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 * $$sqrt{2E_f/M_e} / Mean Free Path$$

$$Probability = e^{-E_g/kT}$$

$$E_g Silicon = 1.12 eV$$

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

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

thin depletion region (0.7-0.8 um)

Make sure to do it in pixels

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

$$Volume = 0.0033mm^3$$

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

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

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

$$Rate of Scattering = Velocity of Valence Electrons / Mean free path$$

Mean velocity of valence elctrons = Fermi Velocity

Fermi Velocity = Fermi momentum / Mass of electron

$$Fermi Velocity = sqrt{2E_f/M_e}$$

$$Mass of Electron = 9.109 * 10^{-31} kg$$

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