Basic questions from a new user - based on 1D capacitor

Hi Juan, hi all!

I have recently started to look into ways of simulating electronic properties of semiconductor structures I am dealing with in my research (I have very little experience in this regard, was so far primarily using optically pumped, “non-electric” samples) and I came across DEVSIM.

First of all - thanks for the opportunity to use the software! It looks very promising and I am eager to try it!

I have a question regarding the 1D capacitor example:

The result for the 1D capacitor example is a charge of ~3.45x10^(-13) from the simulation. The manual gives as a unit F/(cm²). I was wondering about this unit. I tried to estimate the result (as expected) from a simple plate capacitor:

Q = C*U
Q = epsiolon_r * epsilon_0 * A / d * U
Q/A = epsiolon_r * epsilon_0 / d * U

epsilon_r being the relative permittivity (3.9 for SiO2 in the example)
epsilon_0 being the vacuum permittivity (~8.85x10^(-12) As/(V*m) or 8.85x10^(-14) As/(Vcm) as used in the example)
A being the area of the capacitor plates
U being the Bias voltage (1 V in the example)
d being the distance between the plates (1 m if I understand the mesh creation according to the manual correctly, meaning 100 cm)

Using the above values I get a result of
Q/A = 3.45x10^(-11) As/(Vm²) = 3.45*10^(-11) F/m² = 3.45x10^(-15) F/cm²
I would also get this value if I set the position to 100 (cm) and leave the vacuum permittivity at 8.85x10^(-14) As/(Vcm).

Did I overlook something, or is the answer given in the manual incorrect, and should rather be 3.45x10^(-11) F/m² = 3.45x10^(-15) F/cm²?
Or am I making a mistake, because the distance simulated is not 1 m, but actually 1 cm?

I would also be interested what the “spacing” as a parameter in the add_1d_mesh_line() command is?
Does it mean a 0.1(unit?) extension of the contact? Or is it a parameter for the mesh?
And if it is an extension of the contact, and both contacts are extended by 0.1 in the same (positive) direction, is the distance then not 0.9, if one contact is at position 0.0 and the other at 1.0, and would we then not expect other charge values?

Thank you very much for your help! And please excuse the long post, if I simply overlooked something or made a mistake elsewhere.

Welcome @SinglePhotonGuy !

DEVSIM does not perform any unit conversions and relies strictly on any parameters as given. The length of the device is assumed to be consistent with the other units and is not scaled in any way.

The capacitance is:

C = \frac{\epsilon A}{d}

where

\epsilon = 3.9 \cdot 8.84\cdot 10^{-14} = 3.4515 \cdot 10^{-13}

with units of \mathrm{F}/\mathrm{cm}^2. Being a 1D simulation, the cross sectional area is

A = 1

and does not have a unit. To be consistent with the permittivity, the integration of the Poisson equation along the mesh of the device is equivalent to:

d = 1 \mathrm{cm}

so that the capacitance is then 3.4515 10^{-13} \mathrm{F}/\mathrm{cm}^2. If we assume the device cross section is 1 \mathrm{cm}^2 then the results would be in 3.4515 10^{-13} \mathrm{F}.

When performing a simulation, it is necessary that any parameters and mesh have a consistent length unit.

The contacts are points at 0 and 1 \mathrm{cm}.
The spacing, ps, is necessary to resolve the solution of the Potential in the device. For the 1D internal mesher, the spacing is logarithmically interpolated to the spacing at the next mesh line.

In contacts are points in 1D, lines in 2d, and triangles in 3d.

Hello Juan,

thank you very much for your quick answer! I understand the obtained value then, I just did not understand that the distance was 1 cm.

At the following point in the manuscript regarding the 1D capacitor, the mesh “is said to be 1 m long”, and I thought this would then also set the value for d as 1 meter. Can you tell me please, what this “1 m” refer to in the manuscript?

And does this then mean, that the default unit for pos in add_1d_mesh_line (mesh, pos, ps, tag) is cm?

I am asking because in the 1D diode example, the pos-values given are 0, 0.5e-5 and 1.0e-5, but in the manual it says it would create a mesh with 1e-6 cm extension.

Thank you once again for your time!

That is a typo. The units should be in cm. If you change the permittivity to F/\mathrm{m}^2, then the device would be 1 m long. I will fix that in a future update. Pull requests are also accepted at:
https://github.com/devsim/devsim_documentation

Thank you for the help, that makes things clear for me now!