Better explicating the strengths and shortcomings of these models will help refine projections and improve transparency in the years ahead.
Image credit: Witsawat.S.
Edited by David Goldhaber-Gordon, Stanford University, Stanford, CA, and accepted by Editorial Board Member Evelyn L. Hu March 1, 2017 (received for review December 14, 2016)
Significance
The use of epitaxial graphene has been less favored over the use of chemical vapor deposition (CVD)-grown polycrystalline graphene because graphene formed near SiC vicinal steps accompanies carrier scattering, which makes the practical domain size of epitaxial graphene much smaller than that of CVD-grown graphene. Nonetheless, the origin of carrier scattering at the SiC vicinal steps has not been fully understood. Here, we experimentally reveal that graphene formed at side walls is pristine, and the scattering near the steps mainly originates from the deformation of graphene and partially from stripes of bilayer graphene. This understanding of the origin of scattering allows us to demonstrate large-size single-domain graphene, removing major scattering sources through a layer-resolved transfer.
Abstract
Graphene epitaxy on the Si face of a SiC wafer offers monolayer graphene with unique crystal orientation at the wafer-scale. However, due to carrier scattering near vicinal steps and excess bilayer stripes, the size of electrically uniform domains is limited to the width of the terraces extending up to a few microns. Nevertheless, the origin of carrier scattering at the SiC vicinal steps has not been clarified so far. A layer-resolved graphene transfer (LRGT) technique enables exfoliation of the epitaxial graphene formed on SiC wafers and transfer to flat Si wafers, which prepares crystallographically single-crystalline monolayer graphene. Because the LRGT flattens the deformed graphene at the terrace edges and permits an access to the graphene formed at the side wall of vicinal steps, components that affect the mobility of graphene formed near the vicinal steps of SiC could be individually investigated. Here, we reveal that the graphene formed at the side walls of step edges is pristine, and scattering near the steps is mainly attributed by the deformation of graphene at step edges of vicinalized SiC while partially from stripes of bilayer graphene. This study suggests that the two-step LRGT can prepare electrically single-domain graphene at the wafer-scale by removing the major possible sources of electrical degradation.
Since the first discovery of graphene (1), its outstanding properties have drawn a great deal of attention (2⇓⇓⇓⇓⇓⇓⇓⇓–11). Among the methods to synthesize large-scale graphene (12⇓–14), the growth of epitaxial graphene on a SiC wafer has been investigated as one of the most promising methods. Specifically, graphene growth on the Si face of a SiC (0001) wafer offers unique crystallographic orientation and monolayer controllability at the wafer-scale via a self-limiting sublimation of Si (15⇓⇓–18). However, graphene formed near SiC vicinal steps exhibits high resistance; thus, the region of graphene demonstrating high uniform carrier mobility is limited to the size of the terrace on a SiC substrate (19⇓⇓⇓–23). The resistivity jump at the 10-nm-high single step on a SiC substrate was reported to be 21 kΩ⋅μm (21), whereas the intergrain resistivity from chemical vapor deposition (CVD)-grown polycrystalline graphene is measured to be 5 kΩ/sq (24). Thus, the use of this oriented graphene on SiC has been less favored over the use of CVD-grown polycrystalline graphene because the practical domain size of oriented graphene is much smaller than that of CVD-grown graphene (typically ranging from tens to hundreds of microns) (25). To overcome the limitation of graphene grown on SiC substrates, it is necessary to elucidate the cause of carrier scattering near vicinal steps and progress toward removing the factors causing this phenomena. However, the cause of enhanced carrier scattering in graphene near the SiC vicinal steps has not been fully understood yet. This is mainly due to the difficulty of resolving the complicated form of graphene near the step edges—(i) monolayer graphene formed at the step edges is subject to deformation, (ii) bilayer stripes of graphene are known to form near the edges, and (iii) the side-wall surface is not a hexagonal (0001) plane, which may not allow the formation of high-quality graphene at the side wall (15, 16, 18).
Here, we revealed the role of each parameter affecting carrier transport in epitaxial graphene by performing a layer-resolved graphene transfer (LRGT) process. We also confirmed that the graphene fabricated by the LRGT process is electrically single-domain graphene, whereas its ability to produce crystallographically single-crystalline graphene has been proven in the previous work (26). A one-step LRGT causes flattening of the epitaxial graphene on SiC step edges, which contains deformed monolayer, bilayer stripes, and graphene formed at the side wall of steps (26). We discovered that resistance of flattened graphene across the single bilayer stripe is ∼2.9 kΩ⋅μm where the measured area contains a bilayer stripe and side-wall graphene. Our simulation showed that such a resistance jump is solely due to the mobility drop at the bilayer, suggesting that the side-wall graphene is pristine. We additionally confirmed this by fabricating the field effect transistors (FETs) on the stripe-removed region and terrace region of the transferred graphene, both of which exhibit comparable FET mobility. Thus, we conclude that the graphene prepared by the two-step LRGT, where the all-bilayer stripes are completely removed, is electrically single domain at the wafer-scale. This is clear contrast to our previous report where we have shown only crystallographic single crystallinity in graphene through LRGT due to the uncertainty of the quality of graphene near the terrace edges of SiC (26). Further elimination of the process residues during the LRGT leads to a notable maximum mobility of 7,496 cm2/V⋅s measured at room temperature for a single-crystalline, single-domain graphene transferred on a SiO2/Si substrate, which supersedes as the highest value ever reported from graphene formed on the Si face of an SiC wafer (15, 16, 21⇓–23, 27⇓–29).
Results and Discussion
We have performed a one-step LRGT process using a graphitized SiC wafer where graphene is mechanically exfoliated using a high-stress Ni film (26) (Materials and Methods for the detailed process parameters). The entire graphene, successfully released from the SiC surface, was then transferred onto an oxidized Si wafer followed by Ni etching. Fig. 1A shows a photograph of 4-inch wafer-scale graphene transferred on an 8-inch oxidized Si wafer using the LRGT process. A schematic of this process is depicted in Fig. 1B, showing the flattening of deformed graphene at the step edge and side-wall graphene. We first measured a Raman spectra on graphene/SiC to evaluate the quality of grown graphene on SiC (Fig. S1). As shown in the map of the 2D/G peak ratio from a Raman spectra taken on a transferred single-crystalline graphene layer (Fig. 1C) (30), this graphene is composed of a monolayer sheet and around 20% bilayer stripes, called 1.2 ML hereafter (blue, bilayer; green, monolayer). Through atomic force microscopy (AFM), we investigated the surface topography of original epitaxial graphene on the Si-face SiC wafer and transferred epitaxial graphene on the SiO2/Si substrate. As shown in Fig. 1 D and E, ∼10-nm-high steps periodically exist at every ∼10-μm-wide terrace; after transferring graphene to a flat SiO2/Si surface, these steps in graphene were no longer present and graphene was well-flattened to the substrate without formation of wrinkles (31). The flattening of graphene may improve carrier transport because mobility degradation in epitaxial graphene on SiC is known to arise from the curved morphology of graphene at step edges (19, 20). However, the presence of bilayer stripes in the transferred graphene can still increase carrier scattering.
Fig. 1.
Optical properties and topography of single-oriented graphene. (A) Four-inch wafer-scale single-oriented graphene on 8-inch oxidized Si wafers via LRGT. (B) Schematic graphene structures before and after LRGT. (C) Map of the 2D/G peak ratio from Raman spectra (green color, monolayer graphene; blue color, bilayer graphene). (D) Tapping mode AFM images from graphene on Si-face SiC wafer and profile information. (E) Tapping mode AFM images from graphene transferred on SiO/Si wafer via LRGT and profile information.
Fig. S1.
Raman spectrum of graphene grown on SiC wafer. Raman spectrum was taken with 514-nm wavelength to confirm the quality of graphene. Low D peak intensity and strong G and 2D peak intensity indicate that the quality of graphene is suitable enough to be analyzed.
It has been known that the resistance of bilayer graphene was substantially greater than that of monolayer graphene due to enhanced backscattering in bilayer graphene (32, 33). Therefore, periodically distributed bilayer stripes in flat 1.2-ML graphene transferred on SiO2/Si would certainly account for carrier scattering. For further investigation on carrier transport in 1.2 ML, we fabricated backgated FETs on the transferred graphene on SiO2/Si substrates. (Fig. S2) FET channels were formed orthogonal to the bilayer stripes as shown in Fig. 2 A and B, which contain bilayer stripes of varying periodicity across the channel, where the width of stripes had a uniformly distributed average of 800 nm. The scanning electron microscope (SEM) images shown in Fig. 2 A and B represent the graphene FET channels, including one and four bilayer stripes located in a 10-μm-long channel, respectively. Field effect (FE) electron mobility and channel resistance were extracted at a maximum transconductance where the carrier density was ∼1 × 1012 cm−2 at a room temperature. Fig. 2 C and D show average resistance and average electron FE mobility of a graphene channel with 10-μm length and 2-μm width as a function of the number of stripes in the channel, respectively. A monotonic increase in the average resistivity of graphene was observed as the number of stripes in the channel increased, reducing the mobility of graphene. The resistance increment attributed by one bilayer stripe in the channel was measured by taking a slope of the plot in Fig. 2C; the value normalized by the channel width was 2.94 kΩ⋅μm. This resistance value is an order of magnitude lower than the reported value of 21 kΩ⋅μm obtained from a 10-nm-high single step in our graphene on SiC (21) where the resistance jump occurs from the multiple causes such as graphene bending, local thickness variation due to bilayer stripes, and lower-quality graphene at the side wall of the step. This indicates that most of the carrier-scattering sources in epitaxial graphene before exfoliation were removed during the graphene transfer process in LRGT. However, graphene near bilayer stripes still plays a role in disturbing carrier transport due to backscattering at the body of bilayer graphene (32) or variations in electrical quality of graphene formed at the SiC side wall. However, wavefunction mismatch at a bilayer–monolayer junction does not play a major role in the mobility of 1.2-ML graphene (19) because the extra resistance from the wavefunction mismatch is much smaller (at least an order of magnitude lower) compared with what we observed. The effect of intensified scattering at the bilayer on the resistance of 1.2-ML graphene can be isolated by modeling electrical characteristics of flat monolayer graphene FETs containing periodic bilayer stripes. Under the assumption that the rise in resistance with increasing number of stripes is solely due to enhanced backscattering at the body of a bilayer stripe, we simulated a graphene FET with a channel that had a series connection of monolayer graphene and bilayer graphene stripes (average width of 700 nm) by varying the number of bilayers in the channel (Fig. S3). This allowed us to predict the increase in resistance from adding a single bilayer stripe in a graphene channel, which was measured to be 3 kΩ⋅μm, comparable to the value obtained from experiment. Moreover, simulated resistance-gate voltage characteristics of graphene channels for varying number of stripes showed excellent agreement with those experimentally measured (Fig. 2 E and F and Table S1). In the simulation result, monolayer mobility, residual carrier density, and the contact resistance were taken from the monolayer resistance without any bilayer stripe (Fig. S4 and Fig. 2E), and then the bilayer device parameters were extracted from samples with bilayer stripes. We simulated the result with extracted parameters, which are summarized in Table S2. With extracted information, we ensure that the resistance increase with stipes originates from the carrier transport through the monolayer and bilayer regions connected in series (see SI Text for details). This confirms that (i) electrical degradation in flat graphene transferred from SiC is solely attributed to the existence of bilayer stripes, (ii) substantial resistance jump at epitaxial graphene on SiC steps is mainly attributed to the sharp bending of graphene that may cause π–σ hybridization (19, 20), and (iii) graphene grown at the side wall of a SiC step does not contribute to electrical degradation in transferred graphene.
Fig. 2.
Influence of bilayer stripes. (A) SEM images on graphene FET channels containing one bilayer stripe in a 10-μm-long channel and (B) four bilayer stripes in a 10-μm-long channel. (C) Monotonic increase in average resistance as a function of number of stripes in the channel. The resistance increment by a single bilayer stripe is 1,470 Ω. (D) Average electron FE mobilities of a graphene channel according to the number of stripes in FET channel. (E) Experimentally measured RCH–VG characteristics and (F) simulated RCH–VG characteristics of graphene channel vs. number of stripes.
Fig. S2.
Schematic illustration for the graphene transfer and the device fabrication. First, graphene is grown on SiC wafers through graphitization process. After Ni deposition, graphene can be transferred on SiO2/Si substrates. After defining channel areas using e-beam lithography, contact electrodes are prepared through evaporators.
Fig. S3.
Scheme for modeling to numerically calculate resistance in bilayer stripes. Scheme shows one example to describe how the channel looks for calculation. The channel consists of four monolayer parts and three bilayer strip parts.
View this table:
Table S1.
Calculated carrier density according to the resistance values measured from the graphene with stripes and without a stripe
Fig. S4.
Contact resistance measurement. The contact resistance measurement through TLM structures with different channel lengths including 0.5, 1, 2, 5, and 10 μm.
View this table:
Table S2.
Device parameters extracted by analytical model in the presence of bilayer stripes
For further confirmation, we fabricated FETs following specific locations pointed in the SEM image in Fig. 3A: (A) between the bilayer stripes, (B) on the graphene where the stripe was accidentally removed during the process, and (C) on the bilayer stripe. The electron mobility measured from regions A and B were comparable, whereas region C showed degradation of mobility (Fig. 3B). This suggests that graphene on the location where the bilayer stripe was accidentally removed during the transfer process does not have any memory effect of having had a bilayer stripe or having been deformed, and again graphene grown at the SiC step side wall is pristine. To support this claim, scanning tunneling microscopy (STM) was performed to obtain atomic-resolution images. A scan was performed across the bilayer stripes in the graphene; the trace of the scan is depicted by the red line in Fig. 3A. Fig. 3 C and D shows STM surface topologies, and we could identify (i) a honeycomb lattice structure with a lattice constant of 2.4 Å from monolayer graphene and (ii) a hexagonal lattice structure from bilayer graphene due to the AB stacking of the layers breaking the symmetry, leading to two inequivalent C atoms per unit cell. Throughout scanning across the stripe along the red line in Fig. 3A, we could only identify perfect hexagonal monolayer and bilayer images, which supports the fact that the graphene coming from the SiC step side wall is pristine.
Fig. 3.
Graphene grown at side-wall surfaces of SiC vicinal steps. (A) SEM images of graphene after LRGT on SiO/Si wafer. FET was fabricated on three different regions: A region, between the bilayer stripes; B region, on the graphene where the stipe was removed during the process; and C region, on the bilayer stripe. (B) FET output characteristics from three different sites at A region, B region, and C region. From the result, we can conclude the device performances from A region and B region are similar, whereas the device performance from C regions shows degradation of mobility. (C and D) Atomic-resolution STM images of single-crystalline graphene from monolayer graphene and bilayer graphene.
Although carrier scattering arising from geometric factors can be suppressed by flattening, uniform electrical quality of our single-crystalline graphene is still limited by the existence of periodic bilayer stripes. Considering the fact that the mobility measured from the location where the stripe was locally removed is comparable to that from the location between the stripes (Fig. 3A), the graphene transferred from SiC can be domain-free if the stripes are completely removed. We have performed a two-step LRGT process to selectively remove the bilayer stripes with single-atom thickness precision (25). In this process, Au is deposited on the as-exfoliated graphene on Ni film. Because the Au–graphene interface bonding energy is higher than that of the graphene–graphene interface, graphene stripes on a graphene sheet can be selectively lifted off by Au. During the exfoliation process, the monolayer graphene sheet remains bonded to Ni because the bonding energy between Ni and graphene is much higher than the bonding energy between Au and graphene. As shown in the map of the 2D/G peak ratio from a Raman spectra taken on the graphene layer transferred by this two-step LRGT process (Fig. 4A), bilayer stripes were completely removed from the monolayer graphene sheet, leaving only a monolayer sheet. This monolayer graphene sheet was transferred on a SiO2/Si wafer. To quantify the electrical properties and uniformity of graphene, FETs were fabricated on the monolayer of graphene prepared using the two-step LRGT (1-ML graphene) as well as on monolayer graphene with 20% bilayer stripes prepared by a one-step LRGT (1.2-ML graphene). The electron FE mobility was recorded at the maximum transconductance; the mobility distribution is shown in Fig. 4B. The 1-ML graphene presented a marked improvement in mobility compared with 1.2-ML graphene with measured values concentrating near 4,000–5,000 cm2/V⋅s.
Fig. 4.
Device performances of monolayer, single-oriented graphene. (A) Raman mapping result of the 2D/G peak ratio on the graphene. Because the bilayer stripes were removed by LRGT, the mapping color is almost uniform. (B) The electron FE mobility distribution comparison between device based on graphene before and after LRGT. (C) Microspot electron diffraction from low-energy electron microscope (LEEM). Identical diffraction patterns across the sample were observed. (D) Channel resistance as a function of gate voltage from single-crystalline graphene. Maximum electron mobility of 7,496 cm2/V⋅s was obtained.
The single crystallinity was confirmed by microspot electron diffraction measurements using a low-energy electron microscope (LEEM), where we observed identical diffraction patterns across the sample (Fig. 4C). A maximum FE electron mobility of 7,496 cm2/V⋅s obtained from our single-crystalline, single-domain graphene at room temperature (Fig. 4D and Fig. S5) is the highest value ever reported from the graphene grown on Si-face SiC wafer (Fig. S6) (15, 16, 21⇓–23, 27⇓–29). It should be noted that, in our previous report (26), enhanced mobility due to flattening the epitaxial graphene is screened by the Ni residues on graphene after chemical etching of the Ni stressor. As shown in Fig. S7, choice of Ni etching solution substantially affects the mobility of single-domain graphene due to the effectiveness of removing the residues. When typical acid solutions such as HCl and FeCl3 for metal etching are used to remove Ni stressors, the substantial Ni residues reside on the graphene surface, resulting in the mobility of around 3,000 cm2/V⋅s, which is a comparable value typically measured from the epitaxial graphene on SiC substrates. Substantial mobility enhancement to 7,496 cm2/V⋅s is observed from the epitaxial graphene with the reduction of Ni residues with postetching treatment by a TFB transene Ni etchant. The device result shows the actual improvement of the mobility of epitaxial graphene by separating it from the SiC substrate and flattening it on the flat SiO2 surface. There is more room for improving the mobility of this graphene because Ni residues with average size of 2 nm still remained after etching, as shown in the AFM image (Figs. S7 and S8) (33), and graphene FETs fabricated on SiO2 substrates accompany carrier scattering from charged surface states and impurities of SiO2 (34, 35).
Fig. S5.
Transconductance gm as a function of gate voltage Vg for the device with 2 μm of channel width and 1 μm of channel length at VD = 0.01 V.
Fig. S6.
Mobility comparison of graphene transistors on SiO2/Si substrate at room temperature (RT). Comparing the mobility results from several studies dealing with graphene grown on Si-face SiC wafers. Maximum mobility of our work is 7,496 cm2/V⋅s, which is the highest value ever reported from graphene grown on Si faces on SiC wafer.
Fig. S7.
Topography and corresponding device results before the optimization of the process. (A) AFM was used to see the surface residue on the graphene. (B) Corresponding performance of FETs (2-μm width and 2-μm length).
Fig. S8.
Topography and corresponding device results after the optimization of the process. (A) Topographical imaging. AFM image of graphene on the SiO2/Si substrate. There are small nickel residues on the surface. However, we observe no wrinkle on the graphene. (B) Corresponding performance of FETs (2-μm width and 2-μm length).
Conclusions
In summary, we demonstrated that geometry-induced carrier scattering at epitaxial graphene on SiC can be avoided by transferring this graphene to a flat surface. Finally, this graphene is rendered domain-free by selectively removing intrinsically present bilayer stripes. We further identified the origin of carrier scattering at SiC vicinal steps, the role of each bilayer stripe, and evidence that the LRGT process can prepare domain-free graphene.
Materials and Methods
Growth of Epitaxial Graphene.
A 4-inch epitaxial graphene was grown on a Si-face (0001) 4H-SiC wafer with 0.05° miscut. The SiC substrate was annealed at 850 °C for 20 min for surface cleaning in vacuum (<1 × 10−6 mbar). The substrate temperature was raised to 1,555 °C for 30 min, and H2 was introduced into the chamber (800 mbar) for 30 min for a second surface cleaning by thermally etching the top layers of SiC. The graphene was subsequently formed on the SiC surface in Ar ambient (100 mbar) at 1,575 °C for 60 min by sublimating the Si atoms from the SiC surface.
LRGT (One-Step Exfoliation).
Epitaxial graphene formed on SiC was exfoliated from the SiC wafer by depositing highly strained, adhesive nickel (Ni) film on graphene followed by application of a thermal-release tape handler for mechanical exfoliation of Ni bonded with graphene. Because the bonding energy of Ni–graphene is greater than that of SiC–graphene (16), Ni was used as an adhesive layer to compete for graphene bonding during the exfoliation process. In the graphene release process, SiC–graphene bonding energy was overcome by the strain energy provided by Ni film, leading to complete mechanical exfoliation of graphene from SiC (12). It was essential to evaporate 30-nm Ni initially to protect the damage on graphene and subsequently sputter 500-nm Ni to provide the strain energy. The graphene released from the SiC surface was then transferred onto an oxidized Si wafer, followed by removal of the handling tape and wet etching of the nickel film.
LRGT (Two-Step Exfoliation).
To obtain a domain-free graphene, the bilayer stripes must be completely removed from the one-step–exfoliated graphene. A two-step LRGT process was applied to selectively remove the bilayer stripes with single-atom thickness precision. In this process, after the graphene exfoliation using a Ni film, Au is deposited on the as-exfoliated graphene on Ni. Because the Au–graphene interface bonding energy is higher than that of the graphene–graphene interface, graphene stripes on a graphene sheet can be selectively lifted off by Au. During the selective exfoliation process, monolayer graphene sheet remains bonded to Ni because the bonding energy of the Ni–graphene interface is much higher than that of the Au–graphene interface. The complete monolayer graphene on Ni/tape was then transferred onto an oxidized Si wafer, followed by removal of the tape and wet etching of the nickel film.
Device Fabrications and Electrical Characterizations.
The FETs were fabricated on graphene sheet on oxidized Si wafers (90-nm-thick SiO2/highly doped n-type Si). The channel length of transistors was defined from 0.5 to 10 μm with 2-μm width by LEICA VB6 e-beam writer. The electrodes were made of Ti (0.2 nm)/Pd (20 nm)/Au (20 nm). After patterning electrodes via electron beam lithography, Agilent B5100 semiconductor parameter analyzer was used for all current–voltage measurement at room temperature in ∼10−7 torr. The SiO2 was used as a gate insulator and Si worked as a backgate.
Surface Imaging via STM.
STM experiments were performed with a cryogenic ultrahigh-vacuum STM system combined with SEM. The ability to carry out SEM in our system allowed us to easily locate and measure monolayer and bilayer graphene, respectively. The STM topography was taken in the constant current mode using a Pt–Ir tip for imaging. All of the STM measurements were conducted at 77 K.
SI Text
Graphene Growth.
Single-oriented graphene was grown on a 4H (0001) SiC wafer, mechanically polished, epitaxy-ready surface, under ∼3 × 10−10 torr of pressure in ultrahigh-vacuum chamber. First, a cleaning step under a Si-containing gas was conducted at around 850 °C to remove oxides from the SiC surface for 20 min, and graphitization was followed at a higher temperature (1,550 °C) in argon atmosphere at ∼3.5 × 10−4 torr. After cooling down in argon atmosphere, the graphene on 4H (0001) SiC was obtained (15). The quality of graphene film can be verified by the small intensity of the D peak in the Raman spectrum, which dictates whether the graphene film is suitable for further experimentations (Fig. S1).
Expecting Internal Stress of Ni Stressors by Stoney’s Formula.
We first deposited Ni protection film (30 nm) using the thermal evaporator to prevent sputtering damage on graphene film. Subsequently, the Ni stressor layer was deposited to a certain thickness to vary the internal stress in the film. The relation between film thickness and internal stress was estimated by using Stoney’s formula:
Device Fabrication and Electrical Characterization.
To characterize the electrical properties of single-oriented graphene, we fabricated FETs using the graphene transferred onto an oxidized Si substrate (90-nm-thick SiO2/highly doped n-type Si). Electron beam lithography was used to define the channel area of graphene on oxidized Si. Subsequently, Ti (0.2 nm), Pd (20 nm), and Au (20 nm) were sequentially deposited for source and drain electrodes and patterned through electron beam lithography (36). The various kinds of transistors were prepared with different channel length from 0.5 to 10 μm with 2-μm width (Fig. S2). Here, highly doped Si was used as a backgating layer, and transistors were measured using a semiconductor parameter analyzer (Agilent B5100).
Carrier Density According to the Resistance.
Because the Hall measurement has not been measured, we instead calculated the carrier density based on well-known equation about carrier density (Table S1):
Channel Resistance Simulation of Graphene FETs with Bilayer Graphene Stripes.
We develop an analytical model to explain and further understand the observed device resistance characteristics in our graphene FETs with bilayer stripes. Our modeling process is summarized as following: first, we extract the core transport parameters—mobility and residual carrier density—of monolayer graphene from the device with no bilayer stripe, and use these parameters to estimate and subtract the contribution of the monolayer graphene from the resistance measured in devices with bilayer stripes. Then, using the isolated resistance and total length of the bilayer stripe regions, we extract the parameters of bilayer graphene and calculate a gate voltage-dependent resistivity for the bilayer regions. Finally, we show that the extracted bilayer mobility and residual carrier density values are consistent across the devices with different numbers of bilayer stripes, which confirms that the higher device resistance observed with added bilayer stripes is caused by increase of low-mobility bilayer graphene region in the channel.
The detailed derivation of our model is discussed here. We divide the total resistance of a graphene FET, Rtotal, into three elements: (i) resistance of the monolayer graphene region, which is a function of VG (Rmono[VG]); (ii) resistance of bilayer stripes, which is also a function of VG (Rbi[VG]); and (iii) other gate-independent resistances included in the measurement (Rcontact) as shown in the following equation:
Because the quasi–free-standing epitaxial graphene bilayer grown on SiC terraces is known to be Bernal stacking verified by quantum Hall measurement (38), one can use the following equations to obtain the expression for Rbi[VG]:
One important experimental observation that supports our model is that the resistance contribution due to the introduced bilayer stripes is a function of the applied gate bias as shown in Fig. 2E and not a constant. If it were independent of VG, the resistance curve would be simply shifted upward with a constant amount regardless of the gate bias. Another important observation is that the average size of the bilayer stripe, 0.8 μm, is of a significant size compared with the channel length, 10 μm. In the case of a device with five bilayer stripes, for example, the total area of bilayer stripes indeed occupies 40% of the channel area. Therefore, gate modulation of carrier density in bilayer region and consequent resistance change cannot be ignored. A single resistance peak found in all of the experimental data also supports the use of identical Dirac points for both monolayer and bilayer graphene.
Now, we show that our model exhibits an excellent agreement with the experimental data. Using our model, we extract monolayer mobility, residual carrier density, and the contact resistance from the monolayer resistance curve without any bilayer stripe (red curve in Fig. 2E), and the result is shown in the first column of Table S2 (32, 39). Then, we extract the bilayer device parameters from the experimental data taken at samples with bilayer stripes using the extracted monolayer parameters. The extracted device parameters are listed in Table S2, and fitting parameters are marked as red color. Interestingly, the extracted bilayer mobility and other parameters are consistent in the three-stripe and five-stripe cases, evincing that the resistance increase with the introduced stripes is due to the carrier transport through the monolayer and bilayer regions connected in series. Minor variation in extracted Rcontact values (less than 2% of the peak device resistance) across the different devices is expected because Rcontact is supposed to capture gate-independent resistance components of various sources such as probe-to-pad, pad-to-device, and metal-to-graphene contact resistances accumulated at device terminals. The relatively low mobility of bilayer graphene, ∼1,300 cm2/V⋅s, compared with that of monolayer, ∼5,100 cm2/V⋅s, clearly explains the trend of increasing resistance as the number of bilayer stripes in the channel increases.
Numerical Calculation for Resistance in Bilayer Stripes.
Based on our electrical measurement, numerical modeling was also conducted to estimate resistance in each bilayer stripe. As shown in Fig. S3, the total resistance is the sum of each resistance. Therefore, we can calculate the Rsbi through comparing the resistance of the channel having one stripe with resistance of the channel not having any stripes. They can be expressed as follows:
Contact Resistance from Transmission Line Model.
Contact resistivity was required to understand dimensionless property and is given as follows:
Transconductance of Graphene FETs.
We also show the transconductance (gm) result according to the gate bias (VG). As shown in Fig. S5, the mobility can show the highest value near at the lowest carrier concentration according to following equation where gm, L, W, CGI, and VD are the transconductance, the channel length, the channel width, the capacitance of the gate insulator, and the drain voltage, respectively (Fig. S5):
Remaining Residue and Wrinkle Issues on Graphene Films.
In the case of our transfer process, graphene accompanies Ni-adhesive stressors to produce external stresses. Thus, the unnecessary Ni-adhesive stressors must be removed after transfer onto target substrates. Here, we used FeCl3 etchant to etch Ni film away, but the residue of Ni still remained after the etching process. Especially a lot of residue was observed at the beginning, which seriously affected the carrier scattering. On the whole, the corresponding device showed poor performance as shown in Fig. S7 (μ = 3,260 cm2/V⋅s). Because the residue effect had to be exclusive to understand the carrier-scattering sources, we tried to minimize the residue on the graphene. Therefore, we further developed the process, which allowed us to quantitatively study main sources of carrier scattering (Fig. S7). To confirm the residue on the surface, we carried out atomic force microscope (AFM), and the result is shown. The AFM measurement was conducted in noncontact mode for the purpose of a mild scan. Wet chemical etching left behind residues on the graphene, which possibly degrades the electrical properties of the transferred graphene (40). On the other hand, after processing optimization, we observed much improvement on the surface, which enhanced overall mobility more than two times. Fig. S8 shows enhanced mobility, 6,521 cm2/V⋅s, and it allowed us to make the residue effect exclusive. There are no wrinkles, unlike graphene prepared from wet transfer method. Therefore, it is possible to produce wrinkle-free graphene on arbitrary substrates.
Footnotes
- ↵1To whom correspondence should be addressed. Email: jeehwan{at}mit.edu.
Author contributions: H.P. and J.K. designed research; S.-H.B., X.Z., S.K., Y.S.L., and J.K. performed research; S.-H.B., X.Z., S.K., Y.S.L., S.S.C., Y.K., J.B.H., Y.Y., D.K.S., F.M.R., H.P., and J.K. analyzed data; and S.-H.B., X.Z., S.K., S.S.C., Y.K., H.P., and J.K. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. D.G. is a Guest Editor invited by the Editorial Board.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1620176114/-/DCSupplemental.
References
Carrier transport mechanism in epitaxial graphene
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