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Understanding Charge Dynamics in PIN Photodiodes: Implications of the Shockley-Ramo Theorem

This work delves into the application of the Shockley-Ramo theorem in PIN photodiodes, analyzing factors such as charge dynamics, diffusion mechanisms, and recombination times under varying electric field conditions. It explores the quenching mechanisms necessary for efficient photodiode operation and the role of resistance in current behavior, providing insights into the interaction of excess carriers and their lifetime in P-type and N-type materials. Through rigorous derivation and analysis, we highlight the significance of charge diffusion and electric field variation on pulse behavior within photonic systems.

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Understanding Charge Dynamics in PIN Photodiodes: Implications of the Shockley-Ramo Theorem

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  1. Quenching Scenario H.Otono, H.Oide 21/Dec/2007

  2. Shockley-Ramo Theorem Q -Q xi xf v v q q E E j j If j(Xi)=0 and j(Xf)=j,

  3. S-R Theorem in PIN Photo Diode photon Q -Q h v v e E j Finally,

  4. Derivation of S-R theorem (1.a) (1.b) (1.c) xi xi r(x) No Charge q q E1i E E0 + V V -Q -Q Q Q xf xf (2.a) (2.b) (2.c) r(x) No Charge q q E1f E0 E + V V

  5. S-R Theorem w/ Resistor photon Q’ -Q’ Q v v -Q E R V ’ consist with S-R theorem @RO ’

  6. Excess Carrier Lifetime P-type N-type e h photon 1018 [cm-3] 1018 [cm-3] Q’ -Q -Q’ Q E=0 E>0 E=0 Induced Charge Q’ is a minor carrier  Diffuse time ~ 10-13s Multiplied Charge Q is a major carrier Diffuse time ~ 10-13s Recombination timedepends on G-R center density (<10-4s) Multiplied charge is accumulated in diffusion layer After induced current, complementary charge (Q-Q’) flows. . G-R center

  7. S-R Theorem w/ Resistor photon Q v v -Q R Q’ v Q’ -Q’ v R Q’ Q-Q’ Q’-Q Q-Q’ R

  8. S-R Theorem w/ Resistor We have to take into account E variation due to current fed into attached resistor, but it is about O(⊿V/ V). Therefore we can estimate the ratio of the1st pulse to total pulse. j = 63.5 [v] G = 5.0e5 E = 3.0e7 [V/m] v = 1.0e5 [m/s] ( )

  9. Pulse Shape 200K 77K 300K Tail Tail Spike Spike Overestimating….?

  10. Ratio @ cut position is 1.75ns~2.00ns

  11. Well-known Quench Mechanism V-IR>V0 V I I e- h+ R R V V V-I0R=V0 V-IR>V0 I0 I0 I I e- h+ R R V V

  12. Expected Pulse Height We need another quenching mechanism.

  13. Our Proposing Quench Mechanism E>E0 E I I h+ e- R R V V E=E0 E>E0 I0 h+ e- I0 I I R R V V

  14. Evidence of Diffusion

  15. Gain Locality in pixel y-point (1 mm pitch) x-point (1 mm pitch)

  16. Electric Field Calculation Electric field has to be reduced about Multiplied carriers as a condenser generate Our mechanism decides multiplication factor (=G) w/o capacitance value. But the carriers have to be diffuse in every corner in pixel.

  17. Diffusion Mechanism • Lattice scattering Low energy  Scattering by doping ion High energy  Scattering by phonon • Charge Repulsion (where r 0=10nm, r=20nm)

  18. Velocity Saturation （C.Jacoboni et al."Solid-State Electron,20,77(1977)）

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