# Presentation: 201912

## Pixel Clustering

- Simplified presentation today ignores:
- Cross column clustering
- Magnetic field effects
- Radiation damage effects

## Mobile charge creation
Factors that determine cluster size:
Track Angle
Charge carrier diffusion
Discriminator threshold
Sensor bias voltage
Optimal use of charge sharing information

- Factors that determine cluster size:
- Track Angle
- Charge carrier diffusion
- Discriminator threshold
- Sensor bias voltage
- Optimal use of charge sharing information

## Mobile charge creation in silicon

- One e-hole pair is created per 3.62 eV lost by a particle.  On average, 24000 e-hole pairs are created per 300 of track length for a minimum-ionizing particle (~87 KeV lost by track).
- We have been using 300 thick sensors so far; nominally expect to use 250 thick sensors in BTeV.
- Pulse height distribution is well fit with a Landau function convoluted with a Gaussian.
- Fluctuations are large: FHWM(300 Si)  10000 e-.
- Distribution is asymmetric (long high-energy tail).

## Data from 1999 testbeam run

- ADC saturation

- Charge loss at
- one pixel boundary

## Charge creation & collection

- Most e-hole pairs are created within ~3 of track.
- Exceptions are due to “-rays” – electrons with energy of many 10’s of KeV (up to MeV) – these are the cause of the long high energy tail in dE/dx.
-  -rays are produced nearly perpendicular to track (elastic scattering kinematics).
- Diffusion adds to “width” of track.
- Depends on _**discriminator threshold**_ and bias voltage.
- Less diffusion at higher bias voltage.

-     Effective “width” of track  10

- (Simulation)

## Dependence of Cluster Fraction on Bias Voltage and Discriminator Threshold

- Bias Voltage

- Discriminator Threshold

- CAN get 50% charge sharing at normal incidence (50 wide pixels) with sensor just depleted.

## Dependence of cluster size on track angle

- 1

- 2

- 2

- 3

- 4

- n-side

- p-side

- 50

- 300

- Arctan(1/6) = 9.5°

## Dependence of cluster size on track angle (data from 1999 testbeam run)

## -rays

- 3.3% have more than 2 pixels on.

- -rays

## Use of pulse height information

- Without knowledge of track angle, the best estimate of track position is given by the digital center of cluster (ignoring pulse height)  x0.
- Once the track angle is known, the best estimate of track position is given by x0 + f(,N,PHL,PHR).
- For each angle , there are 2-3 possible values of N (others arise from -rays).
- PHL,PHR are the pulse heights on the left and right edges of the cluster.
- The pulse heights in the center of the cluster contain NO INFORMATION.
- Knowing the track angle means knowing the track length in the central pixels!
- The function f is determined from data & simulation.

## Determination of f(,N,PHL,PHR)

- Determination of f(,N,PHL,PHR)

- Example from 1999 test beam ( = 0°)

- Eta = (PHL-PHR)/(PHL+PHR) ... really would create a lookup table;
- 3 bits of pulse height  only 64 possibilities.

## Residual distributions for tracks at normal incidence

- xpredicted – x0

## Resolution as a function of track angle

- G = standard deviation of Gaussian fit.

## Comments on pulse height measurement

- When more than one pixel is hit, either
- Most of the information is in the small pulse height.
- No pulse height is more than ~1/2 MIP.
- No need for fine binning of pulse height (fluctuations in dE/dx are large).
- 1+2  We use only 3 bits for pulse height.
- Dynamic range still not finally decided.
- Probably >1/2 MIP, but <1 MIP.

## Small pulse height measurements on cluster edges have large information content --- Low discriminator threshold is important! 

- Small pulse height measurements on cluster edges have large information content --- Low discriminator threshold is important!