Avalanche Photodiode Gain
APD multiplication gain, excess noise factor (McIntyre), and material comparison.
V/V_br
0.9333
Gain M
5.349
Excess Noise F
1.884
F = M^0.378
Noise Current Gain √F·M
7.34
M = 1 / [1 − (V/V_br)^n] [Miller 1955, empirical]
F(M) = k·M + (1 − k)·(2 − 1/M) [McIntyre 1966]
k = ratio of the smaller to the larger ionization coefficient, for injection of the more ionizing carrier
Large-M asymptote: F ≈ kM + 2(1 − k), linear in M
n is fitted per device: an InGaAs APD with M = 10 at 4 V below a 50 V breakdown has n = 1.26
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
Miller's empirical law with an entered exponent n (a device fit, not a material constant) and McIntyre's excess noise for a uniform field and injection of the more ionising carrier. The k presets are Si 0.02 (Excelitas C30902EH), InGaAs/InP 0.5 and Ge 0.85 from Agrawal's ranges; dead-space effects in thin layers and mixed injection are not modelled, and series-resistance and space-charge gain limits near V_br are not modelled.
- Miller S. L. (1955). Avalanche breakdown in germanium. Phys. Rev. 99, 1234–1241. Empirical gain M = 1/[1 − (V/V_br)^n]. doi:10.1103/PhysRev.99.1234
- 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
- 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. V_br = 225 V at 22 °C, 0.7 V/°C. excelitas.com