Finite Element Analysis
Derek Shuman did a finite element analysis for several pixel array sizes (3x3 and 7x7). His results for the 3x3 array were biased by edge effects, so he increased the array size to 7x7. Unfortunately he gave us only his numerical results and it took some time to decode this into similar pictures as seen before.
His setup was slightly different from mine, but this is not expected to affect the results shown below.
Level 1
Level 2
Level 3
Level 4
Level 5
To measure something like the size of the peak I added the signal of the highest bins together. The next plot shows the percentage of the full signal which is collected in 1 up to 10 bins.
Two pixels contain already about ~40% of the full signal, three pixels contain about 50%. That's much closer to reality than my own studies using the random walk approach. The reason for has to be checked, still.
The distribution in the highest bin can be compared to the measurement of ADC0 (the signal in the highest bin) in section 1. Therefore I took the data I'd just taken for testing the photogate of section 5 and 6 (240.000 events in total) and analysed section 1. The distribution of ADC0 was scaled so that the single conversion peak was sitting at 100%. Both, the simulated plot and the real data plot were divided by their integral.
The comparison looks reasonable, but not perfect. We can probably enhance the tail of the simulated distribution by deploying the charge at more positions within the epi layer. (The strong tail of the real data is the main reason why the height of the blue plot is lower that for the red one.)
As in my simulations the distance of the measured peak position and the actual charge generation (in x and y) is peaked at about 5 um (as expected). As explained ibid. it makes no sense to fit a Gaussian to improve this situation.
This plot gives me troubles, actually. While it seems to be a bit easier to measure the depth of the signal generation in the first 5 layers, I don't understand this high value at the farthest distance to the pixel array. This high entry there makes no sense. The same behavior was observed with the 'fixed step' simulation. While I accused this to the funny way of generating the next step there (at least part of), I don't understand at all, what is going on here. This needs further investigantion.
Markus Oldenburg
Last modified: Mon Nov 10 15:55:28 PST 2003