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Modeling of a field emitter array

Assignment for BSc or MSc student 

Field emission is characterized by a discharge of electrons from a surface whenever an electric field is applied, [1]. Electrons have to overcome a surface energy barrier which is achieved by tunneling of electrons through the energy barrier that is altered with the application of an electric field. The emitted current is then an exponential function of the local electric field and the work-function among other factors, [2]. The geometry of the emitter is related to a field enhancement factor, which considers the normal component of the field strength near a nanostructured surface against the normal component of the field strength near a flat counter electrode, [3], [4]. Strong local field enhancements can be achieved by altering the emitter’s geometry,[3]–[5], which in turn may increase the current density of the emitted electrons.

Furthermore, considering an array of field emitters, a high surface concentration of emitter sites may induce a screening effect that negatively affects the field enhancement factor, [6]–[8]. In general, the density of the emitter sites affects the current density in two ways, either increasing (a high amount of sites gives more emitters) or decreasing (high density of sites induces a screening effect that decreases the magnitude of the local field). In summary, to optimize the field emitter, there are three key variables to consider when designing an emitter.

  • The chemical and physical composition of the emitter
  • The geometry of a single emitter
  • Morphology of an array of emitters


The assignment is to optimize a field emitter array towards a high current density by implementing point II and III in a mathematical model designed with COMSOL. A design of experiment approach may be taken in order to evaluate the different factors that could influence the modeling outcomes.

We offer an internship at the Mesoscale Chemical Systems (MCS) chair at the University of Twente. MCS exists of a multidisciplinary team concerning physicists, chemists, and biochemists alike. The link between the different disciplines is found in a large amount of work conducted at the micro- and nanoscale. Focal points in the research are:

  • The development of 3D nanostructures for solar to electricity to chemical conversion;
  • Microreactors as a means of chemical process intensification (sonochemistry, high pressure, electricity-driven);
  • Miniaturized analytical tools and MEMS-based sensors for a variety of application fields (forensics, health, environment, chemical process control);
  • Microfluidic systems for life science applications (e.g. drug delivery).

Moreover, MCS is a great place to get in contact with students from all levels of education as well as from different fields, and nationalities.


More information can be obtained from Dirk Jonker (


  1. W. P. Dyke and W. W. Dolan, “Field Emission,” Adv. Electron. Electron Phys., vol. 8, pp. 89–185, 1956.
  2. R. H. Fowler and L. Nordheim, “Electron Emission in Intense Electric Fields,” Proc. R. Soc. A Math. Phys. Eng. Sci., vol. 119, no. 781, pp. 173–181, 1928.
  3. A. N. Zartdinov and K. A. Nikiforov, “Studying electric field enhancement factor of the nanostructured emission surface,” J. Phys. Conf. Ser., vol. 741, no. 1, pp. 9–11, 2016.
  4. H. Qiu, R. P. Joshi, A. Neuber, and J. Dickens, “A model study of the role of workfunction variations in cold field emission from microstructures with inclusion of field enhancements,” Semicond. Sci. Technol., vol. 30, no. 10, 2015.
  5. M. Morassutto, R. M. Tiggelaar, M. A. Smithers, and J. G. E. Gardeniers, “Vertically aligned carbon nanotube field emitter arrays with Ohmic base contact to silicon by Fe-catalyzed chemical vapor deposition,” Mater. Today Commun., vol. 7, pp. 89–100, 2016.
  6. O. Gröning, O. M. Küttel, C. Emmenegger, P. Gröning, and L. Schlapbach, “Field emission properties of carbon nanotubes,” J. Vac. Sci. Technol. B Microelectron. Nanom. Struct., vol. 18, no. 2, p. 665, 2000.
  7. L. Nilsson et al., “Scanning field emission from patterned carbon nanotube films,” Appl. Phys. Lett., vol. 76, no. 15, pp. 2071–2073, 2000.
  8. S. Sridhar et al., “Field emission with ultralow turn on voltage from metal decorated carbon nanotubes,” ACS Nano, vol. 8, no. 8, pp. 7763–7770, 2014.