Commit 89911322 authored by Simon Spannagel's avatar Simon Spannagel
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Merge branch 'p-efield-docs' into 'master'

Manual for ElectricFieldReader

Closes #253

See merge request allpix-squared/allpix-squared!926
parents a8dd2f87 5709967e
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@@ -18,15 +18,16 @@ The reader provides the following models for electric fields:

- For **linear** electric fields, the field has a constant slope determined by the bias voltage and the depletion voltage.
  The sensor is depleted either from the implant or the back side, the direction of the electric field depends on the sign of
  the bias voltage (with negative bias voltage the electric field vector points towards the backplane and vice versa). If the
  sensor is depleted from the implant side, the electric field is calculated using the formula
  the bias voltage (with negative bias voltage the electric field vector points towards the backplane and vice versa).
  The sign of depletion voltage is always ignored.
  If the sensor is depleted from the implant side, the absolute value of the electric field is calculated using the formula
  ```math
  E(z) = \frac{U_{bias} - U_{depl}}{d} + 2 \frac{U_{depl}}{d}\left( 1- \frac{z}{d} \right),
  E(z) = \frac{|U_{bias}| - |U_{depl}|}{d} + 2 \frac{|U_{depl}|}{d}\left( 1- \frac{z}{d} \right),
  ```
  where d is the thickness of the sensor, and $`U_{depl}`$, $`U_{bias}`$ are the depletion and bias voltages, respectively.
  In case of a depletion from the back side, the electric field is calculated as
  In case of a depletion from the back side, the absolute value of the electric field is calculated as
  ```math
  E(z) = \frac{U_{bias} - U_{depl}}{d} + 2 \frac{U_{depl}}{d}\left( \frac{z}{d} \right).
  E(z) = \frac{|U_{bias}| - |U_{depl}|}{d} + 2 \frac{|U_{depl}|}{d}\left( \frac{z}{d} \right).
  ```
- For **parabolic** electric fields, a parabola is defined in order to emulate a double-peaked field such as the electric
  fields observed in sensors after irradiation. The parabola is calculated from the position $`z_{min}`$ and value