Introduction

Graphene-based quantum dots (QDs) provide a promising platform for spin qubits, which can have long spin coherence times because of their low nuclear spin density and weak spin–orbit interaction1,2,3. Graphene-based QD devices can be fabricated by the simple etching of two-dimensional (D) monolayer graphene4,5,6 and local-gate controlled bi-layer graphene with perpendicular electric fields7. Narrow and short graphene nanoribbons (GNRs) can be also used as QD devices8,9,10. Several fundamental features, such as electron-hole crossover11, the excitation spectrum6, spin and valley states12, and charge relaxation times13, have been reported, indicating the potential abilities of graphene-based QD devices. Despite these promising fundamental studies, the use of graphene-based QDs in real applications is yet to be realized. One of the critical subjects for further investigation is integration. Large-scale integration of QD devices is essential for realizing quantum computing14,15, sensors16,17,18, and other devices19. However, the integration of graphene-based QDs remains a challenge20,21. The lack of scalability of current fabrication processes is a critical barrier preventing this research field from further development toward commercial use, as has been demonstrated for Si and GaAs QD devices22,23,24.

We previously developed a unique method for the site- and alignment-controlled synthesis of GNRs25. Through the use of Ni nanobars and advanced plasma processing, high-yield synthesis of 1,000,000 GNRs has been realized at the wafer scale26. Non-volatile memory operation based on persistent photoconductivity and enhanced thermoelectric performance have also been demonstrated with our highly-integrated GNRs27,28. Although this scalable fabrication process possesses a potential for the practical use of graphene-based QD devices, detailed-quantum features have not been investigated because of the relatively long GNR length (~1 µm).

We modified our scalable GNR fabrication method for the synthesis of QDs, and the efficient synthesis of GNR-based QD devices was realized with accurate site controllability through adjustment of the Ni nanobar length and growth conditions. Furthermore, a clear orbital-level spacing between the ground state (GS) and excited state (ES) is observed in our GNR-based QD device. Surprisingly, the orbital-level spacings were stable even at 20 K, which is much higher than that of a QD device composed of Si and GaAs (up to ~1 K29). These scalable QD devices with high-temperature stability will strongly contribute to the next stage of the development of graphene-based QDs.

Results and discussion

Fabrication of GNR-based QD device

GNR growth was performed using a homemade plasma chemical vapor deposition (CVD) system25,26. Detailed information can be found in the Methods section. Most of the GNR-QDs used in our studies are not monolayer but multi-layer, which was confirmed by Raman scattering spectra (Supplementary Fig. 1). The electrical transport properties were measured using a low-temperature probe station (~15 K) (“15 K system”) and He-pum** refrigerator (~2.2 K) (“2.2 K system”), in which systematic measurements for many devices with moderate resolution and high-resolution measurements for specific devices were possible, respectively. In this study, more than 100 devices were fabricated by varying the growth conditions and nanobar lengths (Fig. 1a). The features observed in our devices can be divided into several categories (Fig. 1b–e). The first selection is related to Coulomb blockade (CB) (Fig. 1b, c). A CB can be identified from a drain-source current (Ids) versus a drain-source voltage (Vds) curve under a specific gate bias (Vg). If the Ids-Vds curve shows linear features or a continuous off-current region, these devices can be identified as No-CB (Fig. 1b) or CB (Fig. 1c) devices, respectively. There are two different sub-categories of CB devices: Coulomb diamond (CD) (Fig. 1d) and No-CD (Fig. 1e) devices, as determined by the shape of the off-current region, i.e., depending on whether diamond-like shapes can be observed. For CD devices, there is a critical difference in the appearance of the ES (Fig. 1f, g). The ES can appear as parallel lines on the edge (GS) of CD (Fig. 1g). The appearance of the ES indicates that the orbital-level spacing is sufficient to identify the up- and down-spin levels due to Zeeman splitting under a magnetic field (Fig. 1g). The up- and down-spin states provide information about the spin qubits in quantum devices. Thus, obtaining QD devices with clear orbital-level spacings between the GS and ES or ES and ES is very important for the realization of spin-qubit applications.

Fig. 1: Schematic illustration of GNR fabrication and categorization of quantum features.
figure 1

a Device structure with different LNi values. b–e Categorization of device features for b No-CB, c CB, d CD, and e No-CD devices. f, g Difference of CD device f without and g with orbital-level spacing.

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Based on these systematic investigations, it was determined that the Ni nanobar length (LNi) is a critical factor in determining the quantum transport properties of GNRs. First, we focused on the device fabrication yield (Yd), which is the percentage of devices in which the on-current at Vds = 100 mV was greater than 100 pA. In the case of short LNi, Yd reached ~90% and clearly decreased when LNi was ≥200 nm (Fig. 2a). This can be correlated to the unique growth mode of our GNR device (discussed further below). The quantum transport properties also showed an obvious dependence on LNi; the CB appearance rate increased with longer LNi (Fig. 2b). These Yd and CB trends can be explained as follows: a low Yd indicates that most of the Ni nanobars are broken during the CVD process. However, just before a Ni nanobar is broken, very fine structures called “break points” (BP) are formed. If the GNR can be nucleated from such BPs, a fine GNR may be formed from a relatively long LNi, resulting in the frequent occurrence of CBs.

Fig. 2: Efficient fabrication of GNR-based QD devices.
figure 2

a–c LNi dependence of a Yd, relative appearance rate of b CB, and c (red) CD and (blue) No-CD devices. d Plot of G/G0 vs. on/off ratio (room temperature) for CB (〇) and No-CB (×) devices. e, f Arrhenius plot of Gmin/G0 for e No-CB and f CB device. g Plot of RT for No-CB, single-like dot, and multi-dot devices. h Typical model of correlation between λPR and fine structure in GNR (i, state of Ni nanobar just before segregation of GNRs; ii, after segregation of GNRs from Ni nanobar with a BP at the nose point of the PR instability wave; iii, GNR with fine structure). i Typical (top)Ids and (bottom) dIds/dVds map** as functions of Vg and Vds for a CD device. j (left) Low and (right) high magnification SEM images of the GNR device used for (i).

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Further detailed analyses were performed to prove the accuracy of this hypothesis. The contribution of the fine GNR structures to the occurrence of CBs can also be determined from the conductance (G) vs. on/off plot, where G is normalized by the quantum conductance (G0). Because the bandgap of a GNR is related to its width, it can be conjectured that the on/off ratio increases when a fine structure is formed within the GNR. When the room temperature on/off ratio was low, CBs were not observed—even at low temperatures (Fig. 2d). In contrast, for a relatively high on/off ratio, CBs were frequently observed (Fig. 2d), indicating that the formation of a fine structure in the GNR is directly correlated with the appearance of CBs. In this study, most GNR device exhibit on/off ratios of 1–100 (Fig. 2d), which is lower than that fabricated by other methods. This can be explained by the multi-layer dominant structure of our GNR.

For CB to occur, not only a fine structure but also a large contact barrier is required. The contact barrier height was estimated as the activation energy (Ea) from the temperature dependence of the minimum conductance (Gmin) of the No-CB and CB devices. For a No-CB device, Ea is approximately 5.3 meV (Fig. 2e), which can be attributed to the contact barrier between the Ni electrode and the GNR. The Ea of a GNR device with a CB is approximately 218 meV (Fig. 2f), which is more than 40 times greater than that of a No-CB device, indicating that a sufficient contact barrier is formed in a CB device.

The correlation between the fine structure of GNRs and the appearance of CBs can be rationalized as follows. CB devices can be classified as either CD or No-CD devices (Fig. 1d, e, respectively). For an LNi of 100–200 nm, the CD device becomes dominant, whereas a longer LNi enhances the formation of a No-CD device (Fig. 2c). This LNi dependence could be related to the number of fine structures within the GNR. A nanobar with a longer LNi can form multiple fine structures, resulting in a decrease in Yd (Fig. 2a) and promotion of QD formation, resulting in No-CD (Fig. 2c). When plotting the room temperature resistance (RT) of GNRs in No-CB devices, the RT values of the CD and No-CD devices were in different ranges (Fig. 2g). The RT values of all the No-CB devices were below 100 kΩ, while those of CD and No-CD devices were in the ranges of 102–104 and 105–107 kΩ, respectively (Fig. 2g). These RT differences between the CD and No-CD devices can be explained by the variation in the number of fine structures within a single GNR channel. It can be assumed that each fine structure has a relatively similar RT order, and No-CD devices can be seen as a series connection of these fine structures (Supplementary Fig. 2).

As shown in Fig. 2c, a CD device became dominant for LNi in the range of 100–200 nm. It can be conjectured that the unique growth mechanism of GNRs from Ni nanobars played an important role in explaining this result26. In a previous study, we demonstrated that Ni nanobars have a liquid phase during CVD that breaks into two pieces after the segregation of GNRs26. Droplets of Ni nanobars move in opposite directions along the GNR axis owing to capillary forces, resulting in the formation of suspended GNRs. The breaking of liquid-phase Ni can be explained by the Plateau-Rayleigh (PR) instability arising within liquid-phase Ni nanobars26. The calculated wavelength of PR instability (λPR) was approximately 100 nm (Supplementary Fig. 3). This implies that when LNi is a few multiples of λPR, a few QDs are formed (Fig. 2c). Thus, it is expected that the fine structure formation in GNRs is directly correlated with the BPs of liquid-phase Ni that may arise at the node point of the PR instability wave (Fig. 2h and S3). If GNR nucleation occurs during the breaking of liquid-phase Ni, a very fine structure of the GNRs can be formed. Therefore, a fine structure, considered to be the origin of quantum features within our GNR, may be formed at the node point of the PR instability arising in liquid-phase Ni.

To support this hypothesis, we performed a direct comparison between quantum features and the GNR structure. When we observed the shape of the GNRs, which showed a clear CD (Fig. 2i), a very fine structure was formed in the middle of the GNR (Fig. 2j). This finding is consistent with the explanation discussed above.

Integration of GNR-based QD devices

Large-scale integration is critical for the use of QDs as quantum devices. Because LNi = 100–200 nm shows the highest probability of CD device fabrication (Fig. 2c), large-scale integrations were carried out with a suitable device geometry (LNi = 200 nm). The 16 GNR devices were designed within the same substrate (~10 mm × 10 mm) (Fig. 3a) and the stability diagram was measured for each. Noticeably, nine devices exhibited CD features (Fig. 3b), indicating that the fabrication yield of the quantum GNR device with CD features was greater than 56%. As our approach is scalable, further large-scale integration of GNR-QD devices is possible.

Fig. 3: Site-controlled fabrication of integrated GNR-based QD devices.
figure 3

a Typical illustration of device patterns and detailed device structures. (b) All 16 GNR-device features measured at 15 K were fabricated within the same substrate. c Typical SEM image and d, e Coulomb oscillation features of GNR-based QD devices operated by d sg1 and e sg2. Contour plot of G/G0 as functions of Vsg1 and Vsg2 swept in f wide and g narrow ranges. h (top) Time profile of VSG1 switched between V0 and V1 and (bottom) its Ids response.

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Controlling the state of carriers in QDs is also important and can be achieved with a side-gate operation (Fig. 3a, c). It should be noted that the side-gate patterns were initially formed together with the Ni nanobars and other electrodes. Thus, a side-gate device can be fabricated without post-processing for electrode formation, i.e., a clean as-grown surface of the GNR can be maintained during the measurement of quantum features. In both sweeps of side gate1 (sg1) and side gate2 (sg2), a similar Coulomb oscillation was observed (Fig. 3d, e). When we measured Ids as a function of sg1 and sg2, clear straight-line patterns were obtained, indicating that carriers confined within GNR-QDs can be well controlled by side gates (Fig. 3f). Similar side-gate operations can also be realized using other devices (Supplementary Figs. 4, 5). Furthermore, the carrier state within a GNR-QD can be quickly switched by applying V0 and V1 to sg1 (Fig. 3g, h, respectively), indicating that the quantum state in the GNR is very stable without any hysteresis, which may be useful for various quantum applications.

Detailed-quantum features in GNR-based QD device

As mentioned above, for the application of QD devices as spin qubits, control of the carrier and spin state is important. To address this issue, maintaining a sufficiently large orbital-level spacing is critical (Fig. 1g). To confirm the possibility of spin-qubit application of our GNR-QD device, further detailed measurements of the quantum features were carried out at cryogenic temperatures (~2.2 K). Large CDs with ΔVds ~100 mV were observed with closed shapes at zero bias, indicating the formation of a single QD (Fig. 4a). Outside the CDs (GS), ESs parallel to the edges of the diamonds were also observed, demonstrating that a large orbital-level spacing between the GS and ES was maintained in our GNR device. These ESs correspond to the orbitals in the QD formed by size quantization. Similar transport properties were also observed in other devices, as shown in Fig. 4b, c. It should be noted that the density of state in graphene lead can be modulated by Vg, which can show multiple lines outside of CD regions30. However, those lines are known to be shown as non-parallel lines to the edge of the CD. Therefore, parallel lines observed in this study should be coming from not a lead state but ES.

Fig. 4: GS and ES of CDs in our GNR device.
figure 4

a–c Typical Coulomb diamonds with GS and ES lines measured at 2.2 K for various GNR devices (a Device 1, b Device 2, and c Device 3).

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Figure 5 shows the temperature dependence of the transport properties (Fig. 5a:2.2 K, 5b:20 K, 5c:50 K, and 5d:80 K). With increasing temperature, the ES and CBs became blurred because of the broadening of the electron energy distribution in the leads. The ESs disappeared at 50 K, and CDs were maintained up to ~80 K (Fig. 5a–d). We analyzed the width of the ES by varying the temperature. Figure 5e shows the current peak at the ES in Device 2 (Fig. 4b). The peak width increased with increasing temperature. The peak width (σ) at Vds ≈ 0.15 V was extracted by Gaussian fitting and is plotted as a function of temperature in Fig. 5f. The width increased linearly, indicating that peak broadening due to the tunneling rate was less than that due to temperature. From the slope of the linear fit, the conversion factor was evaluated as α = 2.75, which describes the real Vds applied through the quantum dot Vds_dot = Vds /α around this ES. α is induced by in-series resistive components in the GNR and at the interface between the GNR and metal31. From the stability diagram in Fig. 4b, the charging energy corresponds to Ec = ΔVds_c = 25 mV and the excited-level spacing is ΔVds_ex = 13 mV. The excited-level spacing can be calibrated by α, resulting in Eex = ΔVds_ex/2.75 = 5.1 meV. These results are consistent with the temperature dependence shown in Fig. 5.

Fig. 5: Temperature dependence of orbital levels and CDs in GNR.
figure 5

a–d Transport properties of Device 2 were measured at a 2.2 K, b 20 K, c 50 K, and d 80 K. e Temperature dependence of the differential conductance in Device 2. f Extracted widths obtained from Gaussian fitting of the current peak at the excited line located at Vsd = 0.15 V as a function of temperature (dots). The line shows the linear fit.

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We estimated the dot size using a capacitance model26. The area of dot A was calculated as follows:

$$A=\frac{w}{{d}_{0}+{d}_{1}}\cdot \frac{{C}_{g}}{C{E}_{c}}\left(\frac{{d}_{0}}{{\varepsilon }_{0}}+\frac{{d}_{1}}{{\varepsilon }_{1}}\right)$$

where d0 is the distance between the GNR and wafer surface, d1 is the SiO2 thickness, ε0 is the permittivity of a vacuum, ε1 is the permittivity of SiO2, w is the GNR width, Cg is the capacitance of the gate, and C is the overall capacitance of the dot. Using this equation, the dot size was estimated to be 14 nm2. This size is much smaller than that of the entire GNR geometry, indicating that the dot is locally formed inside the GNR, as discussed previously.

We now discuss why the orbital-level spacing in our GNR was stable under high-temperature conditions (~20 K). To observe the ES under high-temperature conditions, ΔVds_ex must be larger than the thermal energy. ΔVds_ex is inversely proportional to the multiple of a carrier (electron or hole) effective mass (m*) and area of the QD (A) (ΔVds_ex ∝ ћ2/m*A). Thus, smaller dots with lighter m* are ideal candidates for increasing the threshold temperature of the ES. The largest ΔVds in our GNR was 129 meV, which clearly differs from previously reported results (10–25 meV), where orbital levels were observed below 4.2 K6,7,8,9,10,11,12,13. Only one report has a similar or higher ΔVds (300 meV) with a very short GNR (~5 nm) bridged between graphene electrodes29. In this device, an ES was observed even at 75 K32. This structure is similar to that of our GNR, where a very fine structure of GNR is formed within wider GNRs (Fig. 2j), indicating that size is a dominant factor in the stability of the orbital-level spacing in our GNR-QD device. The threshold temperature of 20 K is much higher than that of Si-based QDs (~1 K)29. It has been theoretically predicted that m* in GNRs is much lower than that in Si33. This may also be one of the reasons for the high-temperature observations of orbital-level spacing in our GNR-QD devices.

It should be mentioned that although the appearance rate of CD is relatively high (>56%), clear ES observations were rare (below 10%), which can be due to the difficulty of (i) obtaining a single GNR-QD and (ii) increasing the bandgap of GNR-QDs. Further shortening the GNR length and reducing the number of layers of GNR-QDs may be possible approaches to solve these issues, which are the future work of our study toward future applications of GNR-QD-based integrated quantum devices. Uniformity and device-to-device variation should also be discussed for future industrial applications of integrated quantum devices. Previously, most quantum devices comprising nanocarbon materials had very low fabrication yields. Because our study improves the yield up to 56%, it is now feasible to discuss uniformity and device-to-device variation. To address these issues, it is necessary to establish a novel measurement system that can measure many quantum devices within a short time. This is an important subject for the practical use of integrated quantum devices. To improve uniformity and reduce device-to-device variation, the fabrication process also needs to be improved, similar to current Si-based technology, by scaling up the reaction chamber and improving the uniformity of the plasma source, temperature, gas flow, etc., which is one of the next subjects of our research.

Conclusion

We have demonstrated the scalable fabrication (fabrication yield >56%) of GNR-QD devices by adjusting growth conditions and LNi. A systematic investigation revealed that very fine structures that formed in the middle of the GNR were possible candidates for QDs. More than 56% of devices showed clear CD features. Detailed measurements of quantum features were also performed, which revealed clear orbital-level spacings between the GS and ES in our GNR-QD device. Furthermore, the orbital levels were stable at relatively high temperatures (~20 K). The scalable fabrication of GNR-QD devices with clear orbital-level spacings at relatively high temperatures have the potential to accelerate the development of GNR-based quantum devices for future applications.

Methods

Device fabrication

Multiple Ni patterns of nanobars, source-drain electrodes, and side-gate electrodes were fabricated using conventional electron beam lithography (ELS-7500, Elionix) and a liftoff process followed by vacuum evaporation of the Ni film (typically 50 nm).

Plasma CVD

A homemade plasma CVD system was used for the GNR synthesis. Before plasma CVD growth, an electric furnace was heated to the desired temperature (typically 800–900 °C) under a flow of hydrogen (50 Pa). A substrate with Ni patterns was transferred to the central area, and rapid heating was performed. CH4 and H2 gases (250 Pa) were allowed to flow after reaching a fixed heating time (typically 60 s), during which the Ni nanobars were not dissipated. Subsequently, radiofrequency power (30–60 W, 13.56 MHz) was applied to the coils outside the quartz tube. The plasma irradiation time was typically 5–30 s. Following plasma CVD, the substrate was moved from the center to the outside of the electric furnace to rapidly decrease the temperature of the substrate.

Characterization

The structure of the GNR sample was characterized by scanning electron microscopy (SEM; Hitachi, SU1510, Japan). Electrical measurements of the GNR devices were performed using a vacuum probe station with a semiconductor parameter analyzer (HP 4155 C) from ~15 K to room temperature (15 K system). Further detailed-quantum features were measured using a He-pum** refrigerator, which can decrease the temperature to ~2.2 K (2.2 K system). The devices were mounted on chip carriers and sample holders in a refrigerator. The currents were measured using a semiconductor parameter analyzer and a sensitive current preamplifier (DL 1211).