A reverse-biased avalanche photodiode (APD) sandwiches a high-field multiplication region between the light-absorbing layer (here, quantum dots tuned to the target wavelength) and the collecting contact. A photo-generated electron entering this region is accelerated by the field until it gains enough kinetic energy to knock a bound electron across the bandgap — impact ionization — creating a fresh electron-hole pair while the original carrier survives and keeps going. Each new carrier can trigger further ionizations, producing an exponentially branching cascade for every single absorbed photon.
Ionization coefficients (Chynoweth law): α(E), β(E) — pairs created per unit
path length by an electron / a hole. Ratio k = β / α.
McIntyre local-field gain (pure electron injection, region length L):
M = (1 − k) / [ exp(−(1−k)·αL) − k ]
Breakdown ((1−k)·αL → −ln k): M → ∞
Excess noise factor (McIntyre, 1966):
F(M) = k·M + (1 − k)·(2 − 1/M)
- Reverse bias sets the field, and therefore αL relative to the breakdown value for the current k — pushing it toward 98% shows the cascade run away exactly as the formula predicts.
- Ionization ratio k is a material property: silicon APDs have k ≈ 0.02–0.05 (electrons ionize far more readily than holes), giving low excess noise; InGaAs/InP-class and many quantum-dot-based near-infrared APDs run k closer to 0.4–1, trading noise for infrared sensitivity. Dragging k toward 1 makes both electrons and holes ionize equally, which is why F(M) rises fastest there.
- Photon injection rate / Inject single photon spawn primary electrons at the quantum-dot absorber; each one may seed its own cascade. The 3D view shows every carrier as it drifts and multiplies; blue = electron, orange-red = hole.
- Measured gain M̂ is reconstructed from actual carriers collected at the two contacts (for N injected pairs, total collected ≈ N·(2M−1)), so it fluctuates event-to-event around the analytic M — that fluctuation is the physical origin of the excess noise factor F(M).