Field Emission and Radial Distribution Function Studies of Fractal-like Amorphous Carbon Nanotips
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The short-range order of individual fractal-like amorphous carbon nanotips was investigated by means of energy-filtered electron diffraction in a transmission electron microscope (TEM). The nanostructures were grown in porous silicon substrates in situ within the TEM by the electron beam-induced deposition method. The structure factorS(k) and the reduced radial distribution functionG(r) were calculated. From these calculations a bond angle of 124° was obtained which suggests a distorted graphitic structure. Field emission was obtained from individual nanostructures using two micromanipulators with sub-nanometer positioning resolution. A theoretical three-stage model that accounts for the geometry of the nanostructures provides a value for the field enhancement factor close to the one obtained experimentally from the Fowler-Nordheim law.
KeywordsCarbon nanotips Graphite-like a-C EELS EFED Field emission
Nanotips made of carbon can have many different applications such as scanning microscope probes  and field emission (FE) sources . For instance, recently carbon nanofibers were used as the electron source in order to test and build an FE display device prototype where a new nanocrystalline silicon—polymer film—was used as the phosphor material . Carbon nanotubes, from single to film dispersed cases, have been extensively studied due to their tensile strength, electrical properties, chemical inertness, and high aspect ratio [4, 5, 6, 7, 8, 9, 10]. However, an advantage that amorphous carbon (a-C) nanotips have over carbon nanotubes is that when a-C nanotips are synthesized using the electron beam-induced deposition method with a transmission electron microscope (TEM-EBID) their growth process can be followed in real-time and the nanostructures can be grown at preferred positions by controlling the electron beam . Recently, FE studies were done on an individual one-dimensional a-C nanotip grown by the TEM-EBID method, where a field enhancement factor of the order of 10 was found . In this study, a field enhancement factor of the order of 103 was obtained for fractal-like a-C nanotips consisting of several branches, each branch similar in shape to the previously mentioned one-dimensional nanotips. A theoretical three-stage model that accounts for those findings is presented and discussed. Multistage models have been used for other types of nanostructures such as carbon nanotubes and tungsten oxide nanowires [7, 13, 14, 15]. In addition, we also present information of the short-range order of our nanostructures, using the radial distribution function (RDF) obtained by electron diffraction patterns. With this information average nearest-neighbor distances and their bond angle were obtained. The results are consistent with distorted graphitic-like structure that can account for the moderate conductivity of the tips observed in the FE results.
The nanostructures were grown in situ in a TEM by the TEM-EBID method  using porous silicon (PSi) substrates. Full details about the PSi preparation procedure can be found elsewhere . Pieces of the PSi films of the order of 2 mm2 were attached to copper TEM grids. TEM-EBID experiments were made in a JEOL JEM-100S TEM at 100 kV. Electron energy loss spectroscopy (EELS) measurements were made in a Carl Zeiss LEO-922 TEM equipped with an Omega filter. Energy-filtered electron diffraction studies were done in a Phillips CM-200 TEM at 200 kV using a Gatan imaging filter. The energy selecting window used to filter the electron diffraction pattern was 10 eV and was centered at the zero loss peak of the electron energy loss spectrum. The inverse space was calibrated using a polycrystalline aluminum standard sample.
FE studies were done in an FEI Strata 235 Dual Beam FIB (DB-FIB) with a vacuum better than 10−5 Torr. Two electrochemically etched tungsten tips were connected to two Kleindiek micromanipulators, each having a positioning resolution of 0.25 nm. One of the tungsten tips is landed on a platinum contact which ends at the base of the nanostructure and the other is positioned close to the outer branches of the nanostructure to collect the FE current. The platinum contact was carefully deposited by SEM-EBID method using only the electron source of the DB-FIB. FE experiments were controlled with a LabView program and the beam was blanked before collecting the FE currents. Inspection of the samples after the FE measurements did not show additional growth of nanotrees.
Results and Discussion
From this expression, a bond angle of 124° was obtained. This bond angle differs from a sp2 trigonally bonded carbon, which has a bond angle of 120°. This difference suggests that our nanostructures have a distorted graphitic structure which is consistent with our previous Raman and EELS results. From these findings it is expected that the a-C fractal nanotips will present good FE properties .
The expression for βi was derived by Huang et al. . The factor βs is a factor that accounts for the screening effect of adjacent tips [28, 29, 30], where s is interpreted here as the average distance between adjacent tips, L is the sum of the lengths of three stages, and a is a fitting parameter . Taking the common fitting parameter a equal to 2.3172 [28, 29], and measuring average values for li as 491 nm (i = 1), 146 nm (i = 2) and 74 nm (i = 3), average values of ri as 13.4, 5.6, and 2.1 nm and with s equal to 54.7 nm, we obtain (from Eqs. 7 and 8) a field enhancement factor, β, equal to 981. This result agrees well with the value found experimentally of 889.
In summary, the reduced RDF analysis on the fractal-like a-C nanotips grown by the TEM-EBID method shows first and second bond lengths at 1.49 and 2.65 Å. Those nearest-neighbors distances defined an average bond angle of 124° which deviates from a trigonallysp2bonded carbon (120°) indicating a distorted graphite-like structure, which explains the moderate conductivity of the tips observed in the FE results. The electron FE measurements of the individual fractal-like a-C nanorods showed a turn on field of 24 V/μm. A three-stage model that accounts for the geometry of the nanostructures described well the value of the enhancement factor obtained experimentally from the FN law, and hence suggests a possible explanation of our observations. Hence, our observations show that these nanostructures are promising to be used in FE applications. In particular, the growth mechanism of the nanotrees’ tips follows the path of maximum local field at the tips thus forming a nanostructure where the relationship between the density of tips and the local electric field intensity at the tips is optimized. It is worth to mention that for our calculations of the emission current densities we have used as the active emitting area the cross section of the total nanotree such that the values for the current density per branch’s tip are lowest bound values.
This study was supported by the following grants numbers and projects: NASA NNX08BA48A, NASA Space Grant NNG05GG78H, NSF 0701525, Fundamental Aeronautics Program and Subsonic Fixed Wing Project. The authors acknowledge the National Center for Electron Microscopy, Lawrence Berkeley Lab, which is supported by the U.S. Department of Energy under Contract #DE-AC02-05CH11231, and in particular to Dr. A. Minor for helping us with the FE experimental setup. F·S. kindly acknowledges Dr. D. J. H. Cockayne from Oxford University and D. Hull from NASA GRC for providing helpful information related to the electron diffraction analysis.
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