1. PIXEL Slow Simulation Status Report
Xin Li
8/30/2008

2. Simulation Process Input:
Momentum (GeV), sumE, direction, path length (cm)
PIXEL Geometry:
A ladder: 640 x6400 pixel array
Output:
Sum of electrons collected
PIXEL response :
Diffusion, recombination and reflection at boundaries
Reference:
“Modeling, Design, and Analysis of Monolithic
Charged particle Image Sensors” by Shengdong Li, Univ. of California, Irvine

3. PIXEL Geometry Model: a chip of 640(x)x640(z) PIXEL array
PIXEL size: 30um(x) x 50um(y) x 30um(z)
Diode size: 4.5um x 2um x 4.5um
30um
50um x z y
Readout electronics layer: 6um
Diode layer: 2um
Epi layer: 14um
Sub layer: 28um

4. Simulation Result After Update
Incident angle 45
Incident angle 0
In the sum of collected electrons:
Contribution from sub: 21%
Contribution from epi: 68%
Contribution from diode: 11%
( much larger contribution from sub (21%) compared to the previous result (1%) due the correction of the step length).
45 0 y z

5. Comparison with Experimental and Simulation Result
Reference:
“Modeling, Design, and Analysis of Monolithic
Charged particle Image Sensors” by Shengdong Li, Univ. of California, Irvine
Shendong’s experiment and MC comparison
STAR test result, from Howard Matis

6. Simplified Slow Simulator
Every ionized electron from any track are independent of each other.
One can map out the probability of one electron being collected by different pixels when it is generated at a specific location in the PIXEL, and deduce the distribution of collected electron generated along a track.
This map is a function of (x, y, z, theta, phi) , where x, y, z is the origin of the electron where it is generated, theta, phi are the direction of the first step of random walk during electron diffusion.
Since the step length is very small (10-9m) and direction at every step is totally random in space, the direction of the first step has little effect on the map. Then the map can be only a function of x, y, z.
This map is produced using the real slow simulator mentioned in previous slides.

7. Further Simplification
First we can ignore electrons generated in the diode layer (2um), since electrons will be collected by nwell or absorbed by pwell in this layer.
Second, according to the simulation result, we can ignore electrons generated 19um deep in the sub layer.
So in total 50um thickness (y axis) of a pixel, only need to make samples in 33um (19um sub + 14um epi). If one sample per 1um along x, y, z axis, totally there are 30x30x33=29700 samples.
Layer thickness (cm)
epi
sub
19um deep
30um
Sampling region (33um)
epi
sub
50um z y
30um x

8. Result Comparison between Original and Simplified Slow Simulator
Result along x axis
Pixel ID
Result along z axis

9. Ultimate Simulator
Simplified Slow Simulator is still not fast enough to fit in STAR software.
We use it to Build another lookup table of collected electron distribution for 640 x 640 pixel array with track hit on central pixel, make samples as function with parameters r(0~15um), (0~90), (0~360). Here r is the distance from track incident position to the origin (center of the PIXEL), ,  are the incident angle of the track.
The ultimate slow simulator will be 3-D histograms which should be fast enough to be plugged in STAR software. r

10. Assume the simulation result of a track is only dependent on its entering and exiting positions. In this case, if two tracks has symmetric entering and exiting positions relative to x or z axis, their collected electron distribution in the PIXEL array will also be symmetric to the axis. For example, results of track 1 and 2 is symmetric relative to x axis, while results of track 2 and 3 is symmetric relative to z axis. So we only need to make samples in one quarter region (x>0, z>0) in the total PIXEL array. p1 - 1 2 3 4 x z

11. Symmetric Distributions
Track1
Track2
Symmetric relative to x axis
Track3
Track2
Symmetric relative to z axis

12. Result Comparison between Original and Ultimate Simulator
Result along x axis
Result along z axis

13. Thank you