Transcript HFT_simulation_2

PIXEL Slow Simulation
Status Report
Xin Li
8/30/2008
Simulation Process
Input:
PIXEL Geometry:
Momentum (GeV), sumE,
direction, path length (cm)
A ladder: 640
x6400 pixel array
Output:
PIXEL response :
Sum of electrons
collected
Diffusion, recombination and
reflection at boundaries
Reference:
“Modeling, Design, and Analysis of Monolithic
Charged particle Image Sensors” by Shengdong Li,
Univ. of California, Irvine
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
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.
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
•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
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.
z
1
4
1
3
p1 2
-1
x
Symmetric Distributions
Track1
Track2
Symmetric relative
to x axis
Track3
Track2
Symmetric relative
to z axis
Result Comparison between Original and
Ultimate Simulator
Result along x axis
Result along z axis
Thank you