Ion Range Benchmark

When ions strike the surface of a solid material at extremely high energy, they may penetrate a significant distance into the target material or even pass through it. The exchange of energy between the incident ions and atoms within the target material forms the basis of a class of interactions known broadly as Single Event Effects (SEEs).

In harsh radiation environments, SEEs can cause a variety of undesirable phenomena in sensitive electronic equipment, ranging from soft errors such as bit flips to hard/permanent problems such as single event latchup or burnout. For this reason, understanding of SEEs is vital when designing electronic devices for harsh radiation environments such as outer space.

This example demonstrates an approach to modeling the interaction of energetic ions with a target material using dedicated features in the Charged Particle Tracing interface. These features are used to compute the average distance traversed by protons in silicon, which is then compared to empirical data over a range of initial energy values.

Model Definition

The Charged Particle Tracing interface includes dedicated nodes for modeling the interaction of ions with solid materials. The node accounts for the energy loss and scattering of incident ions in the solid material by supporting dedicated subnodes for the following types of interactions:

•

The subnode treats the interaction between incident ions and electrons in the target material as a continuous force that acts opposite the direction of the particle’s motion.

•

The subnode treats the interaction between incident ions and nuclei in the target material as a discrete force that both slows the ion and deflects it by a random angle with a certain probability.

The validity of this approach is confirmed by this simple benchmark model. Protons are released into a block of silicon with a specified initial energy. They are then subjected to the deterministic ionization losses and stochastic nuclear interactions until their average velocity becomes negligibly small. By using an to compute the path length of each ion in the target, the average range of the ions is computed. This average range is then compared to the tabulated range under the Continuous Slowing Down Approximation (CSDA range) as given by Ref. 1. Under the CSDA, the ions are assumed to decelerate so that rate of energy loss is the same at every point along the ion’s trajectory:

where Ei and Ef are the initial and final energy of the ion, respectively, and S(E) is the total stopping power as a function of the ion energy.

An alternative means of reporting the ion range is the projected range, which indicates the approximate penetration depth into the target material. The projected range is computed by first projecting the ion velocity onto the initial direction of propagation.

Results and Discussion

The particle trajectories are computed for initial energy values ranging from 1 keV to 100 MeV. In general, as the energy increases, the particles move in more linear trajectories as their deceleration is dominated by ionization loss. At lower initial energy values, the ion trajectories are dominated by nuclear interactions and the ions tend to move in random directions. A typical plot of the ion trajectories is shown in Figure 1.

The average ion range is reported in Figure 2 and compared to published values from Ref. 1. Both the CSDA range and the projected range are shown. As the initial ion energy increases, the agreement between the CSDA range and computed range improves because the decrease in ion energy is dominated by ionization losses, which cause the ions to decelerate continuously over time. The agreement between the CSDA range and the projected range improves as well because the ionization losses do not cause any change in the direction of ion propagation.

At lower initial energy, the CSDA range and projected range differ significantly because the ion trajectories are dominated by nuclear stopping, which causes their energy to change discontinuously and also deflects them from their initial direction of propagation. The computed path lengths then show closer agreement to the projected range than the CSDA range.

Figure 1: Trajectories of 0.1 MeV protons in silicon. The changes in direction are due to collisions with target nuclei. The continuous decrease in energy is from ionization loss.

Figure 2: Comparison of the average path length of the computed ion trajectories to the published values of the ion range. Both the CSDA range and projected range are reported.

Reference

1. NIST Stopping-Power and Range Tables for Electrons, Protons, and Helium Ions, http://www.nist.gov/pml/data/star/index.cfm

Particle_Tracing_Module/Charged_Particle_Tracing/ion_range_benchmark

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Load the model’s parameters.

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file ion_range_benchmark_parameters.txt.

Definitions

Load data for the CSDA range of protons in silicon.

Interpolation 1 (int1)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Click

Browse to the model’s Application Libraries folder and double-click the file ion_range_benchmark_ranges.txt.

In the text field, type 1.

Click

Find the subsection. In the table, enter the following settings:


Function name	Position in file
CSDA	1

Locate the section. In the table, enter the following settings:


Argument	Unit
Column 1	MeV

In the table, enter the following settings:


Function	Unit
CSDA	g/cm^2

Load data for the projected range of protons in silicon.

Interpolation 2 (int2)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Click

Browse to the model’s Application Libraries folder and double-click the file ion_range_benchmark_ranges.txt.

In the text field, type 1.

Find the subsection. In the table, enter the following settings:


Function name	Position in file
Proj	2

Click

Locate the section. In the table, enter the following settings:


Argument	Unit
Column 1	MeV

In the table, enter the following settings:


Function	Unit
Proj	g/cm^2

Create a block of silicon of length L centered at the origin. The value of L will be varied as a function of the particles’ initial energy E0 -- see the Parameters list.

Geometry 1

Block 1 (blk1)

In the toolbar, click

In the window for , locate the section.

In the text field, type L.

Locate the section. From the list, choose .

Click

At the maximum simulated energy of 100 MeV, the proton velocity is comparable in magnitude to the speed of light, so select the option.

Charged Particle Tracing (cpt)

In the window, under click .

In the window for , locate the section.

Select the check box.

Particle-Matter Interactions 1

In the toolbar, click

and choose .

Select Domain 1 only.

Ionization Loss 1

In the toolbar, click

and choose .

Particle-Matter Interactions 1

In the window, click .

Nuclear Stopping 1

In the toolbar, click

and choose .

Enter the particles’ rest mass and charge number using the variables defined in the model parameters.

Particle Properties 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Create a release of 1001 particles of initial energy E0 directed in the positive x direction. The particles will be released at x = −L/4 in order to observe backscattered ions at low initial energies.

Release from Grid 1

In the toolbar, click