Supplemental Material

Graphene Field Emission Devices

S. Kumar*

Centre for Nanoscience and Engineering, Indian Institute of Science, Bengaluru, India

G. S. Duesberg

Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN) and School of Chemistry, Trinity College Dublin, D2, Ireland

R. Pratap

Centre for Nanoscience and Engineering and Department of Mechanical Engineering, Indian Institute of Science, Bengaluru, India

S. Raghavan

Centre for Nanoscience and Engineering, Indian Institute of Science, Bengaluru, India

*E-mail:

1. Process Details

A. Chemical vapour deposition (CVD) growth and transfer of graphene.

FIG S1. (a) Typical Raman spectra of CVD graphene transferred to SiO2substrates. The position of D, G and 2D peaks are marked. (b) Scanning electron microscope (SEM) image of graphene lying on copper foils. Bilayer graphene is seen as few faint islands. The white dots are Cu nanoparticles. The scale bar is 2μm.

The copper foils (Sigma Aldrich, 25μm thick) were kept in an evacuated quartz tube and heated to 1000°C under 100sccm flow of hydrogen and a pressure of 650Torr. Under the same conditions, the foils were annealed for 15min and the tube was evacuated at the end of this period. A mixture of 35sccm methane and 2sccm of hydrogen was then flown for 4min at same pumping settings. The methane flow was then stopped and the tube was allowed to cool down under 100sccm flow of hydrogen. The foil with graphene on it was coated with a thin layer of poly-(methyl-methacrylate) (PMMA) and put in an etchant (0.25M FeCl3) solution to remove copper. After the etch, graphene supported by PMMA was dredged on top of desired substrate. The substrate was then allowed to dry at room temperature and PMMA was dissolved in acetone bath.

Representative Raman spectra of the CVD graphene transferred onto SiO2 substrates is shown in Fig. S1(a), with D (~1350cm-1), G (~1585cm-1) and 2D (~2680cm-1) peaks as indicated. The ratio of 2D to G peaks shows that graphene is primarily monolayered. The small D peak can appear due to impurities from the transfer process. SEM image in Fig. S1(b) shows that some bilayered islands of graphene are also present, which can be seen faintly in the image.

B. Fabrication details for device arrays.

All the e-beam lithography (EBL) steps were performed on Raith E-line system. PMMA (A4, 950K, spin-coated at 3000rpm) exposure dose was 180μCcm-2 and developer used was MIBK:IPA in 1:3 ratio for 45s. Sputtering of metals was done in a Tecport Optics sputtering unit. Reactive ion etching (RIE) was done in Oxford Instruments PlasmaLab 80 system.

FIG S2. Steps in fabrication process of GFEDs. The numbers shown correspond to steps listed below. Note that diagrams shown for steps 1 and 2' depict side view of the sample, rest of steps have top view.

The detailed process steps are as follows (the steps are also shown in Fig. S2).

1. A p-doped Si wafer was used as the substrate. These wafers were wet oxidized to produce a layer of 300nm of silica.

2. A thin coating of SiC (30nm) was deposited on these wafers using plasma enhanced CVD (PECVD) in Oxford Instrument PlasmaLab 100 system. SiC layer is used in later stages as mask for etching underlying SiO2 with HF. A thin layer of PECVD Si3N4 was also tested, but it could not withstand HF etch.

3. Alignment marks (Cr 10nm then Au 60nm) were deposited on this layer using EBL.

4. Rectangular openings (2μm wide, 300μm long) were now exposed in PMMA using EBL.

5. SiC layer was etched through these openings in SF6 and O2 plasma (18sccm of SF6, 9sccm of O2 flows, 100W of radio-frequency(RF) and 1000 W of inductively coupled plasma(ICP) power, chamber pressure of 2Torr). Cool grease is needed between the substrate and table to allow PMMA survive the plasma. A 10s exposure is sufficient to etch SiC. PMMA mask was then removed with acetone.

6. Graphene was transferred from Cu by using a PMMA support.

7. PMMA was spin-coated on the substrate and openings for etch mask for graphene were made in it with EBL. Cu (~30nm) was evaporated and PMMA was lifted off in acetone. These patterned were aligned to overlie on rectangular openings in SiC layer.

8. Graphene was etched in O2 plasma. (20sccm O2 flow, 3Torr chamber pressure, 60W RF power for 50s). Cu mask was removed now by dipping the substrate in ammonium persulphate solution for a few minutes.

9. Another EBL step was used to deposit contact pads (Cr 10nm, then Au 60nm) on the graphene ribbons obtained in last step. A bilayer stack of EL-9 and PMMA (A4, 950K) was used for this.

10. Nano-gaps opening were exposed in another layer of PMMA (spin-coated at 6000rpm) using EBL. Vigorous shaking was generally effective in clearing the polymer in the nano-gaps.

11. Again, O2 plasma (same conditions as step 8, 35s duration) was used to transfer these nano-gaps to graphene. PMMA was then removed in acetone.

12. Finally, the substrate was put in HF to etch SiO2 exposed in SiC openings. After the etch was complete (1-3min at 70nmmin-1 etch rate), the substrate was dried in a critical point dryer (Tousimis Autosamdri-815B).

2. Modified Fowler-Nordheim (FN) equation for sheet emitter like graphene

The FN equation:

I = Aφ-1F2exp(-Bφ3/2/F) = Aφ-1(βV/d)2exp(-Bdφ3/2/βV) (S1)

have been derived for point emitters (symbols have same meaning as main text). Recently, Qin et al.1 have derived a modified FN equation for sheet emitters; the end result being:2

I ~ F3/2exp(-Bφk3/2/F) (S2)

for high fields, and

I ~ F3exp(-Bφk3/2/(κF2)) (S3)

for low fields. Here φk is 4.7eV and κ is another constant and other terms are as defined in main text. The fit of I-F data to both FN and modified FN (Equation S2) are good, and resulting β values differ by ~ 10% in all cases (Fig. S3), which is smaller than the variation in β values between the devices. Therefore, we have used FN equation for calculations, as is the case in wider literature.

FIG S3. (a) I-F characteristic of two separate GFEDs, L1 and L2. (b) modified FN plot using equation (S2) for data shown in (a). The slopes of line fits were used for determining field enhancement factors β. The field enhancement factors β are smaller than those obtained from fitting FN Equation S1. Compare with Fig. 2 in main text.

1X.-Z. Qin, W.-L. Wang,N.-S. Xu, Z.-B. Li,R. G. Forbes, Proc. R. Soc. A467, 1029 (2011).

2 Z. Xiao, J. She, S. Deng, Z. Tang, Z. Li, J. Lu, and N. Xu, ACS Nano 4, 6332 (2010).

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