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Transmission Electron Microscopy

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References

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Author information

Authors and Affiliations

  1. Faculty of Applied Sciences, Delft University of Technology, Delft, Netherlands

    Pieter Kruit

Authors
  1. Pieter Kruit
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Corresponding author

Correspondence to Pieter Kruit .

Editor information

Editors and Affiliations

  1. University of Connecticut, Storrs, Connecticut, USA

    C. Barry Carter

  2. Ohio State University, Columbus, Ohio, USA

    David B. Williams

Appendix

Appendix

1.1.1 People

Walter Schottky was born in Zurich on 23 July 1886 and died in Pretzfeld, Germany, on 4 March 1976. He contributed to many technological inventions and discoveries, including the Schottky defect, Schottky barrier and Schottky diode.

1.1.2 Self-Assessment Questions

Q1.1:

Why is the total emission current not a good parameter to characterize a source?

Q1.2:

What is the difference between the virtual source size and the physical size of the emitting area of an electron source?

Q1.3:

Why can we assume that the angular current density in a microscope is uniform, while the spatial density in the virtual source is approximately Gaussian?

Q1.4:

Explain the difference between differential brightness, reduced brightness, and practical brightness.

Q1.5:

Compute the electron wavelength for acceleration voltage 1 kV, 30 kV, 100 kV, 300 kV.

Q1.6:

Use the interdependencies of the parameters in the equation for reduced brightness to show that the reduced brightness is not affected by:

  1. a.

    the choice of the magnification from source to probe

  2. b.

    the size of the beam-limiting aperture

  3. c.

    acceleration or deceleration (for ease of explanation assume the acceleration in the plane of a lens) from energy V 1 to V 2 .

Q1.7:

Why are there three different spatial coherence lengths defined?

Q1.8:

Derive the relation between current within a coherent area I coh and the reduced brightness.

Q1.9:

Explain how electrons are forced to leave the emitter in respectively a Schottky emitter and a cold field emitter.

Q1.10:

What is the relation between brightness and temperature in respectively a Schottky emitter and a field emitter?

Q1.11:

(Advanced) Use your favorite math program to perform a simulation that gives you practical brightness and the full-width-50 value of the energy spread of a thermionic electron source as a function of temperature.

Q1.12:

If a Schottky source in the electron microscope seems not to deliver the expected brightness, how can a Schottky plot show whether this is a result of a blunt tip or an increased work function or neither?

Q1.13:

Give two reasons why the energy spread of a beam from a Schottky source increases when more current is extracted from the tip.

Q1.14:

What limits the lifetime of a Schottky source if all goes well?

Q1.15:

Give at least three incidents that can end the life of a Schottky source prematurely.

Q1.16:

What is a Fowler–Nordheim plot and which information on a field emission source can be obtained from it?

Q1.17:

Why is the short-term current stability of a cold field emission source intrinsically less than that of a Schottky source?

Q1.18:

Why is the energy spread of a cold field emission source intrinsically smaller than that of a Schottky source?

Q1.19:

What is the difference between a FWHM and a FW50 of an electron probe, in definition, and in practice?

Q1.20:

What is the numerical difference between the FWHM, the FW50 of a probe and the 25–75 edge resolution for a Gaussian current density distribution in the probe?

Q1.21:

Compute the difference in total probe size after adding two equal distributions either linearly or by the two-power rule or by the four-power rule.

Q1.22:

Consider a lens system that images a Schottky electron source (effective d source = 30 nm, B r ,pract = 108 A/(m2. sr. V), FW50dE = 1 V) onto a sample at electron energy 80 kV. Assume aberration coefficients C s = 1 mm, C c = 2 mm. Calculate all contributions to the probe size for an aperture angle of 10 mrad and a source to probe magnification of M = 1/150. Also calculate the total probe size and the current in the probe.

Q1.23:

(Advanced) Use your favorite math program to calculate and plot all contributions to the probe size as a function of half angle α and determine the optimum angle. Use realistic estimates for all parameters.

Q1.24:

How does the current in a probe at the highest resolution setting in STEM depend on the aberrations of the microscope?

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Kruit, P. (2016). Electron Sources. In: Carter, C., Williams, D. (eds) Transmission Electron Microscopy. Springer, Cham. https://doi.org/10.1007/978-3-319-26651-0_1

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