shows a lower value due to the strong suppression of the carrier transport by the localized potential barriers of the charged impurities as indicated by Fig. 3. www.nature.com/scientificreports/ Note that σ max (T) in the grown multilayer GNR-FET significantly improves as the measurement temperature decreases as shown in Fig. 8b. The improvement of the σ max (T) is caused by reducing the phonon scattering. Since the carrier scattering of the charged impurities is greatly reduced by the screening effect of the multi-stacking, the dominate factor of the carrier scattering is phonon scattering. This leads to the anomalous enhancements of the conductivity and carrier mobility as shown in Figs. 4 and 5. Figure 9 shows an overview of the device characteristics in the turbostratic multilayer GNR-FET measured at room temperature. The device characteristics greatly change in the vicinity of the 5th layer as a crossover point. At the turbostratic multilayer GNR with 5 or less layers, the zero-conductance state as a transport gap keeps even at room temperature due to a strong suppression effect of the carrier transport by the charged impurities on the substrate. Moreover the I on /I off ratio and carrier mobility in the GNR-FET are improved with increasing the additional graphene layers with the turbostratic stacking. As a result, the transfer characteristic in the turbostratic multilayer GNR exhibits the excellent semiconducting property. When the grown multilayer GNR is 6 layers or more, the suppression of the conductance leading to the carrier scattering dramatically reduces by the efficient www.nature.com/scientificreports/ screening effect of the multi-stacking. As a result, the transfer characteristic in the multilayer graphene shows the metallic property with the significantly higher conductance without the transport gap.

Summary
We investigated the carrier transport properties of the turbostratic multilayer GNR with various number of layers. At the grown multilayer GNR with a thin film thickness of 5 layers or less, the excellent I on /I off ratio and carrier mobility were observed due to the suppression of the carrier transport and the turbostratic effect. When the number of layers exceeds 6 layers, the conductance at the ON state region extremely enhances by reducing the carrier scattering due to the screening effect for the charges of the impurity on the substrate. We conclude that the semiconducting and metallic characteristics in the narrow width GNR system can be controlled by modulating the strength of the screening effect to the surrounding environment such as charged impurity.

Methods
Synthesis of the multilayer GNR. The pristine GNRs used as a growth template were synthesized by unzipping of double-walled CNTs (Tokyo Ohka Kogyo Co. Ltd.) 22 . The synthesized GNRs were dispersed on the SiO 2 (300 nm)/Si substrate, and the samples were preheated at 350 °C for 20 min in air under atmospheric pressure to remove the poly (m-phenylenevinylene-co-2,5-dioctoxy-p-phenylenevinylene (PmPV) used as a surfactant for the stabilization of unzipped GNRs in the solution. Subsequently, the graphene layers were grown on the GNR template using a sloped-temperature CVD apparatus with ethanol 60, 61 . The CVD apparatus can www.nature.com/scientificreports/ regulate the temperatures separately in three zones, resulting in individual control over the decomposition reaction of the carbon feedstock and the growth of graphene layers by activated carbon species. The temperatures used in this study were 900 °C and 720-744 °C for the decomposition and graphene layer growth, respectively.
Structural and electrical analysis of the multilayer GNR. The structural analysis of the synthesized GNR was performed by atomic force microscope (AFM: HITACHI AFM5100N) observations with the dynamic force mode and Raman spectroscopy (Horiba HR800UV) with a laser excitation of 532 nm (typical spot diameter is 1 μm). The GNR-FET devices were fabricated by a conventional photolithographic process. The electrical transport measurements were carried out for the FET devices with just only single GNR channel. The carrier mobility were evaluated from the source-drain current (I sd ) as a function of the gate voltage (V g ) in the FET using a standard formula [62][63][64] , expressed by where W ch , L ch and C g are the width of the GNR, the channel length and the gate capacitance, respectively. The gate capacitance is given by C g = ε i ε 0 /d. The ε i and ε 0 are the relative permittivity of SiO 2 and the permittivity of a vacuum, and d is the film thickness of the SiO 2 (300 nm).
Simulation method. The electron mobility in a turbostratic multilayer GNR on the SiO 2 substrate with a rectangle shape of L ch × W ch was calculated using a semiclassical Monte Carlo approach considering the surface phonon scattering and the charged impurity scattering induced by the substrate 65,66 . The gapless energy dispersion at K 1 and K 2 points was used as the band structure because the inter-layer coupling interaction between GNR sheets to mimic the turbostratic stacking in the multilayer GNR.