Extremefill2D - Comparison with 1D

This blog post compares the new 2D model as described in the previous blog post with the older 1D model (already published). Firstly, the single parameter studies are compared. These include the adsorption coefficient $k^+$, the consumption coefficient $k^-$, the depth of the trench $h$ and the distance between the counter electrode and the reference electrode $L$, the suppressor concentration $C_{\text{SUPP}}^{\infty}$ and the applied potential $E_{\text{APPLIED}}^{\infty}$. I was planning on including the contour plots (figures 5 and 10 from the 1D paper) as well, but I had issues with the cluster and those simulations are not finished at the time that I wrote this blog post. To get a better feel for how these parameters influence the filling see the equations for the extreme fill system.

Helper Functions

The functions plot1DFigure and plotFeatures can be found at Github. The function plot1DFigure plots figures from the 1D Extreme Fill paper in an IPython friendly manner and plotFeatures shows an array of features along with a corresponding table of Sumatra records.

from multiViewer import plot1DFigure
from multiViewer import plotFeatures

Comparing $k^+$

The following cells show a comparison between the 1D steady and 2D extreme fill simulations. The first image is a plot of the deposition rate, $v$, versus the feature depth, $z$, with $z=0$ at the top of the feature for the 1D code. If the curve is not monotonically decreasing it represents a failure (or chance of a failure) in the 1D model.

Comparing the 1D and 2D models it seems like the results do not show any real discrepancies. Obviously, the 1D model does not predict a shutdown of deposition in the $k^+=1000$, just that there will be extreme fill initially. In the $k^+=50$ case, the 1D model shows a fairly flat profile at the bottom of the feature, hence, it is not surprising to see the void in the 2D case.

plot1DFigure(3)

plotFeatures(parameter='kPlus',
             parameterValues=(0.01, 5.0, 25.0, 50.0, 100.0, 1000.0),
             Nxs=(300, 600, 1200),
             tags=['serialnumber9', 'serialnumber10'],
             title=r'$k^+$={0:1.1e}')

Comparing $k^-$

The lower values for $k^-$ for which the deposition is highly segregated tend to shutdown more quickly.

plot1DFigure(4)

plotFeatures(parameter='kMinus',
             parameterValues=(1e7, 1.5e7, 2e7, 2.5e7, 3e7),
             Nxs=(300, 600),
             tags=['serialnumber11'],
             title=r'$k^-$={0:1.1e}')

Comparing $h$

In the deepest features, small voids appear near the bottom.

plot1DFigure(6)

plotFeatures(parameter='featureDepth',
             parameterValues=(8.5e-5, 7.5e-5, 6.5e-5, 5.5e-5, 4.5e-5, 3.5e-5, 2.5e-5, 1.5e-5),
             Nxs=(300, 600),
             tags=['serialnumber19'],
             title=r'$h$={0:1.1e}')

Comparing $\delta_{\text{REF}}$

The inverted curved all fail dramatically as expected. The $L=0.02$ (cyan curve) shows small voids although is doesn’t differ substantially from the $L=0.03$ (pink) and $L=0.04$ yellow curves.

plot1DFigure(7)

from smtext import getSMTRecords, smt_ipy_table
smt_ipy_table(getSMTRecords(tags=['serialnumber20']), fields=['label', 'timestamp', 'parameters', 'repository', 'version', 'duration'], parameters=['deltaRef', 'Nx'])

plotFeatures(parameter='deltaRef',
             parameterValues=(0.001, 0.005, 0.01, 0.02, 0.03, 0.04),
             Nxs=(300, 600),
             tags=['serialnumber20'],
             title=r'$L$={0:1.1e}')

Comparing $E_{\text{APPLIED}}$

The $E=-0.2$ curve shuts down early on. It is evident that there is a critical point for shut down as the deposition becomes more segregated. The $E=-0.3$ curve is flat near the bottom of the feature and, hence, a void results in the 2D case.

plot1DFigure(8)

plotFeatures(parameter='appliedPotential',
             parameterValues=(-0.3, -0.25, -0.2),
             Nxs=(300, 600),
             tags=['serialnumber21'],
             title=r'$E$={0:1.2f}')

Comparing $C_{\text{SUPP}}^{\infty}$

The comparison between the 1D and 2D fits well with the previous results above.

plot1DFigure(9)

plotFeatures(parameter='bulkSuppressor',
             parameterValues=(0.005, 0.01, 0.02, 0.04),
             Nxs=(300, 600),
             tags=['serialnumber22'],
             title=r'$C_}}^$={0:1.2f}')