Gain vs Temperature
APD gain drift at fixed bias from the breakdown-voltage temperature coefficient, and PMT gain drift.
Gain @ 0 °C
40.47
Gain @ 60 °C
4.81
Gain Ratio 0/60 °C
×8.415
Gain Coefficient @ 22 °C
-3.18 %/°C
Fitted Miller Exponent n
1.2636
Fixed Bias V
46.00 V
Breakdown Reached Below
-6.6 °C
APD: V_br(T) = V_br,ref + γ·(T − T_ref), M(T) = 1 / [1 − (V/V_br(T))^n]
n fitted through the operating point: n = ln(1 − 1/M_ref) / ln(V/V_br,ref)
(1/M)·dM/dT = −n·(M − 1)·γ / V_br: the drift grows with the gain
PMT: M(T) = M_ref·exp(β·ΔT), β entered
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
APD at fixed bias: Miller's law with n fitted through the entered operating point and a breakdown voltage linear in temperature. The defaults are the Excelitas C30662 InGaAs APD (M = 10 at 4 V below a 50 V breakdown, 0.14 V/°C), which reaches breakdown below −6.6 °C; V_br(T) scales the whole Miller curve (M = 1/[1 − (V/V_br(T))^n]); a bias that tracks γ·ΔT still leaves a residual drift of order (V_br − V)/V_br. The PMT branch applies an entered constant coefficient; the −0.3 %/°C default is a mid value between about −0.1 %/°C (CuBe dynodes, Photonis 2002) and −0.5 %/°C (nine Cs-Sb stages at −0.06 %/°C each, Burle 1980).
- 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
- Crowell C. R., Sze S. M. (1966). Temperature dependence of avalanche multiplication in semiconductors. Appl. Phys. Lett. 9, 242–244. The breakdown voltage rises with temperature. doi:10.1063/1.1754731
- Excelitas Technologies. C30645 and C30662 InGaAs avalanche photodiodes, datasheet Rev. 2025.11. V_br = 50 V (45–70 V), 0.14 V/°C; M = 10 at 4 V below breakdown. excelitas.com
- 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. excelitas.com
- Hamamatsu Photonics (2006). Photomultiplier Tubes: Basics and Applications, 3rd ed., §13.1.1. The gain's temperature characteristic hardly depends on wavelength or supply voltage; Fig. 13-1 plots photocathode anode-sensitivity coefficients on a −1 to +1.5 %/°C scale.
- Photonis (2002). Photomultiplier tubes: principles and applications, p. 28. Gain temperature coefficient about −0.1 %/°C for CuBe dynodes with bialkali and trialkali cathodes. psec.uchicago.edu
- Burle Industries (1980). Photomultiplier Handbook TP-136, p. 48, Fig. 53. Stage gain of Cs-Sb dynodes changes by about −0.06 %/°C. psec.uchicago.edu