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Materials Science on CD-ROM User Guide

Beam-Specimen Interactions

Version 2.1

Ian Jones, MATTER
Peter Goodhew, University of Liverpool

Assumed Pre-knowledge

Before starting this module, it is assumed that the student is familiar with the Poisson distribution, and understands the concept of Mean Free Path. However both of these terms are defined in the glossary.

Module Structure

This Module gives an introduction to the effect of interactions between high energy electrons and solid specimens. It has been designed to complement the other MATTER modules on Microscopy, especially those relating to SEM and TEM.

It includes an interactive simulation using Monte Carlo modelling methods.

Introduction

This section begins by examining the interactions that occur when electrons meet solid specimens. It reveals what secondary effects can be produced when electrons interact with solids.

The theory of statistical scattering is introduced and experimentation can be performed with a variable mean free path, to show the effect this has on the distribution of the scattering events.

Further investigation shows how Monte Carlo methods are used to synthesise these scattering events.

This leads to a sophisticated simulation program which by experimentation shows the relationships between the variables in the system (e.g. material of specimen, incident voltage, incident angle and thickness) and the effect on the trajectory of the beam as it travels within the specimen.

All parameters of the simulation are adjustable so their effect can be visualised.

Important parameters which can be deduced at least semi-quantitatively from the simulation, include beam penetration in solid specimens and backscattering efficiency in all conditions.

Bibliography

The student is referred to the following resources in this module:

Appendix A

The Poisson Distribution

The Poisson distribution is given by:

(1)

Statistical Error

Statistical error incurred in Monte Carlo Simulations is given by:

Statistical Error =

(2)

where n is the number of trials.

Appendix B

Monte Carlo Simulation - Understanding the Menu options

Element:

Use this menu option to specify the material of the specimen.

Voltage:

Choose from a wide range of incident voltages. 5 k eV Þ 300 k eV

Tilt:

Select the incident angle of the electron. 0° Þ 70° with respect to the specimen normal.

Thickness Dialog:

Values are truncated to 3dp, and this consequently gives a minimum thickness of 0.001 m m (or 1 nm). There is an upper limit of 1000 m m. Any higher value entered will be set to this maximum.

Xray - cut off:

A blue colour is used for electrons which have an energy below that of the Xray threshold. This value can be set low if this visual effect is not desired. Values lower than 0.1 keV are considered as off, as electrons with energies below this are not tracked.

The value of the threshold can be given either directly as a voltage, or it can be expressed as a percentage of the incident voltage being used at the time.

Use the same dialog to view the current value for the threshold, choose the Xray menu option, then the format to view it in. Click the cancel button on this dialog to discard changes.

Display:

Two different modelling methods are available.

• Plural method: Fast, 50 steps per whole line are calculated. This can make the path look jagged with very thin specimens.
• Single method: This methods uses more complicated approximations and at smaller intervals. i.e. >2000 steps per whole line. This has an obvious effect on speed. It is better suited to fast machines or thin specimens where many electrons leave the specimen before undergoing very many scattering events.

The mathematical models used are approximations. Many trials are necessary to reduce statistical scatter, because of the random nature of the simulation. Using the single scattering model with relatively few trials could produce less accurate results than if the plural scattering model was used with the larger number of trials which could be calculated in the same time.

See Appendix A for further information on statistical error incurred in the simulation.

• Show Primaries and Secondaries:

It is possible to view either primary electrons only, secondary electrons only or both, by checking the menu items as required.

• Clear display after each primary:

When this option is unchecked, electron trajectories are allowed to build up on the screen. After a short while the picture will accumulate, giving an impression of the volume of the specimen being interacted with.  If the box is checked, each trajectory is clearly visible in succession. Change the speed of the simulation or pause it to capture an individual trajectory. With a little luck it is possible to freeze some interesting occurrences.

• Pause/Resume, Speed and Reset:

Pause/Resume can be used to freeze the simulation between trajectory plots.

The speed of the simulation can be set to three levels. Choose a level which suits your computer and how quickly you want new trajectories to be calculated.  Resetting will clear all the graphs and you will lose all the data that has been accumulated.

Graphs:

The two graphs that are displayed are customisable.

The upper graph detects backscattered electrons and the lower represents any transmitted electrons.

By selecting the four graph options in this menu it is possible to select whether either of the graphs should detect primary electrons, secondary electrons or both.

Miscellaneous:

Clicking the left mouse button anywhere in the appropriate area of the screen will

pause/resume the simulation.

Clicking the right mouse button anywhere in the appropriate area will initiate termination.