Dionne

Presentation

This model provides the SEEY \(\delta\). All the terms in its expression have a physical meaning. In its original version [Dio73, Dio75, LD57], it does not take the incidence angle of PEs into account. For a 3D version, see Dionne 3D.

Input files

This model should preferably be fitted to SEEY data, although it can also be fitted to TEEY data.

	Emission Yield	Emission energy distribution	Emission angle distribution
“True” secondaries	✅	❌	❌
Elastically backscattered	❌	❌	❌
Inelastically backscattered	❌	❌	❌
Total	✅	❌	❌

Definitions

The SEEY is given by:

\[\delta = G \cdot T \cdot S\]

Where \(G\) is the mean number of SEs generated by a PE of energy \(E\). \(T\) is their probability of reaching the surface. \(S\) is their probability of crossing the surface.

Range

\(G\) and \(T\) depend on the range, denoted \(R\), which is the depth reached by the PE in the material. We assume that the PE loses its energy following a power law. This is called the power law or Thomson-Whiddington model [Whi14].

\[R = \frac{E^n}{A\cdot n}\]

where \(A\) and \(n\) are obtained by fitting.

Note

This is currently the only energy loss model implemented. However, it has been shown that it was not suitable at low energies. Continuous Slowing-Down Approximation (CSDA) [You56] may be better suited:

\[\frac{\mathrm{d}E}{\mathrm{d}x} = - E / R\]

CSDA may also be inaccurate at low-energies, were the range is almost constant. See Refs. [IPBP17a, IPBP17b] for an alternative model.

Generation term

This is the probability for an incident electron with an energy \(E\) to generate a secondary electron.

\[G = \frac{1}{R}\frac{E}{\xi}\]

\(\xi\) is the energy required to excite a secondary electron in the material. We set it to the work function of the material [Dio75] even if, in reality, \(\xi > W_f\). Note that, in reality, this parameter can be set to anything, as the product \(A\cdot\xi\) appears in the final expression and \(A\) is fitted.

Transport term

This is the probability that a generated secondary electron reaches the sample surface.

\[T = d\left(1-\mathrm{e}^{-R/d}\right)\]

where the diffusion length \(d\) is the typical distance between to SE-material interactions. It is determined by fitting.

Escape term

This is a constant obtained by fitting.

Other expression

In the original Dionne paper [Dio73], the SEEY expression is:

\[\delta = \frac{B}{\xi} \left( \frac{An}{\alpha} \right)^{1/n} \left( \alpha d \right)^{(1-n)/n} \left( \mathrm{e}^{-\alpha d} \right)\]

As this expression is not simplified and does not make appear physical parameters explicit, it is not used. Correspondency between the notations used here and in Dionne’s paper are listed below.

Quantity	Notation in EEmiLib	Notation in [Dio73]
Escape term	\(S\)	\(B\)
Diffusion length/attenuation	\(d\)	\(1/\alpha\)
Range	\(R\)	\(d\)

Model parameters

The parameters list is dynamically created here: Dionne API documentation.

To-do list

Todo

• Handle SEEY vs TEEY files.

• Set up tests.