Geometric Effects in the Field Emission of Surfaces with Factional Dimension

  • (a) Fractal Conducting Polymer, obtained  of AFM measurements, result from the deposition of 1 layer.(a) Fractal Conducting Polymer, obtained of AFM measurements, result from the deposition of 1 layer.
  • (a) Fractal Conducting Polymer, obtained  of AFM measurements, result from the deposition of 1 layer.
  • (b) Normalized electronic current as a function of the local fractal dimension for the surface present in (a).

The study of effective cold sources of high intensity electron beam couplings is one of actual problems of modern vacuum micro and nanoelectronics. As far as it is known, the difficulties for determining significant absolute values for the field emission current are connected to extremely small values of the effective emission area, which is very small compared with the macroscopic area of a cathode substrate [1]. With the scale properties related to real surfaces, it is possible to simulate the enhancement of the effective area at low anode voltages. The fractal structure of the real surfaces allows to support the idea that the surface micro and nanostructure irregularities can be referred to the self-affine topology of fractal dimensions [2].
In this work, we theoretically analyze the role of the geometry (represented by the local roughness and local fractal dimension) of real fractal surfaces, resulting from the deposition of conducting polymers with the profiles obtained from AFM measurements, in the corresponding field emission properties. The growth of these surfaces outside the grains, was found to follow the Kardar-Parisi-Zhang model [3], that describes stochastic formation of an interface, and can be related to the growth of surface film. To compute the electronic current density, the formalism of field emission models, based on the methods proposed by Fowler-Nordheim, Good-Muller and Forbes [4,5] , which provides the framework to obtain a reasonable approximation for the elliptical functions, which are key elements of the Fowler-Nordheim theory. Our results suggest a defined relation between the local fractal dimension and the local current density in all surfaces used for our calculations (see Figs. (a),(b)). For larg values of local fractal dimensions, we encounter low electronic current intensity contributions. We believe that this result can offer a connection between a physical effect represented by the field-screening, that affects the local value of the field amplification factor [6], and the corresponding local fractal dimension.

[1] R. G. Forbes, J. Vac. Sci. Technol. B, 27 (2009) 1200.
[2] T. A. de Assis, F.

Borondo, R. M. Benito, R. F. S. Andrade, Phys.: Rev. B, 78 (2008) 235427.
[3] N. C. de Souza et al., Nanotechnology, 18 (2007) 75713.
[4] R. G. Forbes, Appl. Phys. Lett., 89 (2006) 113122.
[5] R. G. Forbes, J. H. B. Deane, Proc. R. Soc. Lond. A, 463 (2007) 2907.
[6] T. A. de Assis, F. Borondo, C. M. C. de Castilho, F. de B. Mota, R. M. Benito J. Phys. D: Appl. Phys. 42 (2009) 195303.

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This poster was presented on NanoBioView, 6-7 October 2010

T. Albuquerque1,2*, F. Borondo1, C. M. C. de Castilho3, R.F.S. Andrade3, J. G. V. Miranda3, F. de B. Mota3, J.C. Losada2, R. M. Benito2

1- Departamento de Química Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain.
2- Grupo de Sistemas Complejos, Departamento de Física y Mecánica, ETSI Agrónomos, Universidad Politécnica de Madrid, Ciudad Universitaria, 28040 Madrid, Spain.
3- Instituto de Física, Universidade Federal da Bahia, Campus Universitário da Federação, 40210--340, Salvador, BA, Brazil.

*corresponding author:


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