Models

Chung and Everhart

Presentation

This is a model for emission energy distribution of SEs [CE74]. It does not take into account incidence angle of PEs.

Input files

You must provide an emission energy distribution at normal incidence. Currently, the fitting on several emission distribution files at different PE energies is not supported.

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

Definitions

Emission energy distribution is given by:

\[f(E_\mathrm{SE}) = \frac{E_\mathrm{SE}}{\left( E_\mathrm{SE} + W_f \right)^4}\]

\(W_f\) is the material work function in \(\mathrm{eV}\). In order to set it’s maximum to unity, we scale it by \(256W_f/27\).

Model parameters

The parameters list is dynamically created here: Chung and Everhart API documentation.

To-do list

Todo

• Allow fitting on several distribution files with different PE energy.

• Set up tests.

Dionne 3D

Presentation

What the model is for. References. Model.

Input files

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

Output parameters

The list of parameters with associated units.

Sombrin

Presentation

This model was designed to be particularly precise on the first cross-over energy [Som93]. Implementation is taken from [FBHP16, FBHP20]. It gives the TEEY, and does not take the incidence angle of PEs into account.

Input files

You must provide measured TEEY at normal incidence.

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

Definitions

The TEEY is given by:

\[\sigma(E) = \frac{ 2\sigma_\mathrm{max} \left( \frac{E}{E_\mathrm{max}} \right)^{E_\mathrm{param}} }{ 1 + \left( \frac{E}{E_\mathrm{max}} \right)^{2E_\mathrm{param}} }\]

\(E_\mathrm{param}\) is defined by:

\[E_\mathrm{param} = \frac{ \ln{\left( \sigma_\mathrm{max} - \sqrt{\sigma_\mathrm{max}^2 - 1} \right)} }{ \ln{\left( \frac{E_\mathrm{c,\,1}}{E_\mathrm{max}}\right)} }\]

Model parameters

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

Vaughan

Presentation

This is the most basic Vaughan model, as defined in original Vaughan paper [Vau89, Vau93]. It gives the TEEY, and takes the incidence angle of PEs into account.

Input files

You must provide measured TEEY at normal incidence.

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

Definitions

The TEEY is given by:

\[\begin{split}\sigma(E, \theta) &= \sigma_\mathrm{max}(\theta) \times (\xi \mathrm{e}^{1-\xi} )^k \mathrm{\quad if~} \xi \leq 3.6 \\ &= \sigma_\mathrm{max}(\theta) \times \frac{1.125}{\xi^{0.35}} \mathrm{\quad if~} \xi > 3.6\end{split}\]

\(\xi\) is defined by:

\[\xi = \frac{E - E_0}{E_\mathrm{max} - E_0}\]

Under the limit \(E_0\) (\(12.5\mathrm{\,eV}\) by default), the TEEY is set to a unique value (\(0.5\) by default).

\[ \begin{align}\begin{aligned}\sigma_\mathrm{max}(\theta) = \sigma_\mathrm{max}(\theta = 0^\circ) \times \frac{1}{k_s\theta^2/\pi}\\E_\mathrm{max}(\theta) = E_\mathrm{max}(\theta = 0^\circ) \times \frac{1}{k_{se}\theta^2/\pi}\end{aligned}\end{align} \]

The \(k_s\) and \(k_{se}\) are both set to unity by default.

The factor \(k\) is given by:

\[\begin{split}k &= 0.56 \mathrm{\quad if~} \xi \leq 1 \\ &= 0.25 \mathrm{\quad if~} 1< \xi \leq 3.6 \\\end{split}\]

Model parameters

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

Implementations

Two alternative implementations for Vaughan are implemented: CST and SPARK3D. Just instantiate your model with:

model = Vaughan(implementation="CST") # or "SPARK3D"
# alternative:
model = Vaughan()
model.preset_implementation("CST")

From the GUI, manually reproduce the steps described in the vaughan.Vaughan.preset_implementation() method. More specific documentation is also listed in vaughan.Vaughan.preset_implementation().

Parameter Vaughan with \(E_{\mathrm{c,\,1}}\) instead of \(E_0\)

When \(E_0\) is unlocked, a fit over this variable is performed to match \(E_{\mathrm{c,\,1}}\). You must provide either a TEEY file path, either enter the other Vaughan parameters yourself (see image below), and click Fit!.

To-do list

Todo

• Unlock \(k_s\), \(k_{se}\) to have better overall fit? In particular: if several incidence angles are provided.

• Instructions to match CST Vaughan.

• Instructions to match SPARK3D Vaughan.