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Sample Data: Breakdown Spots R169

Source Notebook

Locations of electrical breakdown spots on a circular electrode of radii 169 microns in a microelectronic capacitor

Details

Locations of electrical breakdown spots on a circular electrode of radii 169 microns in a microelectronic capacitor in a polygonal observation region bounded by the region Rectangle[{-169., -169.}, {169., 169.}] microns.

Examples

Basic Examples (1) 

In[1]:=
ResourceData[\!\(\* TagBox["\"\<Sample Data: Breakdown Spots R169\>\"", #& , BoxID -> "ResourceTag-Sample Data: Breakdown Spots R169-Input", AutoDelete->True]\), "Data"]
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Summary of the spatial point data:

In[2]:=
ResourceData[\!\(\* TagBox["\"\<Sample Data: Breakdown Spots R169\>\"", #& , BoxID -> "ResourceTag-Sample Data: Breakdown Spots R169-Input", AutoDelete->True]\), "Data"]["Summary"]
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Visualizations (2) 

Plot the spatial point data:

In[3]:=
ListPlot[ResourceData[\!\(\* TagBox["\"\<Sample Data: Breakdown Spots R169\>\"", #& , BoxID -> "ResourceTag-Sample Data: Breakdown Spots R169-Input", AutoDelete->True]\), "Data"], AspectRatio -> 1]
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Visualize smooth point density:

In[4]:=
density = SmoothPointDensity[ResourceData[\!\(\* TagBox["\"\<Sample Data: Breakdown Spots R169\>\"", #& , BoxID -> "ResourceTag-Sample Data: Breakdown Spots R169-Input", AutoDelete->True]\), "Data"]]
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In[5]:=
Show[ContourPlot[density[{x, y}], {x, y} \[Element] ResourceData[\!\(\* TagBox["\"\<Sample Data: Breakdown Spots R169\>\"", #& , BoxID -> "ResourceTag-Sample Data: Breakdown Spots R169-Input", AutoDelete->True]\), "ObservationRegion"], ColorFunction -> "Rainbow"], ListPlot[ResourceData[\!\(\* TagBox["\"\<Sample Data: Breakdown Spots R169\>\"", #& , BoxID -> "ResourceTag-Sample Data: Breakdown Spots R169-Input", AutoDelete->True]\), "Data"], PlotStyle -> Black]]
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Analysis (6) 

Compute probability of finding a point within given radius of an existing point - NearestNeighborG is the CDF of the nearest neighbor distribution:

In[6]:=
nnG = NearestNeighborG[ResourceData[\!\(\* TagBox["\"\<Sample Data: Breakdown Spots R169\>\"", #& , BoxID -> "ResourceTag-Sample Data: Breakdown Spots R169-Input", AutoDelete->True]\), "Data"]]
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In[7]:=
maxR = nnG["MaxRadius"]
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In[8]:=
DiscretePlot[nnG[r], {r, maxR/100, maxR, maxR/100}, AxesLabel -> {"radius", "probability"}]
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NearestNeighborG as the CDF of nearest neighbor distribution can be used to compute the mean distance between a typical point and its nearest neighbor - the mean of a positive support distribution can be approximated via a Riemann sum of 1- CDF. To use Riemann approximation create the partition of the support interval from 0 to maxR into 100 parts and compute the value of the NearestNeighborG at the middle of each subinterval:

In[9]:=
step = maxR/100; middles = Subdivide[step/2, maxR - step/2, 100]; values = nnG[middles];

Now compute the Riemann sum to find the mean distance between a typical point and its nearest neighbor:

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Total[(1 - values)*step]
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Account for scale and units:

In[11]:=
%*ResourceData[\!\(\* TagBox["\"\<Sample Data: Breakdown Spots R169\>\"", #& , BoxID -> "ResourceTag-Sample Data: Breakdown Spots R169-Input", AutoDelete->True]\), "RegionScale"]
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Test for complete spatial randomness:

In[12]:=
SpatialRandomnessTest[ResourceData[\!\(\* TagBox["\"\<Sample Data: Breakdown Spots R169\>\"", #& , BoxID -> "ResourceTag-Sample Data: Breakdown Spots R169-Input", AutoDelete->True]\), "Data"], {"PValue", "TestConclusion"}] // Column
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Fit a Poisson point process to data:

In[13]:=
Clear[\[Mu]]; EstimatedPointProcess[ResourceData[\!\(\* TagBox["\"\<Sample Data: Breakdown Spots R169\>\"", #& , BoxID -> "ResourceTag-Sample Data: Breakdown Spots R169-Input", AutoDelete->True]\), "Data"], PoissonPointProcess[\[Mu], 2]]
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Gosia Konwerska, "Sample Data: Breakdown Spots R169" from the Wolfram Data Repository (2022)  

Data Resource History

  • Date Created:

Source Metadata

  • Citation:
    • Miranda, E. and O’Connor, E. and Hurley, P.K. (2010)
      Simulation of the breakdown spots spatial distribution in high-K dielectrics and model validation using the spatstat package for R language. ECS Transactions 33 (3) 557--562.

      Miranda, E., Jimenez, D., Sune, J., O’Connor, E., Monaghan, S., Povey, I., Cherkaoui, K. and Hurley, P. K. (2013)
      Nonhomogeneous spatial distribution of filamentary leakage current paths in circular area Pt/HfO2/Pt capacitors. J. Vac. Sci. Technol. B 31, 01A107.

Publisher Information

  • Prepared for the Wolfram Data Repository By: Gosia Konwerska
    (Wolfram Research, Inc.)
  • Publisher of Record: Gosia Konwerska