Open Access Article

This Open Access Article is licensed under a Creative Commons Attribution-Non Commercial 3.0 Unported Licence

Young-Jun
Yu‡
*^{a},
Jong-Ho
Choe‡
^{b},
Jong Yun
Kim
^{a},
Oh Hun
Gwon
^{a},
Hong Kyw
Choi
^{c},
Jin Sik
Choi
^{d},
Jin Hong
Kim
^{d},
Jin-Soo
Kim
^{b},
Jin Tae
Kim
^{c},
Jun-Hwan
Shin
^{c} and
Young Kyu
Choi
^{c}
^{a}Department of Physics, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon, 34134, Korea. E-mail: yjyu@cnu.ac.kr
^{b}Department of Physics, Korea University, Anam-dong 5, Seonbuk-gu, Seoul, 02841, Korea
^{c}Electronics and Telecommunications Research Institute (ETRI), 218 Gajeong-ro, Yuseong-gu, Daejeon, 34129, Korea
^{d}Department of Physics, Konkuk University, 120 Neungdong-ro, Gwangjin-gu, Seoul 05029, Korea

Received
28th December 2018
, Accepted 18th February 2019

First published on 4th March 2019

To utilize graphene as interconnection electrodes in high-density nanoelectronic structures, the electrical stability of graphene should be guaranteed under nanometer-scale deviations. Graphene-ribbon (GR) junctions with accessible dimensions (i.e., sub-micrometer widths) are used in diverse interconnection electrode applications and should be characterized properly if they are to be applied in high-density nanoelectronics. Analyzing the effects of nanoscale GR width variations on the conductance of the entire graphene electrode is necessary for their proper characterization. Here, we diagnose the conductance and thermal effect of graphene electrode junctions constructed from GRs of various widths and directions under gate-tuned voltages. On applying partial gate voltages, we identify the effect of local potential variance on the entire graphene electrode junction. As a result, we were able to perceive precise and minute conductance variations for the entire graphene electrode, arising mainly from different sub-micrometer-scale widths of the GRs, which could not be distinguished using conventional global gating methods.

In this work, to diagnose the effect of sub-micrometer variations in GRs on conductance, we demonstrate junction structures composed of GRs with various widths. We investigate the conductance variation as a function of width by applying electrical biases and gate voltages. As a result, while conductance variations generally expected for GR junctions with a sub-micrometer width range, on the application of a global gating voltage through the SiO_{2} substrate, are from 40% to 69%, we could detect precise and minute conductance variations (ranging from 0.3% to 3.0%) over the GR junction, which were contributed by individual GRs on applying a partial gating voltage with a conductive SPM probe.

Fig. 2(a) shows an electric field microscopy (EFM, V_{EFM}) image of a GR junction with V_{DS} = 0.5 V. Here, the represented GR junction is type (I), as shown in Fig. 1(a), constructed with 470, 290, and 200 nm widths and ∼1 μm length for the individual GRs. In the EFM image exhibiting the conductance of the graphene area (Fig. 2(a)), the electrical isolation of the GR junctions from the initially exfoliated graphene flakes corresponding to the AFM image of type (I) (Fig. 1(a)) is guaranteed and a gradually sloping electric potential is observed between the ends of the GR junction marked with A and B (Fig. 2(a)), owing to the application of a bias voltage V_{DS} = 0.5 V. Here, we can observe that the variation of the potential is the largest in the widest part of the GR due to a larger electric field, exhibiting greater slope for GR with 470 nm width than for GR with 290 and 200 nm widths (see ESI, Fig. S5†). Although the width-dependent Joule self-heating temperature difference (ΔT = 5 to 15 K for 470 to 200 nm width with V_{DS} = 2 V) in the GR junction was not large, the ΔT variation agreed well with the conductance of the GR junctions, as a function of width and V_{BG} (Fig. 2(b) and (c), respectively; see also ESI, Fig. S3 and S4†). This indicates that the width-dependent conductance of GR is dominant among the electrical and thermal properties of a GR junction.

Fig. 2 (a) EFM image of applying V_{DS} = 0.5 V for the type (I) GR junction shown in Fig. 1. Here, the points marked A and B in the color scale bar correspond to ΔV_{EFM} ∼ 0.5 V for positions marked by A and B on the EFM image of the GR junction and the dashed box indicates the same area of (b) SThM and (Fig. 3) SGM images. (b) Temperature distribution images of a Joule self-heated type (I) GR junction for applied V_{DS} = 2 V and V_{BG} = 0–25 V. (c) Temperature variation at GR widths of 200 nm (red dots), 290 nm (purple dots) and 470 nm (blue dots), as a function of V_{BG}. Temperature values were extracted from (b) SThM images as a function of V_{BG}. The current variation (dashed line) of the GR junction as a function of V_{BG} is the same as that in Fig. 1(c). |

For the direct measurement of the gate voltage contribution to the individual conductance of the GR in the junction structure constructed with different widths or directions, we employed scanning gate microscopy (SGM) (Fig. 1(b)).^{27–31} By applying a partial gate voltage to each different strip width area, the conductance variation of the GR junction contributed by the ribbon structure could be investigated, as shown in Fig. 3(a–c). From the SGM measurements, by applying a partial gate voltage V_{T} = ±8 V using a conductive SGM probe at a constant height of 100 nm, we deduce the Fermi level of the GR junction tuned in the hole-doping region to be E_{0} ± ΔE_{T} = ħν_{F}[( ± Δn)π]^{1/2} = 169–206 meV by roughly estimating Δn = C_{Air}·V_{T}/e = ±0.5 × 10^{12} cm^{−2}, as proposed in the schematic diagrams in the inset of Fig. 3(a) and (b), where Δn and C_{Air} are the charge-carrier density induced by applying a gate voltage (V_{T} or V_{BG}) and capacitance of air with 100 nm distance between the SGM probe and GR, respectively. Based on this charge-carrier density variation of graphene, induced by V_{T}, the SGM images of the GR junctions (Fig. 3(a) and (b)) exhibited a width dependency leading to conductance variations around (I − I_{0})/I_{0} = 0.29% to 0.94% for widths between 470 and 200 nm (see Fig. 3(c)). Here, I and I_{0} are the current values of the entire GR junction, with and without a gating voltage applied over individual GR areas, respectively. The (I − I_{0})/I_{0} values used in this work were absolute values for comparing the variations as a function of the width and gate voltage.

Fig. 3 (a) and (b) SGM images for V_{T} = ±8 V for the type (I) GR junction biased by V_{DS} = 0.5 V. Inset: Schematic diagrams of graphene energy potential exhibiting doping change with E_{0} ± ΔE_{T}. (c) Conductance profiles of (a) and (b) SGM images along the GR junction. Here, the V_{T} (470 nm), V_{T} (290 nm), and V_{T} (200 nm) marks indicate the partial gating by V_{T} on individual GRs with widths of ∼470 nm, ∼290 nm, and ∼200 nm, respectively. The cropped EFM image of Fig. 2(a) is shown at the center of the plots for correlating current variations with GR features. |

GR junction structures of various widths and paths have been fabricated and characterized (Fig. 1(a) and Fig. S2†), and we confirmed that the width variation was significantly more dominant than the path change for our specimens. Namely, although type (II) and (III) GR junctions with a ribbon of 1 μm length had path changes of 45° and 90°, respectively, variations were not observed in the transport characteristics owing to a short mean free path in graphene on SiO_{2} (see ESI, Fig. S3 and S4†).^{13,32–35} Note that, upon employing the ballistic conditions for suspended graphene or graphene on a hexagonal boron nitride (hBN) substrate, which can suppress charge impurities and improve carrier mobility above 500000 cm^{2} V^{−1} s^{−1}, the mean free path can be increased to micrometer scales.^{32–35} However, our GR junctions on SiO_{2} possessing a few hundred nanometers width and few micrometers length, exhibited a carrier mobility of approximately several thousand cm^{2} V^{−1} s^{−1} (i.e., 2000 to 4000 cm^{2} V^{−1} s^{−1} for 2.61 × 10^{12} cm^{−2} of the hole carrier density region for our specimens) because of the electron–hole puddles created by the SiO_{2} substrate. Therefore, the mean free path should have been smaller than 1 μm. Conventional dielectric substrates such as SiO_{2} lead to short mean free paths and do not allow path-dependent transport variations in graphene. On the other hand, because we observed substantial width-dependent conductance variations (see also ESI, Fig. S3 and S4†), we focused our analysis on the width-dependent conductance variations of GR junctions on the application of gate voltages.

For comparing the electric-field effect on the GR/SiO_{2} structure by gating either V_{T} or V_{BG} (Fig. 4(a)), we numerically calculated electric potential distributions, reflecting notably different electric potential distributions between the GR and the dielectric areas under gating of either V_{T} or V_{BG} in Fig. 4(b) or (c), respectively (for details of the calculations, see the Experimental section and ESI, Fig. S6–S8†). Applying V_{T} = 8 V via the SGM probe at a distance of 100 nm from the GR surface created an electric potential at the exact desired position of the GR, with almost invariant electric potential of the SiO_{2} substrate (see Fig. 4(b)). The global gating voltage V_{BG} = 8 V applied through the 280 nm thick SiO_{2} substrate caused a doping change in the entire GR in both SiO_{2} and air (see Fig. 4(c)). As a result, the global gating voltage V_{BG} produced a carrier-density change over the entire GR area, as shown by the large carrier density Δn ∼ 1.54 × 10^{12} cm^{−2} at the center of the GR (x = 0) (Fig. 4(d–f)). On the other hand, the application of V_{T} by the SGM probe induced a carrier density change in graphene, which could be exactly ascribed to the SGM probe position (x = y = 0 nm), as well as its rapid suppression on increasing |y| (red line in Fig. 4(e)), while Δn by V_{BG} was invariant along the length direction (blue line in Fig. 4(e)). Furthermore, we found that Δn under both V_{BG} and V_{T} was enhanced at the edge of the GR owing to the geometry, the state of the graphene edge, and the electric field strength.^{26} The Δn for V_{T} was slightly smaller than that for V_{BG}, albeit the SGM probe was applied at the GR edge (see also ESI, Fig. S7†). Here, although the GR with 100 nm width is representatively exhibited in Fig. 4, we calculated and employed Δn for all width conditions from 500 nm to 100 nm, with the aim of extracting the conductivities of the GR junctions (see ESI, Fig. S8†).

Since the global gate-induced large Δn derived the conductivity of graphene σ_{GR-BG}, (I − I_{0})/I_{0} = (σ_{GR-BG} − σ_{GR0})/σ_{GR0} as a function of width (W) for the GR under global gating V_{BG} = 8 V was assumed to vary from ∼40% for W = 500 nm to ∼69% for W = 100 nm, owing to the large electric field over the entire GR area through both air and the SiO_{2} substrate by global gating, where σ_{GR-BG} and σ_{GR0} are the conductivities of GR under V_{BG} = 8 V and 0 V, respectively (see the inset of Fig. 5(a) and ESI, Fig. S9†). Under the global gating of V_{BG} (i.e., when applying an electric field to the entire graphene nanoribbon structure), the behavior of conductance variation of the narrowest nanoribbon part (< several tens of nanometers) was dominant. Therefore, the previously reported research concept was employed for focusing the analysis of conductivity on the narrowest target graphene nanoribbon area alone.^{22–25} However, for graphene electrodes constructed with subtle differences in width (∼ several hundreds of nanometers) of the GR junctions, since each partial width difference dominantly contributed to the conductance variation of the entire GR junction, global gating was unsuitable for the inspection of each partial width-difference-dependent conductivity of the entire GR electrode junction. Based on the gate-tuned Δn in Fig. 4, which employed enough length of Δy to reflect almost the entire induced carrier density over the GR length, the conductivities σ_{GR-T} of GR could be extracted as a function of W on the application of V_{T} (Fig. 5(a), for more details see the Experimental section and ESI, Fig. S9 and S10†). The σ_{GR-T} and σ_{GR0} under V_{T} = 8 V and 0 V exhibited suppression and invariance, respectively, as a function of W (Fig. 5(a)), which led to a conductance variation from 1.7% for W = 500 nm to 4.1% for W = 100 nm, according to the relationship (I − I_{0})/I_{0} = (σ_{GR-T} − σ_{GR0})/σ_{GR0} (see the solid line in Fig. 5(b)). Here, the σ_{GR-T} for V_{T} = 8 V and σ_{GR0} for V_{T} = 0 V was acquired by applying the averaged value of the induced carrier density from type (I), (II), and (III) GRs (see ESI, Fig. S10†). Although similar to the suppression behavior of (I − I_{0})/I_{0} for increasing W, an offset was observed, when compared with the experimental results (black, red, and blue dots with a conductance variation from 0.29% for W = 470 nm to 2.8% for W = 95 nm). During SGM probe gating on the target GR, since the extra resistance (R_{ext}) included in other GR junctions under V_{T} = 0 was still connected, the total current in all GR junctions could be expressed as I = V_{DS}/(R_{GR-T} + R_{ext}), where R_{GR-T} = L/(W·σ_{GR-T}) (for more details see the Experimental section and the section on the simulation of the conductance variation and electric potential of GR junctions in ESI, Fig. S9 and S10†). Upon employing theoretical fitting (dashed lines and the gray area in Fig. 5(b)) with the parameter R_{ext} = 7 to 13 kΩ, we confirmed the range of gradual escalation of (I − I_{0})/I_{0}, depending on W for type (I) (blue dots), (II) (red dots), and (III) (black dots) GR junctions (Fig. 5(b)). In particular, because the (I − I_{0})/I_{0} of W ∼ 170 nm (black dots in Fig. 5(b)) for the type (III) GR junction, which included the cracked area leading to a few tens of nanometers width during fabrication (see ESI, Fig. S4†), corresponded well with the value of (I − I_{0})/I_{0} between ∼133 nm and ∼200 nm widths for type (I) and (II) of GR junctions, respectively, we can assume that the resistance of the crack area in the type (III) GR junction was within the range of 7 to 13 kΩ. This indicates that we can expect the conductance behaviors of the entire GR junctions with (I − I_{0})/I_{0} to be a function of the target GR width under various R_{ext} and V_{T} (see ESI, Fig. S11†). Consequently, although there is extra-GR with large resistance connected to the target GR, the analysis of the conductance contribution of the target GR to the entire GR junction is guaranteed by SGM characterization, while global gating methods such as those reported previously^{20–26} are limited to the measurement of the width-dependent conductance for individual GRs constructed with invariant width.

Fig. 5 (a) Conductivities of the GR (σ_{GR}) as a function of width (W) on the application of either V_{T} = 0 V (dashed line) or 8 V (solid line) marked with σ_{GR0} or σ_{GR-T}, respectively. Inset: σ_{GR} as a function of W on the application of either V_{BG} = 0 V (dashed line) or 8 V (solid line) marked with σ_{GR0} or σ_{GR-BG}, respectively. (b) Current variation around (I − I_{0})/I_{0} as a function of the GR width from ∼95 nm to ∼470 nm and its theoretically fitted results on the application of V_{T} = 8 V (dashed line). Here, (I − I_{0})/I_{0} for each width was extracted from the AFM and SGM images of GR type (I) (blue dots), type (II) (red dots), and type (III) (black dots) shown in Fig. 1, 2 and Fig. S3, S4.† Here, the calculated lines were extracted for the GR junction structure (dashed lines and the gray area) or the individual GR structure (solid line) with the parameters of R_{ext} = 7 to 13 kΩ or 0 kΩ, respectively. Inset: Schematic diagram of the GR connected with the R_{ext} structure on the application of V_{T}. |

where Δn, , n

where C

where σ

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## Footnotes |

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c8nr10469g |

‡ These authors contributed equally to this work. |

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