Graphene, a mono-layer of carbon atoms arranged in a honeycomb lattice, has extraordinary electrical properties, such as the gapless linear dispersion 1 2 3 4 . In order to realize graphene-based nanoelectronic device applications, many research groups tried to open the energy bandgap in the gapless linear dispersion in different ways, for instance, graphene nanoribbons 5 6 and bilayer graphene applied by the electric field 7 8 9 . Recently, hydrogenated graphene attracts a great deal of attention because of its bandgap behavior driven by the chemical functionalization 10 11 12 13 14 15 16 17 . The adsorbed atomic hydrogen atoms form three-dimensional C-H sp ³ covalent bonds with carbon atoms by interrupting C-C sp ² bonds, thus, removing the conducting π bonds and opening a bandgap 11 18 19 . In 2010, Singh and co-workers proposed that graphane could form natural host for graphene multi-quantum dots, clusters of vacancies in hydrogen sublattice 20 . According to the surface dynamics, thermally energetic hydrogen atoms adsorbed on graphene could be desorbed from the graphene surface or migrate to the proper bonding sites or nucleate randomly (due to short diffusion length) to form dense islands of coexisting two-dimensional phases, C-H and C-C 14 20 21 . On the other hand, some reports proposed that the multi-quantum dots were unintentionally formed by impurities or defects in single-wall carbon nanotubes, which belong to the same honeycomb lattice as single-layer graphene 22 23 24 .

In this study, we propose a possible explanation based on the aforementioned mechanism for the formation of multi-quantum dots on our single-layer graphene flake and supported by the low-temperature electrical transport measurements.

A graphene field-effect transistor (FET) device was fabricated for the investigation described in this work. A single-layer graphene flake, mechanically exfoliated from natural graphite, was deposited onto a highly doped Si substrate capped with a 300-nm-thick SiO₂ layer, serving as a back gate 25 . Optical microscopy was used to locate graphene flakes and confirms that it was a single layer shown in the inset to Figure  1a 1 25 . Two Ti/Au contacts (5/50 nm) were patterned, using e-beam lithography and lift-off processing, into the source and drain contacts. To retain the defects and impurities in the graphene flakes to facilitate the formation of multi-quantum dots, the FET device was conditioned by the hydrogen plasma at conditions of power = 16 W and pressure = 0.2 Torr for 6 s without post-exfoliation annealing treatment 10 26 .

An Oxford top-loading He⁴ cryostat was used to carry out the two-terminal conductance measurements using standard AC lock-in technique at 77 Hz with a DC bias at the temperature range between 1.3 and 40 K.

Figure  1a shows the source-drain current (I _SD) dependence on the back gate voltage (V _BG) measured at the charge neutrality point, V _NP = 74 V, with a fixed source-drain voltage V _SD = 0.1 mV at T = 1.32 K before the hydrogen plasma treatment. The charge neutrality point, which is far from the zero voltage, can be attributed to the hole-doping impurities left on the graphene flake 27 28 . Figure  1b shows the I _SD V _BG measurement after hydrogen plasma treatment. Strong suppression of the source-drain current in the Coulomb blockade oscillation region (between the dashed lines) with a fixed source-drain voltage V _SD = 20 mV at T = 1.41 K is observed. To assure the Coulomb peaks in the Coulomb blockade oscillation region, we examined the Coulomb peaks with a fixed V _SD = 1 mV at T = 1.32 K shown in the inset to Figure  1b 29 . To further investigate the Coulomb blockade effect, the Coulomb blockade color scale plot of the conductance G in a V _BG V _SD plane was adopted for a better illustration of the existence of multi-quantum dots in our graphene flake sample; overlapped diamond-shape pattern was expected.

Figure  2 shows a color scale plot of the differential conductance G versus V _BG and V _SD at T = 5 K. The overlap of Coulomb diamonds, so-called ‘Coulomb shards’, was observed 30 . The Coulomb shards, which is also called stochastic Coulomb blockade, occurred due to the multi-quantum dots coupling in series during the carrier transport tunneling process 30 31 32 33 . Results of the measurements indicated that the multi-quantum dots formed in a two-dimensional manner. In other words, carriers could tunnel through the potential barriers of the quantum dots dispersed randomly. Coulomb shards disappeared while the temperature was increased to T = 10 K as shown in Figure  2b, whereby it implied that thermal energy dominated the carrier transport behavior rather than the multi-quantum dot Coulomb blockade tunneling 31 32 33 .

The stochastic Coulomb blockade in the multi-quantum dot system is further supported by investigating the temperature dependence of the number of the Coulomb peaks. Figure  3a shows the differential conductance as a function of V _BG between 40.5 and 44.5 V at different temperatures with a fixed V _SD = 9.5 mV. To distinguish the real Coulomb blockade peaks from the background noise, only reproducible peaks observed at the same V _BG with varying V _SD (V _SD = 6.5, 7.5, and 9.5 mV) are considered, shown in the inset to Figure  3a. The oscillations in Figure  3a are non-periodic, and the number of Coulomb peaks increases monotonically as the temperature is increased as shown in Figure  3b 22 30 31 . Both the aforementioned are the typical characteristics of the stochastic Coulomb blockade which suggests a formation of multi-quantum dots 31 32 33 34 .

For a better visualization of the individual Coulomb diamond in the blockade region, the Coulomb diamond color scale plot of the conductance G with a better resolution ΔV _BG = 10 mV at T = 6.5 K was shown in Figure  4. The clear Coulomb diamonds indicated that the charging effect existed in our hydrogenated graphene system 35 36 37 .

To justify the revealed overlapped Coulomb diamonds in our hydrogenated graphene system, a possible explanation for the formation of the multi-quantum dots is depicted in Figure  5. Without the post-exfoliation annealing process, the impurities or/and as-grown defects, shown as dots in Figure  5a, existed on the single-layer graphene flake 38 39 40 . In the vicinity of defects (mostly vacancies) or impurities, hydrogen passivated the edge carbon atoms on the vacancy sites or substituted impurities by keeping the C-C sp ² bonding structure. In the defect/impurity-free regions, the C-H bonding transformed the C-C bonding from sp ² into sp ³ structure 10 26 . After hydrogen plasma exposure, graphene multi-quantum dots were formed in the proximity of defects/impurities, depicted in Figure  5b. The asymmetric hydrogenated graphene quantum dot array could be treated as the sequential tunneling of charges through the two-dimensional (2D) array of single-layer graphene quantum dots 41 . The experimental results indicated that 2D multi-quantum dot array can be achieved by the hydrogenation of exfoliated graphene flakes experiencing no annealing process. More detailed fundamental understanding of the origin of multi-quantum dots formed on the non-annealed hydrogenated graphene flakes can greatly promote the development of graphene-based multi-quantum dot devices for quantum computation 42 43 .

Two-dimensional multi-quantum dots can be realized on a mechanically exfoliated graphene flake followed by the hydrogen plasma treatment without executing post-exfoliation thermal annealing. The overlapped Coulomb blockade diamonds observed from the electrical measurements, as well as the monotonic increase of the number of Coulomb peaks with the ascending temperature, suggest the formation of two-dimensional multi-quantum dots that is unprecedented on the annealed graphene flakes with similar hydrogenation processes. Therefore, we suggest a defect (or vacancy) and impurity-related mechanism to account for the formation of the multi-quantum dots discovered on our device. Further characterizations, such as AFM or SEM, on the atomic structure of un-annealed graphene layers might shed light on the origin of the quantum dot formation, whereas the degree of post-growth annealing could be utilized to engineer the quantum dots in terms of its size, density, shape, or charging states in a cost-effective way for quantum chip device applications.

FET: field-effect transistor; 2D: two-dimensional.

The authors declare that they have no competing interests.

CC and RKP fabricated the samples. CC, RKP, and MRC performed the measurements. CC and HDL drafted the paper. TMC and STL provided models, interpretation, and possible explanations for the results. CGS and CTL coordinated the project. All authors read and approved the final manuscript.

CC obtained his B.Sc. degree in Physics at NCUE in 2006 and M.Sc. degree in Physics at NTNU in 2009. He is currently pursuing his Ph.D. degree in Physics at NTU. RKP is currently pursuing his Ph.D. degree at the Cavendish Laboratory, University of Cambridge. MRC is currently a postdoctoral research worker at the Cavendish Laboratory, University of Cambridge. STL obtained his B.Sc. degree at NTU in 2010 and is pursuing his Ph.D. degree at the Graduate Institute of Applied Physics, NTU. He won the Dr. An-Tai Chen Scholarship, Mr. Ming Kao Scholarship, and college students participating in special research project of Creative Award provided by the NSC in 2009. HDL obtained his B.S. degree at Chinese Culture University, Taiwan and his Ph.D. degree at Mississippi State University, USA, and currently works as a project engineer at Electronics Testing Center, Tao-Yuan, Taiwan (R.O.C). TMC obtained his B.Sc. degree and M.Sc. degree at NTU, Taiwan and obtained his Ph.D. degree at Cambridge University, UK. He is currently an assistant professor at the Department of Physics, NCKU. CGS obtained his Ph.D. degree at Cambridge University, UK and is currently a professor of Physics at Cambridge University, UK. CTL obtained his B.Sc. degree at NTU in 1990 and his Ph.D. degree in Physics at Cambridge University, UK in 1996 and is currently a professor of Physics at NTU. He is also a topical editor for Current Applied Physics.