Schottky

[Zhi-Gang Yu]

Dear Juan,

Could you advise how to properly set the Schottky contact between a semiconductor and a metal in devsim? In the examples, the metal contact is always Ohmic. Thanks.

Best wishes

Zhi-Gang

[Juan Sanchez]

Hello Zhi-Gang,

Thank you for the interesting question.  I believe this can be done using the current "contact_equation" command.
https://devsim.net/CommandReference.html?highlight=contact_equation#devsim.contact_equation

but I have never done an actual implementation.

The suggested approach would be to set the "node_model" option to the equation describing the limited current at the surface.  This would be based on a nodal quantity like the Electron Densities at the contact nodes.

The "edge_model" option can then be set to the Electron Current.

The node_model and the edge_model are then integrated at each node and added together.

volume_integrationl(J_schottky * ContactSurfaceArea/NodeVolume) + surface_integration(J_electron) = 0

Since the node_model is volume integrated, you would need to apply a scaling of "ContactSurfaceArea/NodeVolume" to change the unit to a surface integration.

A hole schottky current can be done in a similar fashion.

If you have the specific equation you have in mind, please send me the description and I may be able to suggest a trial implementation.

Regards,

Juan

--
You received this message because you are subscribed to the Google Groups "DEVSIM TCAD" group.
To unsubscribe from this group and stop receiving emails from it, send an email to devsim+un...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/devsim/6845b42f-40e2-48a8-9d37-e8e72422894b%40googlegroups.com.

[Zhi-Gang Yu]

Dear Juan,

Thank you for your help.

I'm thinking of modeling the Schottky diode in the diffusion approximation. The boundary conditions at the contact are: 1) carrier density n(0)=Nc * exp(-q phi_b/ kT) and 2) potential \psi(0)= - phi_b if the fermi level is set 0. Certainly we can include thermionic emission later.

Note that the metal contact is no longer charge neutral because of the formation of depletion region in the semiconductor.

Could you help me on this?

Best wishes

Zhi-Gang

[Juan Sanchez]

Hello,

Attached is a script, which simulates a condition at the contact that:

Jn=-ASchottky_e*(n-n0)

Jp=ASchottky_h*(p-p0)

Please run it in the examples/diode directory of the devsim distribution.  It can be compared to the diode_1d.py script which is in the same directory.  It generates some plots at the end that you can visualize.

Please note that n0 and p0 is not currently adjusted by the built in potential.  In order to capture the effect, the built-in potential would have to be added to the n0, and p0 calculation.

The function is
CreateSiliconDriftDiffusionAtContact
in python_packages/simple_physics.py

Also the built-in potential would need to be added to the boundary condition for potential at the contact.

The function is
CreateSiliconPotentialOnlyContact
in python_packages/simple_physics.py

Please let me know if you think this is a step in the right direction.

Regards,

Juan

--
You received this message because you are subscribed to the Google Groups "DEVSIM TCAD" group.
To unsubscribe from this group and stop receiving emails from it, send an email to devsim+un...@googlegroups.com.

To view this discussion on the web visit https://groups.google.com/d/msgid/devsim/41ddc7ea-ff7c-4165-a92f-856e977b8383%40googlegroups.com.

[Zhi-Gang Yu]

Dear Juan,

Thank you for your effort. I'll study your code now.

Zhi-Gang

[Qiusong Chen]

Hello Juan:

I'm reading your script about Schottky contact. In this file, the current at contact is defined by "Jn=-ASchottky_e*(n-n0)", and "n0" is defined as "Electrons - ifelse(NetDoping > 0, {0}, n_i^2/{1})" . 

So in my understanding, "n0" is determined by the dopping condition. But for a real device, the Schottky contact typically connect metal and semiconductor with different the fermi level. Then the energy band would change and the the carriers would redistribution, even with all bias set to 0. 

So can we solve the initial state(set all the biases and all the current densitys to 0) first, and then set the value of electron and hole of initial state at contact as the default "n0"?

Best regards,

QS.C

On Monday, October 28, 2019 at 5:37:48 AM UTC+8, jsanchez wrote:

Hello,

Attached is a script, which simulates a condition at the contact that:

Jn=-ASchottky_e*(n-n0)

Jp=ASchottky_h*(p-p0)

Please run it in the examples/diode directory of the devsim distribution.  It can be compared to the diode_1d.py script which is in the same directory.  It generates some plots at the end that you can visualize.

Please note that n0 and p0 is not currently adjusted by the built in potential.  In order to capture the effect, the built-in potential would have to be added to the n0, and p0 calculation.

The function is
CreateSiliconDriftDiffusionAtContact
in python_packages/simple_physics.py

Also the built-in potential would need to be added to the boundary condition for potential at the contact.

The function is
CreateSiliconPotentialOnlyContact
in python_packages/simple_physics.py

Please let me know if you think this is a step in the right direction.

Regards,

Juan

On Mon, Oct 21, 2019 at 9:36 PM Zhi-Gang Yu <dr.zh...@gmail.com> wrote:

Dear Juan,

Thank you for your help.

I'm thinking of modeling the Schottky diode in the diffusion approximation. The boundary conditions at the contact are: 1) carrier density n(0)=Nc * exp(-q phi_b/ kT) and 2) potential \psi(0)= - phi_b if the fermi level is set 0. Certainly we can include thermionic emission later.

Note that the metal contact is no longer charge neutral because of the formation of depletion region in the semiconductor.

Could you help me on this?

Best wishes

Zhi-Gang

--
You received this message because you are subscribed to the Google Groups "DEVSIM TCAD" group.

To unsubscribe from this group and stop receiving emails from it, send an email to dev...@googlegroups.com.

[Juan Sanchez]

Hi,

In this formulation {0} substitutes either celec_model or chole_model in python_packages/simple_physics.py:

celec_model = "(1e-10 + 0.5*abs(NetDoping+(NetDoping^2 + 4 * n_i^2)^(0.5)))"

chole_model = "(1e-10 + 0.5*abs(-NetDoping+(NetDoping^2 + 4 * n_i^2)^(0.5)))"

The quadratic equation solutions come from a "0.0" net space charge, which is what also would be expected for a Ohmic contact.  At equilibrium, I expect that "n-n0 == 0"

The Fermi level difference is not accounted for in the script.  This can be accounted for by adding the work function difference to the Poisson equation for the contact.  I think this would account well for the Schottky effect, and give us a good calculation for n0.  If necessary, we can also explore other modeling options.

This model was from Siegfried Selberherr, "Analysis and Simulation of Semiconductor Devices", but I am sure can be found elsewhere.

Similar formulations I am sure can be derived for Fermi level pinning

Regards,

Juan

To unsubscribe from this group and stop receiving emails from it, send an email to devsim+un...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/devsim/4b38959c-5e33-44a5-ae8b-6d5ebe43264c%40googlegroups.com.