Prediction

Dark Rate = X events/second

Dark Rate = Probability of occurrence * Volume of Sensitive region * Density of Valence Electrons * Rate of Scattering

Dark Rate = $e^{-(1.12*1.6*10^{-19})/(1.381*10^{-23}*T)}$ * 0.0033 mm^3 * 200 pixels * 2.329g/1000mm^3 * 6.022*10^23molecules/28g * $sqrt{2E_{f}/M_{e}}/MeanFreePath$

$Probability=e^{-E_{g}/kT}$

$E_{g}Silicon=1.12eV$

$k=1.3806503*10^{-23}JK^{-1}$

$Probability=e^{-(1.12*1.6*10^{-19})/(1.381*10^{-23}*T)}$

thin depletion region (0.7-0.8 um)

Make sure to do it in pixels

$Volume=4.4mm^{2}*0.00075mm$

$Volume=0.0033mm^{3}$

$Volume=0.0033mm^{3}*200pixels$

$Density=2.329g/mL*1mL/1cm^{3}*{1cm/10mm}^{3}$

$Density=2.329g/1000mm^{3}$

$RateofScattering=VelocityofValenceElectrons/Meanfreepath$

Mean velocity of valence elctrons = Fermi Velocity

Fermi Velocity = Fermi momentum / Mass of electron

$FermiVelocity=sqrt{2E_{f}/M_{e}}$

$MassofElectron=9.109*10^{-31}kg$

Back