This is a 2D companion to the 3D McIntyre avalanche-photodiode simulator, built from an independent discrete-space Monte Carlo engine rather than a flattened 3D scene. A photo-injected electron enters the high-field multiplication region at the quantum-dot absorber and drifts across it in small sub-steps; at each sub-step it (and every hole it spawns) has an exact ionization probability p = 1 − exp(−α·ds) or 1 − exp(−β·ds) — the true survival probability of a non-homogeneous Poisson process over a path length ds, not the linear p ≈ α·ds approximation, so the statistics stay correct even at high bias where a single frame's drift step would otherwise be too coarse.
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 ]
Excess noise factor (McIntyre, 1966):
F(M) = k·M + (1 − k)·(2 − 1/M)
Per-photon measured gain: for 1 injected electron, total carriers collected
at both contacts across the whole cascade = 2·M_event − 1, so
M_event = (collected + 1) / 2
- Reverse bias / ionization ratio k set αL exactly as in the 3D version — pushing bias toward breakdown or k toward 1 grows both the mean gain and its spread.
- The histogram below the device strip bins the M_event of every completed single-photon cascade. Its running mean ⟨M⟩ and second moment ⟨M²⟩ let this page compute an empirical excess-noise factor from raw event statistics — not read off a formula — and the readouts above show it converging onto the analytic F(M) as more events accumulate. That gap between a single event's gain and the average is the excess noise: an APD's shot noise is worse than a noiseless multiplier of the same mean gain precisely because M_event fluctuates event to event.
- Photon injection rate / Inject single photon seed new cascades; each is tracked independently until every descendant carrier is collected, at which point it contributes exactly one point to the histogram.