Linear-Mode Avalanche Photodiode
SNR of a linear-mode APD receiver versus gain: McIntyre excess noise, shot and thermal noise, and the optimum gain for a given load resistance.
Excess Noise F(M = 100)
3.950
SNR (electrical)
1.153
0.62 dB
Optimum Gain M_opt
215.5
SNR at M_opt
1.912
2.82 dB
Responsivity ℛ₀ = 516.19 mA/W (M = 1)
Primary photocurrent = 5.162e-10 A, multiplied = 5.162e-8 A
Multiplied dark current = 2.200e-11 A
Shot noise = 2.557e-8 A, thermal noise = 4.070e-8 A, total = 4.807e-8 A rms
NEP (no light) = 7.886e-10 W = 7.886e-14 W/√Hz
Key Formulas
ℛ₀ = η·q·λ / (h·c), I_p = ℛ₀·P
F(M) = k·M + (1 − k)·(2 − 1/M) [McIntyre 1966]
σ² = 2q·(I_p + I_d)·M²·F(M)·B + 4k_B·T·B / R
SNR = (M·I_p)² / σ² [Personick 1977]
M_opt: k·M³ + (1 − k)·M = 4k_B·T / [q·R·(I_p + I_d)]
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Shot noise of the multiplied photocurrent and bulk dark current with McIntyre's F, plus Johnson noise of the load; surface dark current, amplifier voltage noise and background light are left out. The default 0.22 pA bulk dark current is the Excelitas C30902EH's, from its noise current i_N = 0.1 pA/√Hz and dark current I_D = I_DS + I_DB·M = 7 nA at M = 150 (i_N² = 2q(I_DS + I_DB·M²F), F = 4.95): the bulk part I_DB·M is 33 pA, 0.5 % of I_D, the rest is unmultiplied surface leakage.
- McIntyre R. J. (1966). Multiplication noise in uniform avalanche diodes. IEEE Trans. Electron Devices ED-13, 164–168. F = kM + (1 − k)(2 − 1/M). doi:10.1109/T-ED.1966.15651
- Personick S. D. (1977). Receiver design for optical fiber systems. Proc. IEEE 65, 1670–1678. Shot and thermal noise of a p-i-n or APD receiver and the optimum gain. doi:10.1109/PROC.1977.10808
- Agrawal G. P. (2010). Fiber-Optic Communication Systems, 4th ed. Wiley. §4.4 (APD receiver noise, optimum gain) and Table 4.2 (k: Si 0.02–0.05, InGaAs 0.5–0.7, Ge 0.7–1.0).
- Excelitas Technologies. C30902EH and C30921EH avalanche photodiodes, datasheet Rev. 2022.02. k_eff = 0.02; V_br = 225 V at 22 °C, 0.7 V/°C; M = 150; dark current 7 nA (typ.), noise current 0.1 pA/√Hz (typ.), NEP 1.23 fW/√Hz; notes 2–3 split I_D into surface and bulk parts. excelitas.com