Edge-Sensitive Semiconducting Behaviour in Low-Defect Narrow Graphene Nanoribbons

3.1 Basic property and 4th annealing

Figure 1f shows the typical drain current (I_sd) values as a function of the drain voltage (V_sd) of an FET fabricated using a short-length GNR (Figure 1d) as the current channel at a temperature (T) of 1.5 K. The current amplitude is small, with the presence of a strong zero-bias conductance (G₀) anomaly (a voltage width of ΔV_SD ∼±1 V even at a back-gate voltage (V_bg) of ±20 V). We observed that most of the fabricated narrow GNRs (width ∼20 nm) were highly resistive (i.e., a small magnitude of I_sd) with strong G₀ anomalies even after the three-step annealing [15] when compared with our previously-fabricated wide GNRs (width >75 nm).

Although the width of the narrower GNRs is less than ∼1/3 of the width of the wider GNRs, the resistivity is at least 10-times larger. This result cannot be understood by the conventional relationship of resistivity vs. the width of the GNRs, which is an inversely proportional relationship. Moreover, the G₀ anomaly cannot be attributed to the single-electron charging effect [15] (see Author's note).

However, after we carried out the fourth annealing process under high vacuum at 700 °C immediately after the formation of the metal electrodes (methods), the amplitude of I_sd exhibited a significant recovery. This implies that the previously-observed high resistivity (Figure 1f) was due to poor interface contact between the metal electrode and the narrow GNRs. After the fourth annealing, further deoxidization from the GNR can at least occur. The GNRs present were fabricated by the unzipping of CNTs by the oxidation of defects. Thus, after the formation of the GNRs, oxygen (O)-atoms remained. Here, even if the number of the remaining O atoms is very small and mostly the same between the wide and narrow GNRs after the three-step annealing, the resistivity at the interface of the electrodes/GNR is significantly affected only in the narrow GNRs because the ratio of the O atoms/GNR width is larger in the narrow GNRs. This can result in larger interface resistivity. After the fourth annealing, O atoms beneath the electrodes move and can be excluded further, resulting in low interface resistivity.

3.2 Semiconducting behaviours on edge termination

Figure 2a shows the typical I_sd vs. V_bg curve for the sample with a 600 nm length at T = 300 K, after the fourth annealing. The I_sd value is significantly enhanced by the fourth annealing step. In the V_bg range between ±20 V, the device does not exhibit ambipolar behaviour but instead evident n-type semiconductor behaviour, where I_sd drastically increases only when the applied V_bg is positive. This behaviour is qualitatively consistent with the behaviour reported in previously fabricated carrier-doped GNRs with sub-10 nm-widths and graphene nanomeshes with an inter-pore distance (i.e., GNR width) of ∼20 nm [18–20]. However, an I_on/I_off ratio as high as ∼10⁴ is observed at V_sd = 0.2 V, even with the leakage I_sd at V_sd = 0 V (Figure 2b with the y-axis representing the logarithmic-scale values of the I_sd value in Figure 2a). This I_on/I_off ratio is 10³ times greater than those observed in previously fabricated ∼20 nm-width GNRs [19, 30]. Surprisingly, this value is equal to ∼10⁶ as reported in 2 nm-wide GNRs, when the I_on is normalized for the GNR width (i.e., normalized I_on ∼ 200 μA/μm = I_on ∼ 4μA/20 nm (Figure 2a) × 1μm/20 nm) [20].

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Figure 2.

a, b, Drain current (I_sd) vs. back-gate (BG) voltage (V_bg) curves at 300 K for the sample shown in Figure 1b (400 nm length) with H-terminated edges. The significant ISD increase observed only in the +V_bg region suggests n-type semiconductive (i.e., electron-dominant) transport. Owing to insufficient isolation between the BG and source pads, leakage current remains even at V_sd=0. In (b), the y-axis represents the logarithmic scale of the values of I_sd shown in the +V_bg region of Figure 2a. c, d, I_sd vs. V_bg curves at 300 K for the sample corresponding to Figure 2a after exposure to atmospheric air for two weeks at room temperature. e, I_sd vs. V_bg curves at 300 K for an O-terminated long sample corresponding to Figure 1e (length of 3,000 nm) obtained after exposure to atmospheric air, similar to Figure 2c.

As mentioned above, the observed semiconducting behaviour that does not exhibit transport gaps (or charge neutrality points, band gaps) in sub-10 nm GNRs has been understood only by the shift in E_F through the VHSs of 1D EDSs caused by edge carrier doping. This shift can also produce large I_on/I_off values due to a significant increase in EDOS caused by the E_F shifting along a VHS. However, in the presence 20 nm-GNRs, no evident 1D EDOS exists because the GNR width is greater than 10 nm and, hence, the observed semiconducting behaviour with the extremely large normalized I_on/I_off values of ∼10⁶ cannot be fully understood by this model alone. We discuss our model (considering E_F pinning at impurity levels) of the origin of this semiconducting behaviour in a later section.

Figure 2c shows the typical I_sd–V_bg relationship obtained for the sample corresponding to Figure 2a when placed in atmospheric air for two weeks at room temperature. Because our fabricated GNRs are not covered with passivation films, the surfaces and edges of the GNRs are directly exposed to air and the edges are automatically oxidized through this process. We found that the initially observed n-type behaviour (Figure 2a) drastically changes to p-type behaviour (Figure 2c). The normalized I_on/I_off ratio (as large as ∼10⁶) observed in Figure 2b is also approximately observed in Figure 2d (with a logarithmic y-axis scale as in Figure 2b), although it is reduced by the larger leakage I_sd. Because the wider GNRs (∼100 nm) showed no such change, this edge-sensitive characteristic is unique to the narrow (<20 nm) GNRs present. We confirmed qualitatively similar changes in five samples.

This is qualitatively consistent with the evident semiconducting behaviour observed in Figure 2a, and this result strongly suggests that the narrow GNRs' electronic structures are extremely sensitive to the termination of the dangling edge bonds by foreign atoms. It is known that the H-termination of GNR edges leads to electron doping and n-type behaviour [40], while O-termination by this process causes hole doping and p-type behaviour [41]. Evident changes between the n- and p-type behaviours in Figs. 2a and 2c may correspond to these edge terminations. Indeed, in the wider GNRs fabricated following the same CNT-derived method, p-type behaviour in an as-grown one and its transformation into ambipolar behaviour were reported after air-pumping in high vacuum for a long time [39]. This supports our results and the argument given above, although our narrow GNRs are much more sensitive to the atmosphere because the GNRs were only placed in air, without performing any intentional procedures. This result indicates that some portions of edge C–H bonds are chemically unstable and tend to be replaced by C=O bonds when the edges are exposed in air for a long time in the absence of covering passivation films. In the narrow and short GNRs (e.g., <20 nm width and <400 nm length), such a partial replacement can drastically change the electronic behaviours of all of the GNRs. The result also indicates that such GNRs are suitable for the fabrication of p- and n-type semiconducting devices via carrier doping from the edges and, hence, for CMOS-like circuits.

Figure 2e shows the typical I_sd–V_bg characteristics of ∼3,600 nm-long GNRs (measured between electrodes 1 and 3 in Figure 1e) after O-termination of the edges by exposing the sample to atmospheric air. The curves indicate p-type semiconducting behaviour, as in the case of Figure 2c. However, the onset value of V_bg, at which point I_sd starts to increase, is different in this case. The onset V_bg shifts to V_bg ∼−4 V in Figure 2e. In contrast, the I_sd–V_bg relationship between electrodes 1 and 2 with a 400 nm distance on the same GNR (Figure 1e) is similar to that observed in Figure 2c, with the onset being V_bg = 0 V. These differences in the onset V_bg at the different portions of the long GNR can also be understood from the perspective of the poor uniformity of O-termination for the long GNR edges, as explained in a later section. This suggests that the electronic transport in narrow-width GNRs is highly sensitive not only to different types of foreign atoms but also to their quantities involved in edge termination.

This result also implies the possibility of fabricating GNR FETs with different threshold voltages by using different-length GNRs; this can prove useful in manufacturing LSI-circuit components using GNRs. In the LSI circuits, the tuning of the threshold voltages (current-onset voltage) is the most important. In the present experiments, the short GNRs with high homogeneous edge termination by the impurity atoms showed the lowest onset V_bg, while the long GNRs with inhomogeneous edge termination showed the highest onset V_bg. Thus, combining and hybridizing such different-length GNRs with different onsets of V_bg make the realization of LSI possible. Of course, the onset V_bg is not controllable in the present work, because only the unintentional termination of the edges was employed. If one could control it in the future, it would lead to the formation of an effective LSI circuit.

3.3 Small activation energy for impurity level

As mentioned, we have previously reported E_a values as large as ∼50 meV in our fabricated wide GNRs, with minimum widths of ∼75 nm. In order to compare the E_a value of the present narrow GNRs with the wide GNRs, we measured the relationship for minimum conductivity (G_min) vs. temperature for V_bg = 0 V in a few of the H-terminated n-type samples (Figure 2a). The corresponding Arrhenius plots are shown in Figure 3. The relationship is mostly linear when T >20 K, following a thermal-activation relationship as indicated by the dotted line, while the relationship is not clearly defined below T = 20 K, and the G_min value becomes extremely low while exhibiting a constant value when T <10 K (i.e., insulating behaviour). The linear part for T >20 K (the dotted line for1/T <0.05) yields E_a ∼35 meV from fitting with G_min ∝ exp(–E_a/2k_BT). Despite the narrow width of the GNRs (20 nm), this E_a value is less than the maximum E_a value of ∼50 meV obtained for our previously-fabricated wider GNRs (minimum width ∼75 nm), for which only the linear part was observed in the Arrhenius plots for the estimation of E_a.

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Figure 3.

a, b, Arrhenius plots for the minimum conductance (G_min) vs. temperature of the sample corresponding to Figure 2a at T >5 K (a) and T >1.5 K (b). The plotted G_min values were those obtained at V_bg = 0 V in Figure 2a. The dotted curve is just a visual guide.

In general, the E_a value is inversely proportional to the GNR width W (i.e., E_a = AW⁻¹, where A denotes the coefficient). Although the A values were small in the previously-fabricated wide GNRs because of the large width region (W >75 nm), these low-defect GNRs exhibited large E_a values because of strong electron confinement in the clean 1D space of the low-defect GNRs [15]. This type of confinement should ideally be induced in the present narrower (W <20 nm) GNRs and, thus, the A value should increase. Moreover, the influence of armchair edges should become also significant in sub-10 nm-width GNRs. In our present near-sub-10 nm GNRs, such an influence should become non-trivial, thereby resulting in the enhancement of E_a. Nevertheless, the E_a observed in the present case is relatively smaller. This suggests that the anomalously small E_a value of ∼35 meV is not characteristic of intrinsic energy band gaps. Because no power-law behaviour (i.e., G_min ∝ T^α for hopping conductance) is observed even in the temperature regions where the linearity is smeared out (i.e., 10 K <T<20 K), the small value of E_a cannot be attributed to defect-originated energy levels, as in the case of lithographically fabricated GNRs [8–10].

On the other hand, it is known that the termination of GNR edges and carrier doping theoretically lead to the introduction of impurity levels

[35–39]. Indeed, this E_a value of ∼35 meV estimated from Figure 3 is close to the impurity levels reported in [35]. The observed E_a value, thus, could be the activation energy of the electrons emitted from the impurity level to the bottom of the conduction band (Figure 4d) because of the measured V_bg = 0V.

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Figure 4.

Conductance peaks at T = 1.5 K (a) and their disappearance at T = 30 K (b) in an H-terminated n-type short GNR. In (a), two evident conductance peaks are observed around V_bg = ±3.5 V. Inset: Magnification of the conductance peak shown in the main panel. c, V_sd dependence of the conductance peak. The z-axis represents I_sd. The yellow portions indicate high-I_sd regions. Two distinct vertical lines, which are attributed to the conductance peak, are observable around V_bg = ±3.5 V along the y-axis. d, Schematic band diagram for n-type behavior (Figure 2a). The activation energy E_a ∼35 meV of the impurity level is estimated from the linear part of the curve shown in Figure 3a. The energy difference ∼180 meV between the impurity level and the top of the valence band is also estimated from the V_bg region for the off-current (Figure 2a).

3.4 Conductance peak at low V_bg fields

Here, in certain such small-E_a GNRs, we observe a sharp and small conductance peak in low V_bg regions (V_bg = ±3.5 V) of the I_sd–V_bg curves at T = 1.5 K (Figure 4a). Five of eight samples which showed the small E_a exhibited the conductance peaks. This suggests the strong correlation of the conductance peak with the impurity level with small E_a values. The conductance peak appears to be mostly independent of V_sd (Figure 4c). As the temperature increases, the conductance peak decreases and it disappears entirely at T ∼30 K (Figure 4b). It can be, however, potentially the main cause for the abovementioned small E_a - which was observed at V_bg ∼0 -over a wide temperature range in Figure 3(a).

When E_F is pinned around this impurity level, it can cause resonant tunnelling [35–37] and, thus, produce this sharp conductance peak. Here, in Figure 4(a), the conductance peaks exist around V_bg = ±3.5 V. This V_bg is the voltage applied from the back side of the silicon substrate and, thus, the applied VBG modulates the electronic states of the GNRs via the silicon substrate, so electronic charging in the substrate (Q_BG = C_BGΔV_BG) gives rise to the true energy values [15].

Considering this, the energy in the single particle energy spectrum is given by Δ = (h/2π) VF√(2πC_BGΔV_BG/|e|), where VF ∼10⁶ m/s is the Fermi velocity of graphene and C_BG is the capacitive coupling of the GNR to the back-gate electrode. When C_BG is taken to be 230 aF μm⁻², which is 1/3 times smaller than that for our previous wide GNR [15], Δ for V_bg = 3.5 V in the present narrow GNRs is estimated to be ∼70 meV. This means that the resonant tunnelling for the conductance peak occurs when E_F shifts in ∼70 meV from the Dirac point at V_bg = 0V and is pinned by the impurity level.

We also discuss this issue in the next section, considering also other phenomena mentioned above.

Alternatively, carrier doping via edge termination by foreign atoms without considering the presence of impurity levels has been considered as the origin of the appearance of n- or p-type semiconductive behaviour, particularly in sub-10 nm-GNRs. However, in the present GNRs with ∼20 nm widths, no 1D EDOS evidently exists because the width is >10 nm. Thus, the impurity levels with the small E_a ∼35 meV introduced by edge termination can consistently explain the observed phenomena, as elucidated below (see Figure 4d).

3.5 Discussion

Theoretically, resonant tunnelling through the impurity levels theoretically produces conductance peaks [36,37]. Semiconducting ultra-narrow-armchair GNRs with impurities exhibited sharp peaks in DOS between VHSs as well as conductance due to resonant tunnelling, depending on the impurity concentration [36]. As the impurity concentration increased, the resonant-peak height increased. Moreover, the two connected GNRs with impurities also showed resonant tunnelling and conductance peaks, depending on the width of the GNRs and the hybridization energy of the impurity atoms in two GNRs [37].

As mentioned above, there is a strong correlation between the observed conductance peak and the impurity level with the small E_a value in the present, narrow GNRs. This suggests the robust possibility that the conductance peak originates from resonant tunnelling through the impurity level with an E_a value of ∼35 meV, when E_F shifts ∼70 meV from the Dirac point at V_bg = 0V and when E_F is pinned by the impurity level. Assuming this, all of the other three phenomena can be consistently understood qualitatively, as follows.

(1) The absence of transport gaps (Figure 2) can be understood by the model whereby E_F is strongly pinned around the high-intensity impurity level, which exists close to the bottom of the conduction band (E_a value of ∼35 meV; Figure 4d) for H-terminated edges and close to the top of the valence band for O-terminated edges (Figure 2c; hole doping). The application of V_bg, thus, cannot shift E_F effectively through all the energy–regions present within the band gaps, resulting in the absence of transport gaps. (2) The high sensitivity upon the appearance of these n- and p-type behaviours to different atmospheres can also be understood by the closest position of E_F to the impurity level and the E_F pinning, especially for the present short GNRs (e.g., <500 nm length). The replacement of C-H bonds by edge C=O bonds can easily change the n-type behaviours to p-type behaviours due to the formation of high-intensity impurity levels in such short and narrow GNRs. (3) The large I_on/I_off value can also be explained by the model whereby drastic electron (hole) emissions can be caused due to the high-intensity of the impurity levels present, even upon slightly varying the applied V_bg and shifting the E_F. Indeed, I_sd rapidly increases right above V_bg = 0 V, both in Figs. 2b and 2d, resulting in the large I_on/I_off value. This is strong evidence for the E_F pinning model.

In the present narrow GNRs of width ∼20 nm and length <∼500 nm, the densities of the impurity levels will not be uniform through all the regions along the longitudinal direction because the termination by impurity atoms (H and O) is not uniform. It is speculated that some very small portions have the highest densities for tunnel barriers. When electrons run through such small tunnel barriers and V_bg is pinned by the impurity level, the electron must engage in resonant tunnelling. Moreover, the combination of two portions including the impurity levels in a GNR may correspond to the hybridization of the impurity level, like [37]. In this case, the emergence of a sharp conductance peak like that in Figure 5(a) can actually be predicted, depending on the hybridization energy. The models that are relevant to the present case should be clarified by further experiments.

Here, the difference in the onset V_bg value for different GNRs' lengths (Figs. 2c and 2e) can also be interpreted by poorer uniformity in the density of the impurity levels, caused by the occasional O-termination of the long GNR edges (i.e., the presence of extremely low-quantity C=O bonds at some edge sections). This is because the GNRs were unintentionally exposed to an air atmosphere.

The onset V_bg is determined by the energy difference between the initial position of E_F at V_bg = 0 V and the impurity levels. In the short GNRs, the edge-termination by H and O is relatively homogeneous with a high density. Thus, the impurity level density is high and homogeneous and hence the initial position of E_F locates close to the impurity level. Indeed, we estimated the initial position of E_F to be only 70 meV from the impurity level, as mentioned above. In contrast, in the unintentionally-oxidized long GNRs, some portions should have much lower O-termination and lower impurity levels as a matter of convention. In such portions, the initial E_F at V_bg = 0 V locates far from the impurity level according to the theory of semiconductors and, hence, the larger V_bg is needed in order to cause the onset to I_sd. The onset V_bg in the overall region of a long GNR is determined by such a portion, which has the largest resistivity. Therefore, the large onset V_bg appears in the long GNRs.

In Figure 2, I_sd cannot easily flow even under the applied maximum V_bg (i.e., V_bg = −20 V for Figure 2a and V_bg = +20 V for Figure 2c), except for the leaked I_sd. When we assume that E_F locates close to the impurity level at V_bg = 0 V and shifts directly following V_bg without undergoing pinning by the impurity level, we can estimate the energy difference Δ between the impurity level and the other band edges (i.e., the top of the valence band for the sample corresponding to Figure 2a and the bottom of the conduction band for that corresponding to Fig 2c). This energy difference can be also given by Δ = (h/2π) VF√(2πC_BGΔV_BG/|e|) ∼180 meV for the present GNR. This suggests that the energy band gaps Δ_gap of the present ∼20 nm-wide GNRs are at least greater than [(Δ = 180) + (E_a = 35) meV = 215 meV]. This result is in qualitatively good agreement with the observed trend of GNR width VS. Δ_gap [15].