tree_ring_validation

Effect: Tree rings

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

Contact person(s) if any:

Craig Lage, Mike Jarvis, Andrei Nomerotski/SAWG

Reference Material

See recent talk by Craig Lage here

Data Provenance:

Data for validation taken from 5 sensors on TS3 at BNL (4 ITL, 1 E2V) by HyeYun Park on ????. (Need more details here).

Sensors include:

1. ITL-017
2. ITL-098
3. ITL-206
4. ITL-283
5. ITL-350
6. E2V-260

(note disagreement with summary numbers above)

Model Details

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.

The tree rings are not be represented well by single sinusoid. The measured spectral power from the BNL data is also shown below:

Based on the Fourier transform of the data, a range of frequencies (20 total) are 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.

Validation Criteria

Area deviations and pixel shifts between the data and several simulated tree rings are compared statistically (need quantitative measure).

Validation Results

Current image (need to learn how to insert image!) show qualitative agreement.

Relevant Project Team for input if any:

Camera

Release and approval log:

03/30/18 - Initial Version - CWW