PIXEL Slow Simulation
Status Report
Xin Li
7/30/2008
Update Since the UC/Davis Collaboration
• Discovered a mistake and rewrote the code to save time.
– Unit error on the step length of random walk. (m to cm).
– Code is written in macro instead of compiled style.
• After the correction, 10~20min per track
– Before the correction, a few hours per track.
• Development of a simplified and faster slow simulator.
– 3 Seconds per track.
• Plan of Building a lookup table which is fast enough to
be plugged into STAR software.
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
Readout electronics layer: 6um
Diode layer: 2um
Epi layer: 14um
Sub layer: 28um
50um
y
z
30um
x
Simulation Result After Update
Incident angle 45
Incident angle 0
In the sum of collected electrons:
45

0
Contribution from sub: 21%
Contribution from epi: 68%
Contribution from diode: 11%
y
z
( much larger contribution from sub (21%)
compared to the previous result (1%) due
the correction of the step length).
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
Simplified Slow Simulator
•Any ionized electron from any track is independent of each other.
•Any electron generated at a specific location has a certain probability
to be collected by each different pixel.
• One can map out the probability using the real slow simulator
mentioned in previous slides.
• This map is a function of (x, y, z, theta, phi) , where x, y, z is the
origin of the electron, 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.
• Segment the central pixel of a chip into fine 3-D grid and generate
the map for electron from every grid point The map of electron
originated from other pixels can be derived directly from this map
through coordinate transformation.
• The collection probability of electrons from a track can be obtained
from these maps which lead to the final number of electrons collected
in each pixel.
How does simulator work
Establish
a coordinate system containing the 640x640 PIXEL array in
one chip, with central PIXEL of the chip as origin. Generate electrons
in a 3-D grid in the central pixel.
calculate
collection probability in all pixels on a chip for electron
generated in a single grid point.
The edge size of the grid unit is 1um along x, y, z axis. Totally there
are 30 x 30 x 50 = 45000 grid points.
build a look-up table containing the probability distribution for all the
grid point in the central pixel.

Get
collected electron distribution of a track:
First
find out in which PIXELs the electrons are generated.
make
coordinate transformation from the central pixel to these
pixels and calculate collection probability of every electron in
every PIXEL using look-up table. Add them up and obtain the
overall collected electron distribution.

Code location: /star/u/lixin044/HFT/sample2/
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.
30um
Sampling
epi region
(33um)
sub
50um
19um deep
y
sub
Layer thickness (cm)
epi
z
30um
x
Result Comparison between Original and
Simplified Slow Simulator
Result along x axis
Pixel ID
Result along z axis
Ultimate Simulator
•The goal is to build the ultimate slow simulator that can simulate a few hundred
tracks per second.
• The Simplified Slow Simulator is still not fast enough to fit in STAR software
but we can use it to build the ultimate slow simulator.
• The ultimate simulator will contains about ten 3-D 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 details will be given in another talk.



r
Thank you