Supplementary Figure S1. AFM image and height profile of GO. (a) AFM image

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1 Supplementary Figure S1. AFM image and height profile of GO. (a) AFM image and (b) height profile of GO obtained by spin-coating on silicon wafer, showing a typical thickness of ~1 nm. 1

2 Supplementary Figure S2. Raman spectra of GO and MPG films on silicon wafer. The Raman signals in the spectra show the broad D band and G band, appearing at 1344 and 1603 cm -1 for GO film and at 1351 and 1594 cm -1 for MPG film, respectively. 2

3 Supplementary Figure S3. XRD patterns of GO and MPG films on silicon wafer. The GO film shows a shape diffraction peak (002) at 9.92, corresponding to a d-spacing of 8.92 Å. After methane plasma reduction, the diffraction peak (002) of MPG film appears at 26.60, with a interlayer d-spacing of 3.36 Å. This indicates the efficient reduction of GO and formation of continous graphene film. The strong peak at around 33 is characteristic of Si(201) from the silicon wafer (JCPDS No ). 3

4 Supplementary Figure S4. XPS spectra of GO and MPG films on silicon wafer. (a) XPS profiles of GO and MPG films recorded in the range of ev. (b) high-resolution C1s XPS profiles of GO and MPG films. It is clearly revealed that, methane plamsa reduction of the GO film leads to a remarkable decreace in the atomic content of oxygen and increase in the content of carbon, as shown in Figure S4a. The C/O ratio increases from 2.3 for GO film to 9.2 for MPG film. Addtionally, the C1s XPS spectrum of GO film suggests a considerable content of oxygen-containing groups, such as sp 2 /sp 3 C (C-C, ev), C in C O bonds (286.4 ev), carbonyl C (287.2 ev), and carboxylate carbon (O=C-O, ev). After methane plasma treatment, most of oxygen-containing groups have been removed for MPG film (Figure S4b). 4

5 Supplementary Figure S5. SEM images of MPG film. SEM images show large-area, continuous and uniform morphology of the produced graphene film. 5

6 Supplementary Figure S6. Electrical conductivity of MPG films as a function of film thickness. With increasing the film thickness from 5 to 100 nm, the electrical conductivity of MPG film decreases from 405 to 120 S cm -1. 6

7 Supplementary Figure S7. AFM image and height profile of MPG film on silicon wafer. (a) AFM image and (b) height profile of the produced MPG film with a thickness of about ~40 nm, revealing continous and uniform morpholgy of MPG film with sharp edge. 7

8 Supplementary Figure S8. AFM image and height profile of GO film on silicon wafter. (a) AFM image and (b) the height profile of GO film obtained by spin-coating GO on silicon wafer, showing a thickness of ~15 nm. 8

9 Supplementary Figure S9. Electrochemical characterization of GO-MSCs. Comparison of CV curves of GO-MSCs and MPG-MSCs with a thickness of 15 nm at (a) 10 V s -1 and (b) 100 V s -1 shows negligible capacitance of GO-MSCs. (c) CV curves of GO-MSCs at different scan rates. (d) Comparison of the discharge current vs. scan rate of GO-MSCs and MPG-MSCs. Inset is the discharge current versus scan rate of GO-MSCs. 9

10 Supplementary Figure S10. The electrochemical characterization of MPG-MSCs. The CV curves of MPG-SSCs (MPG film with a thickness of 2~3 nm) obtained at (a) 1 V s -1, (b) 10 V s -1, (c) 100 V s -1, (d) 1000 V s -1, (e) 2000 V s -1, and (f) 3200 V s -1, indicative of ultrahigh rate capability for thinner MPG-MSCs. 10

11 Supplementary Figure S11. Cycling stability of MPG-MSCs on silicon wafer. (a) CVs obtained at the 1st, 10000th, 50000th and th measured at 50 V s -1, showing similar curve shape before and after cycling. (b) The capacitance retention versus cycle number. The capacitance retention is about 98.3% after cycles, revealing excellent cycling stability at ultrahigh charge and discharge rate of 50 V s

12 Supplementary Figure S12. Self-discharge profile of MPG-MSCs. Self-discharge profile of MPG-MSCs in H 2 SO 4 /PVA gel electrolyte obtained immediately after charging to 1.0 V. 12

13 Supplementary Figure S13. Fabrication illustration and stack geometry of MPG-SSCs. The fabrication process flow includes: (a) the oxygen plasma surface treatment of silicon wafer, spin coating of GO solution on surface-modified silicon, (b) CH 4 plasma reduction, (c) drop casting and solidification of the solid-state gel electrolyte on the surface of MPG film, (d) assembly two separated MPG films with gel electrolyte into one sandwiched device in (e). (f) The stack geometry of MPG-SSCs, revealing that the ions have to cross over from the electrode to the other electrode with a large diffusion distance via separator and electrode during charging and discharging process. Normally, graphene nanosheets are oriented parallel to the current collectors, and the transport direction of ions, driven by electric field (perpendicular to the current collectors in this case), is perpendicular to graphene layers. In this way, the ions are unable to overcome the perfect graphene sheets into the interior surface of graphene film. Alternatively, they have to transport via the defective sites and edge regions of graphene sheets to penetrate into the interior surface of the film electrode 28. Thereby, the electrochemical surface area cannot be fully utilized for charge storage in comparison with the in-plane MPG-MSCs, in particular, at high rate, due to the longer ion diffusion pathway of MPG-SSCs

14 Supplementary Figure S14. The electrochemical characterization of all solid-state MPG-SSCs. The CV curves of MPG-SSCs (MPG film with thickness of 15 nm) obtained at (a) 1 V s -1, (b) 10 V s -1, and (c) 100 V s -1. (d) The discharge current versus scan rate of MPG-SSCs. 14

15 Supplementary Figure S15. AFM image and height profile of TG film on silicon wafer. (a) AFM image and (b) height profile of TG film obtained by spin-coating GO on silicon wafer followed by thermal reducation at 700 C for 20 s, showing a thickness of about ~15 nm. 15

16 Supplementary Figure S16. The electrochemical characterization of all solid-state TG-MSCs. The CV curves of TG-MSCs (TG film with a thickness of 15 nm) obtained at (a) 1 V s -1, (b) 10 V s -1, (c) 100 V s -1, (d) 200 V s -1 and (e) 400 V s -1. (f) The discharge current versus scan rate of TG-MSCs. 16

17 Supplementary Figure S17. Cycling stability of flexible MPG-MSCs-PET. (a) CVs obtained at the 1st, 10000th, 50000th and th measured at 200 V s -1, showing almost similar curve shape. (b) The capacitance retention versus cycle number. The capacitance is retained as high as 99.1% after cycles, revealing excellent cycling stability at ultrahigh charge/discharge rate of 200 V s

18 Supplementary Figure S18. Evaluation of the performance of MPG-MSCs with different film thickness. (a) Evaluation of the stack capacitance versus the thickness of MPG film (with a thickness up to 100 nm). (b) Evaluation of the energy density versus the thickness of MPG film. The electrochemical data of MPG-MSCs with different film thickness was obtained at 10 mv s

19 Supplementary Figure S19. Electrochemcial performance of MPG-MSCs with organic gel electrolyte. (a) Cyclic voltammetry obtained at different scan rates of 1, 10 and 50 V s -1 with an operation volatage of 2.5 V. (b) The area capacitance and stack capacitance as a function of the scan rate. It is worthly noted that the energy denisty of microdevice can be further enhanced through the extension of voltage. The organic gel electrolyte was composed of tetraethyl ammonium tetrafluoroborate/polyacrylamide/propylene carbonate (TEABF 4 /PAN/PC). Typically, the polymer gel electrolytes were prepred according to the previous report 31. Typically, PAN (37 mg) and TEABF 4 (41 mg) were mixed in PC (0.03 mg) at 110 C for 1 h protected in nitrogen gas, and then drop-casted the above gel electrolyte (10 μl) on the patterned electrodes of MPG-MSCs, followed by evaporation of PC in a vacuum oven at 120 C for overnight. 19

Supplementary Figure S20. An all solid-state in-plane MPG-MSC pack with two devices connected in parallel fashion. (a) Schematic illustration of one pack of two parrallel MPG-MSCs.

20 Supplementary Figure S20. An all solid-state in-plane MPG-MSC pack with two devices connected in parallel fashion. (a) Schematic illustration of one pack of two parrallel MPG-MSCs. (b-d) Cyclic voltammetry obtained at (b) 1 V s -1, (c) 10 V s -1, and (d) 100 V s -1 shows that the capacitive current increases by a fator of two under the same operation voltage. 20

Supplementary Figure S21. An all solid-state in-plane MPG-MSC pack with two devices connected in series fashion. (a) Schematic illustration of one pack of two series MPG-MSCs.

21 Supplementary Figure S21. An all solid-state in-plane MPG-MSC pack with two devices connected in series fashion. (a) Schematic illustration of one pack of two series MPG-MSCs. (b-d) Cyclic voltammetry obtained at (b) 1 V s -1, (c) 10 V s -1, and (d) 100 V s -1 shows that the voltage increase from 1 V for single device to 2 V for the devices in series under the same operation current. 21

Supplementary Figure S22. The morphology and capacitance contribution of Au layer. (a) Low- and (b) high-magnification SEM images of the deposited Au layer on MPG film on silicon wafer.

22 Supplementary Figure S22. The morphology and capacitance contribution of Au layer. (a) Low- and (b) high-magnification SEM images of the deposited Au layer on MPG film on silicon wafer. (c) The contact angle measurement of MPG film using the drop shape method (water droplet). (d) The area capacitance of Au-based micro-supercapacitors measured from 0.01 to 1000 V s

23 Supplementary Table S1. Comparison of the electrochemical performance of MPG-MSCs with the state-of-the-art micro-supercapacitors. MPG-MSCs exhibit exceptional electrochemical energy storage in term of scan rate, energy density, power density and time constant. Micro-Supercapacitors (MSCs) MPG-MSCs MPG-SSCs TG-MSCs Onion-like carbon MSCs Laser-written rgo-mscs Electrolyte H 2 SO 4 /PVA gel H 2 SO 4 /PVA gel H 2 SO 4 /PVA gel 1M TEABF 4 in PC graphene oxide/h 2 O Operating voltage (V) Scan rate (V s -1 ) rgo/cnt-mscs 3M KCl Energy density (mwh cm -3 ) 2.5 at 0.01 V s -1 Power density (W cm -3 ) Time constant (ms) 495 at 1000 V s at 0.01 V s at 200 V s at 0.01 V s at 400 V s at 1 V s -1 PC: propylene carbonate; rgo: reduced graphene oxide; CNT: carbon nanotube 250 at Ref This work This work This work 200 V s a 9.4 a at 1 V s at 50 V s a These values were calculated based on the active thickness of the electrodes. 23

24 Supplementary Note 1 Self-discharge profile of MPG-MSCs. Generally, one can use the self-discharge time of supercapacitors measured from V max to 1/2V max to evaluate the self-discharge performance 12, 32. Our MPG-MSCs show the self-discharge time of ~3.3 h from 1.0 to 0.5 V, suggesting the stored charge can be kept for a significant time in such devices. Given that the self-discharge of supercapacitors strongly depend on the nature of device system, such as the electrode materials, the type and purity of electrolyte, and the measured temperature The voltage loss in a charged state may be attributed to (i) the charge redistribution throughout the highly exposed surface area of thin graphene electrodes; (ii) the slow Faradic reaction of the residual oxygen-containing groups may cause the electron-transfer reactions and remove charges from the electrode surface; (iii) oxygen reduction to hydrogen peroxide is probably a main cause of self-discharge because we used aqueous gel electrolyte without any package 36,37. Therefore, the actual charge retention time of MPG-MSCs should be longer than the present results. The in-depth studies of self-discharge mechanism of graphene-based micro-supercapacitors will be essential to better control the self-discharge process and promote the practical applications of the microdevices in the future. 24

25 Supplementary Note 2 The morphology and capacitance contribution of Au layer. The use of gold layer as current collector is a common strategy to build up micro-supercapacitors 10. The morphology of Au layer is strongly dependent on the sputtering condition, such as the evaporation rate of Au, the chamber vacuum and the wetting properties of the used substrates. In our case, SEM images (Supplementary Fig. S22a,b) of Au layer on MPG film on silicon wafer show that the Au layer consists of uniformly-distributed interconnected compacted nanoparticles. This can be attributed to the MPG film that contains residual oxygen-containing groups on the surface. The contact angle of water droplet on MPG film is 62.8±1.1 o, while that on HOPG surface is 81.1±1.8 o, indicative of the relatively hydrophilic property of MPG film (Supplementary Fig. S22c). Therefore, the capacitance contribution of Au (~30 nm) to the device (without graphene electrode) is very lower than that of graphene electrode, as shown in Supplementary Figure S22d. For instance, the capacitance from Au layer is calculated to be ~6.1 μf cm -2 at 0.01 V s -1 and 0.4 μf cm -2 at 1000 V s -1, which is much lower than those of device with graphene electrode (~80.7 μf cm -2 at 0.01 V s -1 and ~4.5 μf cm -2 at 1000 V s -1 ). The contribution of gold layer to the capacitance of the whole device has been deducted in the calculation in this work. 25

26 Supplementary References 31. Ishikawa, M., Ihara, M., Morita, M., & Matsuda, Y., Electric Double-Layer Capacitors with New Gel Electrolytes. Electrochim. Acta 40, (1995). 32. Stoller, M.D. & Ruoff, R.S., Best practice methods for determining an electrode material's performance for ultracapacitors. Energy Environ. Sci. 3, (2010). 33. Ricketts, B.W. & Ton-That, C., Self-discharge of carbon-based supercapacitors with organic electrolytes. J. Power Sources 89, (2000). 34. Zhang, Q., Rong, J.P., Ma, D.S., & Wei, B.Q., The governing self-discharge processes in activated carbon fabric-based supercapacitors with different organic electrolytes. Energy Environ. Sci. 4, (2011). 35. Kowal, J. et al., Detailed analysis of the self-discharge of supercapacitors. J. Power Sources 196, (2011). 36. Black, J. & Andreas, H.A., Prediction of the self-discharge profile of an electrochemical capacitor electrode in the presence of both activation-controlled discharge and charge redistribution. J. Power Sources 195, (2010). 37. Oickle, A.M. & Andreas, H.A., Examination of Water Electrolysis and Oxygen Reduction As Self-Discharge Mechanisms for Carbon-Based, Aqueous Electrolyte Electrochemical Capacitors. J. Phys. Chem. C 115, (2011). 26

Supplementary Figure 1 XPS, Raman and TGA characterizations on GO and freeze-dried HGF and GF. (a) XPS survey spectra and (b) C1s spectra.

Supplementary Figure 1 XPS, Raman and TGA characterizations on GO and freeze-dried HGF and GF. (a) XPS survey spectra and (b) C1s spectra. (c) Raman spectra. (d) TGA curves. All results confirm efficient