tree_ring_validation
During the growing of silicon boules the doping percentage can vary over time building "tree-ring" like structure in doping concentration. Much like a n-p junction, the gradient in doping establishes a static lateral electric field causing electrons to drift laterally into adjacent pixels while traveling through the silicon bulk.
For a more thorough introduction see Need Link
Craig Lage, Mike Jarvis, Andrei Nomerotski/SAWG
See recent talk by Craig Lage here
Data for validation taken from 5 sensors on TS3 at BNL (4 ITL, 1 E2V) by HyeYun Park on ????. (Need more details here).
Data can be found XXX (here... we need to organize all of the input somewhere. E-traveler?)
Sensors include:
- ITL-017
- ITL-098
- ITL-206
- ITL-283
- ITL-350
- E2V-260
(note disagreement with summary numbers above)
It is noticed in the data that the tree ring amplitude increase as moving away from the center. The relationship can be parameterized to a A+B*r^4 model. This effect is shown along with a fitted line to the function for the six sensors in a figure below. Note that there is a wide variation in the magnitude of the tree-ring area distortions (more quantitative description here).
The tree rings do not seem to be represented well by single sinusoid. The measured spectral power from the BNL data is shown below:
Based on the Fourier transform of this data, a range of frequencies (20 total) are randomly drawn to represent the doping variation function. Based on the observed FFT, 75% have a spatial frequency drawn from a Gaussian with a mean of 60 pixels and a sigma of 10 pixels. 25% have a spatial frequency drawn from a Gaussian with a mean of 35 pixels and a sigma of 10 pixels. Each frequency in the model is also given a random phase.
Area deviations and pixel shifts between the data and several simulated tree rings are compared statistically (need quantitative measure).
Current images (which image should we use here?) show qualitative agreement.
Camera
03/30/18 - Initial Version - CWW