Element edge model clarification

[MbolGi]

Hi @Juan,

I’m trying to understand a little better the dynamics of the Element-Edge model. This is in relation to handling of vector quantities.

So, it seems to be straightforward to generate a vector (element) field for a given edge model, which is great. What I can’t get my head around, is why can I not create an edge model from the element model.

So if I understand this correctly (and please correct me) if I need to use a vector field, (e.g., I need vector E to compute field effect on mu) I’d first need to create an element model for E, and then convert all edge models that require this to element models, i.e.,

1. Create element model for mu
2. Create element model for n
3. Create element model for J
4. Substitute edge_model for element_model in equation

Then, how are equations handled? There is element_charge, element_current and element_model in contact_equation but no contact_element_model. Maybe it’d suffice to change edge_current_model by edge_element_model?

Thanks in advance for your help.
@MbolGi

[Juan]

@MbolGi

Hi @Juan,

I’m trying to understand a little better the dynamics of the Element-Edge model. This is in relation to handling of vector quantities.

So, it seems to be straightforward to generate a vector (element) field for a given edge model, which is great. What I can’t get my head around, is why can I not create an edge model from the element model.

You can use an Edge Model in the expression for an Element Edge model. When handling the derivatives the edge model derivaties can be used as:

model@en0 = model@n0
model@en1 = model@n1
model@en2 = 0
model@en3 = 0

Where the @en2 model is the derivative with respect to the node off a triangle edge in 2D. In 3D, @en2, @en3 are the two nodes off of the element edge. Please see this paper for more information about the discretization:
https://doi.org/10.36227/techrxiv.14129081.v3

So if I understand this correctly (and please correct me) if I need to use a vector field, (e.g., I need vector E to compute field effect on mu) I’d first need to create an element model for E, and then convert all edge models that require this to element models, i.e.,

1. Create element model for mu

As described in the paper, and implemented in the accompanying repo:
https://github.com/devsim/devsim_3dmos
the mobility is based off the vector electric fields to get the electric field normal to current flow.

2. Create element model for n

You only need the edge electron densities along the edge. Please see
https://github.com/devsim/devsim_3dmos/blob/405b05806c7f8843e21589eccb59024334367cab/ieee/mos90.py#L150
for an example.

3. Create element model for J

Please see the github link in the previous item. The current direction is based on the element edge model conversion of the conventional edge current to give an estimate of current direction.
https://github.com/devsim/devsim_3dmos/blob/main/ieee/newmodels/mos_physics.py#L77

4. Substitute edge_model for element_model in equation

Yes

Then, how are equations handled? There is element_charge, element_current and element_model in contact_equation but no contact_element_model. Maybe it’d suffice to change edge_current_model by edge_element_model?

Please see this example for the boundary conditions, using only node_model to enforce the boundary condition, and element_current_model to get the external current:
https://github.com/devsim/devsim_3dmos/blob/main/ieee/newmodels/mos_physics.py#L35
Please try:

help(devsim.contact_equation)

or
https://devsim.net/CommandReference.html#devsim.contact_equation and let me know if there is a missing option for what you are trying to do.

Note that the “charge” and “current” models are fed into the external circuit. The other models are for setting the boundary condition.

[MbolGi]

Thanks @Juan ! Your help is very much appreciated!