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Dirac point induced ultralow-threshold laser and giant optoelectronic quantum oscillations in graphene-based heterojunctions

The occurrence of zero effective mass of electrons at the vicinity of the Dirac point is expected to create new paradigms for scientific research and technological applications, but the related discoveries are rather limited. Here, we demonstrate that a simple architecture composed of graphene quantum dots sandwiched by graphene layers can exhibit several intriguing features, including the Dirac point induced ultralow-threshold laser, giant peak-to-valley ratio (PVR) with ultra-narrow spectra of negative differential resistance and quantum oscillations of current as well as light emission intensity. In particular, the threshold of only 12.4 nA cm−2 is the lowest value ever reported on electrically driven lasers, and the PVR value of more than 100 also sets the highest record compared with all available reports on graphene-based devices. We show that all these intriguing phenomena can be interpreted based on the unique band structures of graphene quantum dots and graphene as well as resonant quantum tunneling.


Supplementary Figure 2
Cross-sectional SEM image of the graphene/GQD/graphene composite sandwiched by 300 nm SiO2 and ~300 nm PMMA layer. The GQD layer was fabricated at a spinning speed 2400 rpm. a, and b, The obtained thickness of the GQD layer is ~35 nm and 162 nm respectively.

Supplementary Figure 3
Optical transparency spectrum of top-graphene/PMMA layer. The PMMA was spin coated at a spinning speed 4000 rpm for 45 sec. The calculated thickness of the PMMA layer is 300 nm.

Supplementary Note 2, Raman spectrum of graphene layer
Raman scattering spectrum of the graphene layer is illustrated in Supplementary  Figure 4. The ratio of G to 2D peak centered at 1585 cm -1 and 2636 cm -1 respectively, confirms that the graphene is single layered. Lorentzian shape of G and 2D peaks as well as absence of D peak confirm that the graphene is of high quality. 4 Again, the full width at half maxima (FWHM) of G peak using 633 nm laser is found to be 22 cm -1 , which corresponds a good crystal quality.

Supplementary Figure 4
Raman scattering spectrum of graphene under 633 nm laser excitation. The G and 2D peaks fit with Lorentzian shaped curve with 99.99% accuracy.

Structural characterization
The structural characterization of the GQDs was estimated by employing transmission electron microscopy (TEM) imaging method. The lower magnification TEM image of the GQDs is shown in Supplementary Figure 5a

Raman spectrum of GQDs
The Raman scattering spectrum of GQD is shown in Supplementary Figure 6. The intensity ratio of D to G band is found to be ~ 0.9, indicating that the GQDs are composed of few layer graphene. 3,5 The low energy peak around 125 cm -1 corresponds a low energy vibrational out-of-plane vibration mode of -OH functional groups attached with the aromatic rings. 6

Supplementary Figure 6
Raman scattering spectrum of graphene quantum dots under 633 nm laser excitation.

X-ray photoelectron spectroscopy analysis
The XPS analysis of GQD as shown in Supplementary Figure 7 reveals a dominant C1S and O1S peaks around 285 and 532 eV, respectively. 5, 7-10 A high resolution XPS analysis of C1S peak in Supplementary Figure 8 confirms the dominating presence of hydroxyl and carboxyl functional groups. The weightage of different functional group present in the GQD matrix can be estimated by deconvoluting the C1S peak in to different area corresponding to the peak, which is found to be C-C : 69.92%, C-O : 11.48%, C=O : 9.79%, O-C=O : 3.38% and C-N : 5.43%.

Supplementary Figure 8
High resolution C1s peak of X-ray photoelectron spectroscopy (XPS) spectrum.

Photoluminescence
GQDs possess tunable photoluminescence emission under different excitation energy as shown in Supplementary Figure 9a. Several researches have been concentrated to unveil the nature of the bandgap of GQD, but an explicit explanation of the luminescence properties is still desirable. [11][12][13][14][15][16][17][18][19] The emission process of GQDs are highly influenced by quantum confinement effect (QCE), various oxygen and nitrogen related functional groups and carbon defects. The PL feature is composed of two distinct parts. The blue emission, which is generally excitation independent and caused by carbon defects, and the low energy emission is excitation dependent, which is caused by the combined effect of QCE and the molecular like vibrational energy levels of various functional groups appeared in between sp 2 (π-π * ) energy states. [20][21][22] The emission process can be summarized in the following energy band diagram as shown in Supplementary Figure 9b Figure 6 reveals a presence of low energy peak around 125 cm -1 corresponds a low energy out-of-plane vibration mode of -OH functional groups attached with the aromatic rings. These functional groups produce a core-shell structure in the GQD, where the core is mainly composed of sp 2 carbon networks, which is surrounded by the functional groups. In our sandwiched graphene/GQD/graphene structure, the GQD array produces a multiple quantum well-like energy band structure between the graphene layers as shown in in Figure 1 in the main text, where the injected carriers tunnel between the vibrational energy levels of the GQDs.

Supplementary Note 4, Calculation of Fermi level shift of graphene induced by the change of gate voltage
Considering the gate effect from graphene, it is possible to estimate the relative change of the Fermi level (ΔEF) with respect to the change of gate voltage (ΔVg) using the following expression, where ħ is the Plank constant, vF = 1×10 6 m s -1 is the Fermi velocity and α = 7×10 10 cm -2 V -1 is the gate capacitance in electron charge. 23 The calculated spacing of the vibration energy levels was found ~135 cm -1 , which is consistent with the Raman scattering data of GQDs shown in Supplementary Figure 5 as well as the published report on lower energy out-of-plane vibrational mode energy splitting. 6 ∆ = sign(∆ )ћv F ( |∆ |) 1/2 (1)

Supplementary Note 5, Graphene based tunneling junctions
The scanning tunneling microscopy (STM) analysis of two dimensional graphene layer forms a point junction with STM tip. But the density of states (DOS) of STM tip appears as a quasi-planar states surrounding the neutrality point as shown in Supplementary Figure 10a, which is due to the existence of a large amount of neighboring bulky atoms in the STM tip. 24 Similarly, the DOS of two parallel graphene layers forms a planar-like junction as shown in Supplementary Figure 10b. 24,25 A composite of graphene and GQD forms a T-shaped junction between the DOS of graphene and the vibrational energy levels of GQDs as shown in Supplementary Figure 10c. 25 The periodic zero dimensional vibrational density of states close to 2D density of states of graphene can sample out the carriers of different nature around the Dirac point, i.e. when the Fermi energy is tuned towards the Dirac point, the carriers close to the Fermi energy of graphene produce a resonant tunneling current 25 towards the vibrational energy levels of the same energy. Thus, we obtain oscillations in the tunnel current and at the vicinity of the Dirac point. The current is enhanced abruptly because of massless-like effective mass and high tunnel probability of the carriers.

Supplementary Figure 10
Different graphene based tunnel junctions. a, STM/graphene forms a quasi-planar junction surrounding the Dirac point. b, Two graphene layers in graphene/b-BN/graphene junction forms a planar-like junction. c. GQD on graphene forms a T-shaped junction with the vibrational energy levels of GQD.

Supplementary Note 6, Theoretical calculation
According to equation (1), the tunneling current is largely determined by the density of states of the GQDs when the Fermi energy is apart from the Dirac point. 26 In this situation, the carriers close to the Fermi energy of graphene produce the energy resonant tunneling to the neighboring vibrational energy level of the GQDs. 25 When the Fermi energy gets higher value than the energy of the vibrational level, the tunnel current reduces, which produces a negative differential resistance. The same process repeats when the Fermi energy reaches to the vicinity of next vibrational energy level. Therefore, multiple oscillations in the I-V curve can be generated.
Notably, as the Fermi energy approaches to the Dirac point, the effective mass of the carrier starts to reduce greatly and the carriers behave as a massless-like particle at the Dirac point. Simultaneously, when the Fermi level gradually matches with the vibrational level of the surface functional groups of the GQDs, the resonance tunneling current for the carriers close to the Dirac point can produce an exponentially increasing tunnel current drastically. This can be understood as follows. Firstly, with the effective mass approaching to zero, the tunneling coefficient in equation (2) shows it's giant value. Furthermore, the total energy of the carriers is mainly dominated by its kinetic energy (K.E.) due to the reduction of rest mass according to theory of relativity, which makes the mobility of the injected carriers extremely high. On the other hand, when the Fermi energy reaches to the Dirac point and is away from the vibrational levels of the surface functional groups of the GQDs, the tunnel current goes to zero due to zero density of states of the graphene from where the carriers were tunneling. Thus, at first, the tunnel current will be enhanced dramatically and reduced towards zero. Hence, we observed exponential enhancement and sharply fall of tunnel current as shown in Supplementary Figure 11. Interestingly, these massless-like highly energetic carriers can invert the population of multiple vibrational energy and stimulate the recombination of carriers to produce laser action. Moreover, this characteristics leads to a disequilibrium of the carrier concentrations in the higher vibrational levels of surface functional groups on the GQDs. Thus, when the bias is swept across the Dirac point, the carriers from the higher vibrational levels can produce resonance tunneling to the graphene layer. Therefore, an opposite direction flow of carriers will induce the negative current. The comparison between theoretical calculation and experimental measurement near the Dirac point is shown in Supplementary Figure 11. We can clearly see that the experimental result can be fitted well by the theoretical modeling.

Supplementary Figure 11
Comparison between theoretical calculation and experimentally observed exponentially enhanced and linearly fall of the tunneling current when the Fermi energy of the graphene approaches towards the Dirac point.

Supplementary Note 7, Stability and reproducibility of the device
The device was measured multiple times under ambient condition over wide span of time ~ 6 months. The noted device performance is shown in Supplementary Figure 12. It reveals an important fact that, the device is highly stable under the application of bias as high as 7.0 V. The stability of the device can be correlated to the following factors of our design. The GQD possesses a highly stable and consistent emission spectrum after continuous illumination from Xe lamp at 450 W cm -2 of 440 nm excitation for 1000 hours under ambient condition. Moreover, the GQD layer in our device is sandwiched by single layer graphene. Finally, both of the single layer graphene were protected by Si/SiO2 wafer and PMMA, which keeps the graphene layer isolated from the environment.

Supplementary Figure 12
Stability of graphene/GQD/graphene device. a, Emitted laser intensity after different measurement over time. b, Obtained laser intensity after application of bias voltage for multiple times.
In order to demonstrate the reproducibility of our device we have designed more than 50 devices. The success rate was found to be ~75%. The devices possess identical I-V characteristics. The obtained laser spectrum is also identical in nature with different number of laser peaks. The variation of lasing threshold voltage of the devices are plotted in Supplementary Figure 13a. The threshold pumping voltage for the devices lies between 6.5 ± 0.4 V. Thus, the estimated errors of the threshold value for a particular device is ± 0.4 V. The repetition of the number of peaks is plotted in Supplementary Figure 13b.

Supplementary Figure 13
Reproducibility of the device. a, The variation of the lasing threshold voltage of 50 different devices. b, The repetition of number of peaks in the devices.

Supplementary Note 8, GQD thickness dependence
The thickness dependence of the GQD layer in the device performance in the Supplementary Figure 14. We observed that the device works perfectly within the thickness ranging from 35 nm to 60 nm, which is approximately 6 to 10 layers of GQD. The GQDs thickness over 60 nm causes a gradual disappearance of the resonant behavior. It is found that the threshold voltage increase with increasing GQDs layer thickness, while the emitted light intensity decreases with increasing the GQDs layer thickness. This observation can be understood well based on the fact that when the GQDs layer thickness increases, a large voltage is required to produce the same electric field, which is used to shift the Fermi level of the graphene layer. On the other hand, increasing the GQDs layer thickness will decrease the tunneling probability, and the tunnel current is also reduced. Hence, the emitted photon intensity decreases.

Supplementary Figure 14
Dependence of laser threshold and emitted light intensity on the thickness of the GQD layers.

Supplementary Note 9, Carrier lifetime measurement
We have estimated the change of carrier lifetime of the device before and after the lasing threshold by optical excitation while applying different constant electrical signals that cause the resonance tunneling to the vibrational levels of the GQDs. We have used the constant optical pumping of 374 nm pulsed laser of pulse width 55 ps and frequency 40 MHz with an energy density of 5 µJ m -2 for optical excitation. At the same time, we have varied the bias voltage around the Dirac point to achieve the resonance tunneling to the different vibrational energies of the GQDs closed to and apart from the Dirac point. In the simultaneous application of external bias and optical pulses, we measured the emission spectra and time resolved luminescence (TRL) spectra as shown in Supplementary Figure  15. The emission spectra show a drastic change due to the appearance of sharp peaks when the carrier possesses resonance tunneling near the Dirac point, and the obtained TRL spectrum shows a faster carrier decay time. This can be understood as follow. The obtained longer lifetime at ~ 572 nm is due to the spontaneous emission of the carriers in the GQDs. On the other hand, when the bias voltage is tuned to derive the Fermi energy of graphene closed to the vibrational energy levels near the Dirac point, the resonance tunneling will occur. Because of the massive injection of massless carriers, the carrier distribution at the vibrational levels of the GQDs is changed and population inversion is obtained. As a result, the distribution of the carriers generated by the optical pumping is predetermined by the applied bias, and the measured faster lifetime reflects the laser action driven by the external bias. Figure 15 a, and b, The dependence of emission spectra and lifetime spectra on external bias under a constant optical pumping of 374 nm pulsed laser of pulse width 55 ps and frequency 40 MHz with an energy density of 5 µJ m -2 , respectively.

Supplementary Note 10, Role of the -OH functional group in the device performance
The low energy out of plane vibrational energy levels of -OH functional group attached with the aromatic network of the GQDs as shown in the Raman and XPS analysis in Section III produces several energy states in the quantum confined energy levels, which causes quantum resonant tunneling of charge carriers as well as causes the laser action. To further confirm this effect, we have designed a reduced-GQD (rGQD), where hydroxyl and carboxyl functional groups were eliminated. The rGQDs were used to design the graphene/rGQD/graphene device. Interestingly, a pure diode like behavior in the I-V characteristics was observed. The obtained I-V curve is shown in Supplementary Figure  15a. The XPS study of the rGQD is provided in Supplementary Figure 15b, which shows the presence of a negligible fraction of the hydroxyl and carboxyl functional groups (C-C : 87.49%, C-O : 3.2%, C=O : 2.4%, O-C=O : 0.78% and C-N : 6.13%.). The absence of -OH functional group results absence of the vibrational energy states in between the quantum confined energy levels of the rGQD. Thus, the observed nature of I-V differs from the oscillatory I-V curve as observed in the device using as-derived GQDs. This result is also consistent with the previous report of graphene and GQD based sandwiched photodetector. 27,28 Supplementary Figure 16 Device using reduced-GQD (rGQD) as the active material. a, The pure diode like I-V curve. b, The XPS spectrum of the rGQD materials.

Supplementary Note 12, Effect of graphene quality
The quality of the graphene layer has a great effect in the electronic property of the graphene. Thus, it is expected that the graphene layer with large defect levels has a great influence in our device. To investigate the effect of defects in the present device, we have used an in-situ defective graphene layer, which was grown at the methane flow rate of 13.50 SCCM keeping all the other parameters same. The I-V characteristics of the device is shown in Supplementary Figure 18a. The Raman spectrum of the graphene layer is shown in Supplementary Figure 18b.The device possesses an oscillatory I-V curve. The oscillation in the I-V curve is due to the quantum resonant tunneling of the carriers. Interestingly, the sharp pronounced peak in the I-V curve is not observed in the I-V characteristics of the device, due to the defect induced change in the electronic property of the graphene, which blurs the characteristics of the Dirac point. 29

Supplementary Figure 18
Effect of defects in graphene layer. a, The I-V curve shows quantum oscillation. b, The Raman spectrum of the defective graphene layer.