Materials Science on CDROM User Guide
BeamSpecimen Interactions
Version 2.1
Ian Jones, MATTER
Peter Goodhew, University of Liverpool
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.
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.
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 semiquantitatively from the
simulation, include beam penetration in solid specimens and backscattering efficiency in
all conditions.
The student is referred to the following resources in this module:
Goodhew and Humphreys., Electron Microscopy and Analysis, 2nd edition.,
Taylor & Francis, 1998
Joy, David.C., Monte Carlo Modeling for Electron Microscopy and Microanalysis,
Oxford University Press, 1995
Egerton, R.F., Electron EnergyLoss Spectroscopy in the electron microscope,
Plenum, 1989
Williams, D.B. and Carter, C.B., Transmission Electron Microscopy : A textbook for
Material Science, Plenum, 1996
The Poisson distribution is given by:

(1) 
Statistical error incurred in Monte Carlo Simulations is given by:
Statistical Error = 
(2) 
where n is the number of trials.
Trials, n 
Statistical Error % 
100 
10.000 
500 
4.472 
1,000 
3.162 
2,000 
2.236 
5,000 
1.414 
10,000 
1.000 
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.
